KASOC Data Release
Scientific Publications
On this page you will find a list of all peer reviewed KASC publications that have been published in a scientific journal.
A simple method to measure $\boldsymbol\nu_{\rm\bf max}$ for asteroseismology: application to 16,000 oscillating \kepler red giants
NASA ADS
DOIThe importance of $\rm \nu_{max}$ (the frequency of maximum oscillation power) for asteroseismology has been demonstrated widely in the previous decade, especially for red giants. With the large amount of photometric data from CoRoT, Kepler and TESS, several automated algorithms to retrieve $\rm \nu_{max}$ values have been introduced. Most of these algorithms correct the granulation background in the power spectrum by fitting a model and subtracting it before measuring $\rm \nu_{max}$. We have developed a method that does not require fitting to the granulation background. Instead, we simply divide the power spectrum by a function of the form $\rm \nu^{-2}$, to remove the slope due to granulation background, and then smooth to measure $\rm \nu_{max}$. This method is fast, simple and avoids degeneracies associated with fitting. The method is able to measure oscillations in 99.91 % of Kepler stars, with a small systematic offset in $\rm \nu_{max}$ values that depends upon the evolutionary state. On comparing the seismic radii from this work with Gaia, we see good agreement but with similar deviation to those observed in previous studies. Additionally, our values of width of the power envelope can clearly identify the dipole mode suppressed stars as a distinct population, hence as a way to detect them. We also applied our method to stars with low $\rm \nu_{max}$ (0.39-18.35 $\rm \mu$Hz) and found it works well to correctly identify the oscillations.
Massive peak bagging of red giants in the Kepler field
The NASA satellite Kepler has gathered about 1420 days-long photometric time series for more than 20000 red giant stars. For about 6600 of them also APOGEE spectroscopic parameters are available, making the sample of high interest for various astrophysical investigations. To optimally exploit the full wealth of the seismic information, extraction of mode parameters of all significant individual frequencies is necessary. However, the complex structure of the mixed mode pattern makes it challenging to automate the peak bagging (i.e., the extraction of the individual mode parameters from the stars power density spectra). Even though several approaches have been successfully implemented, the available results are still limited to a handful of stars. Here I present frequencies, amplitudes, and lifetimes of more than a quarter of a million oscillation modes of the spherical degree l=0 to 3, which have been observed in 6179 Kepler red giants. The sample covers evolutionary stages from the lower red-giant branch to high up the asymptotic giant branch. The modes were extracted with the Automated Bayesian Peak-Bagging Algorithm (ABBA) and are publicly available at https://github.com/tkallinger/KeplerRGpeakbagging
K2 photometry on oscillation mode variability: the new pulsating hot B subdwarf star EPIC 220422705
We present analysis of oscillation mode variability in the hot B subdwarf star EPIC 220422705, a new pulsator discovered from $\sim78$ days of K2 photometry. The high-quality light curves provide a detection of 66 significant independent frequencies, from which we identified 9 incomplete potential triplets and 3 quintuplets. Those g- and p-multiplets give rotation periods of $\sim$ 36 and 29 days in the core and at the surface, respectively, potentially suggesting a slightly differential rotation. We derived a period spacing of 268.5 s and 159.4 s for the sequence of dipole and quadruple modes, respectively. We characterized the precise patterns of amplitude and frequency modulations (AM and FM) of 22 frequencies with high enough amplitude for our science. Many of them exhibit intrinsic and periodic patterns of AM and FM, with periods on a timescale of months as derived by the best fitting and MCMC test. The nonlinear resonant mode interactions could be a natural interpretation for such AMs and FMs after other mechanisms are ruled out. Our results are the first step to build a bridge between mode variability from K2 photometry and nonlinear perturbation theory of stellar oscillation.
Amplitude and frequency variations in PG 0101+039 from K2 photometry–A pulsating hot B subdwarf star in an unsynchronized binary system
K2 photometry is suitable for the exploitation of mode variability on short timescales in hot B subdwarf stars, which is important to constrain nonlinear quantities addressed by the stellar theory of high-order perturbation in the future.
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We analyze the $\sim80$ d high-quality K2 data collected on PG 0101+039 and extract the frequency content of oscillation. We then determine its rotational and orbital properties, as well as characterize the dynamics of amplitude and frequency.
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The frequencies are extracted from light curves via a standard prewhitening technique. The binary information is obtained from variations both in brightness and radial velocities. Amplitude and frequency modulation of oscillation modes are measured by piece-wise light curves and characterized by Markov Chain Monte Carl (EMCMC) method.
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We have extracted 137 independent frequencies in PG 0101+039 and derived period spacing of $\sim 252$ s and 144 s for the dipole and quadruple modes, respectively. We derive a rotation rate of $\sim8.81\pm0.06$ d and $\sim8.60\pm0.16$ d based on g- and p-mode multiplets, implying a marginally differential rotation with a probability of $\sim 60\%$. We find that the rotation period is much shorter than the orbital period of $\sim0.57$ d, indicating that this system is not synchronized.
Amplitude and frequency modulation are measurable for 44 frequencies with high enough amplitude, including 12 rotational components. We characterize their modulating patterns and find a clear correlation between amplitude and frequency variation, which is linked to nonlinear resonant couplings. In general, the modulating scale and timescale are on an order of a few dozen of nano hertz and a few tens of days, respectively, whose values are important constraints to future calculations of nonlinear amplitude equations.
PG 0101+039 is an unsynchronized system containing a component whose amplitude and frequency variations are generally on a shorter timescale than previously found in other sdB pulsators. Those findings are essential observational constraints to nonlinear dynamics of resonant mode couplings and orbital solutions.
First Asteroseismic Analysis of the Globular Cluster M80: Multiple Populations and Stellar Mass Loss
Asteroseismology provides a new avenue for accurately measuring the masses of evolved globular cluster (GC) stars through the detection of their solar-like oscillations. We present the first detections of solar-like oscillations in 47 red giant branch (RGB) and early asymptotic giant branch (EAGB) stars in the metal-poor GC M80; only the second ever with measured seismic masses. We investigate two major areas of stellar evolution and GC science; the multiple populations and stellar mass-loss. We detected a distinct bimodality in the EAGB mass distribution. We showed that this is likely due to sub-population membership. If confirmed, it would be the first direct measurement of a mass difference between sub-populations. A mass difference was not detected between the sub-populations in our RGB sample. We instead measured an average RGB mass of $0.782\pm0.009~\msun$, which we interpret as the average between the sub-populations. Differing mass-loss rates on the RGB has been proposed as the second parameter that could explain the horizontal branch (HB) morphology variations between GCs. We calculated an integrated RGB mass-loss separately for each sub-population: $0.12\pm0.02~\msun$ (SP1) and $0.25\pm0.02~\msun$ (SP2). Thus, SP2 stars have greatly enhanced mass-loss on the RGB. Mass-loss is thought to scale with metallicity, which we confirm by comparing our results to a higher metallicity GC, M4. We also find that M80 stars have insignificant mass-loss on the HB. This is different to M4, suggesting that there is a metallicity and temperature dependence in the HB mass-loss. Finally, our study shows the robustness of the $\Delta\nu$-independent mass scaling relation in the low-metallicity (and low-surface gravity) regime.
Stellar spectral-type (mass) dependence of the dearth of close-in planets around fast-rotating stars
In 2013 a dearth of close-in planets around fast-rotating host stars was found using statistical tests on Kepler data. The addition of more Kepler and Transiting Exoplanet Survey Satellite (TESS) systems in 2022 filled this region of the diagram of stellar rotation period (Prot) versus the planet orbital period (Porb). We revisited the Prot extraction of Kepler planet-host stars, we classify the stars by their spectral type, and we studied their Prot–Porb relations. We only used confirmed exoplanet systems to minimize biases. In order to learn about the physical processes at work, we used the star-planet evolution code ESPEM (French acronym for Evolution of Planetary Systems and Magnetism) to compute a realistic population synthesis of exoplanet systems and compared them with observations. Because ESPEM works with a single planet orbiting around a single main-sequence star, we limit our study to this population of Kepler observed systems filtering out binaries, evolved stars, and multi-planets. We find in both, observations and simulations, the existence of a dearth in close-in planets orbiting around fast-rotating stars, with a dependence on the stellar spectral type (F, G, and K), which is a proxy of the mass in our sample of stars. There is a change in the edge of the dearth as a function of the spectral type (and mass). It moves towards shorter Prot as temperature (and mass) increases, making the dearth look smaller. Realistic formation hypotheses included in the model and the proper treatment of tidal and magnetic migration are enough to qualitatively explain the dearth of hot planets around fast-rotating stars and the uncovered trend with spectral type.
To Grow Old and Peculiar: A Survey of Anomalous Variable Stars in M80 and Age Determination using K2 and Gaia
The globular cluster Messier 80 was monitored by the Kepler space telescope for 80 days during the K2 mission. Continuous, high-precision photometry of such an old, compact cluster allows us to study its variable star population in unprecedented detail. We extract light curves for 27 variable stars using differential-image photometry. A search for new variables in the images led to the discovery of two new variable stars: an RR Lyrae and a variable red giant star, respectively. Analysis of the RR Lyrae population reveales multiple RRc stars with additional modes and/or peculiar modulation cycles. We newly classify star V28 as a spotted extreme horizontal branch variable. Despite their faintness, we clearly detect the three SX Phe stars but we did not find new pulsation modes beyond the known ones in them. Spectra taken with the VLT and Magellan Clay telescopes, as well as absolute color-magnitude diagrams of the cluster based on Gaia and Pan-STARRS observations confirm the classification of the peculiar modulated variables as bona-fide RRc stars. We propose that they highlight a subgroup of overtone stars that may have been overlooked before. We fit MESA isochrones to the CMDs to estimate the age and metallicity of the cluster. We confirm that M80 is old and metal-poor, but show that isochrone fitting to old populations comes with numerous uncertainties.
Asteroseismology of RRab variable star EZ Cnc from K2 photometry and LAMOST spectroscopy
EZ Cnc, or EPIC 212182292, is a non-Blazhko RRab variable star located in the field of K2 Campaign 16. Its atmospheric parameters ($T_\mathrm{eff}$, $\log{g}$, [M/H]) and radial velocities are measured from the 55 high-quality LAMOST medium-resolution spectra. The fundamental frequency of pulsation is derived as $f=1.8323(17)$ d$^{-1}$ from the K2 light curves. The amplitude ratios $R_{21} = 0.5115(15), 0.490(8)$, $R_{31} = 0.3249(20), 0.279(7)$ and Fourier phase differences $\varphi_{21}=2.7550(20), 2.764(16)$, $\varphi_{31}=5.7194(25), 5.719(31)$ are determined from the Fourier decomposition of K2 light curve and LAMOST radial velocity curve, respectively. Through the constraints of the parameters, six optimal models are obtained in a time-dependent turbulent convection model survey for EPIC 212182292. The parameters of EPIC 212182292 are derived as $M=0.46\pm0.02$ M$_{\odot}$, $L = 42\pm2$ L$_{\odot}$, $T_\mathrm{eff}=6868\pm45$ K , $\log{g}=2.78\pm0.01$ dex, and $Z = 0.004\pm0.002$, respectively. The precisely determined parameters for RRab variable stars like EPIC 212180092 might help to better understand the period-luminosity relationship of RR Lyrae stars.
LAMOST Observations in 15 K2 Campaigns: I. Low resolution spectra from LAMOST DR6
The LAMOST-K2 (LK2) project, initiated in 2015, aims to collect low-resolution spectra of targets in the K2 campaigns, similar to LAMOST-Kepler project. By the end of 2018, a total of 126 LK2 plates had been observed by LAMOST. After cross-matching the catalog of the LAMOST data release 6 (DR6) with that of the K2 approved targets, we found 160,619 usable spectra of 84,012 objects, most of which had been observed more than once. The effective temperature, surface gravity, metallicity, and radial velocity from 129,974 spectra for 70,895 objects are derived through the LAMOST Stellar Parameter Pipeline (LASP). The internal uncertainties were estimated to be 81 K, 0.15 dex, 0.09 dex and 5 kms$^{-1}$, respectively, when derived from a spectrum with a signal-to-noise ratio in the $g$ band (SNR$_g$) of 10. These estimates are based on results for targets with multiple visits. The external accuracies were assessed by comparing the parameters of targets in common with the APOGEE and GAIA surveys, for which we generally found linear relationships. A final calibration is provided, combining external and internal uncertainties for giants and dwarfs, separately. We foresee that these spectroscopic data will be used widely in different research fields, especially in combination with K2 photometry.
Frequency analysis of the first-overtone RR Lyrae stars based on the Extended Aperture Photometry from the K2 data
Context. Additional low-amplitude signals are observed in many RR Lyrae stars, beside the pulsations in radial modes. The most common ones are short-period signals forming a period ratio of around 0.60–0.65 with the first overtone, or long-period signals forming a period ratio of around 0.68. Some RR Lyrae stars are also known to exhibit quasi-periodic modulation of the light curves, known as the Blazhko effect.
Aims. We used the extensive sample of the first-overtone RR Lyrae stars observed by the Kepler telescope during the K2 mission to search for and characterize these low-amplitude additional signals. The large number of stars and the excellent quality of the space-based photometry are excellent to study the properties of already known groups of RR Lyrae stars with additional signals and to search for additional unexpected periodicities.
Methods. We used K2 space-based photometry for RR Lyrae candidates from Campaigns 0–19. We selected RR Lyrae stars pulsating in the first overtone and performed a frequency analysis for each star to characterize their frequency contents.
Results. We classified 452 stars as first-overtone RR Lyrae. From that sample, we selected 281 RR$_{0.61}$ stars, 67 RR$_{0.68}$ stars, and 68 Blazhko stars. We found particularly interesting stars which show all of the above phenomena simultaneously. We detected signals in RR$_{0.61}$ stars that form period ratios lower than observed for the majority of stars. These signals likely form a new sequence in the Petersen diagram, around a period ratio of 0.60. In 32 stars we detected additional signals that form a period ratio close to that expected in RRd stars, but the classification of these stars as RRd is uncertain. We also report a discovery of additional signals in eight stars that form a new group in the Petersen diagram around the period ratio of 0.465–0.490. The nature of this periodicity remains unknown.
30 to 100-kG magnetic fields in the cores of red giant stars
A red giant star is an evolved low- or intermediate-mass star that has exhausted its central hydrogen content, leaving a helium core and a hydrogen-burning shell. Oscillations of stars can be observed as periodic dimmings and brightenings in the optical light curves. In red giant stars, non-radial acoustic waves couple to gravity waves and give rise to mixed modes, which behave as pressure (p) modes in the envelope and gravity (g) modes in the core. These modes were previously used to measure the internal rotation of red giants, leading to the conclusion that purely hydrodynamical processes of angular momentum transport from the core are too inefficient. Magnetic fields could produce the additional required transport. However, due to the lack of direct measurements of magnetic fields in stellar interiors, very little is currently known about their properties. Asteroseismology can provide direct detection of magnetic fields because, like rotation, the fields induce shifts in the oscillation mode frequencies. Here we report the measurement of magnetic fields in the cores of three red giant stars observed with the Kepler satellite. The fields induce shifts that break the symmetry of dipole mode multiplets. We thus measure field strengths ranging from $\sim$ 30 to $\sim$ 100 kG in the vicinity of the hydrogen-burning shell and place constraints on the field tolopolgy.
Unresolved Rossby and gravity modes in 214 A and F stars showing rotational modulation
Here we report an ensemble study of 214 A- and F-type stars observed by Kepler, exhibiting the so-called hump and spike periodic signal, explained by Rossby modes (r modes) - the hump - and magnetic stellar spots or overstable convective (OsC) modes- the spike, respectively. We determine the power confined in the non-resolved hump features and find additional gravity modes (g modes) humps always occurring at higher frequencies than the spike. Furthermore, we derive projected rotational velocities from FIES, SONG and HERMES spectra for 28 stars and the stellar inclination angle for 89 stars. We find a strong correlation between the spike amplitude and the power in the r and g modes, which suggests that both types of oscillations are mechanically excited by either stellar spots or OsC modes. Our analysis suggests that stars with a higher power in $m=1$ r modes humps are more likely to also exhibit humps at higher azimuthal orders ($m$ = 2, 3, or 4). Interestingly, all stars that show g modes humps are hotter and more luminous than the observed red edge of the $\delta$ Scuti instability strip, suggesting that either magnetic fields or convection in the outer layers could play an important role.
Evidence of structural discontinuities in the inner core of red-giant stars
Red giants are stars in the late stages of stellar evolution. Because they have exhausted the supply of hydrogen in their core, they burn the hydrogen in the surrounding shell. Once the helium in the core starts fusing, the star enters the clump phase, which is identified as a striking feature in the color-magnitude diagram. Since clump stars share similar observational properties, they are heavily used in astrophysical studies, as probes of distance, extinction through the galaxy, galaxy density, and stellar chemical evolution. In this work, we perform the detailed observational characterization of the deepest layers of clump stars using asteroseismic data from Kepler. We find evidence for large core structural discontinuities in about 6.7% of the stars in our sample, implying that the region of mixing beyond the convective core boundary has a radiative thermal stratification. These stars are otherwise similar to the remaining stars in our sample, which may indicate that the building of the discontinuities is an intermittent phenomenon.
Asteroseismic Ages of Subgiant Stars with Deep Learning
With the observations of an unprecedented number of oscillating subgiant stars expected from NASA's TESS mission, the asteroseismic characterization of subgiant stars will be a vital task for stellar population studies and for testing our theories of stellar evolution. To determine the fundamental properties of a large sample of subgiant stars efficiently, we develop a deep learning method that learns from a grid of stellar models varied in eight physical parameters to estimate distributions of fundamental parameters including age, mass, and radius using classical and asteroseismic observations as input. We apply our method to four Kepler subgiant stars and compare our results with previously modelled estimates. Our results show good agreement with previous estimates for three of them (KIC 11026764, KIC 10920273, KIC 11395018). With the ability to explore a vast range of stellar parameters, we identify a candidate solution for the remaining star (KIC 10005473) that is 1 Gyr younger than its previously modelled estimate and reproduces the star's observed asteroseismic and spectroscopic measurements well. We further demonstrate our method's utility for ensemble asteroseismology by characterizing a sample of 30 Kepler subgiant stars, where we find a majority of our age, mass, and radius estimates agree within uncertainties from more computationally expensive grid-based modelling techniques.
Rotational modulation in A and F stars: Magnetic stellar spots or convective core rotation?
The Kepler mission revealed a plethora of stellar variability in the light curves of many stars, some associated with magnetic activity or stellar oscillations. In this work, we analyse the periodic signal in 162 intermediate-mass stars, interpreted as Rossby modes and rotational modulation - the so-called hump & spike feature. We investigate whether the rotational modulation (spike) is due to stellar spots caused by magnetic fields or due to Overstable Convective (OsC) modes resonantly exciting g modes, with frequencies corresponding to the convective core rotation rate. Assuming that the spikes are created by magnetic spots at the stellar surface, we recover the amplitudes of the magnetic fields, which are in good agreement with theoretical predictions. Our data show a clear anti-correlation between the spike amplitudes and stellar mass and possibly a correlation with stellar age, consistent with the dynamo-generated magnetic fields theory in (sub)-surface convective layers. Investigating the harmonic behaviour, we find that for 125 stars neither of the two possible explanations can be excluded. While our results suggest that the dynamo-generated magnetic field scenario is more likely to explain the spike feature, we assess further work is needed to distinguish between the two scenarios. One method for ruling out one of the two explanations is to directly observe magnetic fields in hump & spike stars. Another would be to impose additional constraints through detailed modelling of our stars, regarding the rotation requirement in the OsC mode scenario or the presence of a convective-core (stellar age).
Mode Mixing and Rotational Splittings: II. Reconciling Different Approaches to Mode Coupling
In the mixed-mode asteroseismology of subgiants and red giants, the coupling between the p- and g-mode cavities must be understood well in order to derive localised estimates of interior rotation from measurements of mode multiplet rotational splittings. There exist now two different descriptions of this coupling: one based on an asymptotic quantisation condition, and the other arising from the coupling matrices associated with "acoustic molecular orbitals". We examine the analytic properties of both, and derive closed-form expressions for various quantities — such as the period-stretching function $\tau$ — which previously had to be solved for numerically. Using these, we reconcile both formulations for the first time, deriving relations by which quantities in each formulation may be translated to and interpreted within the other. This yields an information criterion for whether a given configuration of mixed modes may meaningfully constrain the parameters of the asymptotic construction, which is likely not satisfied by the majority of stars in our observational sample. Since this construction has been extensively used to make existing rotational measurements of evolved stars, we examine the robustness of such measurements. While averaged estimates of core rotation seem fairly robust, template-matching using the asymptotic construction appears to have difficulty reliably assigning rotational splittings to individual multiplets, or estimating the mixing fractions $\zeta$ of the most p-dominated mixed modes, where such estimates are most needed. Extending the two-zone model of radial differential rotation, e.g. via rotational inversions, will thus most likely require using the coupling-matrix construction instead.
Surface magnetism of rapidly rotating red giants: single versus close binary stars
According to dynamo theory, stars with convective envelopes efficiently generate surface magnetic fields, which manifest as magnetic activity in the form of starspots, faculae, flares, when their rotation period is shorter than their convective turnover time. Most red giants, having undergone significant spin down while expanding, have slow rotation and no spots. However, based on a sample of about 4500 red giants observed by the NASA Kepler mission, \citetGaulme_2020 showed that about 8 % display spots, including about 15 % that belong to close binary systems. Here, we shed light on a puzzling fact: for rotation periods less than 80 days, a red giant that belongs to a close binary system displays a photometric modulation about an order of magnitude larger than that of a single red giant with similar rotational period and physical properties. We investigate whether binarity leads to larger magnetic fields when tides lock systems, or if a different spot distribution on single versus close binary stars can explain this fact. For this, we measure the chromospheric emission in the Caii H & K lines of 3130 of the 4465 stars studied by \citetGaulme_2020 thanks to the LAMOST survey. We show that red giants in a close-binary configuration with spin-orbit resonance display significantly larger chromospheric emission than single stars, suggesting that tidal locking leads to larger magnetic fields at a fixed rotational period. Beyond bringing interesting new observables to study the evolution of binary systems, this result could be used to distinguish single versus binary red giants in automatic pipelines based on machine learning.
Spinning up the Surface: Evidence for Planetary Engulfment or Unexpected Angular Momentum Transport?
In this paper, we report the potential detection of a nonmonotonic radial rotation profile in a low- mass lower-luminosity giant star. For most low- and intermediate-mass stars, the rotation on the main sequence seems to be close to rigid. As these stars evolve into giants, the core contracts and the envelope expands, which should suggest a radial rotation profile with a fast core and a slower envelope and surface. KIC 9267654, however, seems to show a surface rotation rate that is faster than its bulk envelope rotation rate, in conflict with this simple angular momentum conservation argument. We improve the spectroscopic surface constraint, show that the pulsation frequencies are consistent with the previously published core and envelope rotation rates, and demonstrate that the star does not show strong chemical peculiarities. We discuss the evidence against any close stellar companion. Finally, we discuss the possible origin of this unusual rotation profile, including the potential ingestion of a giant planet or unusual angular momentum transport by tidal inertial waves triggered by a close substellar companion, and encourage further observational and theoretical efforts.
KIC 7955301: a hierarchical triple system with oscillating red giant
KIC 7955301 is a hierarchical triple system with clear eclipse timing and depth variations that was discovered by the \kep satellite during its original mission. It is composed of a non-eclipsing primary star at the bottom of the red giant branch on a 209-day orbit with a K/G-type main-sequence inner eclipsing binary, orbiting in 15.3 days. This system was noted for the large amplitude of its eclipse timing variations (over 4 hours), and the detection of clear solar-like oscillations of the red-giant component, including p-modes of degree up to $l=3$ and mixed $l=1$ modes. The system is a single-lined spectroscopic triple, meaning that only spectral lines from the RG are trackable along the orbit. We perform a dynamical model by combining the 4-year-long \kep photometric data, eclipse timing variations and radial-velocity data obtained with the high resolution spectrometers ARCES of the 3.5-m ARC telescope at Apache Point observatory and SOPHIE of the 1.93-m telescope at Haute Provence Observatory. The “dynamical” mass of the red-giant component is determined with a 2 % precision at $1.30^{+0.03}_{-0.02} M_\odot$. We perform asteroseismic modeling based on the global seismic parameters and on the individual frequencies. Both methods provide an estimate of the mass of the red giant that matches the dynamical mass within the uncertainties. Asteroseismology also reveals the rotation rate of the core ($\approx 15$ days), the envelope ($\sim 150$ days), and the inclination ($\sim75^\circ$) of the red giant. Three different approaches lead to estimating the age to range between 3.3 and 5.8 Gyr, which highlights the difficulty of determining stellar ages despite the exceptional wealth of information available for this system. On short timescales, the inner binary exhibits eclipses with varying depths during a $\approx7.3$ year-long interval, and no eclipses during the consecutive $\approx11.9$ years. This is why Kepler could detect its eclipses, TESS will not, and the future ESA PLATO mission should. Over the long term, the system appears to be stable and owes its evolution to the evolution of its individual components. This triple system could end its current smooth evolution by merging by the end of the red giant branch of the primary star because the periastron distance is $\approx 142 R_\odot$, which is close to the expected radius of the red giant at the tip of the RG branch.
Extension of the Asfgrid for Correcting Asteroseismic Large Frequency Separations
The asteroseismic scaling relation, $\Delta\nu \simeq \rho^{0.5}$, linking a star’s large frequency separation, $\Delta\nu$, and its mean density, $\rho$, is not exact. Yet, it provides a very useful way to obtain fundamental stellar properties. Common ways to make the relation more accurate is to apply correction factors to it. Because the corrections depend on stellar properties, such as mass, Teff , and metallicity, it is customary to interpolate these properties over stellar model grids that include both ∆ν, measured from adiabatic frequencies of the models, and the models’ stellar density; hence linking both sides of the scaling relation. A grid and interpolation tool widely used for this purpose, known as Asfgrid, was published by Sharma & Stello (2016). Here, we present a significant extension of Asfgrid to cover higher- and lower-mass stars and to increase the density of grid points, especially in the low-metallicity regime. [Published in Res. Notes AAS, 6, 168]
Dealing with large gaps in asteroseismic time series
With long data sets available for asteroseismology from space missions, it is sometimes necessary to deal with time series that have large gaps. Because solar-like oscillators have finite mode lifetimes, it has become tempting to close large gaps by shifting time stamps. Using actual data from the Kepler Mission, we show that this results in artificial structures in the power spectrum that compromise the measurements of mode frequencies and linewidths.
Type II and anomalous Cepheids in the Kepler K2 mission
We present the results of the analysis of Type II and anomalous Cepheids using the data from the Kepler K2 mission. The precise light curves of these pulsating variable stars are the key to study the details of their pulsation, such as the period-doubling effect or the presence of additional modes. We applied the Automated Extended Aperture Photometry (autoEAP) to obtain the light curves of the targeted variable stars which were observed. The light curves were Fourier analyzed. We investigated twelve stars observed by the K2 mission, seven Type II and five anomalous Cepheids. Among the Type II Cepheids EPIC 210622262 shows period-doubling, and four stars have modulation present in their light curves which are different from the period-doubling effect. We calculated the high-order Fourier parameters for the short-period Cepheids. We also determined physical parameters by fitting model atmospheres to the spectral energy distributions. The determined distances using the parallaxes measured by the Gaia space telescope have limited precision below 16 mag for these types of pulsating stars, regardless if the inverse method is used or the statistical method to calculate the distances. The BaSTI evolutionary models were compared to the luminosities and effective temperatures. Most of the Type II Cepheids are modeled with low metallicity models, but for a few of them solar-like metallicity ([Fe/H]=0.06) model is required. The anomalous Cepheids are compared to low-metallicity single stellar models. We do not see signs of binarity among our sample stars.
Integrated Mass Loss of Evolved Stars in M4 using Asteroseismology
Mass loss remains a major uncertainty in stellar modelling. In low-mass stars, mass loss is most significant on the red giant branch (RGB), and will impact the star's evolutionary path and final stellar remnant. Directly measuring the mass difference of stars in various phases of evolution represents one of the best ways to quantify integrated mass loss. Globular clusters (GCs) are ideal objects for this. M4 is currently the only GC for which asteroseismic data exists for stars in multiple phases of evolution. Using K2 photometry, we report asteroseismic masses for 75 red giants in M4, the largest seismic sample in a GC to date. We find an integrated RGB mass loss of $\Delta\overline{M} = 0.17 \pm 0.01 ~\mathrm{M}_{\odot}$, equivalent to a Reimers' mass-loss coefficient of $\eta_R = 0.39$. Our results for initial mass, horizontal branch mass, $\eta_R$, and integrated RGB mass loss show remarkable agreement with previous studies, but with higher precision using asteroseismology. We also report the first detections of solar-like oscillations in early asymptotic giant branch (EAGB) stars in GCs. We find an average mass of $\overline{M}_{\text{EAGB}}=0.54 \pm 0.01 ~\mathrm{M}_{\odot}$, significantly lower than predicted by models. This suggests larger-than-expected mass loss on the horizontal branch. Alternatively, it could indicate unknown systematics in seismic scaling relations for the EAGB. We discover a tentative mass bi-modality in the RGB sample, possibly due to the multiple populations. In our red horizontal branch sample, we find a mass distribution consistent with a single value. We emphasise the importance of seismic studies of GCs since they could potentially resolve major uncertainties in stellar theory.
Three ways to solve the orbit of KIC11558725: a 10-day beaming sdB+WD binary with a pulsating subdwarf
The recently discovered subdwarf B pulsator KIC11558725, is one of the 16
pulsating sdB stars detected in the Kepler field, and it features a
rich $g$-mode frequency spectrum, with a few low amplitude $p$-modes
at short periods. This makes it a promising target for a seismic
study aiming to constrain the internal structure of this star, and
of sdB stars in general. We present our discovery of
the binary nature of this star, derive the orbital parameters with
three independent methods, and
present a detailed Fourier analysis of the pulsational signal.
We have obtained spectroscopic radial-velocity measurements of
KIC11558725 based on low-resolution spectra in the Balmer-line region.
We used the Kitt Peak Mayall Telescope, the Nordic Optical Telescope
and the William Herschel Telescope for this purpose, spanning the
2010 and 2011 observing seasons. From these data we have discovered
that KIC11558725 is a binary with period $P$=10.05 d, and that the
radial-velocity amplitude of the sdB star is
58 km s$^{-1}$. Consequently the companion of the sdB star has a
minimum mass of 0.63 M$_{\odot}$, and is therefore most likely to be
an unseen white dwarf. The orbital radius $a_{\rm sdB}\sin
i$ = 11.5 R$_{\odot}$ gives rise to a light-travel time delay of
53.6 s, which causes aliasing and lowers the amplitudes of the
shortest pulsation frequencies, unless the effect is corrected for.
We use our high S/N average spectra to study the atmospheric
parameters of the sdB star, deriving Teff= 27 910 K and
$\log g$ = 5.41 dex, and find that carbon, nitrogen and oxygen are
underabundant relative to the solar mixture.
We analyse the near-continuous 2010–2011 Kepler light curve to
reveal the orbital Doppler-beaming effect, giving rise to light
variations at the 238 ppm level, which is consistent with the
observed spectroscopic orbital radial-velocity amplitude of the
subdwarf.
Furthermore, we analyse the Kepler light curve for its pulsational
content and extract more than 160 significant frequencies. We use
the strongest 70 pulsation frequencies of the subdwarf as clocks to
derive a third consistent measurement of the orbital radial-velocity
amplitude of the subdwarf, from the orbital light-travel delay.
We investigate the pulsation frequencies for expected period
spacings and rotational splittings. We find period-spacing
sequences of spherical-harmonic degrees $\ell$=1 and $\ell$=2, and
we associate a large fraction of the $g$-modes in KIC11558725 with
these sequences.
From frequency splittings we conclude that
the subdwarf is rotating subsynchronously with respect to the orbit.
The Origin of Weakened Magnetic Braking in Old Solar Analogs
The rotation rates of main-sequence stars slow over time as they gradually lose angular momentum to their magnetized stellar winds. The rate of angular momentum loss depends on the strength and morphology of the magnetic field, the mass-loss rate, and the stellar rotation period, mass, and radius. Previous observations suggested a shift in magnetic morphology between two F-type stars with similar rotation rates but very different ages (88 Leo and rho CrB). In this Letter, we identify a comparable transition in an evolutionary sequence of solar analogs with ages between 2-7 Gyr. We present new spectropolarimetry of 18 Sco and 16 Cyg A&B from the Large Binocular Telescope, and we reanalyze previously published Zeeman Doppler images of HD 76151 and 18 Sco, providing additional constraints on the nature and timing of this transition. We combine archival X-ray observations with updated distances from Gaia to estimate mass-loss rates, and we adopt precise stellar properties from asteroseismology and other sources. We then calculate the wind braking torque for each star in the evolutionary sequence, demonstrating that the rate of angular momentum loss drops by more than an order of magnitude between the ages of HD 76151 and 18 Sco (2.6-3.7 Gyr) and continues to decrease modestly to the age of 16 Cyg A&B (7 Gyr). We suggest that this magnetic transition may represent a disruption of the global dynamo arising from weaker differential rotation, and we outline plans to probe this phenomenon in additional stars spanning a wide range of spectral types.
Advanced asteroseismic modelling: breaking the degeneracy between stellar mass and initial helium abundance
Current stellar model predictions of adiabatic oscillation frequencies differ significantly from the corresponding observed frequencies due to the non-adiabatic and poorly understood near-surface layers of stars. However, certain combinations of frequencies – known as frequency ratios – are largely unaffected by the uncertain physical processes as they are mostly sensitive to the stellar core. Furthermore, the seismic signature of helium ionization provides envelope properties while being almost independent of the outermost layers. We have developed an advanced stellar modelling approach in which we complement frequency ratios with parameters of the helium ionization zone while taking into account all possible correlations to put the most stringent constraints on the stellar internal structure. We have tested the method using the Kepler benchmark star 16 Cyg A and have investigated the potential of the helium glitch parameters to constrain the basic stellar properties in detail. It has been explicitly shown that the initial helium abundance and mixing-length parameters are well constrained within our framework, reducing systematic uncertainties on stellar mass and age arising for instance from the well-known anti-correlation between the mass and initial helium abundance. The modelling of six additional Kepler stars including 16 Cyg B reinforces the above findings and also confirms that our approach is mostly independent from model uncertainties associated with the near-surface layers. Our method is relatively computationally expensive, however, it provides stellar masses, radii and ages precisely in an automated manner, paving the way for analysing numerous stars observed in the future during the ESA PLATO mission.
On the stellar core physics of the 16 Cyg binary system: constraining the central hydrogen abundance using asteroseismology
The unprecedented quality of the asteroseismic data of solar-type stars made available by space missions such as NASA's Kepler telescope are making it possible to explore stellar interior structures. This offers possibilities of constraining stellar core properties (such as core sizes, abundances, and physics) paving the way for improving the precision of the inferred stellar ages. We employ 16 Cyg A and B as our benchmark stars for an asteroseismic study in which we present a novel approach aimed at selecting from a sample of acceptable stellar models returned from Forward Modelling techniques, down to the ones that better represent the core of each star. This is accomplished by comparing specific properties of the observed frequency ratios for each star to the ones derived from the acceptable stellar models. We demonstrate that in this way we are able to constrain further the hydrogen mass fraction in the core, establishing the stars' precise evolutionary states and ages. The ranges of the derived core hydrogen mass fractions are [0.01 - 0.06] and [0.12 - 0.19] for 16 Cyg A and B, respectively, and, considering that the stars are coeval, the age and metal mass fraction parameters span the region [6.4 - 7.4] Gyr and [0.023 - 0.026], respectively. In addition, our findings show that using a single helium-to-heavy element enrichment ratio, ($\Delta Y/\Delta Z$), when forward modelling the 16 Cyg binary system, may result in a sample of acceptable models that do not simultaneously fit the observed frequency ratios, further highlighting that such an approach to the definition of the helium content of the star may not be adequate in studies of individual stars.
Classifying Kepler light curves for 12,000 A and F stars using supervised feature-based machine learning
With the availability of large-scale surveys like Kepler and TESS, there is a pressing need for automated methods to classify light curves according to known classes of variable stars. We introduce a new algorithm for classifying light curves that compares 7000 time-series features to find those which most effectively classify a given set of light curves. We apply our method to Kepler light curves for stars with effective temperatures in the range 6500 to 10,000 K. We show that the sample can be meaningfully represented in an interpretable five-dimensional feature space that separates seven major classes of light curves (delta Scuti stars, gamma Doradus stars, RR Lyrae stars, rotational variables, contact eclipsing binaries, detached eclipsing binaries, and non-variables). We achieve a balanced classification accuracy of 82% on an independent test set of Kepler stars using a Gaussian mixture model classifier. We use our method to classify 12,000 Kepler light curves from Quarter 9 and provide a catalogue of the results. We further outline a confidence heuristic based on probability density with which to search our catalogue, and extract candidate lists of correctly-classified variable stars.
Discovery of post-mass-transfer helium-burning red giants using asteroseismology
A star expands to become a red giant when it has fused all the hydrogen in its core into helium. If the star is in a binary system, its envelope can overflow onto its companion or be ejected into space, leaving a hot core and potentially forming a subdwarf-B star. However, most red giants that have partially transferred envelopes in this way remain cool on the surface and are almost indistinguishable from those that have not. Among $\sim$7000 helium-burning red giants observed by NASA's Kepler mission, we use asteroseismology to identify two classes of stars that must have undergone dramatic mass loss, presumably due to stripping in binary interactions. The first class comprises about 7 under-luminous stars with smaller helium-burning cores than their single-star counterparts. Theoretical models show that these small cores imply the stars had much larger masses when ascending the red giant branch. The second class consists of 32 red giants with masses down to 0.5 M$_\odot$, whose implied ages would significantly exceed the age of the universe had no mass loss occurred. The numbers are consistent with binary statistics, and our results open up new possibilities to study the evolution of post-mass-transfer binary systems.
Detection of non-linear resonances among gravity modes of slowly pulsating B stars: Results from five iterative pre-whitening strategies
Context. Slowly pulsating B (SPB) stars are main-sequence multiperiodic oscillators that display non-radial gravity modes. For a fraction of these pulsators, 4-year photometric light curves obtained with the Kepler space telescope reveal period spacing patterns from which their internal rotation and mixing can be inferred. In this inference, any direct resonant mode coupling is usually ignored. Aims. We re-analyse the light curves of a sample of 38 known Kepler SPB stars. For 26 of them, the internal structure, including rotation and mixing, was recently inferred from their dipole prograde oscillation modes. Our aim is to detect direct non-linear resonant mode coupling among the largest-amplitude gravity modes. Methods. We extract up to 200 periodic signals per star with five different iterative pre-whitening strategies based on linear and non-linear regression applied to the light curves. We then identify candidate coupled gravity modes by verifying whether they fulfill resonant phase relations. Results. For 32 of the 38 SPB stars we find at least one candidate resonance that is detected in both the linear and the best non-linear regression model fit to the light curve and involves at least one of the two largest-amplitude modes. Conclusions. The majority of the Kepler SPB stars reveal direct non-linear resonances based on the largest-amplitude modes. These stars are thus prime targets for the non-linear asteroseismic modelling of intermediate-mass dwarfs to assess the importance of mode couplings in probing their internal physics.
Study of Chemically Peculiar Stars-I : High-resolution Spectroscopy and K2 Photometry of Am Stars in the Region of M44
We present a study based on the high-resolution spectroscopy and K2 space photometry of five chemically peculiar stars in the region of the open cluster M44. The analysis of the high-precision photometric K2 data reveals that the light variations in HD73045 and HD76310 are rotational in nature and caused by spots or cloud-like co-rotating structures, which are non-stationary and short-lived. The time-resolved radial velocity measurements, in combination with the K2 photometry, confirm that HD 73045 does not show any periodic variability on timescales shorter than 1.3d, contrary to previous reports in the literature. In addition to these new rotational variables, we discovered a new heartbeat system, HD73619, where no pulsational signatures are seen. The spectroscopic and spectropolarimetric analyses indicate that HD73619 belongs to the peculiar Am class, with either a weak or no magnetic field considering the 200G detection limit of our study. The Least-Squares Deconvolution (LSD) profiles for HD76310 indicate a complex structure in its spectra suggesting that this star is either part of a binary system or surrounded by a cloud shell. When placed in the Hertzsprung-Russell diagram, all studied stars are evolved from main-sequence and situated in the delta Scuti instability strip. The present work is relevant for further detailed studies of CP stars, such as inhomogeneities (including spots) in the absence of magnetic fields and the origin of the pulsational variability in heartbeat systems.
Automated Extended Aperture Photometry of K2 variable stars
Proper photometric data are challenging to obtain in the K2 mission of the Kepler space telescope due to strong systematics caused by the two-wheel-mode operation. It is especially true for variable stars wherein physical phenomena occur on timescales similar to the instrumental signals. We originally developed a method with the aim to extend the photometric aperture to be able to compensate the motion of the telescope which we named Extended Aperture Photometry (EAP). Here we present the outline of the automatized version of the EAP method, an open-source pipeline called autoEAP. We compare the light curve products to other photometric solutions for examples chosen from high-amplitude variable stars. Besides the photometry, we developed a new detrending method, which is based on phase dispersion minimization and is able to eliminate long-term instrumental signals for periodic variable stars.
The Kepler IRIS Catalog: Image subtraction light curves for 9,150 stars in and around the open clusters NGC 6791 and NGC 6819
The four-year Kepler mission collected long cadence images of the open clusters NGC 6791 and NGC 6819, known as “superstamps.” Each superstamp region is a 200-pixel square that captures thousands of cluster members, plus foreground and background stars, of which only the brightest were targeted for long or short cadence photometry during the Kepler mission. Using image subtraction photometry, we have produced light curves for every object in the Kepler Input Catalog that falls on the superstamps. The IRIS catalog includes light curves for 9,150 stars, and contains a wealth of new data: 8,427 of these stars were not targeted at all by Kepler, and we have increased the number of available quarters of long cadence data for 382 stars. The catalog is available as a high-level science product on MAST, with both raw photometric data for each quarter and corrected light curves for all available quarters for each star. We also present an introduction to our implementation of image subtraction photometry and the open source IRIS pipeline, alongside an overview of the data products, systematics, and catalog statistics.
Vetting Asteroseismic $\Delta\nu$ Measurements using Neural Networks
Precise asteroseismic parameters allow one to quickly estimate radius and mass distributions for large samples of stars. A number of automated methods are available to calculate the frequency of maximum acoustic power ($\nu_{\mathrm{max}}$) and the frequency separation between overtone modes ($\Delta\nu$) from the power spectra of red giants. However, filtering through the results requires either manual vetting, elaborate averaging across multiple methods, or sharp cuts in certain parameters to ensure robust samples of stars free of outliers. Given the importance of ensemble studies for Galactic archaeology and the surge in data availability, faster methods for obtaining reliable asteroseismic parameters are desirable. We present a neural network classifier that vets $\Delta\nu$ by combining multiple features from the visual $\Delta\nu$ vetting process. Our classifier is able to analyse large numbers of stars determining whether their measured $\Delta\nu$ are reliable thus delivering clean samples of oscillating stars with minimal effort. Our classifier is independent of the method used to obtain $\nu_{\mathrm{max}}$ and $\Delta\nu$, and therefore can be applied as a final step to any such method. Tests of our classifier's performance on manually vetted $\Delta\nu$ measurements reach an accuracy of 95%. We apply the method to giants observed by K2 Galactic Archaeology Program and find that our results retain stars with astrophysical oscillation parameters consistent with the parameter distributions already defined by well-characterised Kepler red giants.
Towards a systematic treatment of observational uncertainties in forward asteroseismic modelling of gravity-mode pulsators
Context. In asteroseismology the pulsation mode frequencies of a star are the fundamental data that are compared to theoretical predictions to determine a star’s interior physics. Recent significant advances in the numerical, theoretical and statistical asteroseismic methods applied to main sequence stars with convective cores have renewed the interest in investigating the propagation of observational uncertainties within a forward asteroseismic modelling framework. Aims. We aim to quantify the impact of various choices made throughout the observational aspects of extracting pulsation mode frequencies in main sequence stars with gravity modes. Methods. We use a well-studied benchmark slowly pulsating B star, KIC 7760680, to investigate the sensitivity of forward asteroseismic modelling to various sources of observational uncertainty that affect the precision of the input pulsation mode frequencies. Results. We quantify the impact of the propagation of the observational uncertainties involved in forward asteroseismic modelling. We find that one of the largest sources of uncertainty in our benchmark star is in the manual building of period spacing patterns, such that the inclusion of a potentially ambiguous pulsation mode frequency may yield differences in model parameters of up to 10% for mass and age depending on the radial order of the mode. Conclusions. We conclude that future asteroseismic studies of main sequence stars with a convective core should quantify and include observational uncertainties introduced by the light curve extraction, iterative pre-whitening and the building of period spacing patterns, as these propagate into the final modelling results.
Five young delta Scuti stars in the Pleiades seen with Kepler/K2
We perform mode identification for five $\delta$ Scuti stars in the Pleiades star cluster, using custom light curves from K2 photometry. By creating échelle diagrams, we identify radial and dipole mode ridges, comprising a total of 28 radial and 16 dipole modes across the five stars. We also suggest possible identities for those modes that lie offset from the radial and dipole ridges. We calculate non-rotating stellar pulsation models to verify our mode identifications, finding good agreement within the age and metallicity constraints of the cluster. We also find that for all stars, the least dense models are preferred, reflecting the lower density of these oblate, rotating stars. Three of the five stars show rotationally-split multiplets. We conclude that the sample shows promise for asteroseismic rotation rates, masses, and ages with rotating models in the future. Our preliminary modelling also indicates some sensitivity to the helium abundance.
Spectroscopic and seismic analysis of red giants in eclipsing binaries discovered by Kepler
Eclipsing binaries (EBs) are unique targets for measuring precise stellar properties and constraining stellar evolution models. In particular, it is possible to measure masses and radii at the few percent level for both components of a double-lined spectroscopic EB (SB2-EB). On the one hand, detached EBs hosting at least one star with detectable solar-like oscillations constitute ideal test objects to assess the ability of ensemble asteroseismology to determine and understand the fundamental properties of stars. On the other hand, the oscillation and surface activity properties of stars that belong to EBs offer unique information about the evolution of binary systems. This paper builds upon previous works dedicated to red giant stars (RG) observed by the NASA Kepler mission that belong to EBs (20 systems so far) and eccentric “heartbeat” binaries (19). Here we report the discovery of 16 RGs in EBs also from the Kepler data, leading to a total of 36 confirmed RG stars in EBs observed by Kepler in its original mission. This new sample includes three SB2-EBs with oscillations, leading to 14 known SB2-EBs systems including an RG oscillator. Based on dedicated high-resolution spectroscopic observations performed with the échelle spectrometer of the 3.5-m telescope of the Astrophysical Research Consortium at Apache Point Observatory and the SOPHIE spectrograph at Observatoire de Haute Provence, we focus on three main aspects. From the extended sample of 14 SB2-EBs, we first confirm that the simple application of the asteroseismic scaling relations to RGs overestimates masses and radii of RGs, by about 15 percent and 5 percent, and we propose employing modified asteroseismic reference values for RGs, which allows us to correct these systematic biases. Secondly, we confirm that close binarity leads to a high level of photometric modulation (up to 10 percent), and a suppression of solar-like oscillations. In particular, we show that it reduces the lifetime of radial modes by a factor of up to 10. Thirdly, we use our 16 new systems to complete previous observational studies that aimed at constraining tidal dissipation in interacting binaries. We confirm the important role of the dissipation of the equilibrium tide. In addition, we identify a few interesting new cases that seem young to be already on circular orbits. This shows the necessity to explore complementary tidal dissipation mechanisms. Finally, as a by-product, we report the measurements of mass, radius, and age of three M-dwarf companion stars.
A binary with a $\delta$ Scuti star and an oscillating red giant: orbit and asteroseismology of KIC 9773821
We study the $\delta$ Scuti – red giant binary KIC 9773821, the first double-pulsator binary of its kind. It was observed by Kepler during its four-year mission. Our aims are to ascertain whether the system is bound, rather than a chance alignment, and to identify the evolutionary state of the red giant via asteroseismology. An extension of these aims is to determine a dynamical mass and an age prior for a $\delta$ Sct star, which may permit mode identification via further asteroseismic modelling. We determine spectroscopic parameters and radial velocities (RVs) for the red giant component using HERMES@Mercator spectroscopy. Light arrival-time delays from the $\delta$ Sct pulsations are used with the red-giant RVs to determine that the system is bound and to infer its orbital parameters, including the binary mass ratio. We use asteroseismology to model the individual frequencies of the red giant to give a mass of \mga$2.10^{+0.20}_{-0.10}$ M$_{\sun}$ and an age of $1.08^{+0.06}_{-0.24}$ Gyr. We find that it is a helium-burning secondary clump star, confirm that it follows the standard $\nu_{\rm max}$ scaling relation, and confirm its observed period spacings match their theoretical counterparts in the modelling code mesa. Our results also constrain the mass and age of the $\delta$ Sct star. We leverage these constraints to construct $\delta$ Sct models in a reduced parameter space and identify four of its five pulsation modes.
Mixed Modes and Asteroseismic Surface Effects: I. Analytic Treatment
Normal-mode oscillation frequencies computed from stellar models differ from those which would be measured from stars with identical interior structures, because of modelling errors in the near-surface layers. These frequency differences are referred to as the asteroseismic "surface term". The vast majority of solar-like oscillators which have been observed, and which are expected to be observed in the near future, are evolved stars which exhibit mixed modes. For these evolved stars, the inference of stellar properties from these mode frequencies has been shown to depend on how this surface term is corrected for. We show that existing parametrisations of the surface term account for mode mixing only to first order in perturbation theory, if at all, and therefore may not be adequate for evolved stars. Moreover, existing nonparametric treatments of the surface term do not account for mode mixing. We derive both a first-order construction, and a more general approach, for one particular class of nonparametric methods. We illustrate the limits of first-order approximations from both analytic considerations and using numerical injection-recovery tests on stellar models. First-order corrections for the surface term are strictly only applicable where the size of the surface term is much smaller than both the coupling strength between the mixed p- and g-modes, as well as the local g-mode spacing. Our more general matrix construction may be applied to evolved stars, where perturbation theory cannot be relied upon.
Mixed Modes and Asteroseismic Surface Effects: II. Subgiant Systematics
Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modelling error near the surface. This asteroseismic “surface term” must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit solar-like oscillations of mixed acoustic ($p$-mode) and gravity ($g$-mode) character, which defy description by the traditional $p$-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this asymptotic description, they cannot be applied to subgiants directly. In the first paper of this series, we generalised such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. In this paper, we apply those results, modelling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. This is true for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modelling with mixed modes, irrespective of the choice of correction used. We also show that the properties inferred of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from both main-sequence and red giant stars.
An observational testbed for cosmological zoom-in simulations: constraining stellar migration in the solar cylinder using asteroseismology
Large-scale stellar surveys coupled with recent developments in magneto-hydrodynamical simulations of the formation of Milky Way-mass galaxies provide an unparalleled opportunity to unveil the physical processes driving the evolution of the Galaxy. We developed a framework to compare a variety of parameters with their corresponding predictions from simulations in an unbiased manner, taking into account the selection function of a stellar survey. We applied this framework to a sample of over 7000 stars with asteroseismic, spectroscopic, and astrometric data available, together with 6 simulations from the Auriga project. We found that some simulations are able to produce abundance dichotomies in the $[{\rm Fe}/{\rm H}]-[\alpha/{\rm Fe}]$ plane which look qualitatively similar to observations. The peak of their velocity distributions match the observed data reasonably well, however they predict hotter kinematics in terms of the tails of the distributions and the vertical velocity dispersion. Assuming our simulation sample is representative of Milky Way-like galaxies, we put upper limits of 2.21 and 3.70 kpc on radial migration for young ($< 4$ Gyr) and old ($\in [4, 8]$ Gyr) stellar populations in the solar cylinder. Comparison between the observed and simulated metallicity dispersion as a function of age further constrains migration to about 1.97 and 2.91 kpc for the young and old populations. These results demonstrate the power of our technique to compare numerical simulations with high-dimensional datasets, and paves the way for using the wider field TESS asteroseismic data together with the future generations of simulations to constrain the subgrid models for turbulence, star formation and feedback processes.
Asteroseismology of overmassive, undermassive, and potential pastmembers of the open cluster NGC 6791
We perform an asteroseismic investigation of giant stars in the field of NGC 6791 with previous indications of atypical evolution. The analysis makes use of observations from Kepler and Gaia in combination with ground-based photometry, a literature radial-velocity study, and measurements of eclipsing binaries in the cluster. We derive mass, radius, effective temperature, evolutionary stage and apparent distance modulus of each target. Among the investigated cluster giants we find clear evidence of overmassive and undermassive members, and non-members with strong hints of potential past membership. Our results indicate that about 10% of the red giants in the cluster have experienced mass-transfer or a merger. High-resolution high-S/N spectroscopic follow-up could confirm potential past membership of the non-members, and reveal whether certain element abundances might expose the non-standard evolution of overmassive and undermassive stars. If so, field stars of similar type could be identified as what they are, i.e. over- or undermassive stars, and not mistakenly classified as younger or older than they are.
Asteroseismic inference of the central structure in a subgiant star
Asteroseismic measurements enable inferences of the underlying stellar structure, such as the density and the speed of sound at various points within the interior of the star. This provides an opportunity to test stellar evolution theory by assessing whether the predicted structure of a star agrees with the measured structure. Thus far, this kind of inverse analysis has only been applied to the Sun and three solar-like main-sequence stars. Here we extend the technique to stars on the subgiant branch, and apply it to one of the best-characterized subgiants of the Kepler mission, HR 7322. The observation of mixed oscillation modes in this star facilitates inferences of the conditions of its inert helium core, nuclear-burning hydrogen shell, and the deeper parts of its radiative envelope. We find that despite significant differences in the mode frequencies, the structure near to the center of this star does not differ significantly from the predicted structure.
Revisiting the impact of stellar magnetic activity on the detectability of solar-like oscillations by Kepler
Over 2,000 stars were observed for one month with a high enough cadence in order to look for acoustic modes during the survey phase of the \kep mission. Solar-like oscillations have been detected in about 540 stars. The question of why no oscillations were detected in the remaining stars is still open. Previous works explained the non-detection of modes with the high level of magnetic activity of the stars. However, the sample of stars studied contained some classical pulsators and red giants that could have biased the results. In this work, we revisit this analysis on a cleaner sample of main-sequence solar-like stars that consists of 1,014 stars. First we compute the predicted amplitude of the modes of that sample and for the stars with detected oscillation and compare it to the noise at high frequency in the power spectrum. We find that the stars with detected modes have an amplitude to noise ratio larger than 0.94. We measure reliable rotation periods and the associated photometric magnetic index for 684 stars out of the full sample and in particular for 323 stars where the amplitude of the modes is predicted to be high enough to be detected. We find that among these 323 stars 32% of them have a level of magnetic activity larger than the Sun during its maximum activity, explaining the non-detection of acoustic modes. Interestingly, magnetic activity cannot be the primary reason responsible for the absence of detectable modes in the remaining 68$\%$ of the stars without acoustic modes detected and with reliable rotation periods. Thus, we investigate metallicity, inclination angle of the rotation axis, and binarity as possible causes of low mode amplitudes. Using spectroscopic observations for a subsample, we find that a low metallicity could be the reason for suppressed modes. No clear correlation with binarity nor inclination is found. We also derive the lower limit for our photometric activity index (of 20-30 ppm) below which rotation and magnetic activity are not detected. Finally, with our analysis we conclude that stars with a photometric activity index larger than 2,000 ppm have 98.3% probability of not having oscillations detected.
Internal mixing of rotating stars inferred from dipole gravity modes
During most of their life, stars fuse hydrogen into helium in their cores. The mixing of chemical elements in the radiative envelope of stars with a convective core is able to replenish the core with extra fuel. If effective, such deep mixing allows stars to live longer and change their evolutionary path. Yet localized observations to constrain internal mixing are absent so far. Gravity modes probe the deep stellar interior near the convective core and allow us to calibrate internal mixing processes. Here we provide core-to-surface mixing profiles inferred from observed dipole gravity modes in 26 rotating stars with masses between 3 and 10 solar masses. We find a wide range of internal mixing levels across the sample. Stellar models with stratified mixing profiles in the envelope reveal the best asteroseismic performance. Our results provide observational guidance for three-dimensional hydrodynamical simulations of transport processes in the deep interiors of stars.
(You can also view the paper here: https://rdcu.be/ckjRm)
Orbital solutions derived from radial velocities and time delays for four Kepler systems with A/F-type hybrid pulsations
The presence of A/F-type Kepler hybrid stars extending across the entirety of the delta Scuti -gamma Doradus instability strips and beyond remains largely unexplained. In order to better understand these particular stars, we performed a multi-epoch spectroscopic study of a sample of 49 candidate A/F-type hybrid stars and one cool(er) hybrid object detected by the Kepler mission. We determined a lower limit for the multiplicity fraction of 27 %. For six spectroscopic systems, we also reported long-term variations in the time delays (TDs). For four of them, the TD variations are fully coherent with those of the RVs and can be attributed to orbital motion. We aim to improve the orbital solutions for those spectroscopic systems with long orbital periods (order of 4-6 years) among the Kepler hybrid stars that we continued to observe. The orbits are computed based on a simultaneous modelling of the RVs obtained with high-resolution spectrographs and the photometric TDs derived from time-dependent frequency analyses of the Kepler light curves. We refined the orbital solutions of four spectroscopic systems with A/F-type Kepler hybrid component stars: KIC 4480321, 5219533, 8975515 and KIC 9775454. Simultaneous modelling of both data types analysed together enabled us to improve the orbital solutions (all), obtain more robust and accurate information on the mass ratio (some for the first time), and identify the component with short-period delta Sct-type pulsations (all). The information gained is maximized when one of the components, generally the one exhibiting the delta Sct-type pulsations, is a fast rotator. In several cases, we were also able to derive new constraints for the minimum component masses. From a search for regular frequency patterns in the high-frequency regime of the Fourier transforms of each system, we found no evidence of tidal splitting among the triple systems with close (inner) companions. However, some systems exhibit frequency spacings which can be explained by the mechanism of rotational splitting.
Asteroseismology of luminous red giants with Kepler. II. Dependence of mass loss on pulsations and radiation
Mass loss by red giants is an important process to understand the final stages of stellar evolution and the chemical enrichment of the interstellar medium. Mass-loss rates are thought to be controlled by pulsation-enhanced dust-driven outflows. Here we investigate the relationships between mass loss, pulsations, and radiation, using 3213 luminous Kepler red giants and 135000 ASAS–SN semiregulars and Miras. Mass-loss rates are traced by infrared colours using 2MASS and WISE and by observed-to-model WISE fluxes, and are also estimated using dust mass-loss rates from literature assuming a typical gas-to-dust mass ratio of 400. To specify the pulsations, we extract the period and height of the highest peak in the power spectrum of oscillation. Absolute magnitudes are obtained from the 2MASS $K_s$ band and the Gaia DR2 parallaxes. Our results follow. (i) Substantial mass loss sets in at pulsation periods above $\sim$60 and $\sim$100 days, corresponding to Asymptotic-Giant-Branch stars at the base of the period-luminosity sequences C$'$ and C. (ii) The mass-loss rate starts to rapidly increase in semiregulars for which the luminosity is just above the Red-Giant-Branch tip and gradually plateaus to a level similar to that of Miras. (iii) The mass-loss rates in Miras do not depend on luminosity, consistent with pulsation-enhanced dust-driven winds. (iv) The accumulated mass loss on the Red Giant Branch consistent with asteroseismic predictions reduces the masses of red-clump stars by $6.3$%, less than the typical uncertainty on their asteroseismic masses. Thus mass loss is currently not a limitation of stellar age estimates for galactic archaeology studies.
Automated approach to measure stellar inclinations: validation through large-scale measurements on the red giant branch
Measuring stellar inclinations is fundamental to understand planetary formation and dynamics as well as physical conditions during star formation. Oscillation spectra of red giant stars exhibit mixed modes that have both a gravity component from the radiative interior and a pressure component from the convective envelope. Gravity-dominated (g-m) mixed modes split by rotation are well separated inside frequency spectra, making possible accurate measurements of stellar inclinations.
This work aims at developing an automated and general approach to measure stellar inclinations, that can be applied to any solar-type pulsator for which oscillation modes are identified, and at validating it using red giant branch stars observed by Kepler.
The stellar inclination impacts the visibility of oscillation modes with azimuthal orders $m=\lbrace -1, 0, +1 \rbrace$. We use the mean height-to-background ratio of dipole mixed modes with different azimuthal orders to measure stellar inclinations. The underlying statistical distribution of inclinations is recovered in an unbiased way using a probability density function for the stellar inclination angle.
We derive stellar inclination measurements for 1139 stars on the red giant branch, for which Gehan et al. (2018) have identified the azimuthal order of dipole g-m mixed modes. Raw measured inclinations exhibit strong deviation with respect to isotropy which is expected for random inclinations over the sky. When taking uncertainties into account, the reconstructed distribution of inclinations actually follows the expected isotropic distribution of the rotational axis.
This work highlights the biases that affect inclination measurements and provides the way to infer their underlying statistical distribution. When the star is seen either pole-on or equator-on, measurements are challenging and result in a biased distribution. Correcting biases that appear at the low- and high inclination regimes allows us to recover the underlying inclination distribution.
Testing the intrinsic scatter of the asteroseismic scaling relations with Kepler red giants
Asteroseismic scaling relations are often used to derive stellar masses and radii, particulaly for stellar, exoplanet, and Galactic studies. It is therefore important that their precisions are known. Here we measure the intrinsic scatter of the underlying seismic scaling relations for $\Delta\nu$ and $\nu_{\rm max}$, using two sharp features that are formed in the H-R diagram (or related diagrams) by the red giant populations. These features are the edge near the zero-age core-helium-burning phase, and the strong clustering of stars at the so-called red giant branch bump. The broadening of those features is determined by factors including the intrinsic scatter of the scaling relations themselves, and therefore it is capable of imposing constraints on them. We modelled Kepler stars with a Galaxia synthetic population, upon which we applied the intrinsic scatter of the scaling relations to match the degree of sharpness seen in the observation. We found that the random errors from measuring $\Delta\nu$ and $\nu_{\rm max}$ provide the dominating scatter that blurs the features. As a consequence, we conclude that the scaling relations have intrinsic scatter of $\sim0.5\%$ ($\Delta\nu$), $\sim1.1\%$ ($\nu_{\rm max}$), $\sim1.7\%$ (mass) and $\sim0.4\%$ (radius), for the SYD pipeline measured $\Delta\nu$ and $\nu_{\rm max}$. This confirms that the scaling relations are very powerful tools. In addition, we show that standard evolution models fail to predict some of the structures in the observed population of both the HeB and RGB stars. Further stellar model improvements are needed to reproduce the exact distributions.
On the first dSct–roAp hybrid pulsator and the stability of p and g modes in chemically peculiar A/F stars
Strong magnetic fields in chemically peculiar A-type (Ap) stars typically suppress low-overtone pressure modes (p modes) but allow high-overtone p modes to be driven. KIC 11296437 is the first star to show both. We obtained and analysed a Subaru spectrum, from which we show that KIC 11296437 has abundances similar to other magnetic Ap stars, and we estimate a mean magnetic field modulus of $2.8\pm0.5$ kG. The same spectrum rules out a double-lined spectroscopic binary, and we use other techniques to rule out binarity over a wide parameter space, so the two pulsation types originate in one $\delta$ Sct–roAp hybrid pulsator. We construct stellar models depleted in helium and demonstrate that helium settling is second to magnetic damping in suppressing low-overtone p modes in Ap stars. We compute the magnetic damping effect for selected p and g modes, and find that modes with frequencies similar to the fundamental mode are driven for polar field strengths $\lesssim4$ kG, while other low-overtone p modes are driven for polar field strengths up to $\sim$1.5 kG. We find that the high-order g modes commonly observed in $\gamma$ Dor stars are heavily damped by polar fields stronger than 1–4 kG, with the damping being stronger for higher radial orders. We therefore explain the observation that no magnetic Ap stars have been observed as $\gamma$ Dor stars. We use our helium-depleted models to calculate the $\delta$ Sct instability strip for metallic-lined A (Am) stars, and find that driving from a Rosseland mean opacity bump at $\sim$$5\times10^4$ K caused by the discontinuous H-ionization edge in bound-free opacity explains the observation of $\delta$ Sct pulsations in Am stars.
Tango of celestial dancers: A sample of detached eclipsing binary systems containing g-mode pulsating components. A case study of KIC9850387
Eclipsing binary systems with components that pulsate in gravity modes ($g$ modes) allow for simultaneous and independent constraints of the chemical mixing profiles of stars. The high precision of the dynamical masses and radii as well as the imposition of identical initial chemical compositions and equivalent ages provide strong constraints during the modelling of $g$-mode period-spacing patterns. We aim to assemble a sample of $g$-mode pulsators in detached eclipsing binaries with the purpose of finding good candidates for future evolutionary and asteroseismic modelling. In addition, we present a case study of the eclipsing binary KIC9850387, identified as our most promising candidate, and detail the results of the observational spectroscopic, photometric, and asteroseismic analysis of the system. We selected all of the detached eclipsing binaries in the Kepler eclipsing binary catalogue with Kepler Input Catalogue (KIC) temperatures between 6000 K and 10000 K, and performed a visual inspection to determine the presence and density of $g$ modes, and the presence of $g$-mode period-spacing patterns in their frequency spectra. We then characterised our sample based on their $g$-mode pulsational parameters and binary and atmospheric parameters. A spectroscopic follow-up of our most promising candidate was then performed, and the orbital elements of the system were extracted. We then performed spectral disentangling followed by atmospheric modelling and abundance analysis for the primary star. We utilised an iterative approach to simultaneously optimise the pulsational and eclipse models, and subsequently performed an analysis of the pressure- ($p$-) and $g$-mode pulsational frequencies. We compiled a sample of 93 Kepler eclipsing binary stars with $g$-mode pulsating components and identified clear $g$-mode period-spacing patterns in the frequency spectra of seven of these systems. We also identified 11 systems that contained hybrid $p$- and $g$-mode pulsators. We found that the $g$-mode pulsational parameters and the binary and atmospheric parameters of our sample are weakly correlated at best, as expected for detached main-sequence binaries. We find that the eclipsing binary KIC9850387 is a double-lined spectroscopic binary in a near-circular orbit with a hybrid $p$- and $g$-mode pulsating primary with $M_{\text{p}}=1.66_{-0.01}^{+0.01}$ $M_{\odot}$ and $R_{\text{p}}=2.154_{-0.004}^{+0.002}$ $R_{\odot}$, and a solar-like secondary with $M_{\text{s}}=1.062_{-0.005}^{+0.003}$ $M_{\odot}$ and $R_{\text{s}}=1.081_{-0.002}^{+0.003}$ $R_{\odot}$. We find $\ell=1$ and $\ell=2$ period-spacing patterns in the frequency spectrum of KIC9850387 spanning more than ten radial orders each, which will allow for stringent constraints of stellar structure during future asteroseismic modelling.
EPIC 216747137: a new HW Vir eclipsing binary with a massive sdOB primary and a low-mass M-dwarf companion
EPIC 216747137 is a new HW Virginis system discovered by the Kepler spacecraft during its $K2$ “second life”. Like the other HW Vir systems, EPIC 216747137 is a post-common-envelope eclipsing binary consisting of a hot subluminous star and a cool low-mass companion. The short orbital period of 3.87 hours produces a strong reflection effect from the secondary ($\sim$9% in the R band). Together with AA Dor and V1828 Aql, EPIC 216747137 belongs to a small subgroup of HW Vir systems with a hot evolved sdOB primary. We find the following atmospheric parameters for the hot component: Teff = 40400$\pm$1000 K, logg = 5.56$\pm$0.06, log($N$(He)/$N$(H)) = $-2.59\pm$0.05. The sdOB rotational velocity v $\sin$ i = 51$\pm$10 km s$^{-1}$ implies that the stellar rotation is slower than the orbital revolution and the system is not synchronized. When we combine photometric and spectroscopic results with the Gaia parallax, the best solution for the system corresponds to a primary with a mass of about 0.62 Msun close to, and likely beyond, the central helium exhaustion, while the cool M-dwarf companion has a mass of about 0.11 Msun.
Differential Modelling Systematics across the HR Diagram from Asteroseismic Surface Corrections
Localised modelling error in the near-surface layers of evolutionary stellar models causes the frequencies of their normal modes of oscillation to differ from those of actual stars with matching interior structures. These frequency differences are referred to as the asteroseismic surface term. Global stellar properties estimated via detailed constraints on individual mode frequencies have previously been shown to be robust with respect to different parameterisations of this surface term. It has also been suggested that this may be true of a broader class of nonparametric treatments. We examine systematic differences in inferred stellar properties with respect to different surface-term treatments, both for a statistically large sample of main-sequence stars, as well as for a sample of red giants, for which no such characterisation has previously been done. For main-sequence stars, we demonstrate that while masses and radii, and hence ages, are indeed robust to the choice of surface term, the inferred initial helium abundance $Y_0$ is sensitive to the choice of surface correction. This implies that helium-abundance estimates returned from detailed asteroseismology are methodology-dependent. On the other hand, for our red giant sample, nonparametric surface corrections return dramatically different inferred stellar properties than parametric ones. The nature of these differences strongly suggests that such nonparametric methods should be preferred for evolved stars.
Variability of M giant stars based on Kepler photometry: general characteristics
M giants are among the longest-period pulsating stars which is why their studies were traditionally restricted to analyses of low-precision visual observations, and more recently, accurate ground-based data. Here we present an overview of M giant variability on a wide range of time-scales (hours to years), based on analysis of thirteen quarters of Kepler long-cadence observations (one point per every 29.4 minutes), with a total time-span of over 1000 days. About two-thirds of the sample stars have been selected from the ASAS-North survey of the Kepler field, with the rest supplemented from a randomly chosen M giant control sample.
We first describe the correction of the light curves from different quarters, which was found to be essential. We use Fourier analysis to calculate multiple frequencies for all stars in the sample. Over 50 stars show a relatively strong signal with a period equal to the Kepler-year and a characteristic phase dependence across the whole field-of-view. We interpret this as a so far unidentified systematic effect in the Kepler data. We discuss the presence of regular patterns in the distribution of multiple periodicities and amplitudes. In the period-amplitude plane we find that it is possible to distinguish between solar-like oscillations and larger amplitude pulsations which are characteristic for Mira/SR stars. This may indicate the region of the transition between two types of oscillations as we move upward along the giant branch.
Asteroseismology of solar-type stars: systematics from initial helium abundance on the inferred stellar parameters
The excellent precision of the photometric data from space missions such as NASA's Kepler and NASA's Transiting Exoplanet Survey Satellite (TESS) are making it possible to explore the impact of the input physics employed in asteroseismic stellar modelling on the inferred stellar parameters, e.g. mass and age. Among the vital input physics used in the modelling of solar-type stars which remain poorly constrained, is the initial helium abundance. This is because the number of helium lines detectable in the spectra of solar-type stars is insufficient for any strong conclusions on helium abundance to be drawn using spectroscopic observations. To this end, when constructing stellar model grids, the initial helium abundance is estimated either (i) by using the semi-empirical helium-to-heavy element enrichment ratio, (${\Delta Y}/{\Delta Z}$), anchored to the standard Big Bang Nucleosynthesis value or (ii) by setting the initial helium abundance as a free variable. Adopting 35 low-mass, solar-type stars with multi-year Kepler photometry from the asteroseismic “LEGACY” sample, we explore the systematic uncertainties on the inferred stellar parameters (i.e., mean density, radius, mass, and age) arising from the treatment of the initial helium abundance in stellar model grids . The stellar masses and radii derived from grids with free initial helium abundance are lower compared to those from grids based on a fixed ${\Delta Y}/{\Delta Z}$ ratio. We find the systematic uncertainties on mean density, radius, mass, and age arising from grids which employ a fixed value of ${\Delta Y}/{\Delta Z}$ and those with free initial helium abundance to be $\sim$ 0.9%, $\sim$ 2%, $\sim$ 5% and $\sim$ 29%, respectively. We report that the systematic uncertainties on the inferred masses and radii arising from the treatment of initial helium abundance in stellar grids lie within the expected accuracy limits of ESA's PLAnetary Transits and Oscillations of stars (PLATO), although this is not the case for the age.
Probing the interior physics of stars through asteroseismology
Yearslong time series of high-precision brightness measurements have been assembled for thousands of years with telescopes operating in space. Such data have allowed astronomers to measure the physics of stellar interiors via nonradial oscillations, opening a new avenue to study the stars in the Universe. Asteroseismology, the interpretation of the characteristics of oscillation modes in terms of the physical properties of the stellar interior, brought entirely new insights in how stars rotate and how they build up their chemistry throughout their evolution. Data-driven space asteroseismology has delivered a drastic increase in the reliability of computer models mimicking the evolution of stars born with a variety of masses and metallicities. Such models are critical ingredients for modern physics as a whole because they are used throughout various contemporary and multidisciplinary research fields in space science, including the search for life outside the Solar System, archaeological studies of the Milky Way, and the study of single and binary supernova progenitors, among which are future gravitational wave sources. The specific role and potential of asteroseismology for those modern research fields are illustrated. The review concludes with current limitations of asteroseismology and highlights how they can be overcome with ongoing and future large infrastructures for survey astronomy combined with new theoretical research in the era of high-performance computing. This review presents results obtained through major community efforts over the past decade. These breakthroughs were achieved in a collaborative and inclusive spirit that is characteristic of the asteroseismology community. The review’s aim is to make this research field accessible to graduate students and readers coming from other fields of physics, with incentives to enjoy and join future applications in this domain of astrophysics.
Self-consistent method to extract non-linearities from pulsating stars light curves I. Combination frequencies.
Stellar pulsation is a common phenomenon and is sustained because of coherent drivingmechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based.
Active red giants: close binaries versus single rapid rotators
Oscillating red-giant stars have provided a wealth of asteroseismic information regarding their interiors and evolutionary states, and access to their fundamental properties enable detailed studies of the Milky Way. Using confirmed eclipsing binaries with at least one red-giant component, various studies have found that a fraction of the shorter-period systems (less than 150 days or so) commonly had three interesting features: strong modulation of their photometric light curves potentially linked to surface magnetic fields; rapid rotation compared to field giants, possibly as a result of tidal synchronization and circularization; and partially- or fully-suppressed oscillations.
Given the strong correlation between surface activity and binarity found in certain eclipsing systems, we hypothesize that binaries in non-eclipsing configurations can be found in large fractions from photometry alone. We test this hypothesis by selecting a sample of about 4500 relatively bright Kepler red-giant stars. Using a powerful quick-look data-analysis tool, we flag targets that display photometric variations in the Kepler light curves indicative of starspots on a rotating star. For a subset of those, we obtain new spectroscopic observations, and utilize archival APOGEE data, to detect potential radial-velocity variations indicative of binarity. About 370 targets (∼ 8%) show surface modulation, with almost all having oscillation amplitudes below the median of the sample, while 30 of them are not oscillating at all. Of the 85 of these systems chosen for follow-up radial-velocity observation and analysis, 34 show clear evidence of spectroscopic binarity. Surprisingly, 26 of the 30 non-oscillators are in this group of binaries.
In addition, stellar masses and evolutionary status were computed for the oscillating stars. Interestingly, low-mass red-giant branch stars tend to be magnetically inactive, while intermediate-mass ones tend to be highly active. The opposite trends are true for horizontal-branch (red clump) stars, whereby the lower-mass clump stars are comparatively more active and the higher-mass ones less so. We also find that the expected Rossby numbers in many of these stars, computed from models, are consistent with the conditions necessary to generate magnetic fields in convective envelopes.
Binaries are cornerstones of stellar astrophysics that can be used to test different physical processes, so having more well-characterized systems is important. A large fraction of red giants that display strong photometric variations and no solar-like oscillations are indeed highly likely to be in a binary system (which presents an inexpensive way of finding binaries). Thus, there are now established links between rapid rotation from tidal interactions, (surface) magnetic fields, and oscillation suppression. There is a wealth of physics to be studied in these targets not available in the Sun.
Furthermore, the evolutionary characterization points to an interesting finding, that low-mass red-giant branch stars gain angular momentum as they evolve to clump stars, while higher-mass ones lose angular momentum. This finding leads to possible scenarios of planet engulfment or other merging events during the shell-burning phase.
Seismic evidence for near solid-body rotation in two Kepler subgiants and implications for angular momentum transport
Context: Asteroseismic measurements of the internal rotation of subgiants and red giants are all showing the need to invoke a more efficient transport of angular momentum than theoretically predicted. Constraints on the core rotation rate are available starting from the base of the red giant branch (RGB) and we are still lacking information on the internal rotation of less evolved subgiants.
Aims: We identified two young Kepler subgiants (KIC8524425 and KIC5955122) whose mixed modes are clearly split by rotation. We aimed at probing their internal rotation profile and assessing the efficiency of the angular momentum transport during this phase of the evolution.
Methods: Using the full Kepler data set, we extracted the mode frequencies and rotational splittings for the two stars using a Bayesian approach. We then performed a detailed seismic modeling of both targets and used the rotational kernels to invert their internal rotation profiles using the MOLA inversion method.
Results: We found that both stars are rotating nearly as solid bodies, with core-envelope contrasts of $\Omega_{\rm g}/\Omega_{\rm p}=0.68\pm0.47$ for KIC8524425 and $\Omega_{\rm g}/\Omega_{\rm p}=0.72\pm0.37$ for KIC5955122. This result shows that the internal transport of angular momentum has to occur faster than the timescale at which differential rotation is forced in these stars (between 300 Myr and 600 Myr). By modeling the additional transport of angular momentum as a diffusive process with a constant viscosity $\nu_{\rm add}$, we found that values of $\nu_{\rm add}>5\times10^4$ cm$^2$.s$^{-1}$ are required to account for the internal rotation of KIC8524425, and $\nu_{\rm add}>1.5\times10^5$ cm$^2$.s$^{-1}$ for KIC5955122. These values are lower than or comparable to the efficiency of the core-envelope coupling during the main sequence (as given by the surface rotation of stars in open clusters), but higher than the viscosity needed to reproduce the rotation of subgiants near the base of the RGB.
Conclusions: Our results yield further evidence that the efficiency of the internal redistribution of angular momentum is decreasing during the subgiant phase. They bring new constraints that will need to be accounted for by mechanisms that are proposed as candidates for angular momentum transport in subgiants and red giants.
Fast and Automated Peak Bagging with Diamonds (FAMED)
Stars of low and intermediate mass that exhibit oscillations may show tens of detectable oscillation modes each. Oscillation modes are a powerful to constrain the internal structure and rotational dynamics of the star, hence tool allowing one to obtain an accurate stellar age. The tens of thousands of solar-like oscillators that have been discovered thus far are representative of the large diversity of fundamental stellar properties and evolutionary stages available. Because of the wide range of oscillation features that can be recognized in such stars, it is particularly challenging to properly characterize the oscillation modes in detail, especially in light of large stellar samples. Overcoming this issue requires an automated approach, which has to be fast, reliable, and flexible at the same time. In addition, this approach should not only be capable of extracting the oscillation mode properties of frequency, linewidth, and amplitude from stars in different evolutionary stages, but also able to assign a correct mode identification for each of the modes extracted. Here we present the new freely available pipeline FAMED (Fast and AutoMated pEak bagging with Diamonds), which is capable of performing an automated and detailed asteroseismic analysis in stars ranging from the main sequence up to the core-Helium-burning phase of stellar evolution. This, therefore, includes subgiant stars, stars evolving along the red giant branch (RGB), and stars likely evolving toward the early asymptotic giant branch. In this paper, we additionally show how FAMED can detect rotation from dipolar oscillation modes in main sequence, subgiant, low-luminosity RGB, and core-Helium-burning stars. FAMED can be downloaded from its public GitHub repository (https://github.com/EnricoCorsaro/FAMED).
First evidence of inertial modes in $\gamma$ Doradus stars: The core rotation revealed
The advent of space photometry with CoRoT and Kepler has allowed to gather exquisite and long time series for a wealth of main sequence stars, among which $\gamma$ Doradus stars which detailed seismology was unachievable from the ground. $\gamma$ Doradus stars present an incredibly rich pulsation spectra, presenting gravito-inertial modes, in some cases supplemented with $\delta$ Scuti-like pressure modes -for the hybrid stars- and in numerous cases with Rossby modes. The present paper aims at proving that, in addition to these modes established in the radiative envelope, pure inertial modes, trapped in the convective core, can be detected in Kepler observations of $\gamma$ Doradus stars, thanks to their resonance with the gravito-inertial modes. We start by using a simplified model of perturbations in a full sphere of uniform density. Under these conditions, the spectrum of pure inertial modes is known from analytical solutions of the so-called Poincaré equation. We then compute coupling factors which select the pure inertial modes which interacts best with the surrounding dipolar gravito-inertial modes. Using complete calculations of gravito-inertial modes in realistic models of $\gamma$ Doradus stars, we are able to show that the pure inertial/gravito-inertial resonances appear as dips in the gravito-inertial mode period spacing series at spin parameters close to those predicted by the simple model and similar to what was previously observed in some Kepler stars. Finally, using complete calculations in isolated convective cores, we find that the spin parameters of the pure inertial/gravito-inertial resonances are also sensitive to the density stratification of the convective core. We have discovered that certain dips in gravito-inertial mode period spacings observed in some Kepler stars are in fact the signatures of resonances with pure-inertial modes that are trapped in the convective core. This discovery holds the promise to finally access the central conditions , i.e. rotation and density stratification, of intermediate-mass stars on the main sequence.
Establishing the accuracy of asteroseismic mass and radius estimates of giant stars. I. Three eclipsing systems at [Fe/H] -0.3 and the need for a large high-precision sample.
We aim to establish and improve the accuracy level of asteroseismic estimates of mass, radius, and age of giant stars. This can be achieved by measuring independent, accurate, and precise masses, radii, effective temperatures and metallicities of long period eclipsing binary stars with a red giant component that displays solar-like oscillations. We measured precise properties of the three eclipsing binary systems KIC7037405, KIC9540226, and KIC9970396 and estimated their ages be $5.3\pm0.5$, $3.1\pm0.6$, and $4.8\pm0.5$ Gyr. The measurements of the giant stars were compared to corresponding measurements of mass, radius, and age using asteroseismic scaling relations and grid modeling. We found general agreement, and no indications of systematic differences at the precision level of the asteroseismic measurements when theoretical correction factors are taken into account. Comparisons involving a larger sample of eclipsing binaries studied by Gaulme et al. (2016) suggests that the apparent overestimate of mass from the asteroseismic scaling relations in that study is at least partly due to too low precision on the dynamical measurements and systematic overestimates of measured $T_{\rm eff}$ values. However, we cannot rule out that the observed $T_{\rm eff}$ scale is slightly too high or that the model $T_{\rm eff}$ scale could be too cool. We found no indication of a need to correct $\nu_{\rm max}$. An extension of the present precision study to a larger sample of eclipsing systems spanning a range in masses, radii, $T_{\rm eff}$ and metallicity is needed to establish and improve the accuracy of asteroseismology of giant stars.
Asteroseismology of 36 Kepler subgiants – I. Oscillation frequencies, linewidths and amplitudes
The presence of mixed modes makes subgiants excellent targets for asteroseismology, providing a probe for the internal structure of stars. Here we study 36 Kepler subgiants with solar-like oscillations and report their oscillation mode parameters. We performed a so-called peakbagging exercise, i.e. estimating oscillation mode frequencies, linewidths, and amplitudes with a power spectrum model, fitted in the Bayesian framework and sampled with a Markov Chain Monte Carlo algorithm. The uncertainties of the mode frequencies have a median value of 0.206 $\mu$Hz. We obtained asymptotic parameters from the peakbagging, analysed their correlation with stellar parameters, and examined against scaling relations. This sample will be valuable constraints for modelling stars and studying mode physics such as excitation and damping.
Asteroseismic Analyses of Slowly Pulsating B Star KIC 8324482: Ultra-weak Element Mixing Beyond Central Convective Core
Asteroseismology is a powerful tool for probing the inner structure and determining the evolutionary status and the fundamental parameters of stars. The oscillation spectra of slowly pulsating B (SPB) stars show almost uniform period spans, whose pattern is sensitive to the structure of the $\mu$-gradient shell beyond the central convective core and hence can be used to efficiently describe their shapes and constrain the convective core. The SPB star KIC 8324482 was observed by Kepler for over 1470 days with a long-cadence pattern. Nearly equidistant period spacing patterns are found for the 14 connective dipolar modes that are extracted from the oscillation spectrum by Zhang et al. In the present work, we analyze them in depth with the $\chi^2$-matching method and determine their $\chi^2$-minimization models (CMMs). Based on those calculated CMMs, we find that KIC 8324482 is a young ($t_{\rm{age}}=20.96^{+3.85}_{-1.28}$ Myr), metal-poor (${\rm{[Fe/H]}}=-0.6.9^{+0.176}_{-0.115}$ dex), and intermediate-mass ($M=6.075^{+0.1375}_{-0.2500}\,M_{\odot}$) star with a convective core of $M_{\rm{CC}}=1.338^{+0.057}_{-0.091}\,M_{\odot}$ in mass and $R_{\rm{CC}}=0.5175^{+0.0048}_{-0.0103}\,R_{\odot}$ in radius and with a surface rotation velocity $V_{\rm{eq}}=2.61^{+0.13}_{-0.11} \,{\rm{km~s^{-1}}}$. The central hydrogen abundance is of $X_{\rm{C}}=0.5046^{+0.0018}_{-0.0074}$. Asteroseismic analyses indicate that the “propagation time” of g-mode in KIC 8324482 is of $\Lambda_{0}=276.85^{+1.26}_{-0.47}\,\mu$Hz. To well match with the observed period spacing pattern, an extra diffusion mixing ($\log{D_{\rm{mix}}}=3.125^{+0.125}_{-0.250}$) should be considered, but the normal core overshooting $f_{\rm{ov}}$ must be fixed as zero in the best-fitting model. Such ultraweak mixing beyond the convective core corresponds to a fast rotation that is about $20-30$ times the asteroseismic suggested rotation $\Omega_{\rm{rot}}\simeq0.2\,\mu$Hz, if it is thought of as shear mixing induced completely by differential rotation.
An astrophysical interpretation of the remarkable g-mode frequency groups of the rapidly rotating $\gamma$ Dor star, KIC 5608334
The Fourier spectrum of the $\gamma$-Dor variable KIC 5608334 shows remarkable frequency groups at $\sim$3, $\sim$6, $\sim$9, and 11–12 d$^{-1}$. We explain the four frequency groups as prograde sectoral g modes in a rapidly rotating star. Frequencies of intermediate-to-high radial order prograde sectoral g modes in a rapidly rotating star are proportional to $|m|$ (i.e., $\nu \propto |m|$) in the co-rotating frame as well as in the inertial frame. This property is consistent with the frequency groups of KIC 5608334 as well as the period vs. period-spacing relation present within each frequency group, if we assume a rotation frequency of $2.2$ d$^{-1}$, and that each frequency group consists of prograde sectoral g modes of $|m| = 1, 2, 3,$ and 4, respectively. In addition, these modes naturally satisfy near-resonance conditions $\nu_i\approx\nu_j+\nu_k$ with $m_i=m_j+m_k$. We even find exact resonance frequency conditions (within the precise measurement uncertainties) in many cases, which correspond to combination frequencies.
Robo-AO Kepler Asteroseismic Survey. II. Do Stellar Companions Inhibit Stellar Oscillations?
The Kepler space telescope observed over 15,000 stars for asteroseismic studies. Of these, 75% of dwarfs (and 8% of giants) were found to show anomalous behavior: such as suppressed oscillations (low amplitude) or no oscillations at all. The lack of solar-like oscillations may be a consequence of multiplicity, due to physical interactions with spectroscopic companions or due to the dilution of oscillation amplitudes from “wide” (AO detected; visual) or spectroscopic companions introducing contaminating flux. We present a search for stellar companions to \allstars of the Kepler asteroseismic sample, which were expected to display solar-like oscillations. We used direct imaging with Robo-AO, which can resolve secondary sources at $\sim$0\farcs15, and followed up detected companions with Keck AO. Directly imaged companion systems with both separations of $\leq$ 0\farcs5 and amplitude dilutions $>$10% all have anomalous primaries, suggesting these oscillation signals are diluted by a sufficient amount of excess flux. We also used the high-resolution spectrometer ESPaDOnS at CFHT to search for spectroscopic binaries. We find tentative evidence for a higher fraction of spectroscopic binaries with high radial velocity scatter in anomalous systems, which would be consistent with previous results suggesting that oscillations are suppressed by tidal interactions in close eclipsing binaries.
Finding binaries from phase modulation of pulsating stars with Kepler: VI. Orbits for 10 new binaries with mischaracterised primaries
Measuring phase modulation in pulsating stars has proved to be a highly successful way of finding binary systems. The class of pulsating main-sequence A and F variables known as $\delta$ Scuti stars are particularly good targets for this, and the Kepler sample of these has been almost fully exploited. However, some Kepler $\delta$ Scuti stars have incorrect temperatures in stellar properties catalogues, and were missed in previous analyses. We used an automated pulsation classification algorithm to find 93 new $\delta$ Scuti pulsators among tens of thousands of F-type stars, which we then searched for phase modulation attributable to binarity. We discovered 10 new binary systems and calculated their orbital parameters, which we compared with those of binaries previously discovered in the same way. The results suggest that some of the new companions may be white dwarfs.
New Insights for High-precision Asteroseismology: Acoustic Radius of KIC 6225718
Asteroseismology is a powerful tool for probing stellar interiors and determining stellar fundamental parameters. In previous works, $\chi^2$-minimization method is usually used to find the best matching model to characterize observations. In this letter, we adopt the $\chi^2$-minimization method but only using the observed high-precision oscillation to constrain theoretical models for solar-like oscillating star KIC 6225718, which is observed by \kepler satellite. We also take into account the influence of model precision. Finally, we find that the time resolution of stellar evolution can not be ignored in high-precision asteroseismic analysis. Based on this, we find the acoustic radius $\tau_{0}$ is the only global parameter that can be accurately measured by $\chi^2_{\nu}$ matching method between observed frequencies and theoretical model calculations. We obtain $\tau_{0}=4601.5^{+4.4}_{-8.3}$ seconds. In addition, we analyze the distribution of $\chi^2_{\nu}$-minimization models (CMMs), and find that the distribution range of CMMs is slightly enlarged by some extreme cases, which possess both of larger mass and higher (or lower) heavy element abundance, at lower acoustic radius end.
An independent asteroseismic analysis of the fundamental parameters and internal structure of the solar-like oscillator KIC 6225718
Asteroseismology is a useful tool that is usually used to probe stellar interiors and to determine stellar fundamental parameters, such as stellar mass, radius, and surface gravity. In order to probe stellar interiors, making comparisons between observations and models is usually used with the $\chi^2$-minimization method. The work of Wu & Li reported that the best parameter determined by the $\chi^2$-matching process is the acoustic radius for pure p-mode oscillations. In the present work, based on the theoretical calculations of Wu & Li, we will independently analyze the seismic observations of KIC 6225718 to determine its fundamental parameters and to investigate its interior properties. First, in order to test the method, we use it in the Sun to determine its fundamental parameters and to investigate interiors. Second, we independently determine the fundamental parameters of KIC 6225718 without any other non-seismic constraint. Therefore, those determined fundamental parameters are independent of those determined by other methods. They can be regarded as independent references in other analyses. Finally, we analyze the stellar internal structure and find that KIC 6225718 has a convective core with the size of $0.078-0.092$ \rsol. Its overshooting parameter $f_{\rm ov}$ in the core is around 0.010. In addition, its center hydrogen $X_{\rm c}$ is about $0.264-0.355$.
Gravity-mode period spacings and near-core rotation rates of \starnumber $\gamma$ Doradus stars with Kepler
We report our survey of \gdor stars from the 4-yr Kepler mission. These stars pulsate mainly in g modes and r modes, showing period-spacing patterns in the amplitude spectra. The period-spacing patterns are sensitive to the chemical composition gradients and the near-core rotation, hence they are essential for understanding the stellar interior. We identified period-spacing patterns in \starnumber \gdor stars. Almost every star pulsates in dipole g modes, while about 30% of stars also show clear patterns for quadrupole g modes and 16% of stars present r mode patterns. We measure periods, period spacings, and the gradient of the period spacings. These three observables guide the mode identifications and can be used to estimate the near-core rotation rate. We find many stars are hotter and show longer period-spacing patterns than theory. Using the Traditional Approximation of Rotation (TAR), we inferred the asymptotic spacings, the near-core rotation rates, and the radial orders of the g and r modes. Most stars have a near-core rotation rate around $1$ \cpd and an asymptotic spacing around 4000 s. We also find that many stars rotate more slowly than predicted by theory for unclear reasons. \numberfastsplitting stars show rotational splittings with fast rotation rates. We compared the observed slope–rotation relation with the theory and find a large spread. We detected rotational modulations in \numbersurfacemodulation stars and used them to derive the core-to-surface rotation ratios. The interiors rotate faster than the cores in most stars, but by no more than 5%.
Period spacings of $\gamma$ Doradus pulsators in the Kepler field: Rossby and gravity modes in 82 stars
Rossby modes are the oscillations in a rotating fluid, whose restoring force is the Coriolis force. They provide an additional diagnostic to understand the rotation of stars, which complicates asteroseismic modelling. We report 82 $\gamma$ Doradus stars for which clear period spacing patterns of both gravity and Rossby modes have been detected. The period spacings of both show a quasi-linear relation with the pulsation period but the slope is negative for the gravity modes and positive for the Rossby modes. Most Rossby modes have $k=-2, m=-1$. For only one star a series of $k=-1,m=-1$ modes is seen. For each pattern, the mean pulsation period, the mean period spacing, and the slope are measured. We find that the slope correlates with the mean period for Rossby mode patterns. The traditional approximation of rotation is used to measure the near-core rotation rate, assuming the star rotates rigidly. We report the near-core rotation rates, the asymptotic period spacings, and the radial orders of excited modes of these 82 main-sequence stars. The near-core rotation rates lie between $0.6\,\mathrm{d^{-1}}$ and $2.3\,\mathrm{d^{-1}}$. Six stars show surface rotation modulations, among which only KIC 3341457 shows differential rotation while the other five stars have uniform rotations. The radial orders of excited modes show different distributions for the dipole and quadrupole gravity modes versus the Rossby modes.
Regular high-frequency pulsation modes in young intermediate-mass stars
Asteroseismology is a powerful tool for probing the internal structures of stars by using their natural pulsation frequencies. It relies on identifying sequences of pulsation modes that can be compared with theoretical models, which has been done with great success for many classes of pulsators including low-mass solar-type stars, red giants, high-mass stars and white dwarfs. However, a large group of pulsating stars of intermediate mass–the so-called $\delta$ Scuti stars–have rich pulsation spectra for which systematic mode identification has not been possible. This arises because only a seemingly random subset of possible modes are excited, and because rapid rotation tends to spoil the regular patterns. Here we report the detection of remarkably regular sequences of pulsation modes in 60 intermediate-mass main-sequence stars, opening up a new regime in which the power of asteroseismology can be applied to determine masses, ages and internal structure. Some of these stars have space motions that indicate they are members of known associations of young stars, and modelling of their pulsation spectra confirm that these stars are indeed young.
A new C-D-like diagram for SPB stars: The variations of period spacing as a signature of evolutionary status
The Slowly Pulsating B-type (SPB) stars are the upper main-sequence stars on the HR diagram. Their oscillations are high-order, low-degree g-mode and can be used to probe the structure of the radiative zone where is near the outer boundary of the convective core and constrain the chemical mixing in stellar interiors. In SPB stars, the period spacing periodically varies with periods. It has regarded as a signature of the chemical composition gradient beyond the convective core. Based on theoretical calculations, we find that the variation frequency of the period spacings ($f_{\Delta P}$) is related to the width of the $\mu$-gradient region on the buoyancy radius ($\Lambda_{\mu}$) with the relation of $f_{\Delta P}\sim0.5\Lambda_{\mu}$. This indicates that the variation frequency $f_{\Delta P}$ is sensitive to the central hydrogen mass fraction $X_{\rm C}$ (i.e., the evolutionary status). Finally, we find that the variation frequency $f_{\Delta P}$ and the means of the period spacings $\langle\Delta P\rangle$ can be used to construct a new C-D-like diagram ($f_{\Delta P}$ vs. $\langle\Delta P\rangle$) which can be used to roughly decide the stellar evolutionary stages and to approximately determine stellar mass for SPB stars.
Spectroscopy of hot Gamma Doradus and A-F hybrid Kepler candidates close to the hot border of the Delta Scuti instability strip
If $\gamma$-Dor type pulsations are driven by the convective blocking mechanism, a convective envelope at a sufficient depth is essential. There are several hot $\gamma$ Dor, and hybrid star candidates in which there should not be an adequate convective envelope to excite the $\gamma$ Dor-type oscillations. The existence of these hot objects needs an explanation. Therefore, we selected, observed and studied 24 hot $\gamma$ Dor, and hybrid candidates to investigate their properties. The atmospheric parameters, chemical abundances and $v\,\sin i$, values of the candidates were obtained using medium-resolution (R=46000) spectra taken with the FIES instrument mounted at the Nordic Optical Telescope. We also carried out frequency analyses of the Kepler long- and short-cadence data to determine the exact pulsation contents. We found only five bona-fide hot , $\gamma$ Dor and three bona-fide hot hybrid stars in our sample. The other 16 stars were found to be normal $\gamma$ Dor, $\delta$ Sct, or hybrid variables. No chemical peculiarity was detected in the spectra of the bona-fide hot $\gamma$ Dor, and hybrid stars. We investigated the interplay between rotation and pulsational modes. We also found that the hot$\gamma$ Dor, stars have higher Gaia luminosities and larger radii compared to main-sequence A-F stars.
Extended Aperture Photometry of K2 RR Lyrae stars
The Kepler space telescope observed thousands of RR Lyrae stars in the K2 mission. In this paper we present our photometric solutions using extended apertures in order to conserve the flux of the stars to the highest possible extent. With this method we are able to avoid most of the problems that RR Lyrae light curves produced by other pipelines suffer from. For post-processing we apply the K2SC pipeline to our light curves. We provide the EAP (Extended Aperture Photometry) of 432 RR Lyrae stars observed in campaigns 3, 4, 5, and 6. We also provide subclass classifications based on Fourier parameters. We investigated in particular the presence of the Blazhko effect in the stars, and found it to be 44.7% among the RRab stars, in agreement with results from independent samples. We found that the amplitude and phase modulation in the Blazhko stars may behave rather differently, at least over the length of a K2 Campaign. We also identified four anomalous Cepheid candidates in the sample one of which is potentially the first Blazhko-modulated member of its class.
Asteroseismology of luminous red giants with Kepler: Long Period Variables with radial and non-radial modes
While long period variables (LPVs) have been extensively investigated, especially with MACHO and OGLE data for the Magellanic Clouds, there still exist open questions in their pulsations regarding the excitation mechanisms, radial order and angular degree assignment. Here, we perform asteroseismic analyses on LPVs observed by the 4-year Kepler mission. Using a cross-correlation method, we detect unambiguous pulsation ridges associated with radial fundamental modes ($n=1$) and overtones ($n\geqslant2$), where the radial order assignment is made by using theoretical frequencies and observed frequencies. We find that the amplitude of the dominant pulsation modes starts to increase more significantly with period at a period of $P=4.3$ days, which can be a result of the transition of dominant modes between overtones and may suggest significant variations in the mode lifetime. Our results confirm that the amplitude variability seen in semiregulars is consistent with oscillations being solar-like. We identify that the dipole modes, $l=1$, are dominant in the radial orders of $3\leq n \leq6$, and that quadrupole modes, $l=2$, are dominant in the first overtone $n=2$. A test of seismic scaling relations using Gaia DR2 parallaxes reveals the possibility that the relations break down when $\nu_{\rm max}$ $\lesssim$ 3 $\mu {\rm Hz}$ (R $\gtrsim$ 40 R$_{\odot}$, or log $\rm L/L_{\odot}$ $\gtrsim$ 2.6). Our homogeneous measurements of pulsation amplitude and period for 3214 LPVs will be very valuable for probing effects of pulsation on mass loss, in particular in those stars with periods around 60 days, which has been argued as a threshold of substantial pulsation-triggered mass loss.
Systematic search for stellar pulsators in the eclipsing binaries observed by Kepler
Eclipsing binaries are unique targets for measuring precise stellar properties and constrain stellar evolution models. In particular, it is possible to measure at the percent level masses and radii of both components of a double-lined spectroscopic eclipsing binary. Since the advent of high-precision photometric space missions (MOST, CoRoT, Kepler, BRITE, TESS), the use of stellar pulsation properties to infer stellar interiors and dynamics constitutes a revolution for low-mass star studies. The Kepler mission has led to the discovery of thousands of classical pulsators such as $\delta$ Scuti and solar-like oscillators (main sequence and evolved), but also almost 3000 eclipsing binaries with orbital periods shorter than 1100 days. We report the first systematic search for stellar pulsators in the entire Kepler eclipsing binary catalog. The focus is mainly aimed at discovering $\delta$ Scuti, $\gamma$ Doradus, red giant, and tidally excited pulsators. We developed a data inspection tool (DIT) that automatically produces a series of plots from the Kepler light-curves that allows us to visually identify whether stellar oscillations are present in a given time series. We applied the DIT to the whole Kepler eclipsing binary database and identified 303 systems whose light curves display oscillations, including 163 new discoveries. A total of 149 stars are flagged as $\delta$ Scuti (100 from this paper), 115 stars as $\gamma$ Doradus (69 new), 85 stars as red giants (27 new), 59 as tidally excited oscillators (29 new). There is some overlap among these groups, as some display several types of oscillations. Despite many of these systems are likely to be false positives, i. e., when an EB light curve is blended with a pulsator, this catalog gathers a vast sample of systems that are valuable for a better understanding of stellar evolution.
Gaia-derived luminosities of Kepler A/F stars, and the pulsator fraction across the δ Scuti instability strip
We study the pulsator fraction in and around the $\delta$ Scuti instability strip, using Gaia DR2 parallaxes to derive precise luminosities. We use a sample of over 15 000 Kepler A and F stars to classify stars as $\delta$ Sct or non-$\delta$ Sct stars, and pay close attention to variability that could have other origins. We find that 18% of Kepler $\delta$ Sct stars have their dominant frequency above the Kepler long-cadence Nyquist frequency (periods $<$ 1 hr), and 30% have some super-Nyquist variability. We analyse the pulsator fraction as a function of effective temperature and luminosity, finding that not all stars in the $\delta$ Sct instability strip pulsate – the pulsator fraction peaks at just over 70% in a small area in the middle of the instability strip. The results are insensitive to the amplitude threshold used to identify the pulsators. We define a new empirical instability strip based on the observed pulsator fraction, which is systematically hotter than those currently in use. The stellar temperatures, luminosities, and pulsation classifications are provided as a community resource.
Insights from the APOKASC Determination of the Evolutionary State of Red-Giant Stars by consolidation of different methods
The internal working of low-mass stars is of great significance to both the study of stellar structure and the history of the Milky Way. Asteroseismolgy has the power to directly sense the internal structure of stars and allows for the determination of the evolutionary state – i.e. has helium burning commenced or is the energy generated by the fusion of hydrogen in the core? We use observational data from red-giant stars in a combination (known as APOKASC) of asteroseismology (from the Kepler mission) and spectroscopy (from SDSS/APOGEE). The new feature of the analysis is that the APOKASC evolutionary state determination is based on the comparison of diverse approaches to the investigation of the frequency-power spectrum. The high level of agreement between the methods is a strong validation of the approaches. Stars for which there is not a consensus view are readily identified. The comparison also facilitates the identification of unusual stars including those that show evidence for very strong coupling between p and g cavities. The comparison between the classification based on the spectroscopic data and asteroseismic data have led to a new value for the statistical uncertainty in APOGEE temperatures. These consensus evolutionary states will be used as an input for methods that derive masses and ages for these stars based on comparison of observables with stellar evolutionary models (‘grid-based modeling’) and as a training set for machine-learning and data-driven methods of evolutionary state determination.
Testing stellar evolution with asteroseismic inversions of a main sequence star harboring a small convective core
The goal of stellar evolution theory is to predict the structure of stars throughout their lifetimes. Usually, these predictions can be assessed only indirectly, for example by comparing predicted and observed effective temperatures and luminosities. Thanks now to asteroseismology, which can reveal the internal structure of stars, it becomes possible to compare the predictions from stellar evolution theory to actual stellar structures. In this work, we present an inverse analysis of the oscillation data from the solar-type star KIC 6225718, which was observed by the Kepler space observatory during its nominal mission. As its mass is about 20% greater than solar, this star is predicted to transport energy by convection in its nuclear-burning core. We find significant differences between the predicted and actual structure of the star in the radiative interior near to the convective core. In particular, the predicted sound speed is higher than observed in the deep interior of the star, and too low at a fractional radius of 0.25 and beyond. The cause of these discrepancies is unknown, and is not remedied by known physics in the form of convective overshooting or elemental diffusion.
FliPer: A global measure of power density to estimate surface gravities of Solar-like stars
Asteroseismology provides global stellar parameters such as masses, radii or surface gravities using the mean global seismic parameters as well as the effective temperature for thousands of low-mass stars ($0.8 M_\odot <M<3 M_\odot$). This methodology can only be applied to stars in which acoustic modes excited by turbulent convection are measured. Other techniques such as the Flicker can also be used to determine stellar surface gravities, but only works for $\log{g}$ above $2.5$ dex. In this work, we present a new metric called FliPer (Flicker in Power, in opposition to the standard Flicker measurement which is computed in the time domain) that is able to extend the range for which reliable surface gravities can be obtained ($0.1<\log{g}<4.6$ dex) without performing any seismic analysis. FliPer takes into account the average variability of a star measured in the power density spectrum in a given range of frequencies. However, FliPer values calculated on several ranges of frequency are required to better characterize a star. Using a large set of asteroseismic targets it is possible to calibrate the behavior of surface gravity with FliPer through machine learning. This calibration made with a random forest regressor covers a wide range of surface gravities from main-sequence stars to subgiants and red giants, with very small uncertainties from $0.04$ to $0.1$ dex. FliPer values can be inserted in automatic global seismic pipelines to either give estimation of the stellar surface gravity or to assess the quality of the seismic results by detecting any outliers in the obtained surface gravities. FliPer also constrain the surface gravities of main-sequence dwarfs using only long cadence data for which the Nyquist frequency is too low to measure the acoustic-mode properties. This is the first seismic-independent method that allows the estimation of surface gravities below $2.5$ dex with good precision.
Helium settling in F stars: constraining turbulent mixing using observed helium glitch signature
Recent developments in asteroseismology – thanks to space-based missions such as CoRoT and Kepler – provide handles on those properties of stars that were either completely inaccessible in the past or only poorly measured. Among several such properties is the surface helium abundance of F and G stars. We used the oscillatory signature introduced by the ionization of helium in the observed oscillation frequencies to constrain the amount of helium settling in F stars. For this purpose, we identified three promising F stars for which the standard models of atomic diffusion predict large settling (or complete depletion) of surface helium. Assuming turbulence at the base of envelope convection zone slows down settling of the helium and heavy elements, we found an envelope mixed mass of approximately $5 \times 10^{-4}$M$_\odot$ necessary to reproduce the observed amplitude of helium signature for all the three stars. This is much larger than the mixed mass of the order of $10^{-6}$M$_\odot$ found in the previous studies performed using the measurements of the heavy element abundances. This demonstrates the potential of using the helium signature together with measurements of the heavy element abundances to identify the most important physical processes competing against atomic diffusion, allowing eventually to correctly interpret the observed surface abundances of hot stars, consistent use of atomic diffusion in modelling both hot and cool stars, and shed some light on the long-standing cosmological lithium problem.
Influence of magnetic activity on the determination of stellar parameters through asteroseismology
Magnetic activity changes the gravito-acoustic modes of solar-like stars and in particular their frequencies. There is an angular-degree dependence that is believed to be caused by the non-spherical nature of the magnetic activity in the stellar convective envelope. These changes in the mode frequencies could modify the small separation of low-degree modes (i.e. frequency difference between consecutive quadrupole and radial modes), which is sensitive to the core structure and hence to the evolutionary stage of the star. Determining global stellar parameters such as the age using mode frequencies at a given moment of the magnetic activity cycle could lead to biased results. Our estimations show that in general these errors are lower than other systematic uncertainties, but in some circumstances they can be as high as $10\%$ in age and of a few percent in mass and radius. In addition, the frequency shifts caused by the magnetic activity are also frequency dependent. In the solar case this is a smooth function that will mostly be masked by the filtering of the so-called surface effects. However the observations of other stars suggest that there is an oscillatory component with a period close to the one corresponding to the acoustic depth of the He$\,$II zone. This could give rise to a misdetermination of some global stellar parameters, such as the helium abundance. Our computations show that the uncertainties introduced by this effect are lower than the $3\%$ level.
Asteroseismology of solar-type stars
Until the last few decades, investigations of stellar interiors had been restricted to theoretical studies only constrained by observations of their global properties and external characteristics. However, in the last thirty years the field has been revolutionized by the ability to perform seismic investigations of stellar interiors. This revolution begun with the Sun, where helioseismology has been yielding information competing with what can be inferred about the Earth's interior from geoseismology. The last two decades have witnessed the advent of asteroseismology of solar-like stars, thanks to a dramatic development of new observing facilities providing the first reliable results on the interiors of distant stars. The coming years will see a huge development in this field. In this review we focus on solar-type stars, i.e., cool main-sequence stars where oscillations are stochastically excited by surface convection. After a short introduction and a historical overview of the discipline, we review the observational techniques generally used, and we describe the theory behind stellar oscillations in cool main-sequence stars. We continue with a complete description of the normal mode analyses through which it is possible to extract the physical information about the structure and dynamics of the stars. We then summarize the lessons that we have learned and discuss unsolved issues and questions that are still unanswered.
Fundamental properties of Kepler and CoRoT targets: IV. Masses and radii from frequencies of minimum $\Delta \nu$ and their implications
Recently, by analysing the oscillation frequencies of 90 stars, Yıldız, C¸ elik Orhan & Kayhan have shown that the reference frequencies (νmin0, νmin1, and νmin2) derived from glitches due to He II ionization zone have very strong diagnostic potential for the determination of their effective temperatures. In this study, we continue to analyse the same stars and compute their mass, radius, and age from different scaling relations including relations based on νmin0, νmin1, and νmin2. For most of the stars, the masses computed using νmin0 and νmin1 are very close to each other. For 38 stars, the difference between these masses is less than 0.024 M. The radii of these stars from νmin0 and νmin1 are even closer, with differences of less than 0.007 R. These stars may be the most well known solar-like oscillating stars and deserve to be studied in detail. The asteroseismic expressions we derive for mass and radius show slight dependence on metallicity. We therefore develop a new method for computing initial metallicity from this surface metallicity by taking into account the effect of microscopic diffusion. The time dependence of initial metallicity shows some very interesting features that may be important for our understanding of chemical enrichment of Galactic Disc. According to our findings, every epoch of the disc has its own lowest and highest values for metallicity. It seems that rotational velocity is inversely proportional to 1/2 power of age as given by the Skumanich relation.
Bolometric corrections of stellar oscillation amplitudes as observed by the Kepler, CoRoT, and TESS missions
A better understanding of the amplitudes of stellar oscillation modes and surface granulation is essential for improving theories of mode physics and the properties of the outer convection zone of solar-like stars. A proper prediction of these amplitudes is also essential for appraising the detectability of solar-like oscillations for asteroseismic analysis. Comparisons with models, or between different photometric missions, are enabled by applying a bolometric correction, which converts mission-specific amplitudes to their corresponding bolometric (full light) values. We derive the bolometric correction factor for amplitudes of radial oscillation modes and surface granulation as observed by the Kepler, CoRoT, and TESS missions. The calculations are done assuming a stellar spectrum given by a black-body as well as by synthetic spectral flux densities from 1D model atmospheres. We derive a power-law and polynomial relations for the bolometric correction as a function of temperature from the black-body approximation and evaluate the deviations from adopting a more realistic spectrum. Across the full temperature range from $4000-7500$ K, the amplitudes from TESS are in the black-body approximation predicted to be a factor ${\sim}0.83-0.84$ times those observed by Kepler. We find that using more realistic flux spectra over the black-body approximation can change the bolometric correction by as much as ${\sim}30\%$ at the lowest temperatures, but with a change typically within ${\sim}5-10 \%$ around a $T_{\rm eff}$ of $5500-6000$ K. We find that after $T_{\rm eff}$, the bolometric correction most strongly depends on $\rm [M/H]$, which could have an impact on reported metallicity dependencies of amplitudes reported in the literature.
Angular Momentum Transport in Stellar Interiors
Dear KASC/TASC community,
several of you asked me during conferences over the summer if it would be possible to get free access to the final published version of our ARAA on "Angular Momentum Transport in Stellar Interiors". The paper has come out and you can download it free of charge via my personal ARAA e-link.
The review represents a major community effort in that it discusses the asteroseismic rotation and log g estimates of 1210 Kepler/ K2 targets across stellar evolution (assembled until 1 August 2018). You can now download the PDF of the published paper, the figures and supplemental material, and the electronic data file to reproduce Figure 4, from the ARAA website via this link:
http://www.annualreviews.org/eprint/PTFT2M89NRMEAWTEHVE9/full/10.1146/annurev-astro-091918-104359
In order to comply with the ARAA regulations, may I please ask you not to distribute the PDF yourself, but rather to send the above link to the free-of-charge manuscript download to interested readers.
Many thanks,
Conny Aerts,
also on behalf of Stéphane Mathis and Tami Rogers
Deep Learning Applied to the Asteroseismic Modeling of Stars with Coherent Oscillation Modes
We develop a novel method based on machine learning principles to achieve optimal initiation of CPU-intensive computations for forward asteroseismic modeling in a multi-D parameter space. A deep neural network is trained on a precomputed asteroseismology grid containing about 62 million coherent oscillation-mode frequencies derived from stellar evolution models. These models are representative of the core-hydrogen burning stage of intermediate-mass and high-mass stars. The evolution models constitute a 6D parameter space and their predicted low-degree pressure- and gravity-mode oscillations are scanned, using a genetic algorithm. A software pipeline is created to find the best fitting stellar parameters for a given set of observed oscillation frequencies. The proposed method finds the optimal regions in the 6D parameters space in less than a minute, hence providing the optimal starting point for further and more detailed forward asteroseismic modeling in a high-dimensional context. We test and apply the method to seven pulsating stars that were previously modeled asteroseismically by classical grid-based forward modeling based on a $\chi^2$ statistic and obtain good agreement with past results. Our deep learning methodology opens up the application of asteroseismic modeling in +6D parameter space for thousands of stars pulsating in coherent modes with long lifetimes observed by the Kepler space telescope and to be discovered with the TESS and PLATO space missions, while applications so far were done star-by-star for only a handful of cases. Our method is open source and can be used by anyone freely.
The subgiant HR 7322 as an asteroseismic benchmark star
We present an in-depth analysis of the bright subgiant star HR 7322 (KIC 10005473) using Kepler short-cadence photometry, optical interferometry from CHARA, high-resolution spectroscopy using SONG spectra, and stellar modelling using garstec grids and the Bayesian grid-fitting algorithm basta. HR 7322 is only the second subgiant with high-quality Kepler asteroseismology for which we also have interferometric data. We find a limb-darkened angular diameter of $0.443 \pm 0.007$ mas, which combined with a distance derived from the parallax from the second data release of Gaia and a bolometric flux yields a linear radius of $2.00 \pm 0.03$ R$_{\odot}$ and an effective temperature of $6350 \pm 90$ K. HR 7322 exhibits solar-like oscillations and using the asteroseismic scaling relations and revisions thereof, we find excellent agreement between asteroseismic and interferometric stellar radius. The level of precision reached by the careful modelling is to a great extent due to the presence of an avoided crossing in the dipole oscillation mode pattern of HR 7322. We find that the standard models predict radii systematically smaller than the observed interferometric one and that a sub-solar mixing length parameter is needed to achieve an excellent fit to individual oscillation frequencies, interferometric temperature, and spectroscopic metallicity.
Six new rapidly oscillating Ap stars in the Kepler long-cadence data using super-Nyquist asteroseismology
We perform a search for rapidly oscillating Ap stars in the Kepler long-cadence data, where true oscillations above the Nyquist limit of 283.21 $\mu$Hz can be reliably distinguished from aliases as a consequence of the Barycentric time corrections applied to the Kepler data. We find evidence for rapid oscillations in six stars: KIC 6631188, KIC 7018170, KIC 11031749, KIC 10685175, KIC 11296437 and KIC 11409673, and identify each star as chemically peculiar through either pre-existing classifications, or a combination of LAMOST spectroscopy and characteristic spot-based modulation of the light curve. For each star, we identify the principal pulsation mode, and are able to observe several additional pulsation modes in KIC 7018170, allowing for a lower constraint on the large frequency separation $\Delta \nu$. We find that KIC 7018170 and KIC 11409673 both oscillate above their theoretical acoustic cutoff frequency, whilst KIC 11031749 oscillates at the cutoff frequency within uncertainty. All but KIC 11031749 exhibit strong amplitude modulation consistent with the oblique pulsator model, yielding confirmation of their mode geometry and periods of rotation.
gamma Doradus stars as test of angular momentum transport models
Helioseismology and asteroseismology of red giant stars have shown that the distribution of angular momentum in stellar interiors, and its evolution with time remains an open issue in stellar physics. Owing to the unprecedented quality of Kepler photometry, we are able to seismically infer internal rotation rates in gamma Doradus stars, which provide the MS counterpart to the red-giants puzzle. We confront these internal rotation rates to stellar evolution models with rotationally induced transport of angular momentum, in order to test angular momentum transport mechanisms. We used a stellar model-independent method developed by Christophe et al. in order to obtain seismically inferred, buoyancy radii and near-core rotation for 37 gamma Doradus stars observed by Kepler. We show that the buoyancy radius can be used as a reliable evolution indicator for field stars on the MS. We computed rotating evolutionary models including transport of angular momentum in radiative zones, following Zahn and Maeder, with the CESTAM code. This code calculates the rotational history of stars from the birth line to the tip of the RGB. The initial angular momentum content has to be set initially, which is done by fitting rotation periods in young stellar clusters. We show a clear disagreement between the near-core rotation rates measured in the sample and the rotation rates obtained from evolutionary models including rotationally induced transport following Zahn (1992). These results show a disagreement similar to that of the Sun and red giant stars. This suggests the existence of missing mechanisms responsible for the braking of the core before and along the MS. The efficiency of the missing mechanisms is investigated. The transport of angular momentum as formalized by Zahn and Maeder cannot explain the measurements of near-core rotation in main-sequence intermediate-mass stars we have at hand.
The Second APOKASC Catalog: The Empirical Approach
We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and Kepler asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($\Delta \nu$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($\nu_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4%. Median random and systematic mass uncertainties are at the 9% and 8% level respectively for RC stars.
Data tables are online.
The period–luminosity relation for δ Scuti stars using Gaia DR2 parallaxes
We have examined the period–luminosity (P–L) relation for $\delta$ Scuti stars using Gaia DR2 parallaxes. We included 228 stars from the catalogue of Rodriguez et al. (2000), as well as 1124 stars observed in the four-year \kepler mission. For each star we considered the dominant pulsation period, and used DR2 parallaxes and extinction corrections to determine absolute $V$ magnitudes. Many stars fall along a sequence in the P–L relation coinciding with fundamental-mode pulsation, while others pulsate in shorter-period overtones. The latter stars tend to have higher effective temperatures, consistent with theoretical calculations. Surprisingly, we find an excess of stars lying on a ridge with periods half that of the fundamental. We suggest this may be due to a 2:1 resonance between the third or fourth overtone and the fundamental mode.
The period-luminosity relation for delta Scuti stars using Gaia DR2 parallaxes
We have examined the period–luminosity (P–L) relation for $\delta$ Scuti stars using Gaia DR2 parallaxes. We included 228 stars from the catalogue of Rodriguez et al. (2000), as well as 1124 stars observed in the four-year Kepler mission. For each star we considered the dominant pulsation period, and used DR2 parallaxes and extinction corrections to determine absolute $V$ magnitudes. Many stars fall along a sequence in the P–L relation coinciding with fundamental-mode pulsation, while others pulsate in shorter-period overtones. The latter stars tend to have higher effective temperatures, consistent with theoretical calculations. Surprisingly, we find an excess of stars lying on a ridge with periods half that of the fundamental. We suggest this may be due to a 2:1 resonance between the third or fourth overtone and the fundamental mode.
Revised Stellar Properties of Kepler Targets for the Q1-17 (DR25) Transit Detection Run
The determination of exoplanet properties and occurrence rates using Kepler data critically depends on our knowledge of the fundamental properties (such as temperature, radius and mass) of the observed stars. We present revised stellar properties for 197,096 Kepler targets observed between Quarters 1–17 (Q1–17), which were used for the final transiting planet search run by the Kepler Mission (Data Release 25, DR25). Similar to the Q1–16 catalog by Huber et al. the classifications are based on conditioning published atmospheric parameters on a grid of Dartmouth isochrones, with significant improvements in the adopted methodology and over 29,000 new sources for temperatures, surface gravities or metallicities. In addition to fundamental stellar properties the new catalog also includes distances and extinctions, and we provide posterior samples for each stellar parameter of each star. Typical uncertainties are $\sim$ 27% in radius, $\sim$ 17% in mass, and $\sim$ 51% in density, which is somewhat smaller than previous catalogs due to the larger number of improved ogg constraints and the inclusion of isochrone weighting when deriving stellar posterior distributions. On average, the catalog includes a significantly larger number of evolved solar-type stars, with an increase of 43.5% in the number of subgiants. We discuss the overall changes of radii and masses of Kepler targets as a function of spectral type, with particular focus on exoplanet host stars.
The seismic performance
The space missions CoRoT and Kepler have demonstrated the capability of asteroseismology to deliver unique information for stellar physics, stellar evolution, and Galactic archaeology. Many ongoing large-scale surveys use seismology, for instance for measuring the mass and radius of stars hosting exoplanets; future projects seek to use the seismic information too. We aim at predicting the information we can derive from the seismic observation of a low-mass star showing solar-like oscillations in a way as simple as possible, in order to assess what we call the seismic performance: the capability to predict and quantify which information can be inferred, with which precision, from the seismic signal. Previous seismic observations with CoRoT and Kepler are used to define and calibrate a seismic index that can be used as a performance index. This index defined with simple analytical computations is used to build a seismic simulator and to characterize the seismic performance. Two regimes dominate the seismic performance. For evolved stars, the stellar regime is dominated by stellar properties only; neither the stellar magnitude nor the instrumental properties play any role in this regime. In the instrumental regime, the instrumental noise and the photon shot noise dominate; the performance index crucially depends on the stellar magnitude. Main-sequence stars are usually in this instrumental regime. In both regimes, the performance index increases linearly with the observation time. Different thresholds are defined, for the detection of the oscillations and for the measurement of different stellar parameters. The method shows a spread of about 21 %, related to multiple sources as stellar variability or binarity. This new way for considering solar-like oscillations allows us to estimate the seismic performance, calibrated by previous observations, of space missions such as TESS. It can help elaborating the seismic yield of future mission programs as the forthcoming runs of PLATO, in complement to light-curve simulations.
Damping rates and frequency corrections of Kepler LEGACY stars
Linear damping rates and modal frequency corrections of radial oscillation modes in selected LEGACY main-sequence stars are estimated by means of a nonadiabatic stability analysis. The selected stellar sample covers stars observed by Kepler with a large range of surface temperatures and surface gravities. A nonlocal, time-dependent convection model is perturbed to assess stability against pulsation modes. The mixing-length parameter is calibrated to the surface-convection-zone depth of a stellar model obtained from fitting adiabatic frequencies to the LEGACY observations, and two of the nonlocal convection parameters are calibrated to the corresponding LEGACY linewidth measurements. The remaining nonlocal convection parameters in the 1D calculations are calibrated so as to reproduce profiles of turbulent pressure and of the anisotropy of the turbulent velocity field of corresponding 3D hydrodynamical simulations. The atmospheric structure in the 1D stability analysis adopts a temperature-optical-depth relation derived from 3D hydrodynamical simulations. Despite the small number of parameters to adjust, we find good agreement with detailed shapes of both turbulent pressure profiles and anisotropy profiles with depth, and with damping rates as a function of frequency. Furthermore, we find the absolute modal frequency corrections, relative to a standard adiabatic pulsation calculation, to increase with surface temperature and surface gravity.
Stellar ages, masses and radii from asteroseismic modeling are robust to systematic errors in spectroscopy
Context. The search for twins of the Sun and Earth relies on accurate characterization of stellar and the exoplanetary parameters age, mass, and radius. In the modern era of asteroseismology, parameters of solar-like stars are derived by fitting theoretical models to observational data, which include measurements of their oscillation frequencies, metallicity [Fe/H], and effective temperature $T_{\text{eff}}$. Furthermore, combining this information with transit data yields the corresponding parameters for their associated exoplanets.
Aims. While values of [Fe/H] and $T_{\text{eff}}$ are commonly stated to a precision of $\sim$ 0.1 dex and $\sim$ 100 K, the impact of systematic errors in their measurement has not been studied in practice within the context of the parameters derived from them. Here we seek to quantify this.
Methods. We used the Stellar Parameters in an Instant (SPI) pipeline to estimate the parameters of nearly 100 stars observed by Kepler and Gaia, many of which are confirmed planet hosts. We adjusted the reported spectroscopic measurements of these stars by introducing faux systematic errors and, separately, artificially increasing the reported uncertainties of the measurements, and quantified the differences in the resulting parameters.
Results. We find that a systematic error of 0.1 dex in [Fe/H] translates to differences of only 4%, 2%, and 1% on average in the resulting stellar ages, masses, and radii, which are well within their uncertainties ($\sim$ 11%, 3.5%, 1.4%) as derived by SPI. We also find that increasing the uncertainty of [Fe/H] measurements by 0.1 dex increases the uncertainties of the ages, masses, and radii by only 0.01 Gyr, 0.02 $\text{M}_\odot$, and 0.01 $\text{R}_\odot$, which are again well below their reported uncertainties ($\sim$ 0.5 Gyr, 0.04 $\text{M}_\odot$, 0.02 $\text{R}_\odot$). The results for $T_{\text{eff}}$ at 100 K are similar.
Conclusions. Stellar parameters from SPI are unchanged within uncertainties by errors of up to 0.14 dex or 175 K. They are even more robust to errors in $T_{\text{eff}}$ than the seismic scaling relations. Consequently, the parameters for their exoplanets are also robust.
Understanding the Limitations of Gyrochronology for Old Field Stars
Nearly half a century has passed since the initial indications that stellar rotation slows while chromospheric activity weakens with a power-law dependence on age, the so-called Skumanich relations. Subsequent characterization of the mass-dependence of this behavior up to the age of the Sun led to the advent of gyrochronology, which uses the rotation rate of a star to infer its age from an empirical calibration. The efficacy of the method relies on predictable angular momentum loss from a stellar wind entrained in the large-scale magnetic field produced by global dynamo action. Recent observational evidence suggests that the global dynamo begins to shut down near the middle of a star's main-sequence lifetime, leading to a disruption in the production of large-scale magnetic field, a dramatic reduction in angular momentum loss, and a breakdown of gyrochronology relations. For solar-type stars this transition appears to occur near the age of the Sun, when rotation becomes too slow to imprint Coriolis forces on the global convective patterns, reducing the shear induced by differential rotation, and disrupting the large-scale dynamo. We use data from Barnes (2007) to reveal the signature of this transition in the observations that were originally used to validate gyrochronology. We propose that chromospheric activity may ultimately provide a more reliable age indicator for older stars, and we suggest that asteroseismology can be used to help calibrate activity-age relations for field stars beyond the middle of their main-sequence lifetimes.
Asteroseismology of main-sequence F stars with Kepler: overcoming short mode lifetimes
Asteroseismology is a powerful way of determining stellar parameters and properties of stars like the Sun. However, main-sequence F-type stars exhibit short mode lifetimes relative to their oscillation frequency, resulting in overlapping radial and quadrupole modes. The goal of this paper is to use the blended modes for asteroseismology in place of the individual separable modes. We used a peak-bagging method to measure the centroids of radial-quadrupole pairs for 66 stars from the Kepler LEGACY sample, as well as $\theta$ Cyg, HD 49933, HD 181420, and Procyon. We used the relative quadrupole-mode visibility to estimate a theoretical centroid frequency from a grid of stellar oscillation models. The observed centroids were matched to the modelled centroids with empirical surface correction to calculate stellar parameters. We find that the stellar parameters returned using this approach agree with the results using individual mode frequencies for stars, where those are available. We conclude that the unresolved centroid frequencies can be used to perform asteroseismology with an accuracy similar to that based on individual mode frequencies.
Helium abundance in a sample of cool stars: measurements from asteroseismology
The structural stratification of a solar-type main sequence star primarily depends on its mass and chemical composition. The surface heavy element abundances of the solar-type stars are reasonably well determined using conventional spectroscopy, however the second most abundant element helium is not. This is due to the fact that the envelope temperature of such stars is not high enough to excite helium. Since the helium abundance of a star affects its structure and subsequent evolution, the uncertainty in the helium abundance of a star makes estimates of its global properties (mass, radius, age etc.) uncertain as well. The detections of the signatures of the acoustic glitches from the precisely measured stellar oscillation frequencies provide an indirect way to estimate the envelope helium content. We use the glitch signature caused by the ionization of helium to determine the envelope helium abundance of 38 stars in the Kepler seismic LEGACY sample. Our results confirm that atomic diffusion does indeed take place in solar-type stars. We use the measured surface abundances in combination with the settling predicted by the stellar models to determine the initial abundances. The initial helium and metal mass fractions have subsequently been used to get the preliminary estimates of the primordial helium abundance, $Y_p = 0.244\pm0.019$, and the galactic enrichment ratio, $\Delta Y / \Delta Z = 1.226\pm0.849$. Although the current estimates have large errorbars due to the limited sample size, this method holds great promises to determine these parameters precisely in the era of upcoming space missions.
Butterfly diagram of a Sun-like star observed using asteroseismology
Stellar magnetic fields are poorly understood but are known to be important for stellar evolution and exoplanet habitability. They drive stellar activity, which is the main observational constraint on theoretical models for magnetic field generation and evolution. Starspots are the main manifestation of the magnetic fields at the stellar surface. In this study we measure the variation of their latitude with time, called a butterfly diagram in the solar case, for the solar analogue HD 173701 (KIC 8006161). To that effect, we use Kepler data, to combine starspot rotation rates at different epochs and the asteroseismically determined latitudinal variation of the stellar rotation rates. We observe a clear variation of the latitude of the starspots. It is the first time such a diagram is constructed using asteroseismic data.
Chaotic dynamics in the pulsation of DF Cygni, as observed by Kepler
Pulsations of RV Tauri-type variable stars can be governed by chaotic dynamics. However, observational evidence for this happening is usually hard to come by. Here we use the continuous, 4-year-long observations of the Kepler space telescope to search for the signs of chaos in the RVb-type pulsating supergiant, DF Cygni. We use the Global Flow Reconstruction method to estimate the quantitative properties of the dynamics driving the pulsations of the star. The secondary, long-term light variation, i.e., the RVb phenomenon was removed in the analysis with the Empirical Mode Decomposition method. Our analysis revealed that the pulsation of DF Cyg could be described as a chaotic signal with a Lyapunov dimension of $\sim$2.8. DF Cyg is only the third RV Tau star, and the first of the RVb subtype, where the nonlinear analysis indicates that low-dimensional chaos may explain the peculiarities of the pulsation.
Forward asteroseismic modeling of stars with a convective core from gravity-mode oscillations: parameter estimation and stellar model selection
We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of low-degree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used $\chi^2$ statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.
Coefficients of variation for detecting solar-like oscillations
Detecting the presence and characteristic scale of a signal is a common problem in data analysis. We develop a fast statistical test of the null hypothesis that a Fourier-like power spectrum is consistent with noise. The null hypothesis is rejected where the local “coefficient of variation” (CV)—the ratio of the standard deviation to the mean—in a power spectrum deviates significantly from expectations for pure noise ($\mathrm{CV}\approx1.0$ for a $\chi^2$ 2-degrees-of-freedom distribution). This technique is of particular utility for detecting signals in power spectra with frequency-dependent noise backgrounds, as it is only sensitive to features that are sharp relative to the inspected frequency bin width. We develop a CV-based algorithm to quickly detect the presence of solar-like oscillations in photometric power spectra that are dominated by stellar granulation. This approach circumvents the need for background fitting to measure the frequency of maximum solar-like oscillation power, $\nu_\textrm{max}$. In this paper, we derive the basic method and demonstrate its ability to detect the pulsational power excesses from the well-studied APOKASC-2 sample of oscillating red giants observed by Kepler. We recover the cataloged $\nu_\textrm{max}$ values with an average precision of 2.7% for 99.5% of the stars with 4 years of Kepler photometry. Our method produces false positives for $<1\%$ of dwarf stars with $\nu_\textrm{max}$ well above the long-cadence Nyquist frequency. The algorithm also flags spectra that exhibit astrophysically interesting signals in addition to single, solar-like oscillation power excesses, which we catalog as part of our characterization of the Kepler light curves of APOKASC-2 targets.
Nonlinear seismic scaling relations
Context: In recent years the so-called seismic scaling relations for the frequency of maximum power, $\nu_\mathrm{max} \propto g/\sqrt{T_\mathrm{eff}}$, and for the large frequency separation, $\Delta\nu \propto \sqrt{\bar\rho}$, have caught the attention of various fields of astrophysics. This is because these relations can be used to estimate parameters, such as mass and radius of stars that show solar-like oscillations. With the exquisite photometry of Kepler, the uncertainties in the seismic observables are small enough to estimate masses and radii with a precision of only a few per cent. Even though this seems to work quite well for main-sequence stars, there is empirical evidence, mainly from studies of eclipsing binary systems, that the seismic scaling relations systematically overestimate the mass and radius of red giants by about 5 and 15%, respectively. Various model-based corrections of the $\Delta\nu -$scaling reduce the problem but do not solve it. Aims: Our goal is to define revised seismic scaling relations that account for the know systematic mass and radius discrepancies in a completely model-independent way. Methods: We use probabilistic methods to analyse the seismic data and to derive nonlinear scaling relations based on a sample of six red-giant branch (RGB) stars that are members of eclipsing binary systems and about 60 red giants on the RGB as well as in the core-helium burning red clump (RC) in the two open clusters NGC 6791 and NGC 6819. Results: We re-examine the global oscillation parameters of the giants in the binary systems in order to determine their seismic fundamental parameters and find them to agree with the dynamic parameters from the literature if we adopt nonlinear scalings. We note that a curvature and glitch corrected $\Delta\nu_\mathrm{cor}$ should be preferred over a local or average value of $\Delta\nu$. We then compare the observed seismic parameters of the cluster giants to those scaled from independent measurements and find the same nonlinear behaviour as for the eclipsing binaries. Our final proposed scaling relations are based on both samples and cover a broad range of evolutionary stages from RGB to RC stars: $g/\sqrt{T_\mathrm{eff}} = (\nu_\mathrm{max}/\nu_\mathrm{max,\odot})^{1.0075\pm0.0021}$ and $\sqrt{\bar\rho} = (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})[\eta - (0.0085\pm0.0025) \log^2 (\Delta\nu_\mathrm{cor}/\Delta\nu_\mathrm{cor,\odot})]^{-1}$, where $g$, $T_\mathrm{eff}$, and $\bar\rho$ are in solar units, $\nu_\mathrm{max,\odot}=3140\pm5$\mh and $\Delta\nu_\mathrm{cor,\odot}=135.08\pm0.02$\mh , and $\eta$ is equal to one in case of RGB stars and $1.04\pm0.01$ for RC stars. Conclusions: A direct consequence of these new scaling relations is that the average mass of stars on the ascending giant branch reduces to $1.10\pm0.03M$\sun in \na and $1.45\pm0.06M$\sun in \nb, allowing us to revise the clusters' distance modulus to $13.00\pm0.02$ and $11.82\pm0.02$, respectively. We also find strong evidence that both clusters are significantly older than concluded from previous seismic investigations.
Period spacings in red giants IV. A complete description of the mixed-mode pattern
Oscillation modes with a mixed character, as observed in evolved low-mass stars, are highly sensitive to the physical properties of the innermost regions. Measuring their properties is therefore extremely important to probe the core, but requires some care, due
to the complicated nature of the mixed-mode pattern.
This work aims at providing a complete and consistent description
of the mixed-mode pattern, based on the asymptotic expansion, among which the gravity offset $\epsg$. We revisit previous findings and empirically test how period spacings, rotational splittings, mixed-mode widths and amplitudes can be estimated in a consistent view, based on the properties of the mode inertia ratios.
From the asymptotic fit of the mixed-mode pattern of red giants at various evolutionary stages, we derive asymptotic parameters that are not only very precise, but also accurate. We decipher the complex pattern in a rapidly rotating star, and explain how asymmetrical splittings can be inferred. The variation of the asymptotic gravity offsets along stellar evolution is investigated in detail. We also derive generic properties that explain under which conditions mixed modes can be observed.
The rotational shear layer inside the early red-giant star KIC 4448777
We present the asteroseismic study of the early red-giant star KIC 4448777, complementing and integrating a previous work \citep[][Paper I]dimauro2016, aimed at characterizing the dynamics of its interior by analyzing the overall set of data collected by the Kepler satellite during the four years of its first nominal mission. We adopted the Bayesian inference code DIAMONDS \citepCorsaro14 for the peak bagging analysis and asteroseismic splitting inversion methods to derive the internal rotational profile of the star. The detection of new splittings of mixed modes, more concentrated in the very inner part of the helium core, allowed us to reconstruct the angular velocity profile deeper into the interior of the star and to disentangle the details better than in Paper I: the helium core rotates almost rigidly about 6 times faster than the convective envelope, while part of the hydrogen shell seems to rotate at a constant velocity about 1.15 times lower than the He core. In particular, we studied the internal shear layer between the fast-rotating radiative interior and the slow convective zone and we found that it lies partially inside the hydrogen shell above $r \simeq 0.05R$ and extends across the core-envelope boundary. Finally, we theoretically explored the possibility for the future to sound the convective envelope in the red-giant stars and we concluded that the inversion of a set of splittings with only low-harmonic degree $l\leq 3$, even supposing a very large number of modes, will not allow to resolve the rotational profile of this region in detail.
Predicting radial-velocity jitter induced by stellar oscillations based on Kepler data
Radial velocity jitter due to intrinsic stellar variability introduces challenges when charactering exoplanet systems, in particular, when studying the exoplanetary signals of small (sub Neptune-sized) planets orbiting solar-type stars. In this Letter we aim to predict for dwarfs and giants the jitter due to stellar oscillations, which in velocity have much larger amplitudes than noise introduced by granulation on longer timescales. Based on global oscillation parameters measured with Kepler data we fit the jitter in terms of the following sets of stellar parameters: (1) Luminosity, mass, and effective temperature: the fit returns precisions of 17.9% and 27.1% for dwarfs and giants, respectively. (2) Luminosity, effective temperature, and surface gravity: The precisions are the same as using the previous parameter set. (3) Surface gravity and effective temperature: we obtain a precision of 22.6% for dwarfs and 27.1% for giants. (4): Luminosity and effective temperature: the precision is 47.8% for dwarfs and 27.5% for giants. Our method will be valuable for anticipating the potential radial-velocity stellar noise level of exoplanet host stars to be found by the TESS andPLATO space missions, and thus can be useful for their follow-up spectroscopic observations. We provide publicly available code (https://github.com/Jieyu126/Jitter) which can also be used to set a prior for the jitter term as a component when modeling the Keplerian orbits of the exoplanets.
Core rotation braking on the red giant branch for various mass ranges
Asteroseismology allows us to probe stellar interiors. In the case of red giant stars, conditions in the stellar interior are such to allow for the existence of mixed modes, consisting in a coupling between gravity waves in the radiative interior and pressure waves in the convective envelope. Mixed modes can thus be used to probe the physical conditions in red giant cores. However, we still need to identify the physical mechanisms that transport angular momentum inside red giants, leading to the slow-down observed for the red giant core rotation. Thus large-scale measurements of the red giant core rotation are of prime importance to obtain tighter constraints on the efficiency of the internal angular momentum transport, and to study how this efficiency changes with stellar parameters. This work aims at identifying the components of the rotational multiplets for dipole mixed modes in a large number of red giant oscillation spectra observed by Kepler. Such identification provides us with a direct measurement of the red giant mean core rotation. We compute stretched spectra that mimic the regular pattern of pure dipole gravity modes. Mixed modes with same azimuthal order are expected to be almost equally spaced in stretched period, with a spacing equals to the pure dipole gravity mode period spacing. The departure from this regular pattern allows us to disentangle the various rotational components and therefore to determine the mean core rotation rates of red giants. We automatically identify the rotational multiplet components of 1183 stars on the red giant branch with a success rate of 69 % with respect to our initial sample. As no information on the internal rotation can be deduced for stars seen pole-on, we obtain mean core rotation measurements for 875 red giant branch stars. This large sample includes stars with a mass as large as 2.5 $M_{\odot}$, allowing us to test the dependence of the core slow-down rate on the stellar mass. Disentangling rotational splittings from mixed modes is now possible in an automated way for stars on the red giant branch, even for the most complicated cases, where the rotational splittings exceed half the mixed-mode period spacing. This work on a large sample allows us to refine previous measurements of the evolution of the mean core rotation on the red giant branch. Rather than a slight slow down, our results suggest rotation to be constant along the red giant branch, with values independent on the mass.
K2 space photometry reveals rotational modulation and stellar pulsations in chemically peculiar A and B stars
Context. The physics of magnetic hot stars and how a large-scale magnetic field affects their interior properties is largely unknown. Few studies have combined high-quality observations and modelling of magnetic pulsating stars, known as magneto-asteroseismology, primarily because of the dearth of detected pulsations in stars with a confirmed and well-characterised large-scale magnetic field. Aims. We aim to characterise observational signatures of rotation and pulsation in chemically peculiar candidate magnetic stars using photometry from the K2 space mission. Thus, we identify the best candidate targets for ground-based, optical spectropolarimetric follow-up observations to confirm the presence of a large-scale magnetic field. Methods. We employed customised reduction and detrending tools to process the K2 photometry into optimised light curves for a variability analysis. We searched for the periodic photometric signatures of rotational modulation caused by surface abundance inhomogeneities in 56 chemically peculiar A and B stars. Furthermore, we searched for intrinsic variability caused by pulsations (coherent or otherwise) in the amplitude spectra of these stars. Results. The rotation periods of 38 chemically peculiar stars are determined, 16 of which are the first determination of the rotation period in the literature. We confirm the discovery of high-overtone roAp pulsation modes in HD 177765 and find an additional 3 Ap and Bp stars that show evidence of high-overtone pressure modes found in roAp stars in the form of possible Nyquist alias frequencies in their amplitude spectra. Furthermore, we find 6 chemically peculiar stars that show evidence of intrinsic variability caused by gravity or pressure pulsation modes. Conclusions. The discovery of pulsations in a non-negligible fraction of chemically peculiar stars make these stars high-priority targets for spectropolarimetric campaigns to confirm the presence of their expected large-scale magnetic field. The ultimate goal is to perform magneto-asteroseismology and probe the interior physics of magnetic pulsating stars.
A weak modulation effect detected in the light curves of KIC 5950759: intrinsic or instrumental effect?
In this paper, the high-precision light curves of the Kepler target KIC 5950759 are analyzed. The Fourier analysis of the long cadence (LC) light curve reveals three independent frequencies. Two of them are main pulsation modes: F0 = 14.221373(21) $\rm{d^{-1}}$ and F1 = 18.337249(44) $\rm{d^{-1}}$. The third independent frequency, $f_m$ = 0.3193 d$^{-1}$, is found in LC data with a signal-to-noise ratio of 6.2. A weak modulation of $f_m$ to F0 and F1 modes (triplet structures centered on F0 and F1) are detected both in long and short cadence data. This is the first detection of the modulation effect in a double-mode high-amplitude $\delta$ Scuti (HADS) star. The most possible cause of the modulation effect in the light curves is amplitude modulation with the star's rotation frequency of 0.3193 d$^{-1}$. The preliminary analysis suggests that KIC 5950759 is in the bottom of the HADS instability strip and likely situated in the main sequence. Spectroscopic observations are necessary to verify the true nature of the modulation terms.
Surface gravities for 15,000 Kepler stars measured from stellar granulation and validated with Gaia DR2 parallaxes
We have developed a method to estimate surface gravity ($\log g$) from light curves by measuring the granulation background, similar to the “flicker” method by Bastien et al. (2016) but working in the Fourier power spectrum. We calibrated the method using Kepler stars for which asteroseismology has been possible with short-cadence data, demonstrating a precision in $\log g$ of about 0.05 dex. We also derived a correction for white noise as a function of Kepler magnitude by measuring white noise directly from observations. We then applied the method to the same sample of long-cadence stars as Bastien et al. We provide a catalogue of $\log g$ values for about 15,000 stars having uncertainties better than 0.5 dex. We use Gaia DR2 parallaxes to validate that granulation is a powerful method to measure $\log g$ from light curves. Our method can also be applied to the large number of light curves collected by K2 and TESS.
The mass and age of the first SONG target: the red giant 46 LMi.
The Stellar Observation Network Group (SONG) is an initiative to build a worldwide network of 1m telescopes with high-precision radial-velocity spectrographs. Here we analyse the first radial-velocity time series of a red-giant star measured by the SONG telescope at Tenerife. The asteroseismic results demonstrate a major increase in the achievable precision of the parameters for red-giant stars obtainable from ground-based observations. Reliable tests of the validity of these results are needed, however, before the accuracy of the parameters can be trusted. We analyse the first SONG time series for the star 46 LMi, which has a precise parallax and an angular diameter measured from interferometry, and therefore a good determination of the stellar radius. We use asteroseismic scaling relations to obtain an accurate mass, and modelling to determine the age. A 55-day time series of high-resolution, high S/N spectra were obtained with the first SONG telescope. We derive the asteroseismic parameters by analysing the power spectrum. To give a best guess on the large separation of modes in the power spectrum, we have applied a new method which uses the scaling of Kepler red-giant stars to 46 LMi. Several methods have been applied: classical estimates, seismic methods using the observed time series, and model calculations to derive the fundamental parameters of 46 LMi. Parameters determined using the different methods are consistent within the uncertainties. We find the following values for the mass $M$ (scaling), radius $R$ (classical), age (modelling), and surface gravity (combining mass and radius): $M = 1.09\pm0.04$ Msun $R = 7.95\pm0.11$ Rsun, age $t = 8.2\pm1.9$ Gy, and $\log g = 2.674 \pm 0.013$. The exciting possibilities for ground-based asteroseismology of solar-like oscillations with a fully robotic network have been illustrated with the results obtained from just a single site of the SONG network. The window function is still a severe problem which will be solved when there are more nodes in the network.
Surface correction of main sequence solar-like oscillators with the it Kepler LEGACY sample
Poor modelling of the surface regions of solar-like stars causes a systematic discrepancy between the observed and model pulsation frequencies. We aim to characterise this frequency discrepancy for main sequence solar-like oscillators for a wide range of initial masses and metallicities. We fit stellar models to the observed mode frequencies of the 67 stars, including the Sun, in the Kepler LEGACY sample, using three different empirical surface corrections. The three surface corrections we analyse are a frequency power-law, a cubic frequency term divided by the mode inertia, and a linear combination of an inverse and cubic frequency term divided by the mode inertia. We construct a grid of stellar evolution models using the stellar evolution code MESA and calculate mode frequencies using GYRE. Along with the surface correction coefficients, we calculate an empirical homology scaling factor to the model frequencies, which greatly improves the robustness of our grid. We calculate accurate stellar and surface correction parameters for each star using the average of the best-fitting models from each evolutionary track, weighted by the likelihood of each model. The resulting model stellar parameters agree well with an independent reference, the BASTA pipeline. We find that scaling the frequencies by the mode inertia improves the fit between the models and observations. The inclusion of the inverse frequency term produces substantially better model fits to lower surface gravity stars. However, the extra free parameter can cause over-fitting resulting and increased uncertainties for some of the more evolved stars in the sample.
Seismic probing of the first dredge-up event through the eccentric red-giant/red-giant spectroscopic binary KIC9163796
Binaries in double-lined spectroscopic systems (SB2) provide a homogeneous set of stars. Differences of parameters, such as age or initial conditions, which otherwise would have strong impact on the stellar evolution, can be neglected. The observed differences are then determined by the difference in stellar mass between the two components. The mass ratio can be determined with much higher accuracy than the actual stellar mass. In this work, we aim to study the eccentric binary system KIC9163796, whose two components are very close in mass and both are low-luminosity red-giant stars. We analyse four years of Kepler space photometry and we obtain high-resolution spectroscopy with the Hermes instrument. The orbital elements and the spectra of both components are determined using spectral disentangling methods. The effective temperatures, and metallicities are extracted from disentangled spectra of the two stars. Mass and radius of the primary are determined through asteroseismology. The surface rotation period of the primary is determined from the Kepler light curve. From representative theoretical models of the star, we derive the internal rotational gradient, while for a grid of models, the measured lithium abundance is confronted with theoretical predictions. From seismology the primary of KIC9163796 is a star of 1.39$\pm$0.06 M$_\odot$, while the spectroscopic mass ratio between both components can be determined with much higher precision by spectral disentangling to be 1.015$\pm$0.005. With such mass and a difference in effective temperature of 600 K from spectroscopy, the secondary and primary are in the early and advanced stage of the first dredge-up event on the red-giant branch. The period of the primary's surface rotation resembles the orbital period within 10 days. The radial rotational gradient between the surface and core in KIC9163796 is found to be 6.9$^{+2.0}_{-1.0}$. This is a low value but not exceptional if compared to the sample of typical single field stars. The seismic average of the envelope's rotation agrees with the surface rotation rate. The lithium abundance is in agreement with quasi rigidly-rotating models. The agreement between the surface rotation with the seismic result indicates that the full convective envelope is rotating quasi-rigidly. The models of the lithium abundance are compatible with a rigid rotation in the radiative zone during the main sequence. Because of the many constraints offered by oscillating stars in binary systems, such objects are important test beds of stellar evolution.
Amplitude and lifetime of radial modes in red giant star spectra observed by Kepler
The space-borne missions CoRoT and Kepler have provided photometric observations of unprecedented quality. The study of solar-like oscillations observed in red giant stars by these satellites allows a better understanding of the different physical processes occurring in their interiors. In particular, the study of the mode excitation and damping is a promising way to improve our understanding of stellar physics that has, so far, been performed only on a limited number of targets. The recent asteroseismic characterization of the evolutionary status for a large number of red giants allows us to study the physical processes acting in the interior of red giants and how they are modify during stellar evolution. In this work, we aim to obtain information on the excitation and damping of pressure modes through the measurement of the stars’ pressure mode widths and amplitudes and to analyze how they are modified with stellar evolution. The objective is to bring observational constraints on the modeling of the physical processes behind mode excitation and damping. We fit the frequency spectra of red giants with well defined evolutionary status using Lorentzians functions to derive the pressure mode widths and amplitudes. To strengthen our conclusions, we used two different fitting techniques. Pressure mode widths and amplitudes were determined for more than 5000 red giants. We put into light a variation of the mode width with stellar evolution as well as a dependence of this parameter with the stellar mass and temperature. We also confirm observationally the influence of the stellar metallicity on the mode amplitudes, as predicted by models.
Asteroseismology of 16000 Kepler red giants: Global oscillation parameters, Masses, and Radii
The Kepler mission has provided exquisite data to perform an ensemble asteroseismic analysis on evolved stars. In this work we systematically characterize solar-like oscillations and granulation for 16,094 oscillating red giants, using end-of-mission long-cadence data. We produced a homogeneous catalog of the frequency of maximum power (typical uncertainty $\sigma_{\nu_{\rm max}}$=1.6%), the mean large frequency separation ($\sigma_{\Delta\nu}$=0.6%), oscillation amplitude ($\sigma_{\rm A}$=4.7%), granulation power ($\sigma_{\rm gran}$=8.6%), power excess width ($\sigma_{\rm width}$=8.8%), seismically-derived stellar mass ($\sigma_{\rm M}$=7.8%), radius ($\sigma_{\rm R}$=2.9%), and thus surface gravity ($\sigma_{\log g}$=0.01 dex). Thanks to the large red giant sample, we confirm that red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ in the distribution of oscillation amplitude, granulation amplitude, and width of power excess, which is mainly due to the mass difference. The distribution of oscillation amplitudes shows an extremely sharp upper edge at fixed $\nu_{max}$, which might hold clues to understand the excitation and damping mechanisms of the oscillation modes. We find both oscillation amplitude and granulation power depend on metallicity, causing a spread of 15% in oscillation amplitudes and a spread of 25% in granulation power from [Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as reliable distance indicators and age proxies for mapping and dating galactic stellar populations observed by Kepler. They will also provide an excellent opportunity to test asteroseismology using Gaia parallaxes, and lift degeneracies in deriving atmospheric parameters in large spectroscopic surveys such as APOGEE and LAMOST.
Detecting Solar-like Oscillations in Red Giants with Deep Learning
Time-resolved photometry of tens of thousands of red giant stars from space missions like Kepler and K2 has created the need for automated asteroseismic analysis methods. The first and most fundamental step in such analysis, is to identify which stars show oscillations. It is critical that this step can be performed with no, or little, detection bias, particularly when performing subsequent ensemble analyses that aim to compare properties of observed stellar populations with those from galactic models. Yet, an automated and efficient solution to this initial detection step has still not been found, meaning that expert visual inspection of data from each star is required to obtain the highest level of detections. Hence, to mimic how an expert eye analyses the data, we use supervised deep learning to not only detect oscillations in red giants, but also predict the location of the frequency at maximum power, $\nu_{\mathrm{max}}$, by observing features in 2D images of power spectra. By training on Kepler data, we achieve a detection accuracy of 98% on K2 Campaign 6 stars and a detection accuracy of 99% on K2 Campaign 3 stars. We further find that the estimated uncertainty of our deep learning-based $\nu_{\mathrm{max}}$ predictions is about 5%. This is comparable to human-level performance using visual inspection. When examining outliers we find that the deep learning results are more likely to provide robust $\nu_{\mathrm{max}}$ estimates than the classical model-fitting method.
Deep Learning Classification in Asteroseismology Using an Improved Neural Network: Results on 15000 Kepler Red Giants and Applications to K2 and TESS Data
Deep learning in the form of 1D convolutional neural networks have previously been shown to be capable of efficiently classifying the evolutionary state of oscillating red giants into red giant branch stars and helium-core burning stars by recognizing visual features in their asteroseismic frequency spectra. We elaborate further on the deep learning method by developing an improved convolutional neural network classifier. To make our method useful for current and future space missions such as K2, TESS and PLATO, we train classifiers that are able to classify the evolutionary states of lower frequency resolution spectra expected from these missions. Additionally, we provide new classifications for 8633 Kepler red giants, out of which 426 have previously not been classified using asteroseismology. This brings the total to 14983 Kepler red giants classified with our new neural network. We also verify that our classifiers are remarkably robust to suboptimal data, including low signal-to-noise and incorrect training truth labels.
The Impact of Gaia DR1 on Asteroseismic Inferences from Kepler
The Kepler mission has been fantastic for asteroseismology of solar-type stars, but the targets are typically quite distant. As a consequence, the reliability of asteroseismic modeling has been limited by the precision of additional constraints from high-resolution spectroscopy and parallax measurements. A precise luminosity is particularly important to minimize potential biases due to the intrinsic correlation between stellar mass and initial helium abundance. We have applied the latest version of the Asteroseismic Modeling Portal (AMP) to the complete Kepler data sets for 30 stars with known rotation rates and chromospheric activity levels. We compare the stellar properties derived with and without the measured parallaxes from the first data release of Gaia. We find that in most cases the masses and ages inferred from asteroseismology shift within their uncertainties. For a few targets that show larger shifts, the updated stellar properties only strengthen previous conclusions about anomalous rotation in middle-aged stars.
Gravity mode offset and properties of the evanescent zone in red-giant stars
Context:The wealth of asteroseismic data for red-giant stars and the precision with which these data have been observed over the last decade calls for investigations to further understand the internal structures of these stars. Aims: The aim of this work is to validate a method to measure the underlying period spacing, coupling term and mode offset of pure gravity modes that are present in the deep interiors of red-giant stars. We subsequently investigate the physical conditions of the evanescent zone between the gravity mode cavity and the pressure mode cavity. Methods: We implement an alternative mathematical description, compared to what is used in the literature, to analyse observational data and to extract the underlying physical parameters that determine the frequencies of mixed modes. This description takes the radial order of the modes explicitly into account, which reduces its sensitivity to aliases. Additionally, and for the first time, this method allows us to constrain the gravity mode offset $\epsilon_{\rm g}$ for red-giant stars. Results: We find that this alternative mathematical description allows us to determine the period spacing $\Delta\Pi$ and the coupling term $q$ for the dipole modes within a few percent of literature values. Additionally, we find that $\epsilon_{\rm g}$ varies on a star by star basis and should not be kept fixed in the analysis. Furthermore, we find that the coupling factor is logarithmically related to the physical width of the evanescent region normalised by the radius at which the evanescent zone is located. Finally, the local density contrast at the edge of the core of red giant branch models shows a tentative correlation with the offset $\epsilon_{\rm g}$. Conclusions: We are continuing to exploit the full potential of the mixed modes to investigate the internal structures of red-giant stars; in this case we focus on the evanescent zone. It remains, however, important to perform comparisons between observations and models with great care as the methods employed are sensitive to the range of input frequencies.
K2 photometry and HERMES spectroscopy of the blue supergiant rho Leo: rotational wind modulation and low-frequency waves
We present an 80-day long uninterrupted high-cadence K2 light curve of the B1Iab supergiant $\rho\,$Leo, deduced with the method of halo photometry. This light curve reveals a dominant frequency of $f_{\rm rot}=0.0373$ d$^{-1}$ and its harmonics, corresponding with a rotation period of 26.8 d and subject to amplitude and phase modulation. The K2 photometry additionally reveals low-frequency variability ($<1.5\,$d$^{-1}$) and is in full agreement with low-cadence high-resolution spectroscopy assembled during 1800 days. The spectroscopy reveals rotational wind modulation of about 20 km s$^{-1}$ and photospheric velocity variations of a few km s$^{-1}$ at frequencies in the range 0.2 to 0.6 d$^{-1}$. Given the large macroturbulence needed to explain the spectral line broadening of the star, we interpret the detected photospheric velocity as due to travelling super-inertial gravity waves with dominant tangential amplitude.
Model-independent measurement of internal stellar structure in 16 Cygni A & B
We present a method for measuring internal stellar structure based on asteroseismology that we call "inversions-for-agreement." The method accounts for imprecise estimates of stellar mass and radius as well as the relatively limited oscillation mode sets that are available for distant stars. By construction, the results of the method are independent of stellar models. We apply this method to measure the isothermal sound speeds in the cores of the solar-type stars 16 Cyg A and B using asteroseismic data obtained from Kepler observations. We compare the asteroseismic structure that we deduce against best-fitting evolutionary models and find that the sound speeds in the cores of these stars exceed those of the models.
Robo-AO Kepler Asteroseismic Survey. I. Adaptive optics imaging of 99 asteroseismic Kepler dwarfs and subgiants
We used the Robo-AO laser adaptive optics system to image 99 main sequence and subgiant stars that have Kepler-detected asteroseismic signals. Robo-AO allows us to resolve blended secondary sources at separations as close as $\sim$0$.\!\!^{\prime\prime}$15 that may contribute to the measured Kepler light curves and affect asteroseismic analysis and interpretation. We report 8 new secondary sources within 4$.\!\!^{\prime\prime}$0 of these Kepler asteroseismic stars. We used Subaru and Keck adaptive optics to measure differential infrared photometry for these candidate companion systems. Two of the secondary sources are likely foreground objects while the remaining 6 are background sources; however we cannot exclude the possibility that three of the objects may be physically associated. We measured a range of i'-band amplitude dilutions for the candidate companion systems from 0.43% to 15.4%. We find that the measured amplitude dilutions are insufficient to explain the previously identified excess scatter in the relationship between asteroseismic oscillation amplitude and the frequency of maximum power.
KIC 9533489: a genuine $\gamma$ Doradus – $\delta$ Scuti Kepler hybrid pulsator with transit events
Context. Several hundred candidate hybrid pulsators of type A–F have been identified from space-based observations. Their large number allows both statistical analyses and detailed investigations of individual stars. This offers the opportunity to study the full interior of the genuine hybrids, in which both low-radial-order p- and high-order g-modes are self-excited at the same time. However, a few other physical processes can also be responsible for the observed hybrid nature, related to binarity or to surface inhomogeneities. The finding that most $\delta$ Scuti stars also show long-period light variations represents a real challenge for theory. Aims: We aim at determining the pulsation frequencies of KIC 9533489, to search for regular patterns and spacings among them, and to investigate the stability of the frequencies and the amplitudes. An additional goal is to study the serendipitously detected transit events: is KIC 9533489 the host star? What are the limitations on the physical parameters of the involved bodies? Methods: Fourier analysis of all the available Kepler light curves. Investigation of the frequency and period spacings. Determination of the stellar physical parameters from spectroscopic observations. Modelling of the transit events. Results: The Fourier analysis of the Kepler light curves revealed 55 significant frequencies clustered into two groups, which are separated by a gap between 15 and 27 d$^{-1}$. The light variations are dominated by the beating of two dominant frequencies located at around 4 d$^{-1}$. The amplitudes of these two frequencies show a monotonic long-term trend. The frequency spacing analysis revealed two possibilities: the pulsator is either a highly inclined moderate rotator ($v\approx 70$ km s$^{-1}$, $i > 70^\circ$) or a fast rotator ($v\approx 200$ km s$^{-1}$) with $i\approx20^\circ$. The transit analysis disclosed that the transit events which occur with a $\approx197$ d period may be caused by a $1.6\,R_{\rm Jup}$ body orbiting a fainter star, which would be spatially coincident with KIC 9533489.
Automated asteroseismic peak detections
Space observatories such as Kepler have provided data that can potentially revolutionise our understanding of stars. Through detailed asteroseismic analyses we are capable of determining fundamental stellar parameters and reveal the stellar internal structure with unprecedented accuracy. However, such detailed analyses, known as peak bagging, have so far been obtained for only a handful of stars while most of the scientific potential of the available data remains unexplored. One of the major challenges in peak bagging is identifying how many solar-like oscillation modes are visible in a power density spectrum. Identification of oscillation modes is usually done by visual inspection which is time-consuming and has a degree of subjectivity. Here, we present a peak detection algorithm specially suited for the detection of solar-like oscillations. It reliably characterises the solar-like oscillations in a power density spectrum and estimates their parameters without human intervention. Furthermore, we provide a metric to characterise the false positive and false negative rates to provide further information about the reliability of a detected oscillation mode or the significance of a lack of detected oscillation modes. The algorithm presented here opens the possibility for detailed and automated peak bagging of the thousands of solar-like oscillators observed by Kepler.
Finding binaries from phase modulation of pulsating stars with Kepler: V. Orbital parameters, with eccentricity and mass-ratio distributions of 341 new binaries
The orbital parameters of binaries at intermediate periods ($10^2$ – $10^3$ d) are difficult to measure with conventional methods and are very incomplete. We have undertaken a new survey, applying our pulsation timing method to Kepler light curves of 2224 main-sequence A/F stars and found 341 non-eclipsing binaries. We calculate the orbital parameters for 317 PB1 systems (single-pulsator binaries) and 24 PB2s (double-pulsators), tripling the number of intermediate-mass binaries with full orbital solutions. The method reaches down to small mass ratios $q \approx 0.02$ and yields a highly homogeneous sample. We parametrize the mass-ratio distribution using both inversion and MCMC forward-modelling techniques, and find it to be skewed towards low-mass companions, peaking at $q \approx 0.2$. While solar-type primaries exhibit a brown dwarf desert across short and intermediate periods, we find a small but statistically significant (2.6$\sigma$) population of extreme-mass-ratio companions ($q < 0.1$) to our intermediate-mass primaries. We find a large fraction of companions (21% $\pm$ 6%) are white dwarfs in post-mass-transfer systems with primaries that are now blue stragglers, some of which are the progenitors of Type Ia supernovae, barium stars, symbiotics, and related phenomena. Excluding these white dwarfs, we determine the binary fraction of A/F primaries to be 13.9% $\pm$ 2.1% at $q>0.1$ and periods of 100 – 1500 d. Combining our measurements with those in the literature, we find the binary fraction across these periods is a constant 5% for primaries $M_1 < 0.8$ M$_{\odot}$, but then increases linearly with $\log M_1$, demonstrating that natal discs around more massive protostars $M_1 \gtrsim 1$ M$_{\odot}$ become increasingly more prone to fragmentation. Finally, we find the eccentricity distribution of the main-sequence pairs to be much less eccentric than the thermal distribution.
Modelling Kepler Red Giants in Eclipsing Binaries: Calibrating the Mixing-Length Parameter with Asteroseismology
Stellar models rely on a number of free parameters. High-quality observations of eclipsing binary stars observed by Kepler offer a great opportunity to calibrate model parameters for evolved stars. Our study focuses on six Kepler red giants with the goal of calibrating the mixing-length parameter of convection as well as the asteroseismic surface term in models. We introduce a new method to improve the identification of oscillation modes which exploits theoretical frequencies to guide the mode identification ('peak-bagging') stage of the data analysis. Our results indicate that the convective mixing-length parameter ($\alpha$) is $\approx$14% larger for red giants than for the Sun, in agreement with recent results from modelling the APOGEE stars. We found that the asteroseismic surface term (i.e. the frequency offset between the observed and predicted modes) correlates with stellar parameters ($T_{\rm{eff}}$, $\log g$) and the mixing-length parameter. This frequency offset generally decreases as giants evolve. The two coefficients $a_{-1}$ and $a_3$ for the inverse and cubic terms that have been used to describe the surface term correction are found to correlate linearly. The effect of the surface term is also seen in the p-g mixed modes, however, established methods for correcting the effect are not able to properly correct the g-dominated modes in late evolved stars.
Surface rotation of Kepler red giant stars
The long and continuous photometric observations collected by the Kepler satellite of a large number of stars allows the study of the surface rotation and activity variability of thousands of field stars. Such information complements the asteroseismic measurements that constrain the interiors of stars and provides good calibration possibilities for the age-rotation-activity relations. Here, we study the light curves of a large number of red giant stars observed by the Kepler satellite to identify the ones exhibiting surface modulations due to the presence of star spots crossing the visible surface of the star and determine their rotational periods. We use optimized corrections to treat the Kepler data to retrieve the intrinsic modulations present in these light curves. Two different methods based on a wavelet decomposition and on the autocorrelation function of the light curve were then used to get estimates of the rotation period of each star. We also present a new tool which is a combination of the two previous methods, called Composite Spectrum. The results of these various methods are then compared to identify the stars showing clear signs of surface rotation. Out of a sample of 17, 377 red giants, we isolate 361 with a validated rotation rate. This represents 2.08% of our sample, which is consistent with the expectations from spectroscopic measurements. Among the 4881 intermediate mass stars ($M>2M_\odot$), we find a smaller rate of rapid rotators than expected, 1.92%, suggesting enhanced loss or differential rotation in those stars. Finally, we find that 15% of the 575 low-mass clump stars ($M<1.1M_\odot$) are rotating rapidly, which is indicative of a recent interaction.
Multi-technique investigation of the binary fraction among A-F type candidate hybrid variable stars discovered by Kepler
Context.
Hundreds of candidate hybrid pulsators of intermediate type A-F have been revealed by the recent space missions. Hybrid pulsators offer the advantage to study the full stellar interiors, where both low-order p- and high-order g-modes are simultaneously excited. The true hybrid stars must be identified since other processes, related to stellar multiplicity or rotation, might also explain the presence of (some) low frequencies observed in the periodograms of these pulsating stars. \
Aims.
We measured the radial velocities of 50 candidate $\delta$ Scuti - $\gamma$ Doradus hybrid stars from the Kepler mission with the Hermes and Ace spectrographs over a time span of months to years. We aim to derive the fraction of binary and multiple systems, to provide an independent determination of the atmospheric properties and v sini, and to identify the (probable) physical cause of the low frequencies. \
Methods.
We computed 1-D cross-correlation functions (CCFs) in order to find the best set of model parameters in terms of the number of components, spectral type(s) and v sini for each target. Radial velocities were measured from spectrum synthesis and by using a 2-D cross-correlation technique in the case of double- and triple-lined systems. Fundamental parameters were determined by fitting (in casu composite) synthetic spectra to the normalised median spectra corrected for the appropriate Doppler shifts. \
Results.
We report on the analysis of 478 high-resolution Hermes and 41 Ace spectra of A/F-type candidate hybrid pulsating stars from the Kepler field. We determined their radial velocities, projected rotational velocities, atmospheric properties and classified our targets based on the shape of the CCFs and the temporal behaviour of the radial velocities. We derived orbital solutions for seven systems.Three long-period preliminary orbital solutions are confirmed by a photometric time-delay analysis. Finally, we determined a global multiplicity fraction of 27% in our sample of candidate hybrid pulsators. \
Deep Learning Classification in Asteroseismology
In the power spectra of oscillating red giants, there are visually distinct features defining stars ascending the red giant branch from those that have commenced helium core burning. We train a one-dimensional convolutional neural network by supervised learning to automatically learn these visual features from images of folded oscillation spectra. By training and testing on Kepler red giants, we achieve an accuracy of up to 99% in separating helium-burning red giants from those ascending the red giant branch. The convolutional neural network additionally shows capability in accurately predicting the evolutionary states of 5379 previously unclassified Kepler red giants, by which we now have greatly increased the number of classified stars.
NGC 6819: testing the asteroseismic mass scale, mass loss, and evidence for products of non-standard evolution
We present an extensive peakbagging effort on Kepler light curves of $\sim$50 red giant stars in the open star cluster NGC 6819. By employing sophisticated pre-processing of the time series and Markov Chain Monte Carlo (MCMC) techniques we extracted individual frequencies, heights and linewidths for hundreds of oscillation modes in the sample of stars.
We show that the ‘average’ asteroseismic parameter $\delta\nu_{02}$, derived from these, can be used to distinguish the stellar evolutionary state between the red giant branch (RGB) stars and red clump (RC) stars.
The masses and radii of the giants are estimated using asteroseismic scaling relations, both empirically corrected to obtain self-consistency as well as agreement with independent measures of distance and age, and, alternatively, using updated theoretical corrections. Remarkable agreement is found, allowing the evolutionary state of the giants to be determined exclusively from the empirical correction to the scaling relations.
We find a mean mass of the RGB stars and RC stars in NGC 6819 to be $1.61\pm0.02\,\mathrm{M}_\odot$ and $1.64\pm0.02\,\mathrm{M}_\odot$, respectively. The difference $\Delta M=-0.03\pm0.01\,\mathrm{M}_\odot$ is almost insensitive to systematics, suggesting very little RGB mass loss, if any.
Stars that are outliers relative to the ensemble reveal overmassive members that likely evolved via mass-transfer in a blue straggler phase. We also suggest that KIC 4937011, a low-mass Li-rich giant previously studied in the literature, is a cluster member in the RC phase that experienced very high mass-loss during its evolution. Such over- and undermassive stars need to be considered when studying field giants, since the true age of such stars cannot be known and there is currently no way to distinguish them from normal stars.
Anomalies in the Kepler Asteroseismic Legacy Project Data A re-analysis of 16 Cyg A&B, KIC8379927 and 6 solar-like stars
I compare values of the frequencies, separation ratios, errors and covariance matrices from a new analysis of 9 solar-like stars with the Legacy project values reported by Lund et al and, for 16Cyg A&B and KIC8379927, with values derived by Davies et al. There is good agreement between my results and Davies's for these 3 stars, but no such agreement with the Legacy project results. My frequencies differ from the Legacy values, there are inconsistencies in the Legacy frequency covariance matrices which are not positive definite, and the Legacy errors on separation ratios are up to 40 times larger than mine and the values and upper limits derived from the Legacy frequency covariances. There are similar anomalies for 6 other solar-like stars: frequencies and separation ratio errors disagree and 2 have non positive definite covariance matrices. There are inconsistencies in the covariance matrices of 27 the 66 stars in the full Legacy set and problems with the ratio errors for the vast majority of these stars
Metallicity effect on stellar granulation detected from oscillating red giants in Open Clusters
Context. The effect of metallicity on the granulation activity in stars, and hence on the convective motions in general, is still poorly understood. Available spectroscopic parameters from the updated APOGEE-Kepler catalog, coupled with high-precision photometric observations from NASA's Kepler mission spanning more than four years of observation, make oscillating red giant stars in open clusters crucial testbeds.
Aims. We determine the role of metallicity on the stellar granulation activity by discriminating its effect from that of different stellar properties such as surface gravity, mass, and temperature. We analyze 60 known red giant stars belonging to the open clusters NGC 6791, NGC 6819, and NGC 6811, spanning a metallicity range from [Fe/H] $\simeq -0.09$ to $0.32$. The parameters describing the granulation activity of these stars and their frequency of maximum oscillation power, $\nu_\mathrm{max}$, are studied while taking into account different masses, metallicities, and stellar evolutionary stages. We derive new scaling relations for the granulation activity, re-calibrate existing ones, and identify the best scaling relations from the available set of observations.
Methods. We adopt the Bayesian code DIAMONDS for the analysis of the background signal in the Fourier spectra of the stars. We perform a Bayesian parameter estimation and model comparison to test the different model hypotheses proposed in this work and in the literature.
Results. Metallicity causes a statistically significant change in the amplitude of the granulation activity, with a dependency stronger than that induced by both stellar mass and surface gravity. We also find that the metallicity has a significant impact on the corresponding time scales of the phenomenon. The effect of metallicity on the time scale is stronger than that of mass.
Conclusions. A higher metallicity increases the amplitude of granulation and meso-granulation signals and slows down their characteristic time scales toward longer periods. The trend in amplitude is in qualitative agreement with predictions from existing 3D hydrodynamical simulations of stellar atmospheres from main sequence to red giant stars. We confirm that the granulation activity is not sensitive to changes in the stellar core and that it only depends on the atmospheric parameters of stars.
Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes
We present a comparison of parallaxes and radii from asteroseismology and Gaia DR1 (TGAS) for 2200 Kepler stars spanning from the main sequence to the red giant branch. We show that previously identified offsets between TGAS parallaxes and distances derived from asteroseismology and eclipsing binaries have been partially overestimated for stars beyond 100pc, and can be in part compensated by adopting a hotter Teff scale (such as the infrared flux method) instead of spectroscopic temperatures for dwarfs and subgiants. Residual systematic differences are at the 2% level in parallax across three orders of magnitude. We use TGAS parallaxes to empirically demonstrate that asteroseismic radii are accurate to 10% or better for stars between 0.8-8Rsun. We find no significant offset for main-sequence (< 1.5Rsun) and low-luminosity RGB stars ( 3–8Rsun), but seismic radii appear to be systematically underestimated by 5% for subgiants ( 1.5-3Rsun). We find no systematic errors as a function of metallicity between [Fe/H] -0.8 to +0.4 dex, and show tentative evidence that corrections to the scaling relation for the large frequency separation (Dnu) improve the agreement with TGAS for RGB stars. Finally, we demonstrate that beyond 3kpc asteroseismology will provide more precise distances than end-of-mission Gaia data, highlighting the synergy and complementary nature of Gaia and asteroseismology for studying galactic stellar populations.
Near-degeneracy effects on the frequencies of rotationally-split mixed modes in red giants
The Kepler space mission has made it possible to measure the rotational splittings of mixed modes in red giants, thereby providing an unprecedented opportunity to probe the internal rotation of these stars. Asymmetries have been detected in the rotational multiplets of several red giants. This is unexpected since all the red giants whose rotation have been measured thus far are found to rotate slowly, and low rotation, in principle, produces symmetrical multiplets. Our aim here is to explain these asymmetries and find a way of exploiting them to probe the internal rotation of red giants. We show that in the cases where asymmetrical multiplets were detected, near-degeneracy effects are expected to occur, because of the combined effects of rotation and mode mixing. Such effects have not been taken into account so far. By using both perturbative and non-perturbative approaches, we show that near-degeneracy effects produce multiplet asymmetries that are very similar to the observations. We then propose and validate a method based on the perturbative approach to probe the internal rotation of red giants using multiplet asymmetries. We successfully apply our method to the asymmetrical $l=2$ multiplets of the Kepler young red giant KIC7341231 and obtain precise estimates of its mean rotation in the core and the envelope. The observed asymmetries are reproduced with a good statistical agreement, which confirms that near-degeneracy effects are very likely the cause of the detected multiplet asymmetries. We expect near-degeneracy effects to be important for $l=2$ mixed modes all along the red giant branch (RGB). For $l=1$ modes, these effects can be neglected only at the base of the RGB. They must therefore be taken into account when interpreting rotational splittings and as shown here, they can bring valuable information about the internal rotation of red giants.
Beyond the Kepler/K2 bright limit with halo photometry: variability in the seven brightest members of the Pleiades
The most powerful tests of stellar models come from the brightest stars in the sky, for which complementary techniques, such as astrometry, asteroseismology, spectroscopy, and interferometry can be combined. The K2 Mission is providing a unique opportunity to obtain high-precision photometric time series for bright stars along the ecliptic. However, bright targets require a large number of pixels to capture the entirety of the stellar flux, and bandwidth restrictions limit the number and brightness of stars that can be observed. To overcome this, we have developed a new photometric technique, that we call halo photometry, to observe very bright stars using a limited number of pixels. Halo photometry is simple, fast and does not require extensive pixel allocation, and will allow us to use K2 and other photometric missions, such as TESS, to observe very bright stars for asteroseismology and to search for transiting exoplanets. We apply this method to the seven brightest stars in the Pleiades open cluster. Each star exhibits variability; six of the stars show what are most-likely slowly pulsating B-star (SPB) pulsations, with amplitudes ranging from 20 to 2000 ppm. For the star Maia, we demonstrate the utility of combining K2 photometry with spectroscopy and interferometry to show that it is not a ‘Maia variable’, and to establish that its variability is caused by rotational modulation of a large chemical spot on a 10 d time scale.
Characterizing solar-type stars from full-length Kepler data sets using the Asteroseismic Modeling Portal
The Kepler space telescope yielded unprecedented data for the study of solar-like oscillations in other stars. The large samples of multi-year observations posed an enormous data analysis challenge that has only recently been surmounted. Asteroseismic modeling has become more sophisticated over time, with better methods gradually developing alongside the extended observations and improved data analysis techniques. We apply the latest version of the Asteroseismic Modeling Portal (AMP) to the full-length Kepler data sets for 57 stars, comprising planetary hosts, binaries, solar-analogs, active stars, and for validation purposes, the Sun. From an analysis of the derived stellar properties for the full sample, we identify a variation of the mixing-length parameter with atmospheric properties. We also derive a linear relation between the stellar age and a characteristic frequency separation ratio. In addition, we find that the empirical correction for surface effects suggested by Kjeldsen and coworkers is adequate for solar-type stars that are not much hotter (T$_{\rm eff}~\lesssim 6200$ K) or significantly more evolved ($\log g~\gtrsim 4.2$, $\langle \Delta \nu \rangle ~\gtrsim 80\mu$Hz) than the Sun. Precise parallaxes from the Gaia mission and future observations from TESS and PLATO promise to improve the reliability of stellar properties derived from asteroseismology.
Kepler Observations of the Asteroseismic Binary HD 176465
Binary star systems are important for understanding stellar structure and evolution, and are especially useful when oscillations can be detected and analysed with asteroseismology. However, only four systems are known in which solar-like oscillations are detected in both components. Here, we analyse the fifth such system, HD 176465, which was observed by Kepler. We carefully analysed the system's power spectrum to measure individual mode frequencies, adapting our methods where necessary to accommodate the fact that both stars oscillate in a similar frequency range. We also modelled the two stars independently by fitting stellar models to the frequencies and complementary spectroscopic parameters. We are able to cleanly separate the oscillation modes in both systems. The stellar models produce compatible ages and initial compositions for the stars, as is expected from their common and contemporaneous origin. Combining the individual ages, the system is about $3.0\pm0.5\,\mathrm{Gyr}$ old. The two components of HD 176465 are young physically-similar oscillating solar analogues, the first such system to be found, and provide important constraints for stellar evolution and asteroseismology.
Convective-core overshoot and suppression of oscillations: Constraints from red giants in NGC 6811
Using data from the NASA spacecraft Kepler, we study solar-like oscillations in red-giant stars in the open cluster NGC 6811. We determine oscillation frequencies, frequency separations, period spacings of mixed modes and mode visibilities for eight cluster giants. The oscillation parameters show that these stars are helium-core-burning red giants. The eight stars form two groups with very different oscillation power spectra; the four stars with lowest $\Delta\nu$-values display rich sets of mixed $l=1$ modes, while this is not the case for the four stars with higher $\Delta\nu$. For the four stars with lowest $\Delta\nu$, we determine the asymptotic period spacing of the mixed modes, $\Delta$P, which together with the masses we derive for all eight stars suggest that they belong to the so-called secondary clump. Based on the global oscillation parameters, we present initial theoretical stellar modeling which indicate that we can constrain convective-core overshoot on the main sequence and in the helium-burning phase for these $\sim$2 M$_{\odot}$ stars. Finally, our results indicate less mode suppression than predicted by recent theories for magnetic suppression of certain oscillation modes in red giants.
Kepler sheds new and unprecedented light on the variability of a blue supergiant: gravity waves in the O9.5Iab star HD188209
Context. Stellar evolution models are most uncertain for evolved massive stars. Asteroseismology based on high-precision uninterrupted
space photometry has become a new way to test the outcome of stellar evolution theory and was recently applied to a multitude
of stars, but not yet to massive evolved supergiants.
Aims. Our aim is to detect, analyse and interpret the photospheric and wind variability of the O9.5 Iab star HD188209 from Kepler
space photometry and long-term high-resolution spectroscopy.
Methods. We used Kepler scattered-light photometry obtained by the nominal mission during 1460 d to deduce the photometric
variability of this O-type supergiant. In addition, we assembled and analysed high-resolution high signal-to-noise spectroscopy taken
with four spectrographs during some 1800 d to interpret the temporal spectroscopic variability of the star.
Results. The variability of this blue supergiant derived from the scattered-light space photometry is fully in agreement with the one
found in the ground-based spectroscopy.We find significant low-frequency variability that is consistently detected in all spectral lines
of HD188209. The photospheric variability propagates into the wind, where it has similar frequencies but slightly higher amplitudes.
Conclusions. The morphology of the frequency spectra derived from the
long-term photometry and spectroscopy points towards a spectrum of travelling
waves with frequency values in the range expected for an evolved O-type
star. Convectively-driven internal gravity waves excited in the stellar
interior offer the most plausible explanation of the detected variability.
Evidence for compact binary systems around Kepler red giants
We present an analysis of 169 oscillating red giants from NASA's Kepler mission that exhibit anomalous peaks in their Fourier amplitude spectra. These peaks result from ellipsoidal variations which are indicative of binary star systems, at frequencies such that the orbit of any stellar companion would be within the convective envelope of the red giant. Alternatively, the observed phenomenon may be due to a close binary orbiting a red giant in a triple system, or chance alignments of foreground or background binary systems contaminating the target pixel aperture. We identify 88 stars in the sample as chance alignments using a combination of pixel Fourier analysis and difference imaging. We find that in the remaining 81 cases the anomalous peaks are indistinguishable from the target star to within 4$''$, suggesting a physical association. We examine a Galaxia model of the Kepler field of view to estimate background star counts and find that it is highly unlikely that all targets can be explained by chance alignments. From this, we conclude that these stars may comprise a population of physically associated systems.
KIC 8262223: A Post-Mass Transfer Eclipsing Binary Consisting of a Delta Scuti Pulsator and a Helium White Dwarf Precursor
KIC 8262223 is an eclipsing binary with a short orbital period ($P=1.61$ d). The Kepler light curves are of Algol-type and display deep and partial eclipses, ellipsoidal variations, and pulsations of $\delta$ Scuti type. We analyzed the Kepler photometric data, complemented by phase-resolved spectra from the R-C Spectrograph on the 4-meter Mayall telescope at Kitt Peak National Observatory and determined the fundamental parameters of this system. The low mass and oversized secondary ($M_2=0.20M_{\odot}$, $R_2=1.31R_{\odot}$) is the remnant of the donor star that transferred most of its mass to the gainer, and now the primary star. The current primary star is thus not a normal $\delta$ Scuti star but the result of mass accretion from a lower mass progenitor. We discuss the possible evolutionary history and demonstrate with the MESA evolution code that the system can be understood as the result of non-conservative binary evolution similar to that for the formation of EL CVn type binaries. The pulsations of the primary star can be explained as radial and non-radial pressure modes. The equilibrium models from single star evolutionary tracks can match the observed mass and radius ($M_1=1.94M_{\odot}$, $R_1=1.67R_{\odot}$) but the predicted unstable modes associated with these models differ somewhat from those observed. This work presents a preliminary asteroseismic analysis of the abnormal $\delta$ Scuti pulsators, and we discuss the need for better theoretical understanding of such pulsating mass gaining stars.
The Kepler Cepheid V1154 Cyg revisited: light curve modulation and detection of granulation
We present a detailed analysis of the bright Cepheid-type variable star V1154 Cygni using 4 years of continuous observations by the Kepler space telescope. We detected 28 frequencies using standard Fourier transform method.We identified modulation of the main pulsation frequency and its harmonics with a period of 159 d. This modulation is also present in the Fourier parameters of the light curve and the O-C diagram. We detected another modulation with a period of about 1160 d. The star also shows significant power in the low-frequency region that we identified as granulation noise. The effective timescale of the granulation agrees with the extrapolated scalings of red giant stars. Non-detection of solar-like oscillations indicates that the pulsation inhibits other oscillations. We obtained new radial velocity observations which are in a perfect agreement with previous years data, suggesting that there is no high mass star companion of V1154 Cygni. Finally, we discuss the possible origin of the detected frequency modulations.
Asteroseismology of 1523 misclassified red giants using Kepler data
We analyzed solar-like oscillations in 1523 Kepler red giants which have previously been misclassified as subgiants, with predicted νmax values [based on the Kepler Input Catalogue (KIC)] between 280 and 700 μHz. We report the discovery of 626 new oscillating red giants in our sample, in addition to 897 oscillators that were previously characterized by Hekker et al. from one-quarter of Kepler data. Our sample increases the known number of oscillating low-luminosity red giants by 26 per cent (up to ∼1900 stars). About three-quarters of our sample are classified as ascending red giant branch stars, while the remainder is red-clump stars. A novel scheme was applied to determine ∆ν for 108 stars with νmax close to the Nyquist frequency (240 μHz < νmax < 320 μHz). Additionally, we identified 47 stars oscillating in the super-Nyquist frequency regime, up to 387 μHz, using long-cadence light curves. We show that the misclassifications are most likely due to large uncertainties in KIC surface gravities, and do not result from the absence of broad-band colors or from different physical properties such as reddening, spatial distribution, mass or metallicity. The sample will be valuable to study oscillations in low-luminosity red giants and to characterize planet candidates around those stars.
Period spacings in red giants III. Coupling factors of mixed modes
The power of asteroseismology relies on the capability of global oscillations to infer the stellar structure. For evolved stars, we benefit from unique information directly carried out by mixed modes that probe their radiative cores. This third article of the series devoted to mixed modes in red giants focusses on their coupling factors that remained largely unexploited up to now. With the measurement of the coupling factors, we intend to give physical constraints on the regions surrounding the radiative core and the hydrogen-burning shell of subgiants and red giants. A new method for measuring the coupling factor of mixed modes is set up. It is derived from the method recently implemented for measuring period spacings. It runs in an automated way so that it can be applied to a large sample of stars. Coupling factors of mixed modes were measured for thousands of red giants. They show specific variation with mass and evolutionary stage. Weak coupling is observed for the most evolved stars on the red giant branch only; large coupling factors are measured at the transition between subgiants and red giants, as well as in the red clump. The measurement of coupling factors in dipole mixed modes provides a new insight into the inner interior structure of evolved stars. While the large frequency separation and the asymptotic period spacings probe the envelope and the core, respectively, the coupling factor is directly sensitive to the intermediate region in between and helps determining its extent. Observationally, the determination of the coupling factor is a prior to precise fits of the mixed-mode pattern, and can now be used to address further properties of the mixed-mode pattern, as the signature of the buoyancy glitches and the core rotation.
When dipole modes in red giants are simultaneously mixed and depressed
Seismic observations with Kepler have shown that dipole modes in evolved stars sometimes have lower amplitudes than expected from energy equipartition; they are called depressed modes. These observations were used to infer the presence of strong magnetic fields in the stellar core. This conclusion remains indirect, so that further studies are necessary to constrain the analysis and interpretation of depressed modes. The observation of mixed modes in red giants is used to characterize the seismic parameters of stars with low dipole visibility, in order to probe the damping of the oscillation. With the determination of global seismic parameters of mixed modes, we test the relevance of various hypotheses on the processes that construct mixed modes and explain the depressed modes. The observation of stars showing depressed dipole mixed modes is especially useful for deriving model-independent conclusions on the dipole mode damping. We explain with a simple model how mode visibilities provide a measure of the extra damping. Observations prove that dipole modes in red giants are mixed modes. Such a result disconfirms that depressed dipole modes are resulting from the suppression of the oscillation in the radiative core. Understanding the damping of mixed modes is necessary before extrapolating conclusions on the mechanism responsible for the mode depression. Measuring low visibilities is not enough for deriving the presence of a high internal magnetic field inside the red giant cores, so that the magnetic greenhouse effect remains speculative. Moreover, a high magnetic field cannot explain depressed modes in many stars.
Standing on the shoulders of dwarfs: the Kepler asteroseismic LEGACY sample II — radii, masses, and ages
We use asteroseismic data from the Kepler satellite to determine fundamental stellar properties of the 66 main-sequence targets observed for at least one full year by the mission. We distributed tens of individual oscillation frequencies extracted from the time series of each star among seven modelling teams who applied different methods to determine radii, masses, and ages for all stars in the sample. Comparisons among the different results reveal a good level of agreement in all stellar properties, which is remarkable considering the variety of codes, input physics and analysis methods employed by the different teams. Average uncertainties are of the order of $\sim$2% in radius, $\sim$4% in mass, and $\sim$10% in age, making this the best-characterised sample of main-sequence stars available to date. Our predicted initial abundances and mixing-length parameters are checked against inferences from chemical enrichment laws $\Delta Y / \Delta Z$ and predictions from 3D atmospheric simulations. We test the accuracy of the determined stellar properties by comparing them to the Sun, angular diameter measurements, Gaia parallaxes, and binary evolution, finding excellent agreement in all cases and further confirming the robustness of asteroseismically-determined physical parameters of stars when individual frequencies of oscillation are available. Baptised as the Kepler dwarfs LEGACY sample, these stars are the solar-like oscillators with the best asteroseismic properties available for at least another decade. All data used in this analysis and the resulting stellar parameters are made publicly available for the community.
Standing on the shoulders of Dwarfs: the Kepler asteroseismic LEGACY sample I — oscillation mode parameters
The advent of space-based missions like Kepler has revolutionized the study of solar-type stars, particularly through the measurement and modeling of their resonant modes of oscillation. Here we analyze a sample of 66 Kepler main-sequence stars showing solar-like oscillations as part of the Kepler seismic LEGACY project. We use Kepler short-cadence data, of which each star has at least 12 months, to create frequency power spectra optimized for asteroseismology. For each star we identify its modes of oscillation and extract parameters such as frequency, amplitude, and line width using a Bayesian Markov chain Monte Carlo ‘peak-bagging’ approach. We report the extracted mode parameters for all 66 stars, as well as derived quantities such as frequency difference ratios, the large and small separations $\Delta\nu$ and $\delta\nu_{02}$; the behavior of line widths with frequency and line widths at $\nu_{\rm max}$ with $T_{\rm eff}$ , for which we derive parametrizations; and behavior of mode visibilities. These average properties can be applied in future peak-bagging exercises to better constrain the parameters of the stellar oscillation spectra. The frequencies and frequency ratios can tightly constrain the fundamental parameters of these solar-type stars, and mode line widths and amplitudes can test models of mode damping and excitation.
Tidally Induced Pulsations in Kepler Eclipsing Binary KIC 3230227
KIC 3230227 is a short period ($P\approx 7.0$ days) eclipsing binary with a very eccentric orbit ($e=0.6$). From combined analysis of radial velocities and Kepler light curves, this system is found to be composed of two A-type stars, with masses of $M_1=1.84\pm 0.18M_{\odot}$, $M_2=1.73\pm 0.17M_{\odot}$ and radii of $R_1=2.01\pm 0.09R_{\odot}$, $R_2=1.68\pm 0.08 R_{\odot}$ for the primary and secondary, respectively. In addition to an eclipse, the binary light curve shows a brightening and dimming near periastron, making this a somewhat rare eclipsing heartbeat star system. After removing the binary light curve model, more than ten pulsational frequencies are present in the Fourier spectrum of the residuals, and most of them are integer multiples of the orbital frequency. These pulsations are tidally driven, and both the amplitudes and phases are in agreement with predictions from linear tidal theory for $l=2, m=-2$ prograde modes.
Seismic measurement of the locations of the base of convection zone and helium ionization zone for stars in the Kepler seismic LEGACY sample
Acoustic glitches are regions inside a star where the sound speed or its derivatives change abruptly. These leave a small characteristic oscillatory signature in the stellar oscillation frequencies. With the precision achieved by Kepler seismic data, it is now possible to extract these small amplitude oscillatory signatures, and infer the locations of the glitches. We perform glitch analysis for all the 66 stars in the Kepler seismic LEGACY sample to derive the locations of the base of the envelope convection zone and the helium ionization zone. The signature from helium ionization zone is found to be robust for all stars in the sample, whereas the convection zone signature is found to be weak and problematic, particularly for relatively massive stars with large errorbars on the oscillation frequencies. We demonstrate that the helium glitch signature can be used to constrain the properties of the helium ionization layers and the helium abundance.
Metal-Rich SX Phe stars in the Kepler Field
A spectroscopic and photometric analysis has been carried out for thirty-two candidate SX Phe variable blue straggler stars in the Kepler-field (Balona & Nemec 2012). Radial velocities (RVs), space motions ($U,V,W$), projected rotation velocities ($v$ sin $i$), spectral types, and atmospheric characteristics ($T_{\rm eff}$, $\log g$, [Fe/H], $\xi_t$, $\zeta_{\rm RT}$, etc.) are presented for 30 of the 32 stars. Although several stars are metal-weak with extreme halo orbits, the mean [Fe/H] of the sample is near solar, thus the stars are more metal-rich than expected for a typical sample of Pop. II stars, and more like halo metal-rich A-type stars (Perry 1969). Two thirds of the stars are fast rotators with $v$ sin $i$ $>$ 50 km/s, including four stars with $v$ sin $i$ $>$ 200 km/s. Three of the stars have (negative) RVs $>$ 250 km/s, five have retrograde space motions, and 21 have total speeds (relative to the LSR) $>$ 400 km/s. All but one of the 30 stars have positions in a Toomre diagram consistent with the kinematics of bona fide halo stars (the exception being a thick-disk star). Observed Rmer time delays, pulsation frequency modulations and light curves suggest that at least one third of the stars are in binary (or triple) systems with orbital periods ranging from 2.3 days to more than four years.
First observations of W Virginis stars with K2: detection of period doubling
We present the first analysis of W Vir stars observed by the Kepler space telescope in the K2 mission. We detected clear cycle-to-cycle variation in the light curves of KT Sco and the globular cluster member M80-V1. While the variations in the former star seems to be irregular on the short time scale of the K2 data, the latter appears to experience period doubling in its pulsation. Investigation of historical data revealed drastic period changes in both stars. For comparison we reexamine ground-based observations of W Vir, the prototype of the class, and conclude that the it shows period doubling instead of mode beating. These results support the notion that nonlinear dynamics plays an important role in the pulsation of W Virginis-type stars.
A new asteroseismic diagnostic for rotation in $\gamma$ Doradus stars
With four years of nearly-continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to $\gamma$ Doradus stars. In particular several analyses have demonstrated the possibility to detect non-uniform period spacings, which have been predicted to be directly related to rotation. In the present work, we define a new seismic diagnostic for rotation in $\gamma$ Doradus stars that are too rapidly rotating to present rotational splittings. Based on the non uniformity of their period spacings, we define the observable $\Sigma$ as the slope of the period spacing when plotted as a function of period. We provide a univoque relation between this observable $\Sigma$ and the internal rotation, which applies widely in the instability strip of $\gamma$ Doradus stars. We apply the diagnostic to a handful of stars observed by Kepler. Thanks to g-modes in $\gamma$ Doradus stars, we are now able to determine the internal rotation of stars on the lower main sequence, which is still not possible for Sun-like stars.
Asteroseismic properties of solar-type stars observed with the NASA K2 mission: results from Campaigns 1-3 and prospects for future observations
We present an asteroseismic analysis of 33 solar-type stars observed in short cadence during Campaigns (C) 1-3 of the NASA K2 mission. We were able to extract both average seismic parameters and individual mode frequencies for stars with dominant frequencies up to ${\sim}3300\,\rm\mu Hz$, and we find that data for some targets are good enough to allow for a measurement of the rotational splitting. Modelling of the extracted parameters is performed by using grid-based methods using average parameters and individual frequencies together with spectroscopic parameters. For the target selection in C3, stars were chosen as in C1 and C2 to cover a wide range in parameter space to better understand the performance and noise characteristics. For C3 we still detected oscillations in $73\%$ of the observed stars that we proposed. Future K2 campaigns hold great promise for the study of nearby clusters and the chemical evolution and age-metallicity relation of nearby field stars in the solar neighbourhood. We expect oscillations to be detected in ${\sim}388$ short-cadence targets if the K2 mission continues until C18, which will greatly complement the ${\sim}500$ detections of solar-like oscillations made for short-cadence targets during the nominal Kepler mission. For ${\sim}30-40$ of these, including several members of the Hyades open cluster, we furthermore expect that inference from interferometry should be possible. le.
Asteroseismology of the Hyades with K2: first detection of main-sequence solar-like oscillations in an open cluster
The Hyades open cluster was targeted during Campaign 4 (C4) of the NASA K2 mission, and short-cadence data were collected on a number of cool main-sequence stars. Here, we report results on two F-type stars that show detectable oscillations of a quality that allows asteroseismic analyses to be performed. These are the first ever detections of solar-like oscillations in main-sequence stars in an open cluster.
Testing Asteroseismic Scalings for Red Giants with Eclipsing Binaries Observed by Kepler
Given the potential of ensemble asteroseismology for understanding fundamental properties of large numbers of stars, it is critical to determine the accuracy of the scaling relations on which these measurements are based. From several powerful validation techniques, all indications so far show that stellar radius estimates from the asteroseismic scaling relations are accurate to within a few percent. Eclipsing binary systems hosting at least one star with detectable solar-like oscillations constitute the ideal test objects for validating asteroseismic radius and mass inferences. By combining radial velocity (RV) measurements and photometric time series of eclipses, it is possible to determine the masses and radii of each component of a double-lined spectroscopic binary. We report the results of a four-year RV survey performed with the échelle spectrometer of the Astrophysical Research Consortium’s 3.5 m telescope and the APOGEE spectrometer at Apache Point Observatory. We compare the masses and radii of 10 red giants (RGs) obtained by combining radial velocities and eclipse photometry with the estimates from the asteroseismic scaling relations. We find that the asteroseismic scaling relations overestimate RG radii by about 5% on average and masses by about 15% for stars at various stages of RG evolution. Systematic overestimation of mass leads to underestimation of stellar age, which can have important implications for ensemble asteroseismology used for Galactic studies. As part of a second objective, where asteroseismology is used for understanding binary systems, we confirm that oscillations of RGs in
K2P2-reduced data from campaigns 0-4 of the K2 Mission
Context: After the loss of a second reaction wheel the Kepler mission was redesigned as the K2 mission, pointing towards the ecliptic and delivering data for new fields approximately every 80 days. The steady flow of data obtained with a reduced pointing stability calls for dedicated pipelines for extracting light curves and correcting these for use in, e.g., asteroseismic analysis.
Aims: We provide corrected light curves for the K2 fields observed until now (campaigns 0–4), and provide a comparison with other pipelines for K2 data extraction/correction.
Methods: Raw light curves are extracted from K2 pixel data using the "K2-pixel-photometry" (K2P$^2$) pipeline, and corrected using the KASOC filter.
Results: The use of K2P$^2$ allows for the extraction of the order of 90.000 targets in addition to 70.000 targets proposed by the community — for these, other pipelines provide no data. We find that K2P$^2$ in general out-performs other pipelines in the metrics for
photometric variability tested. In addition to stars, pixel masks are properly defined using K2P$^2$ for extended objects such as galaxies for which light curves are also extracted.
Detection of Solar-Like Oscillations, Observational Constraints, and Stellar Models for $\theta$ Cyg, the Brightest Star Observed by the Kepler Mission
$\theta$ Cygni is an F3 spectral-type main-sequence star with visual magnitude V=4.48. This star was the brightest star observed by the original Kepler spacecraft mission. Short-cadence (58.8 s) photometric data using a custom aperture were obtained during Quarter 6 (June-September 2010) and subsequently in Quarters 8 and 12-17. We present analyses of the solar-like oscillations based on Q6 and Q8 data, identifying angular degree $l$ = 0, 1, and 2 oscillations in the range 1000-2700 $\mu$Hz, with a large frequency separation of 83.9 $\pm$ 0.4 $\mu$Hz, and frequency with maximum amplitude $\nu_{\rm max}$ = 1829 $\pm$ 54 $\mu$Hz. We also present analyses of new ground-based spectroscopic observations, which, when combined with angular diameter measurements from interferometry and Hipparcos parallax, give $T_\mathrm{eff}$ = 6697 $\pm$ 78 K, radius 1.49 $\pm$ 0.03 R$_{\odot}$, [Fe/H] = -0.02 $\pm$ 0.06 dex, log $g$ = 4.23 $\pm$ 0.03. We calculate stellar models matching the constraints using several methods, including using the Yale Rotating Evolution Code and the Asteroseismic Modeling Portal. The best-fit models have masses 1.35–1.39 M$_{\odot}$ and ages 1.0–1.6 Gyr. $\theta$ Cyg's $T_\mathrm{eff}$ and log $g$ place it cooler than the red edge of the $\gamma$ Doradus instability region established from pre-Kepler ground-based observations, but just at the red edge derived from pulsation modeling. The best-fitting models have envelope convection-zone base temperature of $\sim$320,000 to 395,000 K. The pulsation models show $\gamma$ Dor gravity-mode pulsations driven by the convective-blocking mechanism, with periods of 0.3 to 1 day (frequencies 11 to 33 $\mu$Hz). However, gravity modes were not detected in the Kepler data; one signal at 1.776 c d$^{-1}$ (20.56 $\mu$Hz) may be attributable to a faint, possibly background, binary. Asteroseismic studies of $\theta$ Cyg, in conjunction with those for other A-F stars observed by Kepler and CoRoT, will help to improve stellar model physics to sort out the confusing relationship between $\delta$ Sct and $\gamma$ Dor pulsations and their hybrids, and to test pulsation driving mechanisms.
The discovery of a planetary candidate around the evolved low-mass Kepler giant star HD 175370
We report on the discovery of a planetary companion candidate with a minimum mass Msini = 4.6 M_J orbiting the K2 III giant star HD 175370 (KIC 007940959). This star was a target in our program to search for planets around a sample of 95 giant stars observed with Kepler. This detection was made possible using precise stellar radial velocity measurements of HD 175370 taken over five years and four months using the coude echelle spectrograph of the 2-m Alfred Jensch Telescope and the fibre-fed echelle spectrograph HERMES of the 1.2-m Mercator Telescope. Our radial velocity measurements reveal a periodic (349.5 days) variation with a semi-amplitude K=133 m/s, superimposed on a long-term trend. A low-mass stellar companion with an orbital period of 88 years in a highly eccentric orbit and a planet in a Keplerian orbit with an ccentricity e=0.22 are the most plausible explanation of the radial velocity variations. However, we cannot exclude the existence of stellar envelope pulsations as a cause for the low-amplitude radial velocity variations and only future continued monitoring of this system may answer this uncertainty. From Kepler photometry we find that HD 175370 is most likely a low-mass red-giant branch or asymptotic-giant branch star.
Finding binary stars from phase modulation of pulsating stars with Kepler: IV Detection limits and radial velocity verification
We explore the detection limits of the phase modulation (PM) method of finding binary systems among multi-periodic pulsating stars, finding that Jupiter-mass planets can be found around stars of $\sim$1.8 M$_{\odot}$ in the $\delta$ Sct instability strip. The difficulty of obtaining precise radial velocity measurements, due principally to rapid stellar rotation, makes PM an attractive method for finding non-transiting planets in the habitable zone of these stars. While such detections require oscillations with amplitudes of a few mmag, many $\delta$ Sct stars with these properties exist. In less favourable cases where the signal-to-noise of the oscillations is lower, objects with masses near the lower-limit for brown dwarfs ($\sim$13 M$_{\rm Jup}$) are detectable at periods longer than about 1 yr, and the lowest mass main-sequence stars ($\sim$75 M$_{\rm Jup}$) are detectable at all periods where the PM method can be applied. We use purpose-written Markov chain Monte Carlo (MCMC) software for the calculation of the orbital parameters of binary systems, which offers robust uncertainties that allow the PM solutions to be compared with radial velocity (RV) solutions. We verify that these two methods are in agreement, even at short orbital periods where the PM method undersamples the orbit. This is a direct consequence of our new theoretical developments detailing the corrections necessary to recover the orbital parameters of undersampled orbits. Such corrections are also necessary for the inclusion of RVs as observational data in the MCMC software. We show that combining RVs with the Rmer delays obtained with PM results substantially refines the orbital parameters because of the complementarity of the mathematical functions governing the spatial (PM) and velocity (RV) domains. We give examples using Kepler data and ground-based RV measurements, whereby 25-s precision on the orbital period and 40-ms precision on the projected light travel time across the orbit ($a_1 \sin i / c$) have been obtained, without transient events such as transits or eclipses for precise timing. Software outputs were tested through an extensive hare and hounds exercise, covering a wide range of orbital configurations including binaries containing two pulsators.
Asteroseismic determination of fundamental parameters of Sun-like stars using multilayered neural networks
The advent of space-based observatories such as Convection, Rotation and Planetary Transits (CoRoT) and Kepler has enabled the testing of our understanding of stellar evolution on thousands of stars. Evolutionary models typically require five input parameters, the mass, initial Helium abundance, initial metallicity, mixing-length (assumed to be constant over time) and the age to which the star must be evolved. These parameters are also very useful in characterizing the associated planets and in studying Galactic archaeology. How to obtain the parameters from observations rapidly and accurately, specifically in the context of surveys of thousands of stars, is an outstanding question, one that has eluded straightforward resolution. For a given star, we typically measure effective temperature, surface metallicity spectroscopically and low-degree oscillation frequencies through space observatories. Here we demonstrate that statistical learning, using artificial neural networks, is successful in determining the evolutionary parameters based on spectroscopic and seismic measurements. Our trained networks show robustness over a broad range of parameter space, and critically, are entirely computationally inexpensive. This method is both computationally cheap and inferentially accurate, paving the way for analyzing the vast quantities of stellar observations from past, current and future missions.
Revisiting old friends with K2 reveals oscillating red giants in the open cluster M67
Observations of stellar clusters have had a tremendous impact in forming our understanding of stellar evolution. The open cluster M67 has a particularly important role as a calibration anchor point for stellar evolution theory due to its near solar composition and age. As a result, it has been observed extensively, including attempts to detect solar-like oscillations in its main sequence and red giant stars. However, any asteroseismic inference has so far remained elusive due to the difficulty in measuring these extremely low amplitude oscillations. Here we report the first unambiguous detection of solar-like oscillations in the red giants of M67. We use data from the Kepler ecliptic mission, K2, to measure the global asteroseismic properties. We find a model-independent seismic-informed distance of 816+/-11pc, or (m-M)o=9.57+/-0.03mag, an average red-giant mass of 1.36+/-0.01Msun, in agreement with the dynamical mass from an eclipsing binary near the cluster turn-off, but we find a lower-than-usual age. We see no evidence of strong mass loss on the red giant branch. We also determine seismic log g of all the cluster giants with a typical precision of 0.01dex. Our results generally show good agreement with independent methods and support the use of seismic scaling relations to determine global properties of red giant stars with near solar metallicity. We further illustrate that the data are of such high quality, that future work on individual mode frequencies should be possible, which would extend the scope of seismic analysis of this cluster.
Fundamental Parameters of Main-Sequence Stars in an Instant with Machine Learning
Owing to the remarkable photometric precision of space observatories like
Kepler, stellar and planetary systems beyond our own are now being
characterized en masse for the first time. These characterizations are pivotal
for endeavors such as searching for Earth-like planets and solar twins,
understanding the mechanisms that govern stellar evolution, and tracing the
dynamics of our Galaxy. The volume of data that is becoming available, however,
brings with it the need to process this information accurately and rapidly.
While existing methods can constrain fundamental stellar parameters such as
ages, masses, and radii from these observations, they require substantial
computational efforts to do so.
We develop a method based on machine learning for rapidly estimating
fundamental parameters of main-sequence solar-like stars from classical and
asteroseismic observations. We first demonstrate this method on a
hare-and-hound exercise and then apply it to the Sun, 16 Cyg A & B, and 34
planet-hosting candidates that have been observed by the Kepler spacecraft. We
find that our estimates and their associated uncertainties are comparable to
the results of other methods, but with the additional benefit of being able to
explore many more stellar parameters while using much less computation time. We
furthermore use this method to present evidence for an empirical diffusion-mass
relation. Our method is open source and freely available for the community to
use.
The source code for all analyses and for all figures appearing in this
manuscript can be found electronically at
https://github.com/earlbellinger/asteroseismology
Asteroseismic modelling of the two F-type hybrid pulsators KIC10080943A and KIC10080943B
Pulsating binary stars are ideal targets for testing the theory of stellar structure and evolution. Fundamental parameters can be derived to high precision from binary modelling and provide crucial constraints for seismic modelling. High-order gravity modes are sensitive to the conditions near the convective core and therefore allow for a determination of parameters describing interior physics, especially the convective-core overshooting parameter. KIC10080943 is a binary system that contains two gravity- and pressure-mode hybrid pulsators. A detailed observational study has provided fundamental and seismic parameters for both components. We aim to find a model that is able to predict the observed g-mode period spacings and stellar parameters of both components of KIC10080943. By calculating model grids with the stellar evolution code MESA and the seismic code GYRE, we can compare theoretical properties to the observed mean period spacing and position in the Hertzsprung-Russell diagram. The masses of our best models are somewhat below the values estimated from binarity, which is a consequence of the low observed mean g-mode period spacing. We find that the amount of core overshooting and diffusive mixing can be well constrained by the equal-age requirement for the two stars, however, we find no significant difference for different shapes of core overshooting. The measured rotation rates are within the limit of validity for the first-order perturbation approximation. We can find a good fit by using the traditional approximation for the pulsations, when taking slightly younger models with a higher asymptotic period spacing. This is because the zonal modes experience a slight shift due to the Coriolis force, which the first-order perturbation approximation ignores.
Probing the deep end of the Milky Way with Kepler: Asteroseismic analysis of 851 faint Red Giants misclassified as Cool Dwarfs
Asteroseismology has proven to be an excellent tool to determine not only the global stellar properties with a good precision but also to infer stellar structure, dynamics, and evolution for a large sample of Kepler stars. Prior to the launch of the mission the properties of Kepler targets were inferred from broadband photometry, leading to the Input Catalog (KIC, Brown et al. 2011). The KIC was later revised in the Kepler Star Properties Catalog (Huber et al. 2014), based on literature values and an asteroseismic analysis of stars which were unclassified in the KIC. Here we present an asteroseismic analysis of 45,400 stars which were classified as dwarfs in the Kepler Star Properties Catalog. We found that around 2% of the sample shows acoustic modes in the typical frequency range that put them in the red-giant category rather than cool dwarfs. We analyse the asteroseismic properties of these stars, derive their surface gravities, masses, and radii and present updated effective temperatures and distances. We show that the sample is significantly fainter than the previously known oscillating giants in the Kepler field, with the faintest stars reaching down to a Kepler magnitude, Kp $\sim$ 16. We demonstrate that 404 stars are at distances beyond 5 kpc and that the stars are significantly less massive than for the original Kepler red-giant sample, consistent with a population of distant halo giants. The detections presented here will provide a valuable sample for galactic archeology studies.
SpaceInn hare-and-hounds exercise: Estimation of stellar properties using space-based asteroseismic data
Context: Detailed oscillation spectra comprising individual frequencies for numerous solar-type stars and red giants are either currently available, e.g. courtesy of the CoRoT, Kepler, and K2 missions, or will become available with the upcoming NASA TESS and ESA PLATO 2.0 missions. These data can lead to a precise characterisation of these stars thereby improving our understanding of stellar evolution, exoplanetary systems, and the history of our galaxy.
Aims: Our goal is to test and compare different methods for obtaining stellar properties from oscillation frequencies and spectroscopic constraints. Specifically, we would like to evaluate the accuracy of the results and reliability of the associated error bars, and see where there is room for improvement.
Methods: In the context of the SpaceInn network, we carried out a hare-and-hounds exercise in which one group, the hares, produced "observed" oscillation spectra for a set of 10 artificial solar-type stars, and a number of hounds applied various methods for characterising these stars based on the data produced by the hares. Most of the hounds fell into two main groups. The first group used forward modelling (i.e. applied various search/optimisation algorithms in a stellar parameter space) whereas the second group relied on acoustic glitch signatures.
Results: Results based on the forward modelling approach were accurate to 1.5 % (radius), 3.9 % (mass), 23 % (age), 1.5 % (surface gravity), and 1.8 % (mean density), as based on the root-mean square difference. Individual hounds reached different degrees of accuracy, some of which were substantially better than the above average values. For the two 1 M(sun) stellar targets, the accuracy on the age is better than 10 % thereby satisfying the requirements for the PLATO 2.0 mission. High stellar masses and atomic diffusion (which in our models does not include the effects of radiative accelerations) proved to be sources of difficulty. The average accuracies for the acoustic radii of the base of the convection zone, the He II ionisation, and the $\Gamma_1$ peak located between the two He ionisation zones were 17 %, 2.4 %, and 1.9 %, respectively. The results from the forward modelling were on average more accurate than those from the glitch fitting analysis as the latter seemed to be affected by aliasing problems for some of the targets.
Conclusions: Our study indicates that forward modelling is the most accurate way of interpreting the pulsation spectra of solar-type stars. However, given its model-dependent nature, such methods need to be complemented by model-independent results from, e.g., glitch analysis. Furthermore, our results indicate that global rather than local optimisation algorithms should be used in order to obtain robust error bars.
Binary star detectability in Kepler data from phase modulation of different types of oscillations
Detecting binary stars in photometric time series is traditionally done by measuring eclipses. This requires the orbital plane to be aligned with the observer. A new method without that requirement uses stellar oscillations to measure delays in the light arrival time and has been successfully applied to $\delta$ Scuti stars. However, application to other types of stars has not been explored. To investigate this we simulated light curves with a range of input parameters. We find a correlation between the signal-to-noise of the pulsation modes and the time delay required to detect binary motion. The detectability of the binarity in the simulations and in real Kepler data shows strong agreement, hence, we describe the factors that have prevented this method from discovering binary companions to stars belonging to various classes of pulsating stars.
Stellar Evidence that the Solar Dynamo may be in Transition
Precise photometry from the Kepler space telescope allows not only the measurement of rotation in solar-type field stars, but also the determination of reliable masses and ages from asteroseismology. These critical data have recently provided the first opportunity to calibrate rotation-age relations for stars older than the Sun. The evolutionary picture that emerges is surprising: beyond middle-age the efficiency of magnetic braking is dramatically reduced, implying a fundamental change in angular momentum loss beyond a critical Rossby number (Ro 2). We compile published chromospheric activity measurements for the sample of Kepler asteroseismic targets that were used to establish the new rotation-age relations. We use these data along with a sample of well characterized solar analogs from the Mount Wilson HK survey to develop a qualitative scenario connecting the evolution of chromospheric activity to a fundamental shift in the character of differential rotation. We conclude that the Sun may be in a transitional evolutionary phase, and that its magnetic cycle might represent a special case of stellar dynamo theory.
Period spacing in red giant II. Automated measurement
The space missions CoRoT and Kepler have provided photometric data of unprecedented quality for asteroseismology. A very rich oscillation pattern was discovered for red giants, including mixed modes that are used to decipher the red giants interiors. They carry information on the radiative core of red giants stars and bring strong constraints on stellar evolution. Since more than 15000 red giant light curves were observed by Kepler, we aim at developing a simple and efficient methods for automatically characterizing the mixed-mode pattern and measuring the asymptotic period spacing. With the asymptotic expansion of the mixed modes, we have revealed the regularity of the gravity-mode pattern. The stretched periods were used to study the evenly-space periods with a Fourier analysis and to measure the gravity period spacing, even when rotation severely complicates the oscillation spectra. We automatically measured gravity period spacing for more than five thousand Kepler red giants. The results confirm and extend previous measurements made by semi-automated methods. We also unveil the mass and metallicity dependence of the relation between the frequency spacings and the period spacings for stars on the red giant branch. The delivery of thousands of period spacings combined with all other seismic and non-seismic information provides new bases for detailed ensemble asteroseismology.
Limits in the application of harmonic analysis to pulsating stars
Using ultra-precise data from space instrumentation we found that the underlying functions of stellar light curves from some AF pulsating stars are non-analytic, and consequently their Fourier expansion is not guaranteed. This result demonstrates that periodograms do not provide a mathematically consistent estimator of the frequency content for this kind of variable stars. More importantly, this constitutes the first counterexample against the current paradigm which consid- ers that any physical process is described by a continuous (band-limited) function that is infinitely differentiable.
Sub-Inertial Gravity Modes in the B8V Star KIC 7760680 Reveal Moderate Core Overshooting and Low Vertical Diffusive Mixing
KIC 7760680 is so far the richest slowly pulsating B star, by exhibiting 36 consecutive dipole ($\ell=1$) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern confirm that KIC 7760680 is a moderate rotator, with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modelling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass $\sim3.25$ M$_\odot$. By simultaneously matching the slope of the period spacing, and the number of modes in the observed frequency range, we deduce that the equatorial rotation frequency of KIC 7760680 is 0.4805 day$^{-1}$, which is 26% of its Roche break up frequency. The relative deviation of the model frequencies and those observed is less than one percent. We succeed to tightly constrain the exponentially-decaying convective core overshooting parameter to $f_{\rm ov}\approx0.024\pm0.001$. This means that convective core overshooting can coexist with moderate rotation. Moreover, models with exponentially-decaying overshoot from the core outperform those with the classical step-function overshoot. The best value for extra diffusive mixing in the radiatively stable envelope is confined to $\log D_{\rm ext}\approx0.75\pm0.25$ (with $D_{\rm ext}$ in cm$^2$ sec$^{-1}$), which is notably smaller than theoretical predictions.
Detection of solar-like oscillations in relics of the Milky Way: asteroseismology of K giants in M4 using data from the NASA K2 mission
Asteroseismic constraints on K giants make it possible to infer radii, masses and ages of tens of thousands of field stars. Tests against independent estimates of these properties are however scarce, especially in the metal-poor regime. Here, we report the detection of solar-like oscillations in eight stars belonging to the red-giant branch (RGB) and red-horizontal branch (RHB) of the globular cluster M4. The detections were made in photometric observations from the K2 Mission during its Campaign 2. Making use of independent constraints on the distance, we estimate masses of the eight stars by utilizing different combinations of seismic and non-seismic inputs. When introducing a correction to the Δν scaling relation as suggested by stellar models, for RGB stars we find excellent agreement with the expected masses from isochrone fitting, and with a distance modulus derived using independent methods. The offset with respect to independent masses is lower, or comparable with, the uncertainties on the average RGB mass (4–10 per cent, depending on the combination of constraints used). Our results lend confidence to asteroseismic masses in the metal-poor regime. We note that a larger sample will be needed to allow more stringent tests to be made of systematic uncertainties in all the observables (both seismic and non-seismic), and to explore the properties of RHB stars, and of different populations in the cluster.
Measuring the extent of convective cores in low-mass stars using Kepler data: toward a calibration of core overshooting
Context: Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. The detection and precise characterization of solar-like oscillations in hundreds of main-sequence stars by CoRoT and Kepler has given the opportunity to revisit this problem.
Aims: Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass-limit for having a convective core.
Methods: We first test and validate a seismic diagnostic that was proposed to probe in a model-dependent way the extent of convective cores using the so-called $r_{010}$ ratios, which are built with $l=0$ and $l=1$ modes. We apply this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we compute grids of stellar models with both the CESAM2k and MESA evolution codes, where the extensions of convective cores are modeled either by an instantaneous mixing or as a diffusion process.
Results: We find that 10 stars or our sample are in fact subgiants. Among the other targets, we are able to unambiguously detect convective cores in eight stars and we obtain seismic measurements of the extent of the mixed core in these targets with a good agreement between the CESAM2k and MESA codes. By performing optimizations using the Levenberg-Marquardt algorithm, we then obtain estimates of the the amount of extra-mixing beyond the core that is required in the CESAM2k code to reproduce seismic observations for these eight stars and we show that this can be used to propose a calibration of this quantity. This calibration depends on the prescription chosen for the extra-mixing, but we find that it should be valid also for the code MESA, provided the same prescription is used.
Conclusions: This study constitutes a first step towards the calibration of the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.
Near-uniform internal rotation of the main sequence gamma Doradus pulsator KIC 7661054
We used Kepler photometry to determine the internal rotation rate of KIC 7661054, a chemically normal $\gamma$ Dor star on the main sequence at spectral type F2.5 V. The core rotation period of $27.25\pm0.06$ d is obtained from the rotational splittings of a series of dipole g modes. The surface rotation period is calculated from a spectroscopic projected rotation velocity and a stellar radius computed from models. Literature data, obtained without inclusion of macroturbulence as a line-broadening mechanism, imply that the surface rotates much more quickly than the core, while our detailed analysis suggests that the surface may rotate slightly more quickly than the core and that the rotation profile is uniform within the 1-$\sigma$ uncertainties. We discuss the pitfalls associated with the determination of surface rotation rates of slow rotators from spectroscopy in the absence of asteroseismic constraints. A broad signal is observed at low frequency, which we show cannot be attributed to rotation, contrary to previous suggestions concerning the origin of such signals.
What asteroseismology can do for exoplanets: Kepler-410A b is a Small Neptune in an eccentric orbit consistent with low obliquity
We confirm the Kepler planet candidate KOI-42b as a Neptune sized exoplanet on a $17.8$ day, eccentric, orbit around the bright ($K_\textrm{p} = 9.4$) star KOI-42A. KOI-42 consists of a blend between the fast rotating planet host star (KOI-42A) and a fainter star (KOI-42B), which has complicated the confirmation of the planetary candidate. Employing asteroseismology, using constraints from the transit light curve, adaptive optics and speckle images, and Spitzer transit observations, we demonstrate that the candidate can only be an exoplanet orbiting KOI-42A. Via asteroseismology we determine the following stellar and planetary parameters with high precision; M$_\star = 1.214 \pm 0.033$ M$_\odot$, R$_\star = 1.352 \pm 0.010$ R$_\odot$, Age $= 2.76 \pm 0.54$ Gyr, planetary radius ($2.838 \pm 0.054$ R$_\oplus$), and orbital eccentricity ($0.17^{+0.10}_{-0.05}$). In addition, rotational splitting of the pulsation modes allows for a measurement of KOI-42A's inclination and rotation rate. Our measurement of an inclination of $82.5^{+5.0}_{-5.2}$ [$^\circ$] indicates a low obliquity in this system.
Analysis of the acoustic cut-off frequency and the HIPs in 6 Kepler stars with stochastically excited pulsations
Gravito-acoustic modes in the Sun and other stars propagate in resonant cavities with a frequency below a given limit known as the cut-off frequency. At higher frequencies, waves are no longer trapped in the stellar interior and they become traveller waves. Those waves produce different patterns of High Interference Peaks (HIPs) above the cut-off frequency depending on whether they are originated by outward waves interfering with inward waves that are either partially reflected at the back of the star or that have been directly refracted in the stellar interior. In this work we study six pulsating solar-like stars at different evolutionary stages observed by the NASA mission Kepler. These high signal-to-noise targets show a peak structure that extends at very high frequencies and are good candidates to study the transition region between the modes and the interference peaks or pseudo modes. Following the same methodology successfully applied on Sun-as-a-star measurements, we uncover the existence of pseudo modes in these stars with one or two dominant interference patterns depending on the evolutionary stage of the star. We also infer their cut-off frequency as the middle point between the last eigenmode and the first peak of the interference patterns. By using the ray theory we show that while the period of one of the interference pattern is very close to half the large separation the other one depends on the time phase of mixed waves thus carrying on additional information on the stellar structure and evolution.
Hot super-Earths stripped by their host stars
Models predict that the envelopes of exoplanets orbiting close to their host star are stripped by evaporation, which should be evident as an absence of very hot super-Earth sized exoplanets. Recently, exoplanets in the midst of this process may have been observed. However, this absence in the distribution of exoplanets caused by evaporation has escaped a secure detection. Here we demonstrate, using asteroseismology on a sample of 162 exoplanets and exoplanet candidates observed during the Kepler mission that, while there is an abundance of super-Earth sized exoplanets with low incident fluxes, none are found with high incident fluxes. We do not find any exoplanets with radii between 2.2 and 3.8 Earth radii with incident flux above 650 times the incident flux on Earth. This gap in the population of exoplanets is explained by the evaporation of volatile elements and thus supports the theoretical predictions. The confirmation of a hot-super-Earth desert caused by evaporation will add an important constraint on simulations of the evolution of planetary systems, since they must be able to reproduce the dearth of close-in super-Earths.
Asteroseismic analysis of solar-like star KIC 6225718: constraints on stellar parameters and core overshooting
We analyze five seasons of short-cadence data of a solar-type star of spectral type F: KIC 6225718 observed by the Kepler . We obtain the power spectrum of this star by applying the Lomb-Scargle Periodogram to the smoothed time series. By applying the autocorrelation technique to the power spectrum, we derive the large frequency separation $\Delta\nu=105.78 \pm 0.65\ \mu$Hz and the frequency of the maximum power spectrum $\nu_{\rm{max}} = 2301 \pm 21\ \mu$Hz. We identify 33 p-modes with angular degrees of $l=0\sim2$ in the frequency range of 1600 - 2800 $\mu$Hz of the power spectrum with Bayesian Markov Chain Monte Carlo algorithms. In order to accurately determine the parameters of the star, we construct a grid of stellar models with core overshooting using the Yale stellar evolution code and then perform preliminary seismological analysis. With both asteroseismic and non-asteroseismic constraints, the range of stellar parameters are estimated: the mass $M=1.10^{+0.04}_{-0.03} M_{\odot}$, the radius $R = 1.22^{+0.01}_{-0.01}\ R_{\odot}$, and the age $t=3.35^{+0.36}_{-0.75}$ Gyr for this star. In addition, we analyze the effects of overshooting on stellar interiors, and find that the upper limit of the overshooting parameter $\alpha_{ov}$ is approximately 0.2 for this star.
Precise stellar surface gravities from the time scales of convectively driven brightness variations
A significant part of the intrinsic brightness variations in cool stars of low and intermediate mass arises from surface convection (seen as granulation) and acoustic oscillations (p-mode pulsations). The characteristics of these phenome- na are largely determined by the stars’ surface gravity g. Detailed photometric measurements of either signal can yield an accurate value of g. However, even with ultraprecise photometry from NASA’s Kepler mission, many stars are too faint for current methods or only moderate accuracy can be achieved in a limited range of stellar evolutionary stages. This means that many of the stars in the Kepler sample, including exoplanet hosts, are not sufficiently characterized to fully describe the sample and exoplanet properties. We present a novel way to measure surface gravities with accura- cies of about 4%. Our technique exploits the tight relation between g and the characteristic time scale of the combined granulation and p-mode oscillation signal. It is applicable to all stars with a convective envelope, including active stars. It can measure g in stars for which no other analysis is now possible. Because it depends on the time scale (and no other properties) of the signal, our technique is largely independent of the type of measurement (for example, photometry or radial velocity measurements) and the calibration of the instrumentation used. However, the oscillation signal must be temporally resolved; thus, it cannot be applied to dwarf stars observed by Kepler in its long-cadence mode.
Tight asteroseismic constraints on core overshooting and diffusive mixing in the slowly rotating pulsating B8.3V star KIC 10526294
Context:
KIC 10526294 was recently discovered to be a very slowly rotating and
slowly pulsating late B-type star. Its 19 consecutive dipole gravity modes
constitute a series with almost constant period spacing. This unique
collection of identified modes probes the near-core environment of this star
and holds the potential to reveal the size and structure of the overshooting
zone above the convective core, as well as the mixing properties of the star.
Aims:
We revisit the asteroseismic modelling of this star with specific emphasis on
the properties of the core overshooting, while considering additional
diffusive mixing throughout the radiative envelope of the star.
Methods:
We pursued forward seismic modelling based on adiabatic eigenfrequencies of
equilibrium models for eight extensive evolutionary grids tuned to
KIC 10526294 by varying the initial mass, metallicity, chemical mixture, and
the extent of the overshooting layer on top of the convective core. We
examined models for both OP and OPAL opacities and tested the occurrence of extra
diffusive mixing throughout the radiative interior.
Results:
We find a tight mass-metallicity relation within the
ranges $M\in [3.13,3.25]$ M$_\odot$ and $Z\in [0.014,0.028]$. We deduce
that an exponentially decaying diffusive core overshooting prescription
describes the seismic data better than a step function formulation and derive a value of
$f_{\rm ov}$ between 0.017 and 0.018. Moreover, the inclusion of extra
diffusive mixing
with a value of $\log D_{\rm mix}$ between 1.75 and 2.00 dex
(with $D_{\rm mix}$ in cm$^2$ s$^{-1}$) improves the goodness-of-fit based on
the observed and modelled frequencies by a factor $\sim\!11$ compared to the case
where no extra mixing is considered, irrespective of the $(M,Z)$ combination
within the allowed seismic range.
Conclusions:
The inclusion of diffusive mixing in addition to core overshooting
is essential to explain the structure in the observed period spacing pattern of this
star. Moreover, for the input physics and chemical mixtures we investigated,
we deduce that an exponentially decaying prescription for the core
overshooting is to be preferred over a step function,
regardless of the adopted mixture or choice of opacity tables.
Our best models for KIC 10526294 approach the seismic data to a level that
they can serve future inversion of its stellar structure.
MODE SUPPRESSION OF QUADRUPOLE AND OCTUPOLE MODES IN RED GIANTS OBSERVED BY KEPLER
The asteroseismology of red giant stars has continued to yield surprises since the onset of high-precision photometry from space-based observations. An exciting new theoretical result shows that the previously observed suppression of dipole oscillation modes in red giants can be used to detect strong magnetic fields in the stellar cores. A fundamental facet of the theory is that nearly all the mode energy leaking into the core is trapped by the magnetic greenhouse effect. This results in clear predictions for how the mode visibility changes with $\nu_{\mathrm{max}}$ as a star evolves up the red giant branch, and how that depends on stellar mass, spherical degree, and mode lifetime. Here we investigate the validity of these predictions with a particular focus on the visibility of different spherical degrees. We find that mode suppression weakens for higher degree modes with average reduced mode visibility of up to 49% for the least evolved stars in our sample, and no detectable suppression of octupole modes, in agreement with the theoretical predictions. We furthermore find evidence for the influence of increasing mode lifetimes on the measured visibilities along the red giant branch, in agreement with with previous independent observations. These results support the theory that strong internal magnetic fields are responsible for the observed suppression of non-radial modes in red giants. We also find preliminary evidence that stars with suppressed dipole modes on average have slightly lower metallicity than normal stars.
Internal rotation of the red-giant star KIC 4448777 by means of asteroseismic inversion
We study the dynamics of the stellar interior of
the early red-giant star KIC 4448777 by asteroseismic inversion of
14 splittings of the dipole mixed modes obtained from Kepler observations.
In order to overcome the complexity of the oscillation pattern typical of
red-giant stars, we present a procedure to extract the rotational splittings from
the power spectrum.
We find not only that the
core rotates from a minimum of 8 to a maximum of 17 times
faster than the surface,
confirming previous inversion results generated for other red giants \citepdeheuvels2012,deheuvels2014, but we also
estimate the variation of the angular velocity within the helium core with a spatial resolution of
$0.001R$ and verify the hypothesis of a sharp discontinuity in the inner stellar rotation.
The results show that the entire core rotates rigidly and
provide evidence for an angular velocity gradient around the base of the hydrogen burning shell; however we
do not succeed to characterize the rotational slope, due to the intrinsic limits of the applied techniques.
The angular velocity, from the edge of the core, appears to decrease with
increasing distance from the center,
reaching an average value in the convective envelope of $68\pm22$ nHz.
We conclude that a set of data which includes only dipolar modes is sufficient to infer quite accurately the rotation of a red giant not only in the dense core but also, with a lower level of confidence,
in part of the radiative region and in the convective envelope.
Oscillation frequencies for 35 Kepler solar-type planet-hosting stars using Bayesian techniques and machine learning.
Kepler has revolutionised our understanding of both exoplanets and their host stars. Asteroseismology is a valuable tool in the characterisation of stars and Kepler is an excellent observing facility to perform asteroseismology. Here we select a sample of 35 Kepler solar-type stars which host transiting exoplanets (or planet candidates) with detected solar-like oscillations. Using available Kepler short cadence data up to Quarter 16 we create power spectra optimised for asteroseismology of solar-type stars. We identify modes of oscillation and estimate mode frequencies by “peak bagging” using a Bayesian MCMC framework. In addition, we expand the methodology of quality assurance using a Bayesian unsupervised machine learning approach. We report the measured frequencies of the modes of oscillation for all 35 stars and frequency ratios commonly used in detailed asteroseismic modelling. Due to the high correlations associated with frequency ratios we report the covariance matrix of all frequencies measured and frequency ratios calculated. These frequencies, frequency ratios, and covariance matrices can be used to obtain tight constraint on the fundamental parameters of these planet-hosting stars.
KIC 9246715: The Double Red Giant Eclipsing Binary With Odd Oscillations
We combine Kepler photometry with ground-based spectra to present a comprehensive dynamical model of the double red giant eclipsing binary KIC 9246715. While the two stars are very similar in mass ($M_1 = 2.171\substack{+0.006 \ -0.008} \ M_{\odot}$, $M_2 = 2.149\substack{+0.006 \ -0.008} \ M_{\odot}$) and radius ($R_1 = 8.37\substack{+0.03 \ -0.07} \ R_{\odot}$, $R_2 = 8.30\substack{+0.04 \ -0.03} \ R_{\odot}$), an asteroseismic analysis finds one main set of solar-like oscillations with unusually low-amplitude, wide modes. A second set of oscillations from the other star may exist, but this marginal detection is extremely faint. Because the two stars are nearly twins, KIC 9246715 is a difficult target for a precise test of the asteroseismic scaling relations, which yield $M = 2.17\pm0.14 \ M_{\odot}$ and $R = 8.26\pm0.18 \ R_{\odot}$. Both stars are consistent with the inferred asteroseismic properties, but we suspect the main oscillator is Star 2 because it is less active than Star 1. We find evidence for stellar activity and modest tidal forces acting over the 171-day eccentric orbit, which are likely responsible for the essential lack of solar-like oscillations in one star and weak oscillations in the other. Mixed modes indicate the main oscillating star is on the secondary red clump (a core-He-burning star), and stellar evolution modeling supports this with a coeval history for a pair of red clump stars. This system is a useful case study and paves the way for a detailed analysis of more red giants in eclipsing binaries, an important benchmark for asteroseismology.
An RR Lyrae family portrait: 33 stars observed in Pisces with K2-E2
A detailed analysis is presented of 33 RR Lyrae stars in Pisces observed with the Kepler space telescope over the 8.9-day long K2 Two-Wheel Concept Engineering Test. The sample includes not only fundamental-mode and first overtone (RRab and RRc) stars but the first two double-mode (RRd) stars that Kepler detected and the only modulated first-overtone star ever observed from space so far. The precision of the extracted K2 light curves made it possible to detect low-amplitude additional modes in all subtypes. All RRd and non-modulated RRc stars show the additional mode at $P_X/P_1\sim0.61$ that was detected in previous space-based photometric measurements. A periodicity longer than the fundamental mode was tentatively identified in one RRab star that might belong to a gravity mode. We determined the photometric [Fe/H] values for all fundamental-mode stars and provide the preliminary results of our efforts to fit the double-mode stars with non-linear hydrodynamic pulsation models. The results from this short test run indicate that the K2 mission will be, and has started to be, an ideal tool to expand our knowledge about RR Lyrae stars. As a by-product of the target search and analysis, we identified 165 bona-fide double-mode RR Lyrae stars from the Catalina Sky Survey observations throughout the sky, 130 of which are new discoveries.
The internal rotation profile of the B-type star KIC 10526294 from frequency inversion of its dipole gravity modes
The internal angular momentum distribution of a star is key to determine its evolution. Fortunately, the stellar internal rotation can be probed through studies of rotationally-split nonradial oscillation modes. In particular, detection of nonradial gravity modes (g modes) in massive young stars has become feasible recently thanks to the Kepler space mission. Our aim is to derive the internal rotation profile of the Kepler B-type star KIC 10526294 through asteroseismology. We interpret the observed rotational splittings of its dipole g modes using four different approaches based on the best seismic models of the star and their rotational kernels. We find that the dipole mode splittings hint towards internal counter-rotation within the radiative envelope if a smooth rotation profile is assumed. We discuss alternative solutions and their viability.
Constraints on the structure of 16 Cyg A and 16 Cyg B using inversion techniques
Context Constraining additional mixing processes and chemical composition is a central problem in stellar physics as their impact on stellar age determinations leads to biases in our studies of stellar evolution, galactic history and exoplanetary systems. In two previous papers, we have shown how seismic inversion techniques could be used to offer strong constraints on such processes by pointing out weaknesses in current theoretical models. The theoretical approach having been tested, we now wish to apply our technique to observations. In that sense, the solar analogues 16CygA and 16CygB, being amongst the best targets in the Kepler field, are probably the current most well observed stars to test the diagnostic potential of seismic inversions. Aims We wish to use seismic indicators obtained with inversion techniques to constrain additional mixing processes in the structure of the components of the binary system 16Cyg. The combination of various seismic indicators will help to point out the weaknesses of stellar models and thus implies more constrained and accurate fundamendal parameters for these stars. Methods First, we will use the latest seismic, spectroscopic and interferometric observational constraints in the litterature for this system to determine suitable reference models independently for both stars. We will then carry out seismic inversions of the acoustic radius, the mean density and of a core conditions indicator. These additional constraints will be used to improve the reference models for both stars. Results The combination of seismic, interferometric and spectroscopic constraints allows us to obtain accurate reference models for both stars. However, we note that a degeneracy exists for these models. Namely, changing the diffusion coefficient or the chemical composition within the observational values could lead to $5 \%$ changes in mass, $3 \%$ changes in radius and up to $8 \%$ changes in age. We used acoustic radius and mean density inversions to further improve our reference models then carried out inversions for a core conditions indicator, denoted $t_{u}$. Thanks to the sensitivity of this indicator to microscopic diffusion and chemical composition mismatches, we were able to reduce the mass dispersion to $2 \%$, namely $\left[ 0.96M_{\odot},1.0M_{\odot} \right]$, the radius dispersion to $1 \%$, namely $\left[ 1.188R_{\odot},1.200R_{\odot} \right]$ and the age dispersion to $3 \%$, namely $\left[7.0,7.4\right]$, for $16$CygA. For $16$CygB, $t_{u}$ offered a consistency check for the models but could not be used to reduce independently the age dispersion. Nonetheless, assuming consistency with the age of $16$CygA could help to further constrain its mass and radius. We thus find that the mass of $16$CygB should be between $0.93$ $M_{\odot}$ and $0.96$ $M_{\odot}$ and its radius between $1.08$ $R_{\odot}$ and $1.10$ $R_{\odot}$
Dynamo-generated magnetic fields common in the convective cores of intermediate-mass stars
Magnetic fields play a role in almost all stages of stellar evolution. Most low-mass stars, including the Sun, show surface fields that are generated by dynamo processes in their convective envelopes. Intermediate-mass stars do not have deep convective envelopes, yet 10% exhibit strong surface fields that are presumed to be residuals from the stellar formation process. These stars do have convective cores that might produce internal magnetic fields, and these might even survive into later stages of stellar evolution, but information has been limited by our inability to measure the fields below the stellar surface. Here we use asteroseismology to study the occurrence of strong magnetic fields in the cores of low- and intermediate-mass stars. We have measured the strength of dipolar oscillation modes, which can be suppressed by a strong magnetic field in the core, in over 3600 red giant stars observed by Kepler. About 20% of our sample have mode suppression but this fraction is a strong function of mass. Strong core fields only occur in red giants above 1.1 solar masses (1.1Msol), and the occurrence rate is at least 60% for intermediate-mass stars (1.6–2.0Msol), indicating that powerful dynamos are very common in the convective cores of these stars.
Period spacings in red giants I. Disentangling rotation and revealing core structure discontinuities
Asteroseismology offers an efficient probe for testing the physical conditions inside the core of red giant stars. This relies on the properties of the oscillations with a mixed character that are highly sensitive to the physical properties of the core. Unfortunately, the mixed-mode pattern is often described as the mixed-mode forest since overlapping rotational splittings and mixed-mode spacings result in complex structures. This motivates further work. % This work aims at making the mixed-mode oscillation pattern as clear as possible in order to disentangle the rotational splittings from the mixed-mode spacings, and then open the way to a fully automated analysis of large data sets. % An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. This expression allows us to correct for the distortion of the mixed-mode pattern induced by the coupling of gravity and pressure waves; it puts in evidence the contribution of the gravity waves, regardless of the coupling. Period-corrected échelle diagrams clearly exhibit the structure of the gravity modes and of the rotational splittings. % We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. We also exhibit the signature of the structural glitches on mixed modes and show that we can distinguish deep and shallow buoyancy glitches. % % This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing.
KIC 10080943: a binary star with two $\gamma$ Doradus/$\delta$ Scuti hybrid pulsators. Analysis of the g modes
We use four years of Kepler photometry to study the non-eclipsing spectroscopic binary KIC 10080943. We find both components to be $\gamma$ Doradus/$\delta$ Scuti hybrids, which pulsate in both p and g modes. We present an analysis of the g modes, which is complicated by the fact that the two sets of $\ell=1$ modes partially overlap in the frequency spectrum. Nevertheless, it is possible to disentangle them by identifying rotationally split doublets from one component and triplets from the other. The identification is helped by the presence of additive combination frequencies in the spectrum that involve the doublets but not the triplets. The rotational splittings of the multiplets imply core rotation periods of about 11 d and 7 d in the two stars. One of the stars also shows evidence of $\ell=2$ modes.
Evidence of amplitude modulation due to Resonant Mode Coupling in the $\delta$ Scuti star KIC 5892969
A study of the star KIC 5892969 observed by the Kepler satellite is presented. Its three highest amplitude modes present a strong amplitude modulation. The aim of this work is to investigate amplitude variations in this star and their possible cause. Using the 4 years-long observations available, we obtained the frequency content of the full light curve. Then, we studied the amplitude and phase variations with time using shorter time stamps. The results obtained are compared with the predicted ones for resonant mode coupling of an unstable mode with lower frequency stable modes. Our conclusion is that resonant mode coupling is consistent as an amplitude limitation mechanism in several modes of KIC 5892969 and we discuss to which extent it might play an important role for other $\delta$ Scuti stars.
KIC 10080943: An eccentric binary system containing two pressure and gravity mode hybrid pulsators
$\gamma$ Doradus and $\delta$ Scuti pulsators cover the transition region between low mass and massive main-sequence stars, and as such, are critical for testing stellar models. When they reside in binary systems, we can combine two independent methods to derive critical information, such as precise fundamental parameters to aid asteroseismic modelling. In the Kepler light curve of KIC 10080943, clear signatures of gravity- and pressure-mode pulsations have been found. Ground-based spectroscopy revealed this target to be a double-lined binary system. We present the analysis of four years of Kepler photometry and high-resolution spectroscopy to derive observational constraints with which to evaluate theoretical predictions of the stellar structure and evolution for intermediate-mass stars. We used the method of spectral disentangling to determine atmospheric parameters for both components and derive the orbital elements. With phoebe, we modelled the ellipsoidal variation and reflection signal of the binary in the light curve and used classical Fourier techniques to analyse the pulsation modes. We show that the eccentric binary system KIC 10080943 contains two hybrid pulsators with masses $M_1=2.0\pm0.1~M_\odot$ and $M_2=1.9\pm0.1~M_\odot$, with radii $R_1=2.9\pm0.1~R_\odot$ and $R_2=2.1\pm0.2~R_\odot$. We detect rotational splitting in the g and p modes for both stars and use them to determine a first rough estimate of the core-to-surface rotation rates for the two components, which will be improved by future detailed seismic modelling.
A seismic and gravitationally-bound double star observed by Kepler: implication for the presence of a convective core
Solar-like oscillations have been observed by Kepler and CoRoT in many solar-type stars, thereby providing a way to probe the stars using asteroseismology.
The derivation of stellar parameters has usually been done using single stars. The aim of the paper is to derive the stellar parameters of a double-star system (HIP93511), for which an interferometric orbit has been observed along with asteroseismic measurements.
We used a time series of nearly two years of data of the double star to detect the two oscillation mode envelopes that appear in the power spectrum. Using a new scaling relation based on the use of luminosity, we derive the radius and mass of each star. We derive the age of each star using two proxies: one based upon the large frequency separation and a new one based upon the small frequency separation. Using stellar modelling, the mode frequencies allowed us to derive the radius, the mass and age of each component. In addition, speckle interferometry performed since 2006 has enabled us to recover the orbit of the system, and the total mass of the system.
From the determination of the orbit, the total mass of the system is 2.34$_{-0.33}^{+0.45}$ $M_{\odot}$ The total seismic mass using scaling relations is 2.47 $\pm$ 0.07 $M_{\odot}$. The seismic age derived using the new proxy based upon the small frequency separation is 3.5 $\pm$ 0.3 Gyr. Based on stellar modelling, the common age of the system is 2.7-3.9 Gyr. The total seismic mass of the system is 2.34-2.53 $M_{\odot}$, consistent to what we determined with the orbit. The stellar models provided the radius, mass and age of the stars as: $R_{A}=1.82-1.87$ $R_{\odot}$, $M_{A}=1.25-1.39$ $M_{\odot}$, ${\rm Age}_{A}$=2.6-3.5 Gyr; $R_{B}=1.22-1.25 R_{\sun}$, $M_{B}=1.08-1.14$ $M_{\odot}$, ${\rm Age}_{B}$=3.35-4.21 Gyr. We detect a convective core in Star A while Star B does not have any. For the metallicity of the binary system of $Z \approx 0.02$, we set the limit between stars having a convective corer or not at about 1.2 $M_{\odot}$.
LAMOST observatons in the Kepler field. I. Database of low-resolution spectra
The nearly continuous light curves with micromagnitude precision provided by the space mission Kepler are revolutionising our view of pulsating stars. They have revealed a vast sea of low-amplitude pulsation modes that were undetectable from Earth. The long time base of Kepler light curves allows an accurate determination of frequencies and amplitudes of pulsation modes needed for in-depth asteroseismic modeling. However, for an asteroseismic study to be successful, the first estimates of stellar parameters need to be known and they can not be derived from the Kepler photometry itself. The Kepler Input Catalog (KIC) provides values for the effective temperature, the surface gravity and the metallicity, but not always with a sufficient accuracy. Moreover, information on the chemical composition and rotation rate is lacking. We are collecting low-resolution spectra for objects in the Kepler field of view with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, Xinglong observatory, China). All of the requested fields have now been observed at least once. In this paper we describe those observations and provide a database of use to the whole astronomical community.
(This is an updated version of the paper with the same title with "status:unpublished" in the list of KASOC Publications)
Determination of fundamental asteroseismic parameters using the Hilbert transform
Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because they give information about e.g. the evolutionary state and the mass of a star.
Aims. We want to develop a robust method to determine the large and small frequency separations for time series with low signal-to-noise ratio. For this purpose, we analyse a time series of the Sun from the GOLF instrument aboard SOHO and a time series of the star KIC 5184732 from the NASA Kepler satellite by employing a combination of Fourier and Hilbert transform.
Methods. We use the analytic signal of filtered stellar oscillation time series to compute the signal envelope. Spectral analysis of the signal envelope then reveals frequency differences of dominant modes in the periodogram of the stellar time series.
Results. With the described method the large frequency separation $\Delta\nu$ can be extracted from the envelope spectrum even for data of poor signal-to-noise ratio. A modification of the method allows for an overview of the regularities in the periodogram of the time series.
KIC 3858884: a hybrid δ Sct pulsator in a highly eccentric eclipsing binary.
The analysis of eclipsing binaries containing non-radial pulsators allows: i) to combine two different and independent sources of information on the internal structure and evolutionary status of the components, and ii) to study the effects of tidal forces on pulsations. KIC 3858884 is a bright Kepler target whose light curve shows deep eclipses, complex pulsation patterns with pulsation frequencies typical of δ Sct, and a highly eccentric orbit. We present the result of the analysis of Kepler photometry and of high resolution phase resolved spectroscopy. Spectroscopy yielded both the radial velocity curves and, after spectral disentangling, the primary component effective temperature and metallicity, and line-of-sight projected rotational velocities. The Kepler light curve was analyzed with an iterative procedure devised to disentangle eclipses from pulsations which takes into account the visibility of the pulsating star during eclipses. The search for the best set of binary parameters was performed combining the synthetic light curve models with a genetic minimization algorithm, which yielded a robust and accurate determination of the system parameters. The binary components have very similar masses (1.88 and 1.86 M⊙) and effective temperatures (6800 and 6600 K), but different radii (3.45 and 3.05 R⊙). The comparison with the theoretical models evidenced a somewhat different evolutionary status of the components and the need of introducing overshooting in the models. The pulsation analysis indicates a hybrid nature of the pulsating (secondary) component, the corresponding high order g-modes might be excited by an intrinsic mechanism or by tidal forces.
Oscillating red giants observed during Campaign 1 of the Kepler K2 mission: New prospects for galactic archaeology
NASA's re-purposed Kepler mission – dubbed K2 – has brought new scientific opportunities that were not anticipated for the original Kepler mission. One science goal that makes optimal use of K2's capabilities, in particular its 360-degree ecliptic field of view, is galactic archaeology – the study of the evolution of the Galaxy from the fossil stellar record. The thrust of this research is to exploit high-precision, time-resolved photometry from K2 in order to detect oscillations in red giant stars. This asteroseismic information can provide estimates of stellar radius (hence distance), mass and age of vast numbers of stars across the Galaxy. Here we present the initial analysis of a subset of red giants, observed towards the North Galactic Gap, during the mission's first full science campaign. We investigate the feasibility of using K2 data for detecting oscillations in red giants that span a range in apparent magnitude and evolutionary state (hence intrinsic luminosity). We demonstrate that oscillations are detectable for essentially all cool giants within the $\log g$ range $\sim 1.9$–3.2. Our detection is complete down to $\mathit{Kp}\sim 14.5$, which results in a seismic sample with little or no detection bias. This sample is ideally suited to stellar population studies that seek to investigate potential shortcomings of contemporary Galaxy models.
Observational $\Delta\nu-\rho$ relation for $\delta$ Sct stars using eclipsing binaries and space photometry
Delta Scuti (δ Sct) stars are intermediate-mass pulsators, whose intrinsic oscillations have been studied for decades. However, modeling their pulsations remains a real theoretical challenge, thereby even hampering the precise determination of global stellar parameters. In this work, we used space photometry observations of eclipsing binaries with a δ Sct component to obtain reliable physical parameters and oscillation frequencies. Using that information, we derived an observational scaling relation between the stellar mean density and a frequency pattern in the oscillation spectrum. This pattern is analogous to the solar-like large separation but in the low order regime. We also show that this relation is independent of the rotation rate. These findings open the possibility of accurately characterizing this type of pulsator and validate the frequency pattern as a new observable for δ Sct stars.
The Blazhko effect and additional excited modes in RR Lyrae stars
Recent photometric space missions, such as CoRoT and Kepler revealed that many RR Lyrae stars pulsate – beyond their main radial pulsation mode – in low amplitude modes. Space data seem to indicate a clear trend, namely overtone (RRc) stars and modulated fundamental (RRab) RR Lyrae stars ubiquitously show additional modes, while non-Blazhko RRab stars never do. Two Kepler stars (V350 Lyr and KIC 7021124), however, apparently seemed to break this rule: they were classified as non-Blazhko RRab stars showing additional modes. We processed Kepler pixel photometric data of these stars. We detected small amplitude, but significant Blazhko effect for both stars by using the resulted light curves and O$-$C diagrams. This finding strengthens the apparent connection between the Blazhko effect and the excitation of additional modes. In addition, it yields a potential tool for detecting Blazhko stars through the additional frequency patterns even if we have only short but accurate time series observations. V350 Lyr shows the smallest amplitude multiperiodic Blazhko effect ever detected.
The potential for super-Nyquist asteroseismology with TESS
The perfect 30-min cadence of the full-frame images from the Transiting Exoplanet Survey Satellite (TESS) will impose a hard Nyquist limit of 24 d$^{-1}$ ($\approx 278$ $\upmu$Hz). This will be problematic for asteroseismology of stars with oscillation frequencies at or around that Nyquist limit, which will have insurmountable Nyquist ambiguities. TESS does offer some observing slots at shorter cadences, but these will be limited in number and competitive, while the full frame images will be the main data product for many types of variable stars. We show that the Nyquist ambiguities can be alleviated if, when TESS resumes observations after a downlink, integrations are not resumed at perfect cadence with those before the downlink. The time spent idling before integrations are resumed need only be around five minutes for satisfactory results, and observing time can be recouped from the downlink event if the telescope does not wait for a return to perfect cadence before resuming integrations. The importance of imperfect cadence after downlink is discussed in light of phase coverage of transit events.
KIC 4768731: a bright long-period roAp star in the Kepler Field
We report the identification of 61.45 d$^{-1}$ (711.2 $\mu$Hz) oscillations, with amplitudes of 62.6-$\mu$mag, in KIC 4768731 (HD 225914) using Kepler photometry. This relatively bright ($V$=9.17) chemically peculiar star with spectral type A5 Vp SrCr(Eu) has previously been found to exhibit rotational modulation with a period of 5.21 d. Fourier analysis reveals a simple dipole pulsator with an amplitude that has remained stable over a 4-yr time span, but with a frequency that is variable. Analysis of high-resolution spectra yields stellar parameters of $T_{\rm eff} = 8100 \pm 200$ K, $\log g = 4.0 \pm 0.2$, [Fe/H] = $+0.31 \pm 0.24$ and $v \sin i = 14.8 \pm 1.6$ km s$^{-1}$. Line profile variations caused by rotation are also evident. Lines of Sr, Cr, Eu, Mg and Si are strongest when the star is brightest, while Y and Ba vary in anti-phase with the other elements. The abundances of rare earth elements are only modestly enhanced compared to other roAp stars of similar $T_{\rm eff}$ and $\log g$. Radial velocities in the literature suggest a significant change over the past 30 yr, but the radial velocities presented here show no significant change over a period of 4 yr.
Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars
The detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the transport of angular momentum in stars. Mosser et al. (2012) have measured the rotation rate in the central regions of intermediate-mass core helium burning stars (secondary clump stars).
Our aim is to exploit the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data.
We select a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we show that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then use these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013).
We obtain evidence of a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating 1.8 +/- 0.3 to 3.2 +/- 1.0 times faster than the envelope. The last target is found to be consistent with a solid-body rotation.
This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase, or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum mechanisms that are at work.
Automated determination of g-mode period spacing of red-giant stars
The Kepler satellite has provided photometric timeseries data of unprecedented length, duty cycle and precision. To fully analyse these data for the tens of thousands of stars observed by Kepler, automated methods are a prerequisite. Here, we present an automated procedure to determine the period spacing of gravity modes in red giant stars ascending the red giant branch. The gravity modes reside in a cavity in the deep interior of the stars and provide information on the conditions in the stellar core. However, for red giants the gravity modes are not directly observable on the surface, hence this method is based on the pressure-gravity mixed modes that present observable features in the Fourier power spectrum. The method presented here is based on the vertical alignment and symmetry of these mixed modes in a period echelle diagram. We find that we can obtain reliable results for both model frequencies and observed frequencies. Additionally, we carried out Monte Carlo tests to obtain realistic uncertainties on the period spacings with different set of oscillation modes (for the models) and uncertainties on the frequencies. Furthermore, this method has been used to improve mode detection and identification of the observed frequencies in an iterative manner.
Helium signature in red giant oscillation patterns observed by Kepler
The space-borne missions CoRoT and $\Kepler$ have provided a large amount of precise photometric data. Among the stars observed, red giants show a rich oscillation pattern that allows their precise characterization. The usual description of red giant solar-like oscillations can be understood at first order in terms of the universal asymptotic oscillation pattern, which corresponds to a second-order asymptotic developement. We aim to, first, investigate the deviations observed from this universal pattern and, second, characterize them and identify them as the signature of sound-speed variations due to the second helium ionisation region. We also intend to characterize its variations along stellar evolution. We first measure the frequencies of radial modes in each spectra using a Maximum Likelihood Estimator method, then we isolate the modulation corresponding to the glitch component by taking the departure to the universal pattern into account. We measure the modulation component of the radial mode frequency spacings in more than one hundred red giants. We attribute the modulation to glitches due to the second ionisation of helium. We find a correlation between the evolutionary status of the stars and the signature of the second helium ionisation zone. We also bring constraints on the position of the second helium ionisation zone for these stars.
Asteroseismic modeling of 16 Cyg A & B using the complete Kepler data set
Asteroseismology of bright stars with well-determined properties from parallax measurements and interferometry can yield precise stellar ages and meaningful constraints on the composition. We substantiate this claim with an updated asteroseismic analysis of the solar-analog binary system 16 Cyg A & B using the complete 30-month data sets from the Kepler space telescope. An analysis with the Asteroseismic Modeling Portal (AMP), using all of the available constraints to model each star independently, yields the same age ($t=7.0\pm0.3$ Gyr) and composition ($Z=0.021\pm0.002$, $Y_{\rm i}=0.25\pm0.01$) for both stars, as expected for a binary system. We quantify the accuracy of the derived stellar properties by conducting a similar analysis of a Kepler-like data set for the Sun, and we investigate how the reliability of asteroseismic inference changes when fewer observational constraints are available or when different fitting methods are employed. We find that our estimates of the initial helium mass fraction are probably biased low by 0.02–0.03 from neglecting diffusion and settling of heavy elements, and we identify changes to our fitting method as the likely source of small shifts from our initial results in 2012. We conclude that in the best cases reliable stellar properties can be determined from asteroseismic analysis even without independent constraints on the radius and luminosity.
Nearly-uniform internal rotation of solar-like main-sequence stars revealed by space-based asteroseismology and spectroscopic measurements
The rotation rates in the deep interior and at the surface of 22 main-sequence stars with masses between $1.0$ and $1.6\,{\rm M}_{\sun}$ are constrained by combining asteroseismological analysis with spectroscopic measurements. The asteroseismic data of each star are taken by the Kepler or CoRoT space mission. It is found that the difference between the surface rotation rate and the average rotation rate (excluding the convective core) of most of stars is small enough to suggest that an efficient process of angular momentum transport operates during and/or before the main-sequence stage of stars. If each of the surface convective zone and the underlying radiative zone, for individual stars, is assumed to rotate uniformly, the difference in the rotation rate between the two zones turns out to be no more than a factor of two in most of the stars independently of their ages.
K2P² - A photometry pipeline for the K2 mission
With the loss of a second reaction wheel, resulting in the inability to point continuously and stably at the same field of view, the NASA Kepler satellite recently entered a new mode of observation known as the K2 mission. The data from this redesigned mission present a specific challenge; the targets systematically drift in position on an ${\sim}6$ hr timescale, inducing a significant instrumental signal in the photometric time series—this greatly impacts the ability to detect planetary signals and perform asteroseismic analysis. Here we detail our version of a reduction pipeline for K2 target pixel data, which automatically defines masks for all targets in a given frame; extracts the target's flux and position time series; corrects the time series based on the apparent movement on the CCD (either in 1D or 2D), combined with the correction of instrumental and/or planetary signals via the Kepler Asteroseismic Science Operations Center (KASOC) filter, thus rendering the time series ready for asteroseismic analysis; computes power spectra for all targets; and identifies potential contaminations between targets. From a test of our pipeline on a sample of targets from the K2 campaign 0, the recovery of data for multiple targets increases the amount of potential light curves by a factor of ${\geq}10$. Our pipeline could be applied to the upcoming TESS and PLATO 2.0 missions.
Finding binaries among Kepler pulsating stars from phase modulation of their pulsations
We present a method for finding binaries among pulsating stars that were observed by the Kepler Mission. We use entire four-year light curves to accurately measure the frequencies of the strongest pulsation modes, then track the pulsation phases at those frequencies in 10-d segments. This produces a series of time-delay measurements in which binarity is apparent as a periodic modulation whose amplitude gives the projected light travel time across the orbit. Fourier analysis of this time-delay curve provides the parameters of the orbit, including the period, eccentricity, angle of ascending node and time of periastron passage. Differentiating the time-delay curve yields the full radial-velocity curve directly from the Kepler photometry, without the need for spectroscopy. We show examples with $\delta$ Scuti stars having large numbers of pulsation modes, including one system in which both components of the binary are pulsating. The method is straightforward to automate, thus radial velocity curves can be derived for hundreds of non-eclipsing binary stars from Kepler photometry alone.
Asteroseismic estimate of helium abundance of a solar analog binary system
16 Cyg A and B are among the brightest stars observed by Kepler. What makes these stars more interesting is that they are solar analogs. 16 Cyg A and B exhibit solar-like oscillations. In this work we use oscillation frequencies obtained using 2.5 years of Kepler data to determine the current helium abundance of these stars. For this we use the fact that the helium ionization zone leaves a signature on the oscillation frequencies and that this signature can be calibrated to determine the helium abundance of that layer. By calibrating the signature of the helium ionization zone against models of known helium abundance, we find that the helium abundance in the envelope of \SCA is $0.243\pm0.008$ and that of \SCB is $0.244\pm0.018$.
Asteroseismic surface gravity for evolved stars
Context: Asteroseismic surface gravity values can be of importance in determining spectroscopic stellar parameters. The independent $\log(g)$ value from asteroseismology can be used as a fixed value in the spectroscopic analysis to reduce uncertainties due to the fact that $\log(g)$ and effective temperature can not be determined independently from spectra. Since 2012, a combined analysis of seismically and spectroscopically derived stellar properties is ongoing for a large survey with SDSS/APOGEE and Kepler. Therefore, knowledge of any potential biases and uncertainties in asteroseismic $\log(g)$ values is now becoming important. Aims: The seismic parameter needed to derive $\log(g)$ is the frequency of maximum oscillation power ($\nu_{\rm max}$). Here, we investigate the influence of $\nu_{\rm max}$ derived with different methods on the derived $\log(g)$ values. The large frequency separation between modes of the same degree and consecutive radial orders ($\Delta\nu$) is often used as an additional constraint for the determination of $\log(g)$. Additionally, we checked the influence of small corrections applied to $\Delta\nu$ on the derived values of $\log(g)$. Methods: We use methods extensively described in the literature to determine $\nu_{\rm max}$ and $\Delta\nu$ together with seismic scaling relations and grid-based modeling to derive $\log(g)$. Results:We find that different approaches to derive oscillation parameters give results for $\log(g)$ with small, but different, biases for red-clump and red-giant-branch stars. These biases are well within the quoted uncertainties of $\sim0.01$ dex (cgs). Corrections suggested in the literature to the $\Delta\nu$ scaling relation have no significant effect on $\log(g)$. However somewhat unexpectedly, method specific solar reference values induce biases of the order of the uncertainties, which is not the case when canonical solar reference values are used.
Asteroseismic inference on the spin-orbit misalignment and stellar parameters of HAT-P-7
The measurement of obliquities – the angle between the orbital and stellar rotation – in star-planet systems is of great importance for the understanding of planet system formation and evolution. The bright and well studied HAT-P-7 (Kepler-2) system is intriguing as several Rossiter-McLaughlin (RM) measurements found a large projected obliquity in this system, but it was so far not possible to determine if the orbit is polar and/or retrograde.
The goal of this study is to measure the stellar inclination and hereby the full 3D obliquity of the HAT-P-7 system instead of only the 2D projection as measured by the RM effect. In addition we provide an updated set of stellar parameters for the star.
We use the full set of available observations from Kepler spanning Q$0$-Q$17$ to produce the power spectrum of HAT-P-7. We extract oscillation mode frequencies via an MCMC peak-bagging routine, and use the results from this to estimate the stellar inclination angle. Combining this with the projected obliquity from RM and the inclination of the orbital plane allows us to determine the stellar obliquity. Furthermore, we use asteroseismology to model the star from the extracted frequencies using two different approaches to the modelling where either the MESA or the GARSTEC stellar evolution codes are adopted.
Using our updated asteroseismic modelling we find, a, the following stellar parameters for HAT-P-7: $M_{\star}=1.51^{+0.04}_{-0.05} \, M_{\odot}$, $R_{\star}=2.00^{+0.01}_{-0.02} \, R_{\odot}$, and age $= 2.07^{+0.28}_{-0.23}$ Gyr. Our asteroseismic modelling offers a high precision on the stellar parameters, for instance is the uncertainty on age of the order ${\sim}11\%$. For the stellar inclination we estimate $i_{\star}<36.5^{\circ}$, which translates to an obliquity of $83^{\circ}<\psi<111^{\circ}$. We find that the planet HAT-P-7b is likely retrograde in its orbit, and that the orbit is close to being polar. The new parameters for the star gives an updated planetary density of $\rho_p=0.65\pm 0.03\, \rm g\, cm^{-3}$, which is lower than previous estimates.
Rotation and magnetism of Kepler pulsating solar-like stars. Towards asteroseismically calibrated age-rotation relations
Kepler ultra-high precision photometry of long and continuous observations provides a unique dataset in which surface rotation and variability can be studied for thousands of stars. Because many of these old field stars also have independently measured asteroseismic ages, measurements of rotation and activity are particularly interesting in the context of age-rotation-activity relations. In particular, age-rotation relations generally lack good calibrators at old ages, a problem that this Kepler sample of old-field stars is uniquely suited to address. We study the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured. The rotation period was determined by comparing the results from two different analysis methods: i) the projection onto the frequency domain of the time-period analysis, and ii) the autocorrelation function of the light curves. Reliable surface rotation rates were then extracted by comparing the results from two different sets of calibrated data and from the two complementary analyses. General photometric levels of magnetic activity in this sample of stars were also extracted by using a photometric activity index, which takes into account the rotation period of the stars. We report rotation periods for 310 out of 540 targets (excluding known binaries and candidate planet-host stars); our measurements span a range of 1 to 100 days. The photometric magnetic activity levels of these stars were computed, and for 61.5% of the dwarfs, this level is similar to the range, from minimum to maximum, of the solar magnetic activity. We demonstrate that hot dwarfs, cool dwarfs, and subgiants have very different rotation-age relationships, highlighting the importance of separating out distinct populations when interpreting stellar rotation periods. Our sample of cool dwarf stars with age and metallicity data of the highest quality is consistent with gyrochronology relations reported in the literature.
Impact on asteroseismic analyses of regular gaps in Kepler data
The NASA Kepler mission has observed more than 190,000 stars in the constellations of Cygnus and Lyra. Around 4 years of almost continuous ultra high-precision photometry have been obtained reaching a duty cycle higher than 90% for many of these stars. However, regular gaps due to nominal operations are present in the light curves at different time scales. In general, most of these gaps are not dealt with in any specific way and are just accepted.In this paper we want to highlight the impact of those regular gaps in asteroseismic analyses and we try to find a method that minimizes their impact in the frequency domain. To do so, we isolate the two main time scales of regular gaps in the data. We then interpolate the gaps and we compare the power density spectra of four different stars: two red giants at different stages of their evolution, a young F-type star, and a classical pulsator in the instability strip. The spectra obtained after filling the gaps in the selected solar-like stars show a net reduction in the overall background level, as well as a change in the background parameters. The inferred convective properties could change as much as ∼200% in the selected example, introducing a bias in the p-mode frequency of maximum power. When global asteroseismic scaling relations are used, this bias can lead up to a variation in the surface gravity of 0.05 dex. Finally, the oscillation spectrum in the classical pulsator is cleaner compared to the original one
Surface Activity and Oscillation Amplitudes of Red Giants in Eclipsing Binaries
Among the 19 red-giant stars belonging to eclipsing binary systems that have been identified in Kepler data, 15 display solar-like oscillations. We study whether the absence of mode detection in the remaining 4 is an observational bias or possibly evidence of mode damping that originates from tidal interactions. A careful analysis of the corresponding Kepler light curves shows that modes with amplitudes that are usually observed in red giants would have been detected if they were present. We observe that the mode depletion is strongly associated with short-period systems, in which stellar radii account for 16-24 % of the semi-major axis, that are likely locked in phase, and where red-giant surface activity is detected. We suggest that when close binary systems lock in phase, the red-giant component is spun up, so that a dynamo mechanism starts and generates magnetic field, leading to observable stellar activity. Pressure modes would then be damped as acoustic waves dissipate in these fields.
Oscillation mode linewidths and heights of 23 main-sequence stars observed by Kepler
Solar-like oscillations have been observed by Kepler and CoRoT in many solar-type stars, thereby providing a way to probe the stars using asteroseismology.
We provide the mode linewidths and mode heights of the oscillations of various stars as a function of frequency and of effective temperature.
We used a time series of nearly two years of data for each star. The 23 stars observed belong to the simple or F-like category. The power spectra of the 23 main-sequence and subgiant stars were analysed using both maximum likelihood estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths, and mode heights. We study the source of systematic errors in the mode linewidths and mode heights, and we give a way to correct to a common reference.
Using the correction, we could explain all sources of systematic errors that could be reduced to less than $\pm$15% for mode linewidths and heights, and less than $\pm$5% for amplitude, when compared to a reference value. The effect of a different stellar background will provide frequency-dependent systematic errors that might affect the comparison with theoretical mode linewidth and mode height, therefore affecting the understanding of the physical nature of these parameters. All other sources of relative systematic errors are independent of frequency. We provide also the dependence of the so-called linewidth depression as a function of effective temperature. We show that the depth of the depression decreases with effective temperature. The dependence of the dip on effective temperature may imply that the mixing length parameter $\alpha$ may increase with effective temperature.
Rotation periods and ages of solar analogs and solar twins revealed by the Kepler mission
A new sample of solar analogs and twin candidates have been constructed and studied, with particular attention to their light curves from NASA's Kepler mission. This letter aims to assess the evolutionary status, derive their rotation and ages and identify those solar analogs or solar twin candidates. We separate out the subgiants that compose a large fraction of the asteroseismic sample, and which show an increase in the average rotation period as the stars ascend the subgiant branch. The rotation periods of the dwarfs, ranging from 6 to 30 days, and averaged 19d, allow us to assess their individual evolutionary states on the main sequence, and to derive their ages using gyrochronology. These ages are found to be in agreement with a correlation coefficient of r = 0.79 with the independent asteroseismic ages, where available. As a result of this investigation, we are able to identify 34 stars as solar analogs and 22 of them as solar twin candidates
Kepler photometry of RRc stars: peculiar double-mode pulsations and period doubling
We present the analysis of four first overtone RR Lyrae (RRc) stars observed with the Kepler space telescope, based on data obtained over a time span of nearly 2.5 yr. All four RRc stars have been found to be multi-mode pulsators. The strongest secondary mode with frequency $f_2$ has an amplitude of a few mmag, $20-45$ times lower than the amplitude of the main radial mode with frequency $f_1$. The two oscillations have a period ratio of $P_2/P_1 = 0.612-0.632$ that cannot be reproduced by any two radial modes. Thus, the secondary mode must be nonradial. Secondary modes with similar period ratios have also recently been discovered in several other variables of the RRc and RRd types. These objects form a homogenous group and constitute a new class of multimode RR Lyrae pulsators, fully analogous to a similar class of multimode classical Cepheids in the Magellanic Clouds. Because a secondary mode with $P_2/P_1\!\sim\! 0.61$ is found in almost every RRc and RRd star observed from space, we argue that this form of multiperiodicity is common. In all four Kepler RRc stars studied, we find subharmonics of the secondary frequency at $\sim 1/2 f_2$ and at $\sim 3/2 f_2$. This is a signature of a period doubling of the secondary oscillation, and is the first detection of period doubling in RRc stars. The amplitudes and phases of $f_2$ and its subharmonics are variable on timescales of 10 to 200 d, depending on the star. The dominant radial modes also shows temporal variations on the same timescales, but with much smaller amplitude. In three of the four Kepler RRc stars we detect additional periodicities (beyond $f_1$, $f_2$ and its subharmonics), with amplitudes below 1 mmag. Some of these frequencies are lower than that of the radial fundamental mode, and must correspond to nonradial $g$-modes. Such modes never before have been observed in RR Lyrae variables.
Determining stellar macroturbulence using asteroseismic rotational velocities from Kepler
The Rossiter-McLaughlin effect observed for transiting exoplanets often requires prior knowledge of the stellar sky-projected equatorial rotational velocity ($v \sin i$). This is usually provided by measuring the broadening of spectral lines, however this method has uncertainties as lines are also broadened by velocity fields in the stellar photosphere known as macroturbulence ($v_{\rm mac}$). We have estimated accurate $v \sin i$ values from asteroseismic analyses of main sequence stars observed by Kepler. The rotational frequency splittings of the detected solar-like oscillations of these stars are determined largely by the near-surface rotation. These estimates have been used to infer the $v_{\rm mac}$ values for 28 Kepler stars, and thus obtain a new calibration between $v_{\rm mac}$, effective temperature and surface gravity. As a result, $v_{\rm mac}$, and thus $v \sin i$, can now be determined with confidence for stars that do not have asteroseismic data available. We present new spectroscopic $v \sin i$ values for the WASP planet host stars, using high resolution HARPS spectra.
Asteroseismic inference on rotation, gyrochronology and planetary system dynamics of 16 Cygni
The solar analogs 16 Cyg A and 16 Cyg B are excellent asteroseismic targets in the \Kepler field of view and together with a red dwarf and a Jovian planet form an interesting system. The dynamics of this system have been studied previously but currently there is no reliable information on the rotation of the stellar components. Here, we use the technique of asteroseimology to determine the period of rotation and the angle of inclination for 16 Cyg A and B. We use the results on rotational period to demonstrate that asteroseismic analyses can provide constraints on mass-period-age relations. We perform a Bayesian model comparison between two gyrochronology relations that produces a decisive Bayes factor. Furthermore, with the excellent constraints available on mass, age, and rotational period we suggest that 16 Cyg A could be used in addition to the Sun as an anchor when calibrating gyrochronology relations. In addition, the results for the angle of inclination in 16 Cyg B do not contradict a low obliquity between the star and its eccentric planet. Given that the time scale to reach a low obliquity due to tidal interactions is much greater than the age of the system, we discuss the star-planet eccentricity and low obliquity which is consistent with Kozai cycling.
Determination of Three-dimensional Spin–orbit Angle with Joint Analysis of Asteroseismology, Transit Lightcurve, and the Rossiter–McLaughlin Effect: Cases of HAT-P-7 and Kepler-25
We develop a detailed methodology of determining three-dimensionally the angle between the stellar spin and the planetary orbit axis vectors, $\psi$, for transiting planetary systems. The
determination of $\psi$ requires the independent estimates of the inclination angles of the stellar spin axis and of the planetary orbital axis with respect to the line-of-sight, $i_\star$ and $i_{\rm orb}$,and the projection of the spin–orbit angle onto the plane of the sky, $\lambda$.
These are mainly derived from asteroseismology, transit lightcurve and the Rossiter-McLaughlin
effect, respectively. The detailed joint analysis of those three datasets enables an accurate and precise determination of the numerous parameters characterizing the planetary system, in addition to $\psi$.
We demonstrate the power of the joint analysis for the two specific systems, HAT-P-7 and Kepler-25. HAT-P-7b is the first exoplanet with significant misalignment $\lambda \approx 180^\circ$, and has been suspected as a retrograde (or polar) planet. Our joint analysis yields $\psi \approx 120^\circ$ with $i_\star \approx 30$ suggesting that its orbit is closer to polar rather than retrograde.
Kepler-25 is one of the few multi-transiting planetary systems with measured $\lambda$, and hosts two short-period transiting planets and one outer non-transiting planet.
The projected spin–orbit angle of the larger transiting planet, Kepler-25c, has been measured to be $\lambda \approx 0^\circ$, implying that the system is well-aligned. Due to the tight constraint from asteroseismology, we obtain $i_\star=65.4^{+10.6}_{-6.4}$ and $\psi=26.9^{+7.0}_{-9.2}$
to find that the system is actually mildly misaligned.
This is the first detection of the spin–orbit misalignment for the multiple planetary system with a main-sequence host star, and points to mechanisms that tilt a stellar spin axis relative to its protoplanetary disk.
Asteroseismic measurement of surface-to-core rotation in a main sequence A star, KIC 11145123
We have discovered rotationally split core g-mode triplets and surface p-mode triplets and quintuplets in a terminal age main sequence A star, KIC 11145123, that shows both $\delta$ Sct p-mode pulsations and $\gamma$ Dor g-mode pulsations. This gives the first robust determination of the rotation of the deep core and surface of a main sequence star, essentially model-independently. We find its rotation to be nearly uniform with a period near 100 d, but we show with high confidence that the surface rotates slightly faster than the core. A strong angular momentum transfer mechanism must be operating to produce the nearly rigid rotation, and a mechanism other than viscosity must be operating to produce a more rapidly rotating surface than core. Our asteroseismic result, along with previous asteroseismic constraints on internal rotation in some B stars, and measurements of internal rotation in some subgiant, giant and white dwarf stars, has made angular momentum transport in stars throughout their lifetimes an observational science.
Kepler detection of a new extreme planetary system orbiting the subdwarf-B pulsator KIC 10001893
KIC 10001893 is one out of 19 subdwarf B (sdB) pulsators observed by the \kep spacecraft in its K1 phase. In addition to tens of pulsation frequencies in the $g$-mode domain, its Fourier spectrum shows three weak peaks at very low frequencies, too low to be explained in terms of $g$-modes. The most convincing explanation is that we are seeing the orbital modulation of three Earth-size planets (or planetary remnants) very close to their parent star, that are illuminated by the strong stellar radiation. The orbital periods are P$_1$=5.273, P$_2$=7.807 and P$_3$=19.48 hours and the period ratios P$_2$/P$_1$=1.481 and P$_3$/P$_2$=2.495 are very close to the 3:2 and 5:2 resonance respectively. One of the main pulsation modes of the star at 210.68 \muHz corresponds to the third harmonic of the orbital frequency of the inner planet, suggesting that we see, for the first time in an sdB star, g-mode pulsations tidally excited by a planetary companion. The extreme planetary system that emerge from the \kep data is very similar to the recent discovery of two Earth-size planets orbiting the sdB pulsator KIC 05807616 (Charpinet et al. 2011).
Mixed modes in red giants: a window on stellar evolution
Determining stellar ages is a central issue in astrophysics because it directly or indirectly impacts all fields, from deciphering exoplanetary structure and evolution, through reconstructing the dynamical and chemical evolution of galactic structures, to setting a lower limit to the age of the Universe. However, measuring ages is challenging. Even determining stellar evolutionary stages and characterizing the transitions between them has been difficult and often impossible for field stars, because there was no observable that would enable us to do so. The situation has dramatically changed with the space-borne missions CoRoT and Kepler. Here, we report seismic observations that directly probe the physical conditions inside the core of low-mass stars, during their evolution from the main sequence to the red giant branch, the commencement of core helium burning, and the asymptotic giant branch. With the detection of global gravity modes for hundreds of stars observed by the Kepler mission, we are able to identify all key transitions between the different stages of stellar evolution. For the first time, we have unambiguous markers of stellar evolution, indicating the end of the subgiant and helium-core burning stages. We also distinguish whether a star is on the red or starting to ascend the asymptotic giant branch. The precise determination of the evolutionary stage during their core helium phase opens new opportunities for the use of red clump stars as accurate distance indicators.
Non-radial oscillations in M-giant semi-regular variables: Stellar models and Kepler observations
The success of asteroseismology relies heavily on our ability to identify the frequency patterns of stellar oscillation modes. For stars like the Sun this is relatively easy because the mode frequencies follow a regular pattern described by a well-founded asymptotic relation. When a solar like star evolves off the main sequence and onto the red giant branch its structure changes dramatically resulting in changes in the frequency pattern of the modes. We follow the evolution of the adiabatic frequency pattern from the main sequence to near the tip of the red giant branch for a series of models. We find a significant departure from the asymptotic relation for the non-radial modes near the red giant branch tip, resulting in a triplet frequency pattern. To support our investigation we analyze almost four years of Kepler data of the most luminous stars in the field (late K and early M type) and find that their frequency spectra indeed show a triplet pattern dominated by dipole modes even for the most luminous stars in our sample. Our identification explains previous results from ground-based observations reporting fine structure in the Petersen diagram and sub ridges in the period-luminosity diagram. Finally, we find ‘new ridges’ of non-radial modes with frequencies below the fundamental mode in our model calculations, and we speculate they are related to f modes.
The connection between stellar granulation and oscillation as seen by the Kepler mission
The long and almost continuous observations by Kepler show clear evidence for a granulation background signal in a large sample of stars, which is interpreted to be the surface manifestation of convection. It has been shown that its characteristic time scale and rms intensity fluctuation scale with the peak frequency (\num ) of the solar-like oscillations. Various attempts have been made to quantify the observed signal, to determine scaling relations for its characteristic parameters, and to compare them to theoretical predictions. Even though consistent on a global scale, large systematic differences of unknown origin remain between different methods as well as between the observations and simulations. We aim to study different approaches to quantify the signature of stellar granulation and search for a unified model that reproduces the observed signal best in a large variety of stars. We then aim to define empirical scaling relations between the granulation properties and \num and various other stellar parameters. We use a probabilistic method to compare different approaches to extract the granulation signal. We fit the power density spectra of a large set of Kepler targets, determine the granulation and global oscillation parameter, and quantify scaling relations between them. We establish that a depression in power at about \num /2, known from the Sun and a few other main-sequence stars, is also statistically significant in red giants, and that a super-Lorentzian function with two components is suited best to reproduce the granulation signal in the broader vicinity of the pulsation power excess. We also establish that the specific choice of the background model can impact the determination of \num , introducing systematic uncertainties that can significantly exceed the random uncertainties. We find the characteristic frequency (i.e., inverse time scale) and amplitude of both background components to tightly scale with \num for a large variety of stars (about 2-2000\mh in \num ), and quantify a mass dependency of the latter. To enable comparison with theoretical predictions (which do not include the observed power depression) we compute effective time scales and bolometric intensity fluctuations and find them to approximately scale as $\tau_\mathrm{eff} \propto g^{-0.86}$ and $A_\mathrm{gran} \propto (g^2M)^{-1/4}$, respectively. Similarly, the bolometric pulsation amplitude approximately scales as $A_\mathrm{puls} \propto (g^2M)^{-1/3}$, which implicitly verifies a separate mass and luminosity dependence of $A_\mathrm{puls}$. We also check our scaling relations with solar reference values and find them in good agreement. We provide a thorough analysis of the granulation background signal in a large sample of stars, from which we establish a unified model that allows us to accurately extract the granulation and global oscillation parameter. The resulting scaling relations allow a simple estimate of the overall spectral shape of any solar-type oscillator and might serve as a starting point for future large-sample studies or as a reference for theoretical modelling of granulation.
HD183648: a Kepler eclipsing binary with anomalous ellipsoidal variations and a pulsating component
KIC 8560861 (HD 183648) is a marginally eccentric ($e=0.05$) eclipsing binary with an orbital period of $P_\mathrm{orb}=31.973$ d, exhibiting mmag amplitude pulsations on time scales of a few days. We present the results of the complex analysis of high and medium-resolution spectroscopic data and Kepler Q0 – Q16 long cadence photometry. The iterative combination of spectral disentangling, atmospheric analysis, radial velocity and eclipse timing variation studies, separation of pulsational features of the light curve, and binary light curve analysis led to the accurate determination of the fundamental stellar parameters. We found that the binary is composed of two main sequence stars with an age of $0.9\pm0.2$ Gyr, having masses, radii and temperatures of $M_1=1.93\pm0.12$ M$_{\odot}$, $R_1=3.30\pm0.07$ R$_{\odot}$, $T_\mathrm{eff1}=7650\pm100$ K for the primary, and $M_2=1.06\pm0.08$ M$_{\odot}$, $R_2=1.11\pm0.03$ R$_{\odot}$, $T_\mathrm{eff2}=6450\pm100$ K for the secondary. After subtracting the binary model, we found three independent frequencies, two of which are separated by twice the orbital frequency. We also found an enigmatic half orbital period sinusoidal variation that we attribute to an anomalous ellipsoidal effect. Both of these observations indicate that tidal effects are strongly influencing the luminosity variations of HD 183648. The analysis of the eclipse timing variations revealed both a parabolic trend, and apsidal motion with a period of $P_\mathrm{apse}^\mathrm{obs}=10\,400\pm3\,000$ y, which is three times faster than what is theoretically expected. These findings might indicate the presence of a distant, unseen companion.
Properties of 42 Solar-type Kepler Targets from the Asteroseismic Modeling Portal
Recently the number of main-sequence and subgiant stars exhibiting solar-like oscillations that are resolved into individual mode frequencies has increased dramatically. While only a few such data sets were available for detailed modeling just a decade ago, the Kepler mission has produced suitable observations for hundreds of new targets. This rapid expansion in observational capacity has been accompanied by a shift in analysis and modeling strategies to yield uniform sets of derived stellar properties more quickly and easily. We use previously published asteroseismic and spectroscopic data sets to provide a uniform analysis of 42 solar-type Kepler targets from the Asteroseismic Modeling Portal (AMP). We find that fitting the individual frequencies typically doubles the precision of the asteroseismic radius, mass and age compared to grid-based modeling of the global oscillation properties, and improves the precision of the radius and mass by about a factor of three over empirical scaling relations. We demonstrate the utility of the derived properties with several applications.
Automated preparation of Kepler time series of planet hosts for asteroseismic analysis
One of the tasks of the Kepler Asteroseismic Science Operations Center (KASOC) is to provide asteroseismic analyses on Kepler Objects of Interest (KOIs). However, asteroseismic analysis of planetary host stars presents some unique complications with respect to data preprocessing, compared to pure asteroseismic targets. If not accounted for, the presence of planetary transits in the photometric time series often greatly complicates or even hinders these asteroseismic analyses. This drives the need for specialised methods of preprocessing data to make them suitable for asteroseismic analysis. In this paper we present the KASOC Filter, which is used to automatically prepare data from the Kepler/K2 mission for asteroseismic analyses of solar-like planet host stars. The methods are very effective at removing unwanted signals of both instrumental and planetary origins and produce significantly cleaner photometric time series than the original data. The methods are automated and can therefore easily be applied to a large number of stars. The application of the filter is not restricted to planetary hosts, but can be applied to any solar-like or red giant stars observed by Kepler/K2.
Long time-scale behavior of the Blazhko effect from rectified Kepler data
In order to benefit from the 4-year unprecedented precision of the Kepler data, we extracted light curves from the pixel photometric data of the Kepler space telescope for 15 Blazhko RR Lyrae stars. For collecting all the flux from a given target as accurately as possible, we defined tailor-made apertures for each star and quarter. In some cases the aperture finding process yielded sub-optimal result, because some flux have been lost even if the aperture contains all available pixels around the star. This fact stresses the importance of those methods that rely on the whole light curve instead of focusing on the extrema (O$-$C diagrams and other amplitude independent methods). We carried out detailed Fourier analysis of the light curves and the amplitude independent O$-$C diagram. We found 12 (80%) multiperiodically modulated stars in our sample. This ratio is much higher than previously found. Resonant coupling between radial modes, a recent theory to explain of the Blazhko effect, allows single, multiperiodic or even chaotic modulations. Among the stars with two modulations we found three stars (V355 Lyr, V366 Lyr and V450 Lyr) where one of the periods dominate in amplitude modulation, but the other period has larger frequency modulation amplitude. The ratio between the primary and secondary modulation periods is almost always very close to ratios of small integer numbers. It may indicate the effect of undiscovered resonances. Furthermore, we detected the excitation of the second radial overtone mode $f_2$ for three stars where this feature was formerly unknown. Our data set comprises the longest continuous, most precise observations of Blazhko RR Lyrae stars ever published. These data which is made publicly available will be unprecedented for years to come.
KIC 4544587: an Eccentric, Short Period Binary System with delta Scuti Pulsations and Tidally Excited Modes
We present Kepler photometry and ground based spectroscopy of KIC 4544587, a short-period eccentric eclipsing binary system with self-excited pressure and gravity modes, tidally excited modes, tidally influenced p modes, and rapid apsidal motion of 182 y per cycle. The primary and secondary components of KIC 4544587 reside within the delta Scuti and gamma Dor instability region of the Hurtzsprung-Russell diagram, respectively. By applying the binary modelling software phoebe to prewhitened Kepler photometric data and radial velocity data obtained using the William Herschel Telescope and 4-m Mayall telescope at KPNO, the fundamental parameters of this important system have been determined, including the stellar masses, 1.98 $\pm$0.07 Msun and 1.60 $\pm$ 0.06 Msun, and radii, 1.76 $\pm$ 0.03 Rsun and 1.42 $\pm$ 0.02 Rsun, for the primary and secondary components, respectively. Frequency analysis of the residual data revealed 31 modes, 14 in the gravity mode region and 17 in the pressure mode region. Of the 14 gravity modes 8 are orbital harmonics: a signature of tidal resonance. While the measured amplitude of these modes may be partially attributed to residual signal from binary model subtraction, we demonstrate through consideration of the folded light curve that these frequencies do infact correspond to tidally excited pulsations. Furthermore, we present an echelle diagram of the pressure mode frequency region (modulo the orbital frequency) and demonstrate that the tides are also influencing the p modes. A first look at asteroseismology hints that the secondary component is responsible for the p modes, which is contrary to our expectation that the hotter star should pulsate in higher radial overtone, higher frequency p modes.
Stroemgren for Asteroseismology and Galactic Archaeology: let the SAGA begin
Asteroseismology has the capability of precisely determining stellar properties which would otherwise be inaccessible, such as radii, masses and thus ages of stars. When coupling this information with classical determinations of stellar parameters, such as metallicities, effective temperatures and angular diameters, powerful new diagnostics for Galactic studies can be obtained. The ongoing Stroemgren survey for Asteroseismology and Galactic Archaeology (SAGA) has the goal of transforming the Kepler field into a new benchmark for Galactic studies, similarly to the solar neighborhood. Here we present first results from a stripe centred at Galactic longitude 74deg and covering latitude from about 8 to 20deg, which includes almost 1000 K-giants with seismic information and the benchmark open cluster NGC 6819. We describe the coupling of classical and seismic parameters, the accuracy as well as the caveats of the derived effective temperatures, metallicities, distances, surface gravities, masses, and radii. Confidence in the achieved precision is corroborated by the detection of the first and secondary clump in a population of field stars with a ratio of 2 to 1, and by the negligible scatter in the seismic distances among NGC 6819 member stars. An assessment of the reliability of stellar parameters in the Kepler Input Catalogue is also performed, and the impact of our results for population studies in the Milky Way is discussed, along with the importance of an all-sky Stroemgren survey.
Old puzzle, new insights: a lithium rich giant quietly burning helium in its core
About 1% of giant stars have been shown to have large surface Li abundances, which is unexpected according to standard stellar evolution models. Several scenarios for lithium production have been proposed, but it is still unclear why these Li-rich giants exist. A missing piece in this puzzle is the knowledge of the exact stage of evolution of these stars. Using low-and-high-resolution spectroscopic observations, we have undertaken a survey of lithium-rich giants in the Kepler field. In this letter, we report the finding of the first confirmed Li-rich core-helium-burning giant, as revealed by asteroseismic analysis. The evolutionary timescales constrained by its mass suggest that Li-production most likely took place through non-canonical mixing at the RGB-tip, possibly during the helium flash.
CHARACTERIZING TWO SOLAR-TYPE KEPLER SUBGIANTS WITH ASTEROSEISMOLOGY: KIC 10920273 AND KIC 11395018
Determining fundamental properties of stars through stellar modeling has improved substantially due to recent advances in asteroseismology. Thanks to the unprecedented data quality obtained by space missions, particularly CoRoT and Kepler, invaluable information is extracted from the high-precision stellar oscillation frequencies, which provide very strong constraints on possible stellar models for a given set of classical observations. In this work, we have characterized two relatively faint stars, KIC 10920273 and KIC 11395018, using oscillation data from Kepler photometry and atmospheric constraints from ground-based spectroscopy. Both stars have very similar atmospheric properties; however, using the individual frequencies extracted from the Kepler data, we have determined quite distinct global properties, with increased precision compared to that of earlier results. We found that both stars have left the main sequence and characterized them as follows: KIC 10920273 is a one-solar-mass star ($M=1.00\pm0.04M_{\odot}$), but much older than our Sun ($\tau=7.12\pm0.47$ Gyr), while KIC 11395018 is significantly more massive than the Sun ($M=1.27\pm0.04M_{\odot}$) with an age close to that of the Sun ($\tau=4.57\pm0.23$ Gyr). We confirm that the high lithium abundance reported for these stars should not be considered to represent young ages, as we precisely determined them to be evolved subgiants. We discuss the use of surface lithium abundance, rotation and activity relations as potential age diagnostics.
The historical vanishing of the Blazhko effect of RR Lyr from GEOS and Kepler surveys
RR Lyr is one of the most studied variable stars. Its light curve has been regularly monitored since the discovery of the periodic variability in 1899. Analysis of all observed maxima allows us to identify two primary pulsation states defined as pulsation over a “long” primary pulsation period (longer than 0.56684 d) and over a “short” one (shorter than 0.56682 d). These states alternate with intervals of 13-16 yr, and are well defined after 1943. The 40.8-d periodical modulations of the amplitude and the period (Blazhko effect) were noticed in 1916. We provide homogeneous determinations of the Blazhko period in the different primary pulsation states and we establish how it suddenly diminished to around 39.0 d in 1975. The monitoring of these periodicities deserved and deserves a continuous and intensive observational effort. For this purpose we have built dedicated, transportable, and autonomous small instruments (Very Tiny Telescopes, VTTs) to observe the times of maximum brightness of RR Lyr. As immediate results the VTTs recorded the last change of $P_0$ state in mid-2009 and extended the time coverage of the Kepler observations, thus recording a maximum O-C amplitude of the Blazhko effect in 2008, followed by the historical smallest O -C amplitude in late 2013. This phase is still ongoing and VTT instruments are ready to monitor the expected increase in the next few years.
Evidence of resonant mode coupling and the relationship between low and high frequencies in a rapidly rotating A star
In the theory of resonant mode coupling, the parent and child modes are directly related in frequency and phase. The oscillations present in the fast rotating Delta Scuti star KIC 8054146 allow us to test the most general and generic aspects of such a theory. The only direct way to separate the parent and coupled (child) modes is to examine the correlations in amplitude variability between the different frequencies. For the dominant family of related frequencies, only a single mode and a triplet are the origins of nine dominant frequency peaks ranging from 2.93 to 66.30 cycles per day (as well as dozens of small-amplitude combination modes and a predicted and detected third high-frequency triplet).
The mode-coupling model correctly predicts the large amplitude variations of the coupled modes as a product of the amplitudes of the parent modes, while the phase changes are also correctly modeled. This differs from the behavior of "normal" combination frequencies in that the amplitudes are three orders of magnitude larger and may exceed even the amplitudes of the parent modes.
We show that two dominant low frequencies at 5.86 and 2.93 cycles per day in the gravity-mode region are not harmonics of each other, and their properties follow those of the almost equidistant high-frequency triplet. We note that the previously puzzling situation of finding two strong peaks in the low-frequency region related by nearly a factor of two in frequency has been seen in other Delta Scuti stars as well.
Asteroseismic Study on Cluster Distance Moduli for Red Giant Branch Stars in NGC 6791 and NGC 6819
Stellar distance is an important basic parameter in stellar astrophysics. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. They are therefore expected to have common properties. These common properties strengthen our ability to constrain theoretical models and/or to determine fundamental parameters, such as stellar mass, metal fraction, and distance when tested against an ensemble of cluster stars. Here we derive a new relation based on solar-like oscillations, photometric observations, and the theory of stellar structure and evolution of red giant branch stars to determine cluster distance moduli through the global oscillation parameters \dnu and \numax and photometric data V. The values of \dnu and \numax are derived from \kepler observations. At the same time, it is used to interpret the trends between V and \dnu. From the analyses of this newly derived relation and observational data of NGC 6791 and NGC 6819 we devise a method in which all stars in a cluster are regarded as one entity to determine the cluster distance modulus. This approach fully reflects the characteristic of member stars in a cluster as a natural sample. From this method we derive true distance moduli of $13.09\pm0.10$ mag for NGC 6791 and $11.88\pm0.14$ mag for NGC 6819. Additionally, we find that the distance modulus only slightly depends on the metallicity [Fe/H] in the new relation. A change of 0.1 dex in [Fe/H] will lead to a change of 0.06 mag in the distance modulus.
Pulsating red giant stars in eccentric binary systems discovered from Kepler space-based photometry - A sample study and the analysis of KIC 5006817
The unparalleled photometric data obtained by NASA's Kepler space telescope led to an improved understanding of red giant stars and binary stars. Seismology allows us to constrain the properties of red giants. In addition to eclipsing binaries, eccentric non-eclipsing binaries, exhibiting ellipsoidal modulations, have been detected with Kepler.
We aim to study the properties of eccentric binary systems containing a red giant star and derive the parameters of the primary giant component.
We apply asteroseismic techniques to determine masses and radii of the primary component of each system. For a selected target, light and radial velocity curve modelling techniques are applied to extract the parameters of the system and its primary component. Stellar evolution and its effects on the evolution of the binary system are studied from theoretical models.
The paper presents the asteroseismic analysis of 18 pulsating red giants in eccentric binary systems, for which masses and radii were constrained. The orbital periods of these systems range from 20 to 440 days. The results of our ongoing radial velocity monitoring program with the HERMES spectrograph reveal an eccentricity range of $e$ = 0.2 to 0.76.
As a case study we present a detailed analysis of KIC 5006817, whose rich oscillation spectrum allows for a detailed seismic analysis.
From seismology we constrain the rotational period of the envelope to be at least 165 d, which is roughly twice the orbital period. The stellar core rotates 13 times faster than the surface. From the spectrum and radial velocities we expect that the Doppler beaming signal should have a maximum amplitude of 300 ppm in the light curve. Fixing the mass and radius to the asteroseismically determined values, from our binary modelling we find a value of the gravity darkening exponent that is significantly larger than expected. Through binary modelling, we determine the mass of the secondary component to be 0.29$\pm$0.03 $M$\sun.
For KIC 5006817 we exclude pseudo-synchronous rotation of the red giant with the orbit. The comparison of the results from seismology and modelling of the light curve shows a possible alignment of the rotational and orbital axis at the 2$\sigma$ level. Red giant eccentric systems could be progenitors of cataclysmic variables and hot subdwarf B stars.
Seismic constraints on the radial dependence of the internal rotation profiles of six Kepler subgiants and young red giants
Context: We still do not understand which physical mechanisms are responsible for the transport of angular momentum inside stars. The recent detection of mixed modes that contain the clear signature of rotation in the spectra of kepler subgiants and red giants gives us the opportunity to make progress on this issue.
Aims: Our aim is to probe the radial dependance of the rotation profiles for a sample of kepler targets. For this purpose, subgiants and early red giants are particularly interesting targets because their rotational splittings are more sensitive to the rotation outside the deeper core than is the case for their more evolved counterparts.
Method: We first extract the rotational splittings and frequencies of the modes for six young kepler red giants. We then perform a seismic modeling of these stars using the evolutionary codes Cesam2k and ASTEC. By using the observed splittings and the rotational kernels of the optimal models, we perform inversions of the internal rotation profiles of the six stars.
Results: We obtain estimates of the core rotation rates for these stars, and upper limits to the rotation in their convective envelope. We show that the rotation contrast between the core and the envelope increases during the subgiant branch. Our results also suggest that the core of subgiants spins up with time, while their envelope spins down. For two of the stars, we show that a discontinuous rotation profile with a deep discontinuity reproduces the observed splittings significantly better than a smooth rotation profile. Interestingly, the depths that are found most probable for the discontinuities roughly coincide with the location of the H-burning shell, which separates the layers that contract from those that expand.
Conclusions: We characterized the differential rotation pattern of six young giants with a range of metallicities, and with both radiative and convective cores on the main sequence. This will bring observational constraints to the scenarios of angular momentum transport in stars. Also, if the existence of sharp gradients in the rotation profiles of young red giants is confirmed, it should help discriminate between the physical processes that could transport angular momentum in the subgiant and red giant branches.
Study of KIC 8561221 observed by Kepler: an early red giant showing depressed dipolar modes
The continuous high-precision photometric observations provided by the CoRoT and Kepler space missions have allowed us to better understand the structure and dynamics of red giants using asteroseismic techniques. A small fraction of these stars shows dipole modes with unexpectedly low amplitudes. The reduction in amplitude is more pronounced for stars with higher frequency of maximum power, nu_max. In this work we want to characterize KIC 8561221 in order to confirm that it is currently the least evolved star among this peculiar subset and to discuss several hypotheses that could help explain the reduction of the dipole mode amplitudes. We used Kepler short- and long-cadence data combined with spectroscopic observations to infer the stellar structure and dynamics of KIC 8561221. We then discussed different scenarios that could contribute to the reduction of the dipole amplitudes such as a fast rotating interior or the effect of a magnetic field on the properties of the modes. We also performed a detailed study of the inertia and damping of the modes. We have been able to characterize 37 oscillations modes, in particular, a few dipole modes above nu_max that exhibit nearly normal amplitudes. The frequencies of all the measured modes were used to determine the global properties and the internal structure of the star. We have inferred a surface rotation period of around 91 days and uncovered the existence of a variation in the surface magnetic activity during the last 4 years. The analysis of the convective background did not reveal any difference compared to “normal†red giants. As expected, the internal regions of the star probed by the l = 2 and 3 modes spin 4 to 8 times faster than the surface. With our grid of standard models we are able to properly fit the observed frequencies. Our model calculation of mode inertia and damping give no explanation for the depressed dipole modes. A fast rotating core is also ruled out as a possible explanation. Finally, we do not have any observational evidence of the presence of a strong deep magnetic field inside the star.
Atmospheric parameters and pulsational properties for a sample of δ Sct, γ Dor, and hybrid Kepler targets
We report spectroscopic observations for 19 $\delta$ Sct candidates observed by the Kepler satellite both in long and short cadence mode. For all these stars, by using spectral synthesis, we derive the effective temperature, the surface gravity and the projected rotational velocity. An equivalent spectral type classification has been also performed for all stars in the sample. These determinations are fundamental for modelling the frequency spectra that will be extracted from the Kepler data for asteroseismic inference. For all the 19 stars, we present also periodograms obtained from Kepler data. We find that all stars show peaks in both low- ($\gamma$ Dor; g mode) and high-frequency ($\delta$ Sct; p mode) regions. Using the amplitudes and considering 5 c/d as a boundary frequency, we classified 3 stars as pure $\gamma$ Dor, 4 as $\gamma$ Dor - $\delta$ Sct hybrid, 5 as $\delta$ Sct - $\gamma$ Dor hybrid, and 6 as pure $\delta$ Sct. The only exception is the star KIC05296877 which we suggest could be a binary.
Measurement of acoustic glitches in solar-type stars from oscillation frequencies observed by Kepler
For the very best and brightest asteroseismic solar-type targets observed by Kepler, the frequency precision is sufficient to determine the acoustic depths of the surface convective layer and the helium ionization zone. Such sharp features inside the acoustic cavity of the star, which we call acoustic glitches, create small oscillatory deviations from the uniform spacing of frequencies in a sequence of oscillation modes with the same spherical harmonic degree. We use these oscillatory signals to determine the acoustic locations of such features in 19 solar-type stars observed by the Kepler mission. Four independent groups of researchers utilized the oscillation frequencies themselves, the second differences of the frequencies and the ratio of the small and large separation to locate the base of the convection zone and the second helium ionization zone. Despite the significantly different methods of analysis, good agreement was found between the results of these four groups, barring a few cases. These results also agree reasonably well with the locations of these layers in representative models of the stars. These results firmly establish the presence of the oscillatory signals in the asteroseismic data and the viability of several techniques to determine the location of acoustic glitches inside stars.
Magnetic activity of F stars observed by Kepler
The study of stellar activity is important because it can provide new constraints for dynamo models, when combined with surface rotation rates and the depth of the convection zone. We know that the dynamo mechanism, which is believed to be the main process to rule the magnetic cycle of solar-like stars at least, results from the interaction between (differential) rotation, convection, and magnetic field. The Kepler mission has already been collecting data for a large number of stars during four years allowing us to investigate magnetic stellar cycles. We investigated the Kepler light curves to look for magnetic activity or even hints of magnetic activity cycles. Based on the photometric data we also looked for new magnetic indexes to characterise the magnetic activity of the stars. We selected a sample of 22 solar-like F stars that have a rotation period smaller than 12 days. We performed a time-frequency analysis using the Morlet wavelet yielding a magnetic proxy for our sample of stars. We computed the magnetic index $S_{\rm ph}$ as the standard deviation of the whole time series and the index $<S_{\rm ph}>$ that is the mean of standard deviations measured in subseries of length five times the rotation period of the star. We defined new indicators to take into account the fact that complete magnetic cycles are not observed for all the stars, such as the contrast between high and low activity. We also inferred the Rossby number of the stars and studied their stellar background. With this analysis we obtained four categories of stars. Five of them show long-lived spots or active regions. We also observe stars that have a cycle-like behaviour. Two stars of our sample seem to have a decreasing or increasing trend in the temporal variation of the magnetic proxies. Finally the last group of stars show magnetic activity (with presence of spots) but no sign of cycle. We looked for correlation between our indexes and the stellar properties of the stars but did not find any clear correlation in our sample of F stars.
Accurate parameters of the oldest known rocky-exoplanet hosting system: Kepler-10 revisited
Since the discovery of Kepler-10, the system has received considerable interest because it contains a small, rocky planet which orbits the star in less than a day. The system’s parameters, announced by the Kepler team and subsequently used in further research, were based on only five months of data. We have reanalyzed this system using the full span of 29 months of Kepler photometric data, and obtained improved information about its star and the planets. A detailed asteroseismic analysis of the extended time series provides a significant improvement on the stellar parameters: not only can we state that Kepler-10 is the oldest known rocky-planet-harboring system at $10.41\pm1.36$ Gyr, but these parameters combined with improved planetary parameters from new transit fits gives us the radius of Kepler-10b to within just 125 km. A new analysis of the full planetary phase curve leads to new estimates on the planetary temperature and albedo, which remain degenerate in the Kepler band. Our modeling suggests that the flux level during the occultation is slightly lower than at the transit wings, which would imply that the nightside of this planet has a non-negligible temperature.
Asteroseismology of evolved stars with Kepler: a new way to constrain stellar interiors using mode inertias
The asteroseismology of evolved solar-like stars is experiencing growing interest due to the wealth of observational data from space-borne instruments such as the CoRoT and Kepler spacecraft. In particular, the recent detection of mixed modes, which probe both the innermost and uppermost layers of stars, paves the way for inferring the internal structure of stars along their evolution through the subgiant and red giant phases. Mixed modes can also place stringent constraints on the physics of such stars and on their global properties (mass, age, etc.). Here, using two Kepler stars (KIC 4351319 and KIC 6442183), we demonstrate that measurements of mixed mode characteristics allow us to estimate the mode inertias, providing a new and additional diagnostics on the mode trapping and subsequently on the internal structure of evolved stars. We however stress that the accuracy may be sensitive to non-adiabatic effects.
Asteroseismic fundamental properties of solar-type stars observed by the NASA Kepler Mission
We use asteroseismic data obtained by the NASA Kepler Mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of Kepler science operations, when these solar-type targets were observed for one month each in a survey mode, were used for this work. Stellar properties were estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures, $T_{\rm eff}$, were available for the entire ensemble using available complementary photometry; spectroscopic estimates of $T_{\rm eff}$ and [Fe/H] were available from a homogeneous analysis of ground-based data on a subset totalling 89 stars. The median final uncertainties for the full ensemble (spectroscopic subset) are approximately $10.8$ % (5.5 %) in mass, 4.4 % (2.2 %) in radius, 0.017 dex (0.010 dex) in $\log\,g$, 4.3 % (2.8 %) in mean density, and about 34 % (25 %) in age.
Classifying stellar populations among 13 000 red giants observed by Kepler
Of the more than 150 000 targets followed by the Kepler Mission, about 10% were selected as red giants. Due to their high scientific value, in particular for Galaxy population studies and stellar structure and evolution, their Kepler light curves have been made public without a proprietary period since late 2011. More than 13 000 of these stars show intrinsic flux variability caused by solar-like oscillations making them ideal for large scale asteroseismic investigations. In a significant fraction we have been able to automatically extract individual frequencies and to measure the period spacings of the dipole modes. These measurements provide a way to classify the stars into various populations, such as the red giant branch, the low-mass ($1.0\lesssim M/$M$_\odot \lesssim 2.0$) helium-core-burning red clump, and the higher-mass ($2.0\lesssim M/$\M$_\odot \lesssim 3.0$) secondary clump. The period spacings also reveal that a large fraction of the stars show rotationally induced frequency splittings. This sample of stars provides an extremely valuable source for studying the stellar population in the direction of the Kepler field, in particular when combined with complementary spectroscopic surveys.
New asteroseismic scaling relations based on Hayashi track relation applied to red-giant branch stars in NGC 6791 and NGC 6819
Stellar mass $M$, radius $R$, and gravity $g$ are important basic parameters in stellar physics. Accurate values for these parameters can be obtained from the gravitational interaction between stars in multiple systems or from asteroseismology. Stars in a cluster are thought to be formed coevally from the same interstellar cloud of gas and dust. The cluster members are therefore expected to have some properties in common. These restrictions strengthen our ability to constrain stellar models and asteroseismically derived $M$, $R$ and $g$ when tested against an ensemble of cluster stars.
Here we derive new scaling relations based on a relation for stars on the Hayashi track ($\sqrt{T_{\rm eff}} \sim g^pR^q$) to determine the masses and metallicities of red giant branch stars in open clusters NGC 6791 and NGC 6819 from the global oscillation parameters \dnu (the large frequency separation) and \numax (frequency of maximum oscillation power). The \dnu and \numax values are derived from \kepler observations.
From the analysis of these new relations we derive: (1) direct observational evidence that the masses of red giant branch stars in a cluster are the same within their uncertainties. (2) new methods to derive $M$ and $z$ of the cluster in a self consistent way from \dnu and \numax. The resulting values for $M$ and $z$ in lower intrinsic uncertainties then previously derived scaling relations which depend on effective temperature. (3) the mass dependence in the \dnu - \numax relation for red giant branch stars.
Stellar granulation as seen in disk-integrated intensity. II. Theoretical scaling relations compared with observations
A large set of stars observed by CoRoT and Kepler shows clear evidence for the presence of a stellar background, which is interpreted to arise from surface convection, i.e., granulation. These observations show that the characteristic time-scale ($\tau_{\rm eff}$) and the root-mean-square (rms) brightness fluctuations ($\sigma$) associated with the granulation scale as a function of the peak frequency ($\nu_{\rm max}$) of the solar-like oscillations. We aim at providing a theoretical background to the observed scaling relations based on a model developed in the companion paper (hereafter paper I). We computed for each 3D model the theoretical power density spectrum (PDS) associated with the granulation as seen in disk-integrated intensity on the basis of the theoretical model published in paper I. For each PDS we derived the associated characteristic time ($\tau_{\rm eff}$) and the rms brightness fluctuations ($\sigma$) and compared these theoretical values with the theoretical scaling relations derived from the theoretical model and the measurements made on a large set of Kepler targets. We derive theoretical scaling relations for $\tau_{\rm eff}$ and $\sigma$, which show the same dependence on $\nu_{\rm max}$ as the observed scaling relations. In addition, we show that these quantities also scale as a function of the turbulent Mach number (${\cal M}_{\rm a}$) estimated at the photosphere. The theoretical scaling relations for $\tau_{\rm eff}$ and $\sigma$ match the observations well on a global scale. Quantitatively, the remaining discrepancies with the observations are found to be much smaller than previous theoretical calculations made for red giants. Our modelling provides additional theoretical support for the observed variations of $\sigma$ and $\tau_{\rm eff}$ with $\nu_{\rm max}$. It also highlights the important role of ${\cal M}_{\rm a}$ in controlling the properties of the stellar granulation. However, the observations made with Kepler on a wide variety of stars cannot confirm the dependence of our scaling relations on ${\cal M}_{\rm a}$. Measurements of the granulation background and detections of solar-like oscillations in a statistically sufficient number of cool dwarf stars will be required for confirming the dependence of the theoretical scaling relations with ${\cal M}_{\rm a}$.
Period-luminosity relations in evolved red giants explained by solar-like oscillations
Solar-like oscillations in red giants have been investigated with
the space-borne missions CoRoT and Kepler, while pulsations in
more evolved M giants have been studied with ground-based
microlensing surveys. After 3.1 years of observation with Kepler,
it is now possible to make a link between these different
observations of the same type of stars.
We aim to identify period-luminosity sequences in evolved red
giants and to interpret them in terms of solar-like oscillations.
Then, we investigate the consequences of the comparison of
ground-based and space-borne results.
We have first measured global oscillation parameters of evolved
red giants observed with Kepler with the envelope autocorrelation
function method. We then used an extended form of the universal
red giant oscillation pattern, extrapolated to very low frequency,
to fully identify their oscillations. The comparison with
ground-based results was then used to obtain a relation between
the large frequency separation and the stellar luminosity.
From the link between red giant oscillations observed by Kepler
and period-luminosity sequences, we have identified these
relations in evolved red giants as radial and non-radial
solar-like oscillations. We were able to expand scaling relations
at very low frequency (periods as high as 100 days, and large
frequency separation less than 0.1 $\mu$Hz). This helped us to
identify the different sequences of period-luminosity relations,
and allowed us to propose an absolute calibration of the K
magnitude with the observed frequency large separation.
Interpreting period-luminosity relations in red giants in terms of
solar-like oscillations allows us to investigate, with a firm
physical basis, the time series obtained from ground-based
microlensing surveys. This can be done with the analytical
expression that describe the low-frequency oscillation spectra.
The different behavior of oscillations at low frequency, with
frequency separations scaling only approximately with the square
root of the mean stellar density, can be used to address precisely
the physics of the most semi-regular variables. This will allow
improved distance measurements and opens the way to extragalactic
asteroseismology.
Metal Abundances, Radial Velocities and Other Physical Characteristics for the RR Lyrae Stars in the Kepler Field
Spectroscopic iron-to-hydrogen ratios, radial velocities, atmospheric parameters, and new photometric analyses are presented for 41 RR Lyrae stars (and one probable high-amplitude $\delta$ Sct star) located in the field-of-view of the Kepler space telescope. Thirty-seven of the RR Lyrae stars are fundamental-mode pulsators (i.e., RRab stars) of which 16 exhibit the Blazhko effect. Four of the stars are multiperiodic RRc pulsators oscillating primarily in the first-overtone mode. Spectroscopic [Fe/H] values for the 34 stars for which we were able to derive estimates range from $-2.54\pm0.13$ (NR Lyr) to $-0.05\pm0.13$ dex (V784 Cyg), and for the 19 Kepler-field non-Blazhko stars studied by Nemec et al. (2011) the abundances agree will with their photometric [Fe/H] values. Four non-Blazhko RR Lyrae stars that they identified as metal-rich (KIC 6100702, V2470 Cyg, V782 Cyg and V784 Cyg) are confirmed as such, and four additional stars (V839 Cyg, KIC 5520878, KIC 8832417, KIC 3868420) are also shown here to be metal-rich. Five of the non-Blazhko RRab stars are found to be more metal-rich than [Fe/H]$\sim -0.9$ dex while all of the 16 Blazhko stars are more metal-poor than this value. New $P$-$\phi_{\rm 31}^s$-[Fe/H] relationships are derived based on $\sim$970 days of quasi-continuous high-precison Q0-Q11 long- and short-cadence Kepler photometry. With the exception of some Blazhko stars, the spectroscopic and photometric [Fe/H] values are in good agreement. Several stars with unique photometric characteristics are identified, including a Blazhko variable with the smallest known amplitude and frequency modulations (V838 Cyg).
Period and light curve fluctuations of the Kepler Cepheid V1154 Cyg
We present a detailed period analysis of the bright Cepheid-type variable star V1154 Cygni (V=9.1 mag, P$\approx$4.9 d) based on 600 days of continuous observations by the Kepler space telescope. The data reveal significant cycle-to-cycle fluctuations in the pulsation period, indicating that classical Cepheids may not be as accurate astrophysical clocks as commonly believed: regardless of the specific points used to determine the $O-C$ values, the cycle lengths do change by about 0.01 days (0.2 per cent) seemingly randomly over the 120 cycles covered by the observations. We compare the measurements with simulated light curves that were constructed to mimic V1154 Cyg as a perfect pulsator modulated only by the light travel time effect caused by low-mass companions. We show that the observed period noise in V1154 Cyg represents a serious limitation in search for binary companions. While the Kepler data are accurate enough to allow the detection of planetary bodies in close orbits around a Cepheid, the astrophysical noise can easily hide the signal of the light-time effect.
Detection of high-degree prograde sectoral mode sequences in the A-star KIC 8054146?
This paper examines the 46 frequencies found in the $\delta$ Sct star KIC 8054146 involving a frequency spacing of exactly 2.814 cycles day$^{-1}$ (32.57 $\mu$Hz), which is also a dominant low-frequency peak near or equal to the rotational frequency. These 46 frequencies range from 7 to 146 cycles day$^{-1}$. We show from three years of Kepler data that these frequencies are comprised of distinct sequences including a basic sequence and
side lobes associated with other dominant frequencies. The observed side-lobe sequences are interpreted as small amplitude modulations of the (other) dominant pulsation modes with the high-frequency basic sequence. The amplitudes of the basic sequence show a high-low pattern. The basic sequence follows the equation $f_m = 2.8519 + m * 2.81421$ cycles day$^{-1}$ with $m$ ranging from 25 to 35. The zero-point offset and the lack of low-order harmonics eliminate an interpretation in terms of a Fourier series of a non-sinusoidal light curve, while the exactness of the spacing eliminates high-order asymptotic pulsation. The frequency pattern is not compatible with simple hypotheses involving single or multiple spots, even with differential rotation.
The basic high-frequency sequence is interpreted in terms of prograde sectoral modes, which can be marginally unstable, while their corresponding low-degree counterparts are stable due to stronger damping. With a measured projected rotation velocity of $v \sin i$ of approximately 300 km s$^{-1}$ the star rotates with $\gtrapprox$ 70% of the Keplerian break-up velocity. The Keplerian break-up limit puts a lower constraint to the inclination angle, hence making a near equator-on view more likely. We qualitatively examine the visibility of prograde sectoral high-degree g-modes in integrated photometric light in such a geometrical configuration. We find that prograde sectoral modes can reproduce the frequencies and the odd-even amplitude pattern of the high-frequency sequence.
KIC 11285625: a double-lined spectroscopic binary with a gamma Dor pulsator discovered from Kepler space photometry
We present the first binary modelling results for the pulsating, eclipsing binary KIC 11285625 that was discovered by the Kepler mission. An automated method to disentangle the pulsation spectrum and the orbital variability in high quality light curves was developed and applied. The goal was to obtain accurate orbital and component properties in combination with essential information derived from spectroscopy. A binary model for KIC 11285625 was obtained, using a combined analysis of high-quality space-based Kepler light curves and ground-based high-resolution HERMES echelle spectra. The binary model was used to separate the pulsation characteristics from the orbital variability in the Kepler light curve in an iterative way. We used an automated procedure based on the JKTEBOP binary modelling code to perform this task, and adapted codes for frequency analysis and prewhitening of periodic signals. Using a disentangling technique applied to the composite HERMES spectra, we obtained a higher signal-to-noise mean spectrum for both the primary and the secondary components. A model grid search method for fitting synthetic spectra was used for fundamental parameter determination for both components. Accurate orbital and component properties of KIC 11285625 were derived, and we have obtained the pulsation spectrum of the gamma Dor pulsator in the system. Detailed analysis of the pulsation spectrum revealed amplitude modulation on a timescale of a hundred days, and strong indications of frequency splittings at both the orbital frequency and the rotational frequency derived from spectroscopy.
KIC 8410637: a 408-day period eclipsing binary containing a pulsating giant star.
Detached eclipsing binaries (dEBs) are ideal targets for accurate measurement of mass $M$ and radius $R$ of the stars. If at least one of the stars has evolved off the main sequence (MS), the masses and radii give a strict constraint on the age of the stars. Several dEBs containing a bright K giant and a fainter MS star have been discovered by the \kepler satellite. The mass $M$ and the radius $R$ of a red giant (RG) star can be derived from its asteroseismic signal. The parameters determined in this way may depend on stellar models and may contain systematic errors. Additional strong constraints on stellar parameters are invaluable in order to narrow down the parameter space for the asteroseismic analysis. Such constraints can be obtained when stars are members of stellar clusters or from dEBs. This paper presents an analysis of the dEB system KIC 8410637, which consists of a RG and a MS star. The aim is to derive accurate masses and radii for both components and provide the foundation for a strong test of the asteroseismic method and the accuracy of the parameters $M$, $R$ and age. We analyse high-resolution, high-signal-to-noise spectra from three different spectrographs for the dEB KIC 8410637. We also calculate a fit to the Kepler lightcurve and use groundbased photometry to determine the flux ratios between the component stars in the $BVRI$ passbands. We measured masses and radii for the stars in the dEB, and the classical parameters $T_{\rm eff}$,$\log g$ and [Fe/H] from the spectra and groundbased photometry. The giant component of KIC 8410637 is most likely in the core helium-burning red clump phase of evolution and has an age and composition very similar to the stars in the open cluster NGC 6819. The mass of the giant component of KIC 8410637 should therefore be similar to the mass of giant stars in NGC 6819, thus lending support to the most up-to-date version of the asteroseismic scaling relations. We find excellent agreement between $\log g$ values derived from the binary analysis and asteroseismic scaling relations, thus providing the first verification that $\log g$ values for giant stars from asteroseismic scaling relations are not only precise, but also accurate.
Atmospheric Parameters of 169 F, G, K and M-type Stars in the Kepler Field
Both the asteroseismic and planetary studies need precise and accurate atmospheric parameters of the stars as input. We aim at deriving the effective temperature ($T_{\rm eff}$), the surface gravity ($\log g$), the metallicity ([Fe/H]), the projected rotational velocity ($v\sin i$) and the MK type for 169 F, G, K, and M-type Kepler targets which were observed spectroscopically from the ground with five different instruments. We use two different spectroscopic methods to analyse 189 high-resolution, high-signal-to-noise spectra acquired for those 169 stars. For 69, $T_{\rm eff}$, $\log g$, [Fe/H], $v\sin i$, and the MK type are derived for the first time. KIC 9025370, 9693187 and 11179629 are discovered to be double-lined spectroscopic binary systems. The results obtained for those stars for which independent determinations of the atmospheric parameters are available in the literature are used for a comparative analysis. As a result, we show that for the solar-type stars the accuracy of the present determinations of $T_{\rm eff}$ is $\pm$ 150 K, $\pm$ 0.15 dex in [Fe/H], and $\pm$ 0.3 dex in $\log g$. Finally, we confirm that the analysis of the curve-of-growth and the method of the spectral synthesis yield systematically different results when they are applied to stars of $T_{\rm eff}$ ranging from 6,000 to 7,000K.
Asteroseismic surface gravity for evolved stars
Context: Asteroseismic surface gravity values can be of importance in determining spectroscopic stellar parameters. The independent $\log(g)$ value from asteroseismology can be used as a fixed value in the spectroscopic analysis to reduce uncertainties due to the fact that $\log(g)$ and effective temperature can not be determined independently from spectra. Since 2012, a combined analysis of seismically and spectroscopically derived stellar properties is ongoing for a large survey with SDSS/APOGEE and Kepler. Therefore, knowledge of any potential biases and uncertainties in asteroseismic $\log(g)$ values is now becoming important. Aims: The seismic parameter needed to derive $\log(g)$ is the frequency of maximum oscillation power ($\nu_{\rm max}$). Here, we investigate the influence of $\nu_{\rm max}$ derived with different methods on the derived $\log(g)$ values. The large frequency separation between modes of the same degree and consecutive radial orders ($\Delta\nu$) is often used as an additional constraint for the determination of $\log(g)$. Additionally, we checked the influence of small corrections applied to $\Delta\nu$ on the derived values of $\log(g)$. Methods: We use methods extensively described in the literature to determine $\nu_{\rm max}$ and $\Delta\nu$ together with seismic scaling relations and grid-based modeling to derive $\log(g)$. Results: We find that different approaches to derive oscillation parameters give results for $\log(g)$ with small, but different, biases for red-clump and red-giant-branch stars. These biases are well within the quoted uncertainties of $\sim0.01$ dex (cgs). Corrections suggested in the literature to the $\Delta\nu$ scaling relation have no significant effect on $\log(g)$. However somewhat unexpectedly, method specific solar reference values induce biases of the order of the uncertainties, which is not the case when canonical solar reference values are used.
Accurate fundamental parameters and detailed abundance patterns from spectroscopy of 93 solar-type Kepler targets
We present a detailed spectroscopic study of 93 solar-type stars that are targets of the NASA Kepler mission and provide detailed chemical composition of each target. We find that the overall metallicity is well-represented by Fe lines. Relative abundances of light elements (CNO) and $\alpha$ elements are generally higher for low-metallicity stars. Our spectroscopic analysis benefit from the accurately measured surface gravity from the asteroseismic analysis of the Kepler light curves. The $\log g$ parameter is known to better than 0.03 dex and is held fixed in the analysis. We compare our $T_{\rm eff}$ determination with a recent colour calibration of $V_{\rm T}-K_{\rm S}$ (TYCHO $V$ magnitude minus 2MASS $K_{\rm S}$ magnitude) and find very good agreement and a scatter of only 80 K, showing that for other nearby Kepler targets this index can be used. The asteroseismic $\log g$ values agree very well with the classical determination using Fei minus Feii balance, although we find a small systematic offset of $0.08$ dex (asteroseismic $\log g$ values are lower). The abundance patterns of metals, $\alpha$ elements, and the light elements (CNO) show that a simple scaling by [Fe/H] is adequate to represent the metallicity of the stars, except for the stars with metallicity below $-0.3$, where $\alpha$-enhancement becomes important. However, this is only important for a very small fraction of the Kepler sample. We therefore recommend that a simple scaling with [Fe/H] be employed in the asteroseismic analyses of large ensembles of solar-type stars.
Discovery of a new AM CVn system with the Kepler satellite
We report the discovery of a new AM CVn system on the basis of broadband photometry obtained with the Kepler satellite supplemented by ground-based optical spectroscopy. Initially retained on Kepler target lists as a potential compact pulsator, the blue object SDSS J190817.07+394036.4 (KIC 004547333) has turned out to be a high-state AM CVn star showing the He-dominated spectrum of its accretion disk significantly reddened by interstellar absorption. We constructed new grids of NLTE synthetic spectra for accretion disks in order to analyze our spectroscopic observations. These models are highly idealized and we use them in an exploratory spirit. On this basis, we find that the accretion disk is seen under a fairly well-constrained angle of 10$-$20$^{\rm o}$. We also estimate that the current rate of mass transfer in the system is in the range 3.5$-$8.5 $\times 10^{-9} M_\odot \mathrm{yr}^{-1}$. By comparing the measured energy distribution with those obtained from our model disk spectra, we further infer a reddening index $E(g-r)$ = 0.26$-$0.29, an absorption coefficient $A_r$ = 0.70$-$0.76, and a distance to the system in the range 250$-$330 pc. The AM CVn nature of the system is also evident in the Kepler light curve, from which we extracted 11 secure periodicities with amplitudes well above 4.3 times the mean local noise. These are found in the range of periods from 212 s to 953 s, and with amplitudes from $\sim0.03$% to $\sim0.31$% of the mean brightness of the star in the Kepler bandpass. The luminosity variations are dominated by a basic periodicity of 938.507 s, likely to correspond to a superhump modulation. In this scenario, the orbital period of the system would be equal to 953.262 s, corresponding to another strong modulation found close to the 938.507 s variation in Fourier space. The light curve folded on the period of 938.507 s exhibits a pulse shape that is very similar to the superhump wavefront seen in AM CVn itself, which is a high-state system and the prototype of the class. Our Fourier analysis also suggests the likely presence of a quasi-periodic oscillation (QPO) similar to those already observed in some high-state AM CVn systems. Furthermore, some very low-frequency, low-amplitude aperiodic photometric activity is likely present, which is in line with what is expected in accreting binary systems. Inspired by previous work, we further looked for and found some intriguing numerical relationships between the 11 secure detected frequencies, in the sense that we can account for all of them in terms of only 3 basic clocks. This is further evidence in favor of the AM CVn nature of the system. Given that the photometric properties of AM CVn systems are still not fully understood, and given the particular importance of such stars as laboratories for testing binary star evolution, it is hoped that SDSS J190817.07+394036.4 will be retained as a long-term target since Kepler can play a vital role for progress on this front.
Kepler's view of KPD1946+4340, a relativistic binary star
The Kepler Mission has acquired 33.5 d of continuous one-minute photometry of KPD1946+4340, a short-period binary system that consists of a subdwarf B star (sdB) and a white dwarf. In the light curve, eclipses are clearly seen, with the deepest occurring when the compact white dwarf crosses the disc of the sdB (0.4%) and the more shallow ones (0.1%) when the sdB eclipses the white dwarf. As expected, the sdB is deformed by the gravitational field of the white dwarf, which produces an ellipsoidal modulation of the light curve. Spectacularly, a very strong Doppler beaming (also known as Doppler boosting) effect is also clearly evident at the 0.1% level. This originates from the sdB’s orbital velocity, which we measure to be $164.0 \pm 1.9 km s^{-1}$ from supporting spectroscopy. We present light curve models that account for all these effects, as well as gravitational lensing, which decreases the apparent radius of the white dwarf by about 6% when it eclipses the sdB. We derive system parameters and uncertainties from the light curve using Markov Chain Monte Carlo simulations. Adopting a theoretical white dwarf mass-radius relation, the mass of the subdwarf is found to be $0.47\pm0.03 M_\odot$ and the mass of the white dwarf $0.59\pm0.02 M_\odot$. The effective temperature of the white dwarf is 15 900 ± 300K. With a spectroscopic effective temperature of $T_\mathrm{eff} = 34 730 \pm 250K$ and a surface gravity of $\log g = 5.43 \pm 0.04$, the subdwarf has most likely exhausted its core helium, and is in a shell He burning stage. The detection of Doppler beaming in Kepler light curves potentially allows one to measure radial velocities without the need of spectroscopic data. For the first time, a photometrically observed Doppler beaming amplitude is compared to a spectroscopically established value. For unknown reasons, the radial velocity derived from the photometry is $7 \pm 2\%$ larger than the spectroscopic value. After subtracting our best model for the orbital effects, we searched the residuals for stellar oscillations but did not find any significant pulsation frequencies.
A large sample of calibration stars for Gaia: logg from Kepler and CoRoT fields
Asteroseismic data can be used to determine stellar surface gravities with precisions of $< 0.05$ dex by using the global seismic quantites $\langle \Delta \nu \rangle$ and $\nu_{\rm max}$ along with standard atmospheric data such as $T_{\rm eff}$ and metallicity. Surface gravity is also one of the four stellar properties to be derived by automatic analyses for 1 billion stars from Gaia data (workpackage GSP_phot). In this paper we explore seismic data from main sequence F, G, K stars (solar-like stars) observed by the Kepler spacecraft as a potential calibration source for the methods that Gaia will use for object characterisation (ogg). We compile a list of bright nearby stars for which radii and masses are known (e.g. from interferometry or binaries), and we compare their $\log g$ with those derived from asteroseismic data using a grid-based method. Agreement to within 1$\sigma$ of the accepted $\log g$ values validates our method. We also find that errors in adopted atmospheric parameters (mainly [Fe/H]) can, however, cause systematic errors on the order of 0.02 dex. We then apply our method to a list of 41 stars to deliver precise values of surface gravity, and we find agreement with recent literature values. Finally we explore the typical precision that we expect in a sample of 400+ Kepler stars which have their global seismic quantities measured. We find typical uncertainties (precision) on the order of better than 0.02 dex in $\log g$. We study sources of systematic errors in $\log g$ and we find possible biases on the order of 0.04 dex in $\log g$ which accounts for errors in the $T_{\rm eff}$ and [Fe/H] measurements, as well as from using a different grid-based method. We conclude that Kepler stars provide a wealth of reliable information that can help to calibrate methods that Gaia will use, in particular, for source characterisation where excellent precision and accuracy in $\log g$ is obtained from Kepler data and this is one of the four stellar parameters to be extracted by GSP_phot.
Kepler photometry of the prototypical Blazhko star RR Lyr: An old friend seen in a new light
We present our analysis of the long cadence Kepler data for the well-studied Blazhko star RR Lyr, gathered during the first two quarters of the satellite's observations and covering a total of 127 d. Besides being of great importance for our understanding of RR Lyrae stars in general, these RR Lyr data can be regarded as a case study for observations of bright stars with Kepler. Kepler can perform high-precision photometry on targets like RR Lyr, as the saturated flux is conserved to a very high degree. The Kepler data on RR Lyr are revolutionary in several respects. Even with long-cadence sampling (one measurement per 29.4 min), the unprecedented precision ( $<$ mmag) of the Kepler photometry allows the study of the star's extreme light curve variations in detail. The multiplet structures at the main frequency and its harmonics, typical for Blazhko stars, are clearly detected up to the quintuplets. For the first time, photometric data of RR Lyr reveal the presence of half-integer frequencies, linked to a period doubling effect. This phenomenon may be connected to the still unexplained Blazhko modulation. Moreover, with three observed Blazhko cycles at our disposal, we observe that there is no exact repetition in the light curve changes from one modulation cycle to the next for RR Lyr. This may be due to additional periodicities in the star, or to transient or quasi-periodic changes.
Solar-like oscillations in red giants observed with Kepler: how to improve knowledge of the global oscillation parameters
The length of the asteroseismic timeseries obtained from the Kepler satellite analysed here span 19 months. Kepler provides the longest continuous timeseries currently available, which calls for a study of the influence of the increased timespan on the accuracy and precision of the obtained results. We aim to investigate how the increased timespan influences the detectability of the oscillation modes, and the absolute values and uncertainties of the global oscillation parameters, i.e., frequency of maximum oscillation power, $\nu_{\rm max}$, and large frequency separation between modes of the same degree and consecutive orders, $\Delta \nu$. We use published methods to derive $\nu_{\rm max}$ and $\Delta \nu$ for timeseries ranging from 50 to 600 days and compare these results as a function of method, timespan and $\Delta \nu$. We find that in general a minimum of the order of 200 day long timeseries are necessary to obtain reliable results for the global oscillation parameters, but that this does depend on $\Delta \nu$. In a statistical sense the quoted uncertainties seem to provide a reasonable indication of the precision of the obtained results in short (50-day) runs, they do however seem to be overestimated for results of longer runs. Furthermore, the different definitions of the global parameters used in the different methods have non-negligible effects on the obtained values. We show that this can be used to identify the evolutionary state of the star using global oscillation parameters determined with high precision. Additionally, we show that there is a correlation between $\nu_{\rm max}$ and the flux variance. We conclude that longer timeseries improve the likelihood to detect oscillations with automated codes and the precision of the obtained global oscillation parameters. The trends suggest that the improvement will continue for even longer timeseries than the 600 days considered here. This work shows that global parameters determined with high precision - thus from long datasets - using different definitions can be used to identify the evolutionary state of the stars. The variance of the flux provides a reliable indication of $\nu_{\rm max}$, which can be used as an additional constraint.
Asteroseismic inferences on red giants in open clusters NGC 6791, NGC 6819 and NGC 6811 using Kepler
Context: Four open clusters are present in the Kepler field of view and timeseries of nearly a year in length are now available. These timeseries allow us to derive asteroseismic global oscillation parameters of red-giant stars in the three open clusters NGC 6791, NGC 6819 and NGC 6811. From these parameters and effective temperatures, we derive mass, radii and luminosities for the cluster as well as field red giants.
Aims: We study the influence of evolution and metallicity on the observed red-giant populations.
Methods: The global oscillation parameters are derived using different published methods and the effective temperatures are derived from 2MASS colours. The observational results are compared with BaSTI evolution models.
Results: We find that the mass has significant influence on the asteroseismic quantities $\Delta \nu$ vs. $\nu_{\rm max}$ relation, while the influence of metallicity is negligible, under the assumption that the metallicity does not affect the excitation / damping of the oscillations. The position of the stars in the H-R diagram depends on both mass and metallicity. Furthermore, the stellar masses derived for the field stars are bracketed by those of the cluster stars.
Conclusions: Both the mass and metallicity contribute to the observed difference in locations in the H-R diagram of the old metal-rich cluster NGC 6791 and the middle-aged solar-metallicity cluster NGC 6819. %Roughly 40% of this difference in location can be attributed to the mass difference between the clusters and $\sim$60% to the difference in metallicity.
For the young cluster NGC 6811, the explanation of the position of the stars in the H-R diagram challenges the assumption of solar metallicity, and this open cluster might have significantly lower metallicity [Fe/H] in the range $-$0.3 to $-$0.7 dex. Also, all the observed field stars seem to be older than NGC 6811 and younger than NGC 6791.
Characterisation of red-giant stars in the public Kepler data
The first public release has now been made of long-cadence stellar photometric data collected by the NASA Kepler mission. In this paper we aim to characterise the red-giant (G-K) stars in this large sample in terms of their solar-like oscillations. We use published methods and well-known scaling relations in the analysis. Just over 70% of the red giants in the sample show detectable solar-like oscillations, and from these oscillations we are able to estimate the fundamental properties of the stars. This asteroseismic analysis reveals different populations: low-luminosity H-shell burning red-giant branch stars, cool high-luminosity red giants on the red-giant branch and He-core burning clump and secondary-clump giants. Furthermore, the detection of solar-like oscillations in red giants does not depend on the long-term variability of the stars.
Solar-like oscillations in red giants observed with Kepler: comparison of global oscillation parameters from different methods
The large number of stars for which uninterrupted high-precision photometric timeseries data are being collected with Kepler and CoRoT initiated the development of automated methods to analyse the stochastically excited oscillations in main-sequence, subgiant and red-giant stars. We investigate the differences in results for global oscillation parameters of G and K red-giant stars due to different methods and definitions. We also investigate uncertainties originating from the stochastic nature of the oscillations. For this investigation we use Kepler data obtained during the first four months of operation. These data have been analysed by different groups using already published methods and the results are compared. We also performed simulations to investigate the uncertainty on the resulting parameters due to different realizations of the stochastic signal. We obtain results for the frequency of maximum oscillation power ($\nu_{\rm max}$) and the mean large separation ($\langle\Delta\nu\rangle$) from different methods for over one thousand red-giant stars. The results for these parameters agree within a few percent and seem therefore robust to the different analysis methods and definitions used here. The uncertainties for $\nu_{\rm max}$ and $\langle\Delta\nu\rangle$ due to differences in realization noise are not negligible and should be taken into account when using these results for stellar modeling.
Orbital properties of an unusually low-mass sdB star in a close binary system with a white dwarf
We have used 605 days of photometric data from the Kepler spacecraft to study KIC6614501, a close binary system with an orbital period of 0.15749747(25) days (3.779939 hours), that consists of a low-mass subdwarf B (sdB) star and a white dwarf. As seen in many other similar systems, the gravitational field of the white dwarf produces an ellipsoidal deformation of the sdB which appears in the light curve as a modulation at two times the orbital frequency. The ellipsoidal deformation of the sdB implies that the system has a maximum inclination of 40 degrees, with i≈20° being the most likely. The orbital radial velocity of the sdB star is high enough to produce a Doppler beaming effect with an amplitude of 432±5 ppm, clearly visible in the folded light curve. The photometric amplitude that we obtain, K1=85.8 km/s, is 12 per cent less than the spectroscopic RV amplitude of 97.2±2.0 km/s. The discrepancy is due to the photometric contamination from a close object at about 5 arcsec North West of KIC6614501, which is difficult to remove. The atmospheric parameters of the sdB star, Teff=23700±500 K and logg=5.70±0.10, imply that it is a rare object below the Extreme Horizontal Branch (EHB), similar to HD188112. The comparison with different evolutionary tracks suggests a mass between 0.18 and 0.25 M⊙, too low to sustain core helium burning. If the mass was close to 0.18-0.19 M⊙, the star could be already on the final He-core WD cooling track. A higher mass, up to 0.25 M⊙, would be compatible with a He-core WD progenitor undergoing a cooling phase in a H-shell flash loop. A third possibility, with a mass between 0.32 and 0.40 M⊙, can not be excluded and would imply that the sdB is a “normal” (but with an unusually low mass) EHB star burning He in its core. In all these different scenarios the system is expected to merge in less than 3.1 Gyr due to gravitational wave radiation.
A uniform asteroseismic analysis of 22 solar-type stars observed by Kepler
Asteroseismology with the Kepler space telescope is providing not only an improved characterization of exoplanets and their host stars, but also a new window on stellar structure and evolution for the large sample of solar-type stars in the field. We perform a uniform analysis of 22 of the brightest asteroseismic targets with the highest signal-to-noise ratio observed for 1 month each during the first year of the mission, and we quantify the precision and relative accuracy of asteroseismic determinations of the stellar radius, mass, and age that are possible using various methods. We present the properties of each star in the sample derived from an automated analysis of the individual oscillation frequencies and other observational constraints using the Asteroseismic Modeling Portal (AMP), and we compare them to the results of model-grid-based methods that fit the global oscillation properties. We find that fitting the individual frequencies typically yields asteroseismic radii and masses to $\sim$1% precision, and ages to $\sim$2.5% precision (respectively 2, 5, and 8 times better than fitting the global oscillation properties). The absolute level of agreement between the results from different approaches is also encouraging, with model-grid-based methods yielding slightly smaller estimates of the radius and mass and slightly older values for the stellar age relative to AMP, which computes a large number of dedicated models for each star. The sample of targets for which this type of analysis is possible will grow as longer data sets are obtained during the remainder of the mission.
Evolutionary influences on the fine structure of red-giant acoustic oscillation spectra from 600d of Kepler observations
Context: It was recently discovered that the period spacings of mixed pressure/gravity dipole modes in red giants permit a distinction between the otherwise unknown evolutionary stage of these stars. The Kepler space mission is reaching continuous observing times long enough to also start studying the fine structure of the observed pressure-mode spectra.
Aims: In this paper, we aim to study the signature of stellar evolution on the radial and pressure-dominated $l$ = 2 modes in an ensemble of red giants that show solar-type oscillations.
Methods: We use established methods to automatically identify the mode degree of $l$ = 0 and 2 modes and measure a local large ($\Delta\nu_c$) and small ($\delta\nu_{02}$) frequency separation around the central radial mode. We then determine the phase shift \epsc of the central radial mode, i.e. the local linear offset in the asymptotic development of acoustic modes. Furthermore we use a straightforward approach to measure the individual frequencies of the radial modes and investigate their average curvature.
Results: We find that $\epsilon_c$ is significantly different for red giants at a given $\Delta\nu_c$ but which burn only H in a shell (RGB) and those that have already ignited core He burning. Even though not directly probing the stellar core the pair of local seismic observables ($\Delta\nu_c$, $\epsilon_c$) can be used as an evolutionary stage discriminator that turned out to be just as reliable as the period spacing of the mixed dipole modes. We find a tight correlation between $\epsilon_c$ and $\Delta\nu_c$ for RGB stars and no indication that their $\epsilon_c$ depends on other properties of the star. It appears that the difference in $\epsilon_c$ between the two populations becomes smaller and eventually undistinguishable if we use a global, i.e. an average of several radial orders, instead of a local, i.e. only around the central radial modes, large separation to determine $\epsilon$. This indicates that the information on the evolutionary stage is encoded locally, more precisely in the shape of the radial mode sequence. This turns out to be approximately symmetric around the central radial mode for RGB stars but asymmetric for core He burning stars. We computed radial mode frequencies for a sequence of red-giant models and find them to qualitatively confirm our findings. We also find a clear signature of the evolutionary stage in $\delta\nu_{02}$ and quantify the mass dependency of this seismic parameter.
Seismic evidence for non-synchronization in two close sdB+dM binaries from Kepler photometry
We report on extended photometry of two pulsating sdB stars in close binaries. In both cases, we show that the sdB component rotates much too slowly to be in synchronous rotation. We use the theory of tidal interaction in binary stars to place upper limits on the mass ratios that are independent of estimates based on the radial velocity curves. The companions have masses below 0.26 $M_{\odot}$. The pulsation spectra show the signature of high–overtone $g$-mode pulsation. One star, KIC 11179657, has a clear sequence of $g$-modes with equal period spacings as well as several periodicities that depart from that trend. KIC 02991403 shows a similar sequence, but has many more modes that do not fit the simple pattern.
Preparation of Kepler lightcurves for asteroseismic analyses
The Kepler mission is providing photometric data of exquisite quality for the asteroseismic study of different classes of pulsating stars. These analyzes place particular demands on the pre-processing of the data, over a range of timescales from minutes to months. Here, we describe processing procedures developed by the Kepler Asteroseismic Science Consortium (KASC) to prepare light curves that are optimized for the asteroseismic study of solar-like oscillating stars in which outliers, jumps and drifts are corrected.
Detection of stochastic gravity modes in the massive binary V380 Cyg from Kepler customized-mask space photometry and high-resolution spectroscopy
We report the discovery of low-amplitude stochastic gravity-mode oscillations in the massive binary V380 Cyg, from 180 d of Kepler custom-aperture space photometry and 5 months of high-resolution high signal-to-noise spectroscopy. The new data are of unprecedented quality and allowed the deduction of improved values of the orbital and fundamental parameters for this important binary. The orbital model was subtracted from the photometric data and seismic signals due to gravity modes were detected in the residual light curve. Spectral disentangling allowed the detection of line-profile variability in the primary. With our discovery of gravity modes, V380 Cyg becomes an important laboratory for future tuning of the near-core physics for B-type stars. The binary is therefore the subject of ongoing and future Kepler measurements.
Early asteroseismic results from Kepler: Structural and core parameters of the hot B subdwarf KPD 1943+4058 as inferred from g-mode oscillations
We present a seismic analysis of the pulsating hot B subdwarf KPD 1943+4058 (KIC 005807616) on the basis of the long-period, gravity-mode pulsations recently uncovered by Kepler. This is the first time that g-mode seismology can be exploited quantitatively for stars on the extreme horizontal branch, all previous successful seismic analyses having been confined so far to short-period, p-mode pulsators. We demonstrate that current models of hot B subdwarfs can explain quite well the observed g-mode periods, while being consistent with independent constraints provided by spectroscopy. We identify the 18 pulsations retained in our analysis as low-degree ($\ell$ = 1 and 2), intermediate-order ($k$ = -9 through -58) g-modes. The periods (frequencies) are recovered, on the average, at the 0.22% level, which is comparable to the best results obtained for p-mode pulsators. We infer the following structural and core parameters for KPD 1943+4058 : $T_\mathrm{eff} = 28,050 \pm 470 K$, $\log g = 5.520 \pm 0.029$, $M_* = 0.4964 \pm 0.0013 M_\odot$, $\log(M_\mathrm{env}/M_{*}) = -2.552 \pm 0.070$, $\log(1-M_\mathrm{core}/M_{*}) = -0.366 \pm 0.010$, and $X_\mathrm{core}(C+O) = 0.2612 \pm 0.0080$. We additionally derive the age of the star since the Zero-Age EHB $18.4 \pm 1.0$ Myr, the radius $R = 0.2026 \pm 0.0070 R_\odot$, the luminosity $L = 22.92\pm3.13 L_\odot$, the absolute magnitude $M_V = 4.21 \pm 0.11$, the reddening index $E(B-V) = 0.094 \pm 0.017$, and the distance $d = 1183 \pm 93$ pc.
First Kepler results on compact pulsators VII. Pulsating subdwarf B stars detected in the second half of the survey phase
We present five new pulsating subdwarf B (sdB) stars discovered by the Kepler spacecraft during the asteroseismology survey phase. We perform time-series analysis on the nearly continuous month-long Kepler datasets of these 5 objects; these datasets provide nearly alias–free time–series photometry at unprecedented precision. Following an iterative prewhitening process we derive the pulsational frequency spectra of these stars, separating out artefacts of known instrumental origin. We find that these new pulsating sdB stars are multiperiodic long-period pulsators of the V1093 Her type, with the number of periodicities ranging from 8 (KIC 8302197) to 53 (KIC 11558725). The frequencies and amplitudes are typical of $g$-mode pulsators of this type. We do not find any evidence for binarity in the five stars from their observed pulsation frequencies. As these are $g-$mode pulsators, we briefly looked for period spacings for mode identification, and found average spacings about 260 s and 145 s. This may indicate $l$ = 1 and 2 patterns. Some modes may show evidence of rotational splitting. These discoveries complete the list of compact pulsators found in the survey phase. Of the 13 compact pulsators, only one star was identified as a short-period ($p$-mode) V361 Hya pulsator, while all other new pulsators turned out to be V1093 Her class objects. Among the latter objects, two of them seemed to be pure V1093 Her while the others show additional low amplitude peaks in the $p-$mode frequency range, suggesting their hybrid nature. Authenticity of these peaks will be tested with longer runs currently under analysis.
A pulsation zoo in the hot subdwarf B star KIC 10139564 observed by Kepler
We present our analyses of 15 months of Kepler data on KIC 10139564. We detected 57 periodicities with a variety of properties not previously observed all together in one pulsating subdwarf B star. Ten of the periodicities were found in the low-frequency region, and we associate them with nonradial g-modes. The other periodicities were found in the high-frequency region, which are likely p-modes. We discovered that most of the periodicities are components of multiplets with a common spacing. Assuming that multiplets are caused by rotation, we derive a rotation period of 25.6$\pm$1.8 days. The multiplets also allow us to identify the pulsations to an unprecedented extent for this class of pulsator. We also detect $l\geq2$ multiplets, which are sensitive to the pulsation inclination and can constrain limb darkening via geometric cancellation factors. While most periodicities are stable, we detected several regions that show complex patterns. Detailed analyses showed these regions are complicated by several factors. Two are combination frequencies that originate in the superNyquist region and were found to be reflected below the Nyquist frequency. The Fourier peaks are clear in the superNyquist region, but the orbital motion of Kepler smears the Nyquist frequency in the barycentric reference frame and this effect is passed on to the subNyquist reflections. Others are likely multiplets but unstable in amplitudes and/or frequencies. The density of periodicities also make KIC 10139564 challenging to explain using published models. This menagerie of properties should provide tight constraints on structural models, making this subdwarf B star the most promising for applying asteroseismology.
To support our photometric analysis we have obtained spectroscopic radial-velocity measurements of KIC 10139564 using low-resolution spectra in the Balmer-line region. We did not find any radial-velocity variation. We used our high S/N average spectrum to improve the atmospheric parameters of the sdB star, deriving T$_{\rm eff}$ = 27,910 K and $\log g$ = 5.41 dex.
Solar-like oscillations from the depths of the red-giant star KIC 4351319 observed with Kepler
We present the results of the asteroseismic analysis of the red-giant star
KIC 4351319 (TYC 3124-914-1), observed for 30 days
with the Kepler satellite. The analysis has allowed us to determine the large and small frequency separations,
$\Delta \nu_{0} = 24.6 \pm 0.2\, \mu$Hz and $\delta \nu_{02} =
2.2 \pm 0.3 \,\mu$Hz respectively, and the frequency of maximum oscillation power, $\nu_{\rm max} = 386.5 \pm 4.0\, \mu$Hz.
The high signal-to-noise ratio of the observations allowed us to
identify $25$ independent pulsation modes whose frequencies range approximately from $300$ to $500\,\mu$Hz.
The observed oscillation frequencies together with the accurate determination of the atmospheric parameters
(effective temperature, gravity and metallicity), provided by additional ground-based spectroscopic observations, enabled us to theoretically interpret the observed oscillation spectrum.
KIC 4351319 appears to oscillate with a well defined solar-type p-modes pattern due to radial acoustic modes and non-radial nearly pure p modes. In addition, several non-radial mixed modes have been identified.
Theoretical models well reproduce the observed oscillation frequencies and indicate that this star, located at the base of the ascending red-giant branch, is in the hydrogen-shell burning phase, with a mass of $\sim 1.3\, {\rm M}_{\odot}$, a radius of $\sim 3.4\,R_{\odot}$ and an age of $\sim5.6$ Gyr.
The main parameters of this star have been determined with an unprecedent level of precision for a red-giant star, with uncertainties of $2\,\%$ for mass, $7\,\%$ for age, $1\,\%$ for radius, and $5\,\%$ for luminosity.
Calibrating Convective properties of Solar-like Stars in the Kepler Field of View
Stellar models generally use simple parametrizations to treat convection. The most widely used parametrization is the so-called “Mixing Length Theory” where the convective eddy sizes are described using a single number, $\alpha$, the mixing-length parameter. This is a free parameter, and the general practice is to calibrate $\alpha$ using the known properties of the Sun and apply that to all stars. Using data from NASA's Kepler mission we show that using the solar-calibrated $\alpha$ is not always appropriate, and that in many cases it would lead to estimates of initial helium abundances that are lower than the primordial helium abundance. Kepler data allow us to calibrate $\alpha$ for many other stars and we show that for the sample of stars we have studied, the mixing-length parameter is generally lower than the solar value. We studied the correlation between $\alpha$ and stellar properties, and we find that $\alpha$ increases with metallicity. We therefore conclude that results obtained by fitting stellar models or by using population-synthesis models constructed with solar values of $\alpha$ are likely to have large systematic errors. Our results also confirm theoretical expectations that the mixing-length parameter should vary with stellar properties.
Asteroseismology of old open clusters with Kepler: direct estimate of the integrated RGB mass loss in NGC6791 and NGC6819
The integrated and instantaneous mass loss of red giant branch (RGB) stars is still poorly determined and understood, despite its crucial role in the chemical enrichment of galaxies. Thanks to the recent detection of solar-like oscillations in G-K giants in open clusters with Kepler, we can now directly determine stellar masses for a statistically significant sample of stars in the old open clusters NGC6791 and NGC6819. The aim of this work is to provide constraints on the integrated RGB mass loss by comparing the average mass of stars in the red clump (RC) with that of stars in the low-luminosity portion of the RGB (i.e. stars with $L\lesssim L({\rm RC})$). Stellar masses are determined by combining the available seismic parameters $\nu_{\rm max}$ and $\Delta\nu$ with additional photometric constraints and with independent distance estimates. We measure the mass of 40 (19) stars in the RGB (RC) of the old metal-rich cluster NGC6791. We find that the difference between the average mass of RGB and RC stars is small, but significant ($\Delta \bar{M}=0.09\pm 0.03$ (random) $\pm 0.04$ (systematic) $M_\odot$). Interestingly, such a small $\Delta\bar{M}$ does not support scenarios of an extreme mass loss for this metal-rich cluster. If we describe the mass-loss rate with Reimers' prescription, a first comparison with isochrones suggests that the observed $\Delta\bar M$ is compatible with a mass-loss efficiency parameter in the range $0.1 \lesssim \eta \lesssim 0.3$. Constraints on the RGB mass-loss rate set by the analysis of the $\sim 2$ Gyr-old NGC6819 are less stringent, largely due to the lower mass loss expected for this cluster, and to the lack of an independent and accurate distance determination. In the near future, additional constraints which comprise frequencies of individual pulsation modes and spectroscopic effective temperatures, will allow further stringent tests of the $\Delta\nu$ and $\nu_{\rm max}$ scaling relations, which provide a novel, and potentially very accurate, means of determining stellar radii and masses.
The complex case of V445 Lyr: Two Blazhko modulations, a non-radial mode, possible triple mode RR Lyrae pulsation, and more
Rapid and strong changes in the Blazhko modulation of RR Lyrae stars, as they have recently been detected in high precision satellite data, have become a crucial topic in finding an explanation of the long-standing mystery of the Blazhko effect. We present here an analysis of the most extreme case detected so far, the RRab star V445 Lyr (KIC 6186029) which was observed with the Kepler space mission. V445 Lyr shows very strong cycle-to-cycle changes in its Blazhko modulation, which are caused both by a secondary long-term modulation period as well as irregular variations. In addition to the complex Blazhko modulation, V445 Lyr also shows a rich spectrum of additional peaks in the frequency range between the fundamental pulsation and the first harmonic. Among those peaks, the second radial overtone could be identified, which, combined with a metallicity estimate of [Fe/H]=-1.5 dex from spectroscopy, allowed to constrain the mass (0.65-0.75 $M_{\odot}$) and luminosity (40-50 $L_{\odot}$) of V445 Lyr through theoretical Petersen diagrams. A non-radial mode as well as possibly the first overtone are also excited. Furthermore, V445 Lyr shows signs of the period doubling phenomenon and a long term period change. A detailed Fourier analysis along with a study of the O-C variation of V445 Lyr is presented, and the origin of the additional peaks and possible causes of the changes in the Blazhko modulation are discussed. The results are then put into context with those of the only other star with a variable Blazhko effect for which a long enough set of high precision continuous satellite data has been published so far, the CoRoT star 105288363.
Kepler photometry of KIC 10661783: a binary star with total eclipses and $\delta\,$Scuti pulsations
We present Kepler satellite photometry of KIC 10661783, a short-period binary star system which shows total eclipses and multi-periodic $\delta$ Scuti pulsations. A frequency analysis of the eclipse-subtracted light curve reveals at least 75 frequencies of which 64 or more can be attributed to pulsation modes. The main limitation on this analysis is the frequency resolution within the 27-day short-cadence light curve. Most of the variability signal lies between in the frequency range 18 to 31 $\mathrm{d}^{-1}$, with amplitudes between 0.1 and 4 mmag. One harmonic term ($2 \times f$) and a few combination frequencies ($f_i + f_j$) have been detected. From a plot of the residuals versus orbital phase we assign the pulsations to the primary star in the system. The pulsations were removed from the short-cadence data and the light curve was modelled using the Wilson-Devinney code. We are unable to get a perfect fit due to the residual effects of pulsations and also to the treatment of reflection and reprocessing in the light curve model. A model where the secondary star fills its Roche lobe is favoured, which means that KIC 10661783 can be classified as an oEA system. Further photometric and spectroscopic observations will allow the masses and radii of the two stars to be measured to high precision and hundreds of $\delta$ Scuti pulsation frequencies to be resolved, leading to unique constraints on theoretical models of $\delta$ Scuti stars.
Oscillation mode frequencies of 61 main-sequence and subgiant stars observed by Kepler
Solar-like oscillations have been observed by Kepler and CoRoT in several solar-type stars, thereby providing a way to probe the stars using asteroseismology.
We provide the mode frequencies required for performing a comparison with those obtained from stellar modelling.
Time series of 9 months of data have been used. The 61 stars observed were categorised in three groups: simple, F-like, mixed-mode. The simple group includes stars for which the identification of the degree is the mode is obvious. The F-like group includes stars for which the identification of the degree is ambiguous. The mixed-mode group includes evolved stars for which the modes do not follow the asymptotic relation of low-degree frequencies. Following the categorisation, the power spectra of the 61 main-sequence and subgiant stars have been analysed using both Maximum Likelihood Estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths, and mode heights. We derived and describe a methodology for extracting a single set of mode frequencies from multiple sets derived by different methods and individuals. We report on how one can assess the quality of the fitted parameters using the likelihood ratio test and the posterior probabilities.
Here we give the mode frequencies of 61 stars (with their 1-$\sigma$ error bars), as well as their associated échelle diagrams.
Deep asteroseismic sounding of the compact hot B subdwarf pulsator KIC02697388 from Kepler time series photometry
Contemporary high precision photometry from space provided by the CoRoT and Kepler satellites generates significant breakthroughs in terms of exploiting the long period, g-mode pulsating hot B subdwarf (sdBV$_{{\rm s}}$) stars with asteroseismology. In this paper, we present a detailed asteroseismic study of the sdBV$_{{\rm s}}$ star KIC02697388 monitored with Kepler, using the rich pulsation spectrum uncovered during the $\sim27$ day long exploratory run Q2.3. We analyse new high-S/N spectroscopy of KIC02697388 using appropriate NLTE model atmospheres in order to provide accurate atmospheric parameters for this star. We also reanalyse the Kepler light curve using standard prewhitening techniques. On this basis, we apply a forward modeling technique using our latest generation of sdB models. The simultaneous match of the independent periods observed in KIC02697388 with those of models leads objectively to the identification of the pulsation modes and, more importantly, to the determination of some of the parameters of the star. The light curve analysis reveals 43 independent frequencies that can be associated with oscillation modes. All the modulations observed in this star correspond to $g$-mode pulsations except one high-frequency signal, which is typical of a $p$-mode oscillation. Although the presence of this $p$-mode is surprising considering the atmospheric parameters that we derive for this cool sdB star ($T_{{\rm eff}}=$25 395 $\pm$ 227 K, $\log g=5.500\pm0.031$, and $\log N({\rm He})/N({\rm H})=-2.767\pm0.122$), we show that this mode can be accounted for particularly well by our optimal seismic models, both in terms of frequency match and nonadiabatic properties. The seismic analysis leads us to identify two model solutions that can both account for the observed pulsation properties of KIC02697388. Despite this remaining ambiguity, several key parameters of the star can be derived with stringent constraints, such as its mass, its H-rich envelope mass, its radius, and its luminosity. Information on the core is also obtained and suggests a relatively young sdB star having burnt less than $\sim 34 \%$ (in mass) of its central helium and having a relatively large mixed He/C/O core. This latter measurement is in line with the trend already uncovered for two other $g$-mode sdB pulsators analysed with asteroseismology and suggests that extra mixing is occurring quite early in the evolution of He cores on the horizontal branch. Additional monitoring with Kepler of this particularly interesting sdB star should further reveal the inner properties of KIC02697388 and provide precious information on the mode driving mechanism and the helium core properties.
Stellar ages and convective cores in field main-sequence stars: first asteroseismic application to two Kepler targets
Using asteroseismic data and stellar evolution models we make the first detection of a convective core in a Kepler field main-sequence star, putting a stringent constraint on the total size of the mixed zone and showing that extra mixing beyond the formal convective boundary exists. In a slightly less massive target the presence of a convective core cannot be conclusively discarded, and thus its remaining main-sequence life time is uncertain. Our results reveal that best-fit models found solely by matching individual frequencies of oscillations corrected for surface effects do not always properly reproduce frequency combinations. Moreover, slightly different criteria to define what the best-fit model is can lead to solutions with similar global properties but very different interior structures. We argue that the use of frequency ratios is a more reliable way to obtain accurate stellar parameters, and show that our analysis in field main-sequence stars can yield an overall precision of 1.5%, 4%, and 10% in radius, mass and age, respectively. We compare our results with those obtained from global oscillation properties, and discuss the possible sources of uncertainties in asteroseismic stellar modeling where further studies are still needed.
The unusual roAp star KIC 8677585
KIC 8677585 is a roAp star in the Kepler field which is unique in that there are four low-frequency variations of unknown origin in addition to more than twenty high-frequency roAp modes. We analysed all available spectroscopy and conclude that the star has a constant radial velocity and most likely not a binary. We estimate its effective temperature to be $T_{\rm eff} = 7300 \pm 200$ K from high-dispersion spectra. We present an analysis of 829 d of Kepler short-cadence data which shows clear frequency and amplitude variations with a timescale of months. The dominant low-frequency peak at 3.142 d$^{-1}$ has the same frequency and amplitude variation as one of the roAp modes. We therefore conclude that the low frequencies are oscillations in the roAp star itself, but the driving mechanism is unknown. We find several frequency spacings among the roAp modes equal to the dominant low frequency, suggestive of nonlinear interactions. There is also a clear spacing of $37.2$ $\mu$Hz which we interpret as the large separation and deduce that $\log g = 3.90 \pm 0.03$. Models with these parameters which take into account the effect of the magnetic field on the oscillations are able to reproduce the observed range of roAp frequencies, but not the observed large separation. It is found that the properties of the oscillations are sensitive to the assumed stellar parameters and that a more detailed analysis is required. The fact that low frequencies are closely coupled to the roAp frequencies calls into question our current understanding of pulsation in these stars.
Kepler photometry and optical spectroscopy of the ZZ Lep central star of the Planetary Nebula NGC 6826: rotational and wind variability
We present three years of long-cadence and over one year of short-cadence photometry of the central star of the Planetary Nebula NGC 6826 obtained with the Kepler spacecraft, and temporally coinciding optical spectroscopy. The light curves are dominated by incoherent variability on time scales of several hours, but contain a lower-amplitude periodicity of 1.23799 d. The temporal amplitude and shape changes of this signal are best explicable with a rotational modulation, and are not consistent with a binary interpretation. We argue that we do not observe stellar pulsations within the limitations of our data, and show that a binary central star with an orbital period less than seven days could only have escaped our detection in the case of low orbital inclination. Combining the photometric and spectroscopic evidence, we reason that the hourly variations are due to a variable stellar wind, and are global in nature. The physical cause of the wind variability of NGC 6826 and other ZZ Leporis stars is likely related to the mechanism responsible for wind variations in massive hot stars.
Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars
Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell. Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion. Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface prior to helium ignition and the amount of internal mixing from rotation and other processes. Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies. Here we report observations of gravity-mode period spacings in red giants that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained with the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars and those that are also burning helium.
Super-Nyquist asteroseismology with the Kepler Space Telescope
Barycentric corrections made to the timing of \kepler observations, necessitated by variations in light arrival time at the satellite, break the regular time-sampling of the data – the time stamps are periodically modulated. A consequence is that Nyquist aliases are split into multiplets that can be identified by their shape. Real pulsation frequencies are distinguishable from these aliases and their frequencies are completely recoverable, even in the super-Nyquist regime, that is, when the sampling interval is longer than half the pulsation period. We provide an analytical derivation of the phenomenon, alongside demonstrations with simulated and real \kepler data for $\delta$ Sct, roAp, and sdBV stars. For Kepler data sets spanning more than one Kepler orbital period (372.5 d), there are no Nyquist ambiguities on the determination of pulsation frequencies, which are the fundamental data of asteroseismology.
Fourier analysis of non-Blazhko ab-type RR Lyr stars observed with the Kepler space telescope
Nineteen of the $\sim$40 RR Lyr stars in the Kepler field have been identified as candidate non-Blazhko (or unmodulated) stars. In this paper we present the results of Fourier decomposition of the time-series photometry of these stars acquired during the first 417 days of operation (Q0-Q5) of the Kepler telescope. Fourier parameters based on $\sim$18400 long-cadence observations per star (and $\sim$150000 short-cadence observations for FN Lyr and for AW Dra) are derived. None of the stars shows the recently discovered ‘period-doubling’ effect seen in Blazhko variables; however, KIC 7021124 has been found to pulsate simultaneously in the fundamental and second overtone modes with a period ratio $P_2/P_0 \sim 0.59305$ and is similar to the double-mode star V350 Lyr. Period change rates are derived from O-C diagrams spanning, in some cases, over 100 years; these are compared with high-precision periods derived from the Kepler data alone. Extant Fourier correlations by Kovács, Jurcsik et al. (with minor transformations from the $V$- to the $Kp$ passband) have been used to derive underlying physical characteristics for all the stars. This procedure seems to be validated through comparisons of the Kepler variables with galactic and LMC field RR Lyr stars and with RR Lyr stars in galactic and LMC globular clusters. The most metal-poor star in the sample is NR Lyr, with [Fe/H]$=-2.25\pm0.11$ dex; fourteen of the stars have metallicities between $-1.3$ and $-2.1$ dex; and the four lowest amplitude stars (KIC 6100702, V2470 Cyg, V782 Cyg and V784 Cyg) are found to be quite metal-rich with [Fe/H] between $-0.4$ and $-0.9$ dex. The metal-rich stars also have the lowest luminosities and masses. Pulsational luminosities and masses are found to be systematically smaller than $L$ and ${\cal M}$ values derived from stellar evolution models, but are favoured over the evolutionary values when periods are computed with the Warsaw non-linear hydrodynamics code. Finally, the Fourier parameters are compared with theoretical values derived using the Warsaw convective pulsation codes (linaer and nonlinear).
Low-frequency variations of unknown origin in the Kepler $\delta$ Scuti star KIC 5988140 = HD188774
We used high-quality Kepler photometry and spectroscopic data to investigate the Kepler target and binary candidate KIC 5988140. We aim to interpret the observed variations of KIC 5988140 by considering three possible scenario's: binarity, co-existence of $\delta$ Scuti- and $\gamma$ Dor-type oscillations, and rotational modulation due to stellar surface spots. We used the spectrum synthesis method to derive the fundamental parameters T$_{\rm eff}$, log $g$, [M/H], and $v$ sin $i$ from the newly obtained high-resolution, high S/N spectra. Frequency analyses of both the photometric and the spectroscopic data were performed. The star has a spectral type of A7.5 IV-III and a metallicity slightly lower than that of the Sun. Both Fourier analyses reveal the same two dominant frequencies $\mathrm{f}_1=2\mathrm{f}_2=0.688$ and $\mathrm{f}_2$=0.344 c\d. We also detected in the photometry the signal of nine more, significant frequencies located in the typical range of $\delta$ Sct pulsation. The light and radial velocity curves, which are not exactly in anti-phase but show a relative phase shift of about 0.1 period between the moment of minimum velocity and that of maximum light, follow a similar, stable double-wave pattern. Such findings are incompatible with the star being a binary system. We next show that, for all possible (limit) configurations of a spotted surface, the predicted light-to-velocity amplitude ratio is almost two orders larger than the observed value, which pleads against rotational modulation. The same argument also invalidates the explanation in terms of pulsations of type $\gamma$ Dor (i.e. hybrid pulsations). We confirm the occurrence of various independent $\delta$ Sct-type pressure modes in the Kepler light curve. With respect to the low-frequency content, however, we argue that the physical cause of the remaining light and radial velocity variations of this late A-type star remains unexplained by any of the presently considered scenarios.
Regularities in frequency spacings of Delta Scuti stars: The Kepler star KIC 9700322
In the faint star KIC 9700322 observed by the Kepler satellite, 76 frequencies with amplitudes from 14 to 29000 ppm were detected. The two dominant frequencies at 9.79 and 12.57 d$^{-1}$ (113.3 and 145.5 $\mu$Hz), interpreted to be radial modes, are accompanied by a large number of combination frequencies. A small additional modulation with a 0.16 d$^{-1}$ frequency is also seen; this is interpreted to be the rotation frequency of the star. The corresponding prediction of slow rotation is confirmed by a spectrum from which $v \sin i = 19 \pm 1$ km s$^{-1}$ is obtained. The analysis of the spectrum shows that the star is one of the coolest $\delta$ Sct variables. We also determine T$_{\rm eff}$ = 6700 $\pm$ 100 K and $\log g$ = 3.7 $\pm$ 0.1, compatible with the observed frequencies of the radial modes. Normal solar abundances are found. An $\ell=2$ frequency quintuplet is also detected with a frequency separation consistent with predictions from the measured rotation rate. A remarkable result is the absence of additional independent frequencies down to an amplitude limit near 14 ppm, suggesting that the star is stable against most forms of nonradial pulsation. The frequency spectrum of this star emphasizes the need for caution in interpreting low frequencies in $\delta$ Sct stars as independent gravity modes. A low frequency peak at 2.7763 d$^{-1}$ in KIC 9700322 is, in fact, the frequency difference between the two dominant modes and is repeated over and over in various frequency combinations involving the two dominant modes. The relative phases of the combination frequencies show a strong correlation with frequency, but the physical significance of this result is not clear.
High frequencies in the $\delta$ Scuti star KIC 4840675
We show that the star KIC 4840675 observed by Kepler is a triple system with a rapidly-rotating A-type star and two solar-type fainter companions. The A-type star is a $\delta$ Scuti variable with a dominant mode and many other modes of lower amplitude, including several low-frequency variations. The low-frequency variation with highest amplitude can be interpreted as rotational modulation with the light curve changing with time. However, the most interesting aspect of this star is a triplet of independent modes in the range 118–129 d$^{-1}$ (1.4–1.5 mHz), which is far outside the range of typical $\delta$ Scuti frequencies. We discuss the possibility that these modes could be solar-like oscillations, oscillations of the roAp type or due to an unseen pulsating compact companion.
Fundamental Properties of Stars using Asteroseismology from Kepler & CoRoT and Interferometry from the CHARA Array
We present results of a long-baseline interferometry campaign using the PAVO beam combiner at the CHARA Array to measure the angular sizes of five main-sequence stars, one subgiant and four red giant stars for which solar-like oscillations have been detected by either Kepler or CoRoT. By combining interferometric angular diameters, Hipparcos parallaxes, asteroseismic densities, bolometric fluxes and high-resolution spectroscopy we derive a full set of near model-independent fundamental properties for the sample. We first use these properties to test asteroseismic scaling relations for the frequency of maximum power (nu_max) and the large frequency separation (Delta_nu). We find excellent agreement within the observational uncertainties, and empirically show that simple estimates of asteroseismic radii for main-sequence stars are accurate to < 4%. We furthermore find good agreement of our measured effective temperatures with spectroscopic and photometric estimates with mean deviations for stars between T_eff = 4600-6200 K of -22+/-32 K (with a scatter of 97K) and -58+/-31 K (with a scatter of 93 K), respectively. Finally we present a first comparison with evolutionary models, and find differences between observed and theoretical properties for the metal-rich main-sequence star HD173701. We conclude that the constraints presented in this study will have strong potential for testing stellar model physics, in particular when combined with detailed modelling of individual oscillation frequencies.
Spin down of the core rotation in red giants
The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. Thanks to the observation of mixed modes, we can probe their deep interior and have now access to the rotation in the innermost region. We aim to measure the rotational splittings in red giants and to derive scaling relations related to seismic and fundamental stellar parameters. We have developed a dedicated method for measuring in an automated way the rotational splittings in a large number of red giants. We have also used the measurements provided by the full identification of the mixed-mode pattern. We then performed ensemble asteroseismology: the examination of a large number of red giants allows us to derive information on their evolution. We have shown that the rotational splittings are in all cases dominated by the core rotation. For the first time, we directly measure this rotation in a large sample of red giants (about 300). We observe a significant change in the core rotation associated with internal angular momentum transfer in stars ascending the red giant branch. This transfer is boosted when the stellar radius reaches $\simeq \Rdredge$, where the first dredge-up is supposed to occur. We also show that, at fixed stellar radius, the specific angular momentum increases with increasing stellar mass, and is smaller for stars in the red clump compared to stars in the red giant branch. Ensemble asteroseismology directly proves what has been indirectly suspected for a while: the core rotation significantly slows down during the red giant phase. It occurs when the convection envelope expands and gives rise to the first dredge-up. This spinning down explains, for instance, the long rotation periods measured in white dwarfs.
Relationship between low and high frequencies in Delta Scuti stars: Photometric Kepler and spectroscopic analyses of the rapid rotator KIC 8054146
Two years of Kepler data of KIC 8054146 ($\delta$ Sct/$\gamma$ Dor hybrid) revealed 349 statistically significant frequencies between 0.54 and 191.36 cd$^{-1}$ (6.3 $\mu$Hz to 2.21 mHz). The 117 low frequencies cluster in specific frequency bands, but do not show the equidistant period spacings predicted for gravity modes of successive radial order, $n$, and reported for at least one other hybrid pulsator. The four dominant low frequencies in the 2.8 to 3.0 cd$^{-1}$ (32 to 35 $\mu$Hz) range show strong amplitude variability with timescales of months and years. These four low frequencies also determine the spacing of the higher frequencies in and beyond the $\delta$ Sct pressure-mode frequency domain. In fact, most of the higher frequencies belong to one of three families with spacings linked to a specific dominant low frequency. In the Fourier spectrum, these family regularities show up as triplets, high-frequency sequences with absolutely equidistant frequency spacings, side lobes (amplitude modulations) and other regularities in frequency spacings. Furthermore, within two families the amplitude variations between the low and high frequencies are related. We conclude that the low frequencies (gravity modes, rotation) and observed high frequencies (mostly pressure modes) are physically connected. This unusual behavior may be related to the very rapid rotation of the star: from a combination of high and low-resolution spectroscopy we determined that KIC 8054146 is a very fast rotator (ini = 300 $\pm$ 20 \kms) with an effective temperature of 7600 $\pm$ 200 K and a surface gravity ogg of 3.9 $\pm$ 0.3. Several astrophysical ideas explaining the origin of the relationship between the low and high frequencies are explored.
Asteroseismology of the Open Clusters NGC 6791, NGC 6811, and NGC 6819 from 19 Months of Kepler Photometry
We studied solar-like oscillations in 115 red giants in the three open clusters, NGC 6791, NGC 6811, and NGC 6819, based on photometric data covering more than 19 months with NASA's Kepler space telescope. We present the asteroseismic diagrams of the asymptotic parameters $\delta\nu_{02}$, $\delta\nu_{01}$, and epsilon, which show clear correlation with fundamental stellar parameters such as mass and radius. When the stellar populations from the clusters are compared, we see evidence for a difference in mass of the red giant branch stars and possibly a difference in structure of the red clump stars, from our measurements of the small separations $\delta\nu_{02}$ and $\delta\nu_{01}$. Ensemble échelle diagrams and upper limits to the linewidths of $\ell = 0$ modes as a function of $\Delta\nu$ of the clusters NGC 6791 and NGC 6819 are also shown, together with the correlation between the $\ell = 0$ ridge width and the $T_{eff}$ of the stars. Lastly, we distinguish between red giant branch and red clump stars through the measurement of the period spacing of mixed dipole modes in 53 stars among all the three clusters to verify the stellar classification from the color-magnitude diagram. These seismic results also allow us to identify a number of special cases, including evolved blue stragglers and binaries, as well as stars in late He-core burning phases, which can be potentially interesting targets for detailed theoretical modeling.
Verifying asteroseismically determined parameters of Kepler stars using Hipparcos parallaxes: self-consistent stellar properties and distances
Accurately determining the properties of stars is of prime importance for characterizing stellar populations in our Galaxy. The field of asteroseismology has been thought to be particularly successful in such an endeavor for stars in different evolutionary stages. However, to fully exploit its potential, robust methods for estimating stellar parameters are required and independent verification of the results is mandatory. With this purpose, we present a new technique to obtain stellar properties by coupling asteroseismic analysis with the InfraRed Flux Method. By using two global seismic observables and multi-band photometry, the technique allows us to obtain masses, radii, effective temperatures, bolometric fluxes, and hence distances for field stars in a self-consistent manner. We apply our method to 22 solar-like oscillators in the Kepler short-cadence sample, that have accurate Hipparcos parallaxes. Our distance determinations agree to better than 5%, while measurements of spectroscopic effective temperatures and interferometric radii also validate our results. We briefly discuss the potential of our technique for stellar population analysis and models of Galactic Chemical Evolution.
Constraining the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler
There are now more than 19 months of long-cadence data available for some of the red giants observed with the Kepler space mission. Consequently we are able to clearly resolve fine detail in their oscillation spectra and see many components of the so-called mixed modes that probe the radiative regions of the stellar core. In this paper, we report for the first time a parametric fit to the pattern of the $\ell=1$ mixed modes in red giants which is a powerful tool in the identification of gravity-dominated mixed modes. With these modes that share the characteristics of both pressure and gravity modes, we are able to probe directly the helium core and the surrounding shell where hydrogen is burning. We propose two ways for describing the so-called mode bumping that affects the locations of the mixed modes. A phenomenological approach is used to describe the main feature of the mode bumping. Alternatively a quasi-asymptotic mixed-mode relation provides a powerful link between seismic observations and the stellar interior structure. We use period échelle diagrams to emphasize the detection of the gravity-dominated mixed modes. The asymptotic law for mixed modes is confirmed. It allows us to measure the unperturbed gravity-mode period spacings in more than hundred red giant stars. The identification of the gravity-dominated mixed modes allows us to complete the identification of all major peaks in a red giant oscillation spectrum, with significant consequences on the true identification of $\ell=3$ modes, of $\ell=2$ mixed modes, and of the mode widths and amplitudes. The accurate measurement of the gravity-mode period spacing provides an effective probe of the inner, g-mode cavity. The derived value of the coupling coefficient between the cavities is different for RGB and clump stars. This provides a probe of the hydrogen-shell burning region which surrounds the helium core. Core contraction as red giants ascend the red giant branch can be explored using the variation of the gravity-mode spacing as a function of the mean large separation.
Nonlinear asteroseismology of RR Lyrae
The observations of the Kepler space telescope revealed that fundamental-mode RR Lyrae stars may show various radial overtones. The presence of multiple radial modes may allow us to conduct nonlinear asteroseismology: comparison of mode amplitudes and frequency shifts between observations and models. Here we report the detection of three radial modes in the star RR Lyr, the eponym of the class, using the Kepler short cadence data: besides the fundamental mode, both the first and the ninth overtones can be derived from the data set. RR Lyrae shows period doubling, but switches occasionally to a state where a pattern of six pulsation cycles repeats instead of two. We found hydrodynamic models that show the same three modes and the period-six state, allowing for comparison with the observations.
Stochastic Brightness Variations in the Central Star of Planetary Nebula NGC 6826
One year of continuous Kepler Space Telescope data for the central object of planetary nebula NGC 6826 (KIC 12071221) were analyzed. KIC 12071221 has long-cadence light curves with stochastic brightness variations and broadband power spectra. The exception is a one-month long period during which variability was detected with a period of 14.8 hr. In search of the origin of this periodicity and in an attempt to better understand the complex NGC 6826 system, long-cadence KIC 12071221 data were analyzed using nonlinear time series methods. Nonlinear projective noise reduction from a phase-space dimension of six lowered the tail of the power spectra at the higher frequencies by factors of 38 to 133, an unexpected result for light curves with no obvious dominant frequencies. Even more notable is the identification of a structured distribution of trajectories, or coherence, in the reconstructed phase space for vectors spanning an interval of 1.5 hr. Organization weakens as the delay increases and is lost for phase-space vectors spanning times longer than 10 hr. This may be indicative of a binary object which shares a common envelope and/or pulsations but for a complete understanding one or both have to be combined with wind structure. Thus, an estimate is made of the timescale of the response to what we propose is stochastic driving. This estimate of the time scale of the organized response is made by monitoring the loss of structure in the distribution of trajectories in phase space, a novel application of nonlinear methodology that may be used on data sampled with any sampling time.
Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with Kepler
Rotation is expected to have an important influence on the structure and the evolution of stars. However, the mechanisms of angular momentum transport in stars remain theoretically uncertain and very complex to take into account in stellar models. To achieve a better understanding of these processes, we desperately need observational constraints on the internal rotation of stars, which until very recently were restricted to the Sun. In this paper, we report the detection of mixed modes — i.e. modes that behave both as g modes in the core and as p modes in the envelope — in the spectrum of the early red giant KIC7341231, which was observed during one year with the Kepler spacecraft. By performing an analysis of the oscillation spectrum of the star, we show that its non-radial modes are clearly split by stellar rotation and we are able to determine precisely the rotational splittings of 18 modes. We then find a stellar model that reproduces very well the observed atmospheric and seismic properties of the star. We use this model to perform inversions of the internal rotation profile of the star, which enables us to show that the core of the star is rotating at least five times faster than the envelope. This will shed new light on the processes of transport of angular momentum in stars. In particular, this result can be used to place constraints on the angular momentum coupling between the core and the envelope of early red giants, which could help us discriminate between the theories that have been proposed over the last decades.
Atmospheric parameters of 82 red giants in the Kepler field.
Context: Accurate fundamental parameters of stars are essential for the asteroseismic analysis of data from the NASA kepler mission. Aims: We aim at determining accurate atmospheric parameters and the abundance pattern for a sample of 82 red giants that are targets for the Kepler mission. Methods: We have used high-resolution, high signal-to-noise spectra from three different spectrographs. We used the iterative spectral synthesis method VWA to derive the fundamental parameters from carefully selected high-quality iron lines. After determination of the fundamental parameters abundances of 13 elements were measured using equivalent widths of the spectral lines. Results: We identify discrepancies in log (g) and [Fe/H], compared to the parameters based on photometric indices in the Kepler Input Catalogue (larger than 2.0 dex for log (g) and [Fe/H] for individual stars). The $T_{eff}$ found from spectroscopy and photometry shows good agreement within the uncertainties. We find good agreement between the spectroscopic log (g) and the log (g) derived from asteroseismology. Also we see indications of a potential metallicity effect on the stellar oscillations. Conclusions: We have determined the fundamental parameters and element abundances of 82 red giants. The large discrepancies between the spectroscopic log (g) and [Fe/H] and values in the Kepler Input catalogue emphasize the need for further detailed spectroscopic follow-up of the Kepler targets in order to produce reliable results from the asteroseismic analyses.
Solving the mode identification problem in asteroseismology of F stars observed with Kepler
Asteroseismology of F-type stars has been hindered by an ambiguity in identification of their oscillation modes. The regular mode pattern that makes this task trivial in cooler stars is masked by increased linewidths. The absolute mode frequencies, encapsulated in the asteroseismic variable $\epsilon$, can help solve this impasse because the values of $\epsilon$ implied by the two possible mode identifications are distinct. We find that the correct $\epsilon$ can be deduced from the effective temperature and the linewidths and we apply these methods to a sample of solar-like oscillators observed with Kepler.
Testing Scaling Relations for Solar-Like Oscillations from the Main-Sequence to Red Giants using Kepler Data
We have analyzed solar-like oscillations in $\sim$1700 stars observed by the Kepler Mission, spanning from the main-sequence to the red clump. Using evolutionary models, we test asteroseismic scaling relations for the frequency of maximum power ($\nu_{\rm max}$), the large frequency separation ($\Delta\nu$) and oscillation amplitudes. We show that the difference of the $\Delta\nu$-$\nu_{\rm max}$ relation for unevolved and evolved stars can be explained by different distributions in effective temperature and stellar mass, in agreement with what is expected from scaling relations. For oscillation amplitudes, we show that neither $(L/M)^s$ scaling nor the revised scaling relation by Kjeldsen & Bedding (2011) are accurate for red-giant stars, and demonstrate that a revised scaling relation with a separate luminosity-mass dependence can be used to calculate amplitudes from the main-sequence to red-giants to a precision of $\sim$25%. The residuals show an offset particularly for unevolved stars, suggesting that an additional physical dependency is necessary to fully reproduce the observed amplitudes. We investigate correlations between amplitudes and stellar activity, and find evidence that the effect of amplitude suppression is most pronounced for subgiant stars. Finally, we test the location of the cool edge of the instability strip in the Hertzsprung-Russell diagram using solar-like oscillations and find the detections in the hottest stars compatible with a domain of hybrid stochastically excited and opacity driven pulsation.
Kepler observations of the high-amplitude delta Scuti star V2367 Cyg
We analyse Kepler observations of the high-amplitude $\delta$ Scuti (HADS) star V2367 Cyg (KIC 9408694). The variations are dominated by a mode with frequency $f_1 = 5.6611$ d$^{-1}$. Two other independent modes with $f_2 = 7.1490$ d$^{-1}$ and $f_3 = 7.7756$ d$^{-1}$ have amplitudes an order of magnitude smaller than $f_1$. Nearly all the light variation is due to these three modes and their combination frequencies, but several hundred other frequencies of very low amplitude are also present. The amplitudes of the principal modes may vary slightly with time. The star has twice the projected rotational velocity of any other HADS star, which makes it unusual. We find a correlation between the phases of the combination frequencies and their pulsation frequencies, which is not understood. Since modes of highest amplitude in HADS stars are normally radial modes, we assumed that this would also be true in this star. However, attempts to model the observed frequencies as radial modes without mode interaction were not successful. For a star with such a relatively high rotational velocity, it is important to consider the effect of mode interaction. Indeed, when this was done we were able to obtain a model in which a good match with $f_1$ and $f_2$ is obtained, with $f_1$ being the fundamental radial mode.
Asteroseismology of the solar analogs 16 Cyg A and B from Kepler observations
The evolved solar-type stars 16 Cyg A and B have long been studied as solar analogs, yielding a glimpse into the future of our own Sun. The orbital period of the binary system is too long to provide meaningful dynamical constraints on the stellar properties, but asteroseismology can help because the stars are among the brightest in the Kepler field. We present an analysis of three months of nearly uninterrupted photometry of 16 Cyg A and B from the Kepler space telescope. We extract a total of 46 and 41 oscillation frequencies for the two components respectively, including a clear detection of octupole ($l$=3) modes in both stars. We derive the properties of each star independently using the Asteroseismic Modeling Portal, fitting the individual oscillation frequencies and other observational constraints simultaneously. We evaluate the systematic uncertainties from an ensemble of results generated by a variety of stellar evolution codes and fitting methods. The optimal models derived by fitting each component individually yield a common age ($t=6.8\pm0.4$ Gyr) and initial composition ($Z_{\rm i}=0.024\pm0.002, Y_{\rm i}=0.25\pm0.01$) within the uncertainties, as expected for the components of a binary system, bolstering our confidence in the reliability of asteroseismic techniques. The longer data sets that will ultimately become available will allow future studies of differential rotation, convection zone depths, and long-term changes due to stellar activity cycles.
The Kepler view of gamma Doradus stars
Visual classification of over 10 000 stars in the Kepler database has revealed a class of stars with almost mono-periodic light variations and characteristic beating. A subset of these stars have a larger light amplitude and asymmetric light curves with larger variation in maximum brightness than in minimum brightness. The beating is mostly a result of two dominant, closely-spaced frequencies. A third group of stars shows multiple low frequencies of comparable amplitudes. All three types of star fall in the region of the HR diagram where $\gamma$ Dor stars are found and we therefore identify them as $\gamma$ Dor variables. However, stars with migrating starspots also have symmetric light curves with beats, so it is likely that the sample is contaminated by non-pulsating stars of this type. If we assume that the dominant frequency in stars with beats is the rotational frequency, the resulting distribution of equatorial rotational velocities matches that of ï¬eld stars of similar temperature and luminosity. We therefore conclude that the pulsation periods of these stars must be close to their rotational periods. The third group with multiple frequencies may be slowly-rotating $\gamma$ Dor stars. This investigation is closely related to the presence of low-frequencies in $\delta$ Scuti stars which we briefly discuss.
First Kepler results on compact pulsators V: Pulsating subdwarf B stars in short-period binaries
The survey phase of the Kepler Mission includes a number of hot subdwarf B (sdB) stars to search for nonradial pulsations. We present our analysis of two sdB stars that are found to be $g$-mode pulsators of the V1093 Her class. These two stars also display the distinct irradiation effect typical of sdB stars with a close M-dwarf companion with orbital periods of less than half a day. Because the orbital period is so short, the stars should be in synchronous rotation, and if so, the rotation period should imprint itself on the multiplet structure of the pulsations. However, we do not find clear evidence for such rotational splitting. Though the stars do show some frequency spacings that are consistent with synchronous rotation, they also display multiplets with splittings that are much smaller. Longer-duration time series photometry will be needed to determine if those small splittings are in fact rotational splitting, or caused by slow amplitude or phase modulation. Further data should also improve the signal-to-noise, perhaps revealing lower amplitude periodicities that would confirm the expectation of synchronous rotation. The pulsation periods seen in these stars show period spacings that are suggestive of high-overtone $g-$mode pulsations.
First Kepler results on compact pulsators II: KIC 010139564, a new pulsating subdwarf B (V361 Hya) star with an additional low-frequency mode
We present the discovery of nonradial pulsations in a hot subdwarf B star based on 30.5 days of nearly continuous time-series photometry using the Kepler spacecraft. KIC 010139564 is found to be a short–period pulsator of the V361 Hya (EC 14026) class with more than 10 independent pulsation modes whose periods range from 130 to 190 seconds. It also shows one periodicity at a period of 3165 seconds. If this periodicity is a high order g-mode, then this star may be the hottest member of the hybrid DW Lyn stars. In addition to the resolved pulsation frequencies, additional periodic variations in the light curve suggest that a significant number of additional pulsation frequencies may be present. The long duration of the run, the extremely high duty cycle, and the well–behaved noise properties allow us to explore the stability of the periodic variations, and to place strong constraints on how many of them are independent stellar oscillation modes. We find that most of the identified periodicities are indeed stable in phase and amplitude, suggesting a rotation period of 2-3 weeks for this star, but further observations are needed to confirm this suspicion.
Characterization of the power excess of solar-like oscillations in red giants with Kepler
The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. This allows us to examine their seismic global properties and to compare them with theoretical predictions. We aim to describe the oscillation power excess observed in red-giant oscillation spectra with global seismic parameters, and to propose empirical scaling relations governing these parameters. From these scalings relations, we derive new physical properties of red-giant oscillation. Various different methods were compared in order to validate the processes and to derive reliable output values. Then, for consistency, a single method was used to determine scaling relations concerning the relevant global asteroseismic parameters: mean mode height, mean height of the background signal superimposed on the oscillation excess power, width of the excess power, bolometric amplitude of the radial modes and visibility of non-radial modes. A method for deriving oscillation amplitudes has been proposed, which relies on the complete identification of the red-giant oscillation spectrum. The comparison of the different methods has shown the important role of the modelling of the background. The convergence reached by the collaborative work enables us to derive significant results concerning the oscillation power excess. We obtained several scaling relations, and identify the influence of the stellar mass and/or of the evolutionary status. We found that none of the amplitude scaling relations motivated from physics considerations predicts the observed mode amplitudes of red-giant stars. In parallel, the degree-dependent mode visibility exhibit important variations. Both effects seem related to the significant influence of the high mode mass of non-radial mixed modes. The clear correlation between the power densities of the background signal and of the stellar oscillation induces important consequences to be considered for deriving a reliable theoretical relation of the mode amplitude. As a by-product of this work, we have verified that red-giant asteroseismology delivers new insights for stellar and Galactic physics, given the evidence for mass loss at the tip of the red-giant branch.
Fundamental properties of five Kepler stars using global seismic quantities and ground-based observations
We present an asteroseismic study of the solar-like stars KIC 11395018, KIC 10273246, KIC 10920273, KIC 10339342, and KIC 11234888 using short-cadence time series of more than eight months from the Kepler satellite. For four of these stars, we derive atmospheric parameters from spectra acquired with the Nordic Optical Telescope. The global seismic quantities (average large frequency separation and frequency of maximum power), combined with the atmospheric parameters, yield the mean density and surface gravity with precisions of 2% and ∼0.03 dex, respectively. We also determine the radius, mass, and age with precisions of 2–5%, 7–11%, and $\sim$35%, respectively, using grid-based analyses. Coupling the stellar parameters with photometric data yields an asteroseismic distance with a precision better than 10%. A v sin i measurement provides a rotational period-inclination correlation, and using the rotational periods from the recent literature, we constrain the stellar inclination for three of the stars. An Li abundance analysis yields an independent estimate of the age, but this is inconsistent with the asteroseismically determined age for one of the stars. We assess the performance of five grid-based analysis methods and find them all to provide consistent values of the surface gravity to $\sim$0.03 dex when both atmospheric and seismic constraints are at hand. The different grid-based analyses all yield fitted values of radius and mass to within 2.4$\sigma$, and taking the mean of these results reduces it to 1.5$\sigma$. The absence of a metallicity constraint when the average large frequency separation is measured with a precision of 1% biases the fitted radius and mass for the stars with non-solar metallicity (metal-rich KIC 11395018 and metal-poor KIC 10273246), while including a metallicity constraint reduces the uncertainties in both of these parameters by almost a factor of two. We found that including the average small frequency separation improves the determination of the age only for KIC 11395018 and KIC 11234888, and for the latter this improvement was due to the lack of strong atmospheric constraints.
Oscillation mode linewidths of main-sequence and subgiant stars observed by Kepler
Solar-like oscillations have been observed by Kepler and CoRoT in several solar-type stars.
We study the variations of stellar p-mode linewidth as a function of effective temperature..
Time series of 9 months of Kepler data have been used. The power spectra of 42 cool main-sequence stars and subgiants have been analysed using both Maximum Likelihood Estimators and Bayesian estimators, providing individual mode characteristics such as frequencies, linewidths and mode heights.
Here we report on the mode linewidth at maximum power and at maximum mode height for these 42 stars as a function of effective temperature.
We show that the mode linewidth at either maximum mode height or maximum amplitude follows a scaling relation with effective temperature, which is a combination of a power law plus a lower bound. The typical power law index is about 13 for the linewidth derived from the maximum mode height, and about 16 for the linewidth derived from the maximum amplitude while the lower bound is about 0.3 $\mu$Hz and 0.7 $\mu$Hz, respectively. We stress that this scaling relation is only valid for the cool main-sequence stars and subgiants, and does not have predictive power outside the temperature range of these stars.
Fast core rotation in red-giant stars revealed by gravity-dominated mixed modes
When the core hydrogen is exhausted during stellar evolution, the central region of a star contracts and the outer envelope expands and cools, giving rise to a red giant, in which convection occupies a large fraction of the star. Conservation of angular momentum requires that the cores of these stars rotate faster than their envelopes, and indirect evidence supports this. Information about the angular momentum distribution is inaccessible to direct observations, but it can be extracted from the effect of rotation on oscillation modes that probe the stellar interior. Here, we report the detection of non-rigid rotation in the interiors of red-giant stars by exploiting the rotational frequency splitting of recently detected mixed modes. We demonstrate an increasing rotation rate from the surface of the star to the stellar core. Comparing with theoretical stellar models, we conclude that the core must rotate at least ten times faster than the surface. This observational result confirms the theoretical prediction of a steep gradient in the rotation profile towards the deep stellar interior.
First Kepler results on compact pulsators VIII: Mode identifications via period spacings in g−mode pulsating Subdwarf B stars
We investigate the possibility of nearly-equally spaced periods in 13 hot
subdwarf B (sdB) stars observed with the Kepler spacecraft and one
observed with CoRoT.
Asymptotic limits for gravity ($g-$)mode pulsations provide relationships between
equal period spacings of modes with differing degrees $\ell$ and relationships
between periods of the same radial order $n$ but differing degrees
$\ell$. Period transforms, Kolmogorov-Smirnov tests, and linear least-squares
fits have been used to
detect and determine the significance of equal period spacings. We have also
used Monte Carlo simulations to estimate the likelihood that the detected
spacings could be produced randomly.
Period transforms for nine of the Kepler stars indicate $\ell =1$
period spacings, with five also showing peaks for $\ell =2$ modes. 12
stars indicate $\ell =1$ modes using the Kolmogorov-Smirnov test while
another shows solely $\ell =2$ modes. Monte Carlo results indicate that
equal period spacings are significant in 10 stars above 99% confidence and
13 of the 14 are above 94% confidence. For 12 stars, the various methods
find consistent regular period spacing values to within the errors, two others
show some inconsistencies, likely caused by binarity, and the last has
significant detections but the mode assignment disagrees between methods.
We use asymptotic period spacing relationships to associate observed periods
of variability with pulsation modes for $\ell =1$ and $2$.
From the Kepler first year survey sample of 13
multiperiodic $g-$mode pulsators, five stars have several consecutive overtones
making period spacings easy to detect, six others have fewer consecutive
overtones but period spacings are readily detected,
%regular period spacings are easily found
%in five stars, while an additional six stars show period
%spacings that are not as regular,
and two stars show marginal indications of
equal period spacings.
We also examine a $g-$mode sdB pulsator observed by CoRoT
with a rich pulsation spectrum and our tests detect regular period spacings.
We use Monte Carlo simulations to estimate the significance of the detections
in individual stars. From the simulations it is determined that regular period
spacings in 10 of the 14 stars is very unlikely to be random, another two
are moderately unlikely to be random and two are mostly unconstrained.
We find a common $\ell =1$ period spacing spanning a range from 231 to
272 s allowing us to correlate pulsation modes with 222 periodicities
and that the $\ell =2$ period spacings are related to the
$\ell =1$ spacings by the asymptotic relationship $1/\sqrt{3}$.
We briefly discuss the impact of equal period spacings which indicate low-degree
modes with a lack of significant mode trappings.
First Kepler results on compact pulsators III: Subdwarf B stars with V1093 Her and hybrid (DW Lyn) type pulsations.
We present the discovery of nonradial pulsations in hot subdwarf B (sdB) stars based on 27 days of nearly continuous time-series photometry using the Kepler spacecraft. We find that every sdB star cooler than $\approx 27\,500\,$K is a long-period pulsator of the V1093 Her (PG 1716) class or a hybrid star with both short and long periods. The apparently single long-period and hybrid pulsators are described here. The V1093 Her periods range from one to 4.5 h and are associated with $g-$mode pulsations. Three stars also exhibit short periods indicative of $p-$modes with periods of 2 to 5 m and in addition, these stars exhibit periodicities between both classes from 15 to 45 m. We detect the coolest and longest-period V1093 Her-type pulsator to date, KIC010670103 ($T_{\rm eff}\approx 20\,900\,$K, $P_{\rm max}\approx 4.5$ h) as well as an extremely cool hybrid pulsator, KIC002697388 ($T_{\rm eff}\approx 23\,900\,$K) and for the first time hybrid pulsators which have larger $g-$mode amplitudes than $p-$mode ones. We find that all of these pulsators are quite rich with many frequencies and apply asymptotic relationships to associate periodicities with modes for KIC010670103. Kepler data are particularly well-suited for these studies as they are long-duration, extremely high duty cycle observations with well-behaved noise properties.
Modelling Kepler observations of solar-like oscillations in the red-giant star HD 186355
We have analysed oscillations of the red giant star HD 186355 observed by the NASA Kepler satellite. The data consist of the first five quarters of science operations of Kepler, which covers around 13 months. The high-precision time-series data allow us to accurately extract the oscillation frequencies from the power spectrum. We find the frequency of the maximum oscillation power, $\nu_{\rm max}$, and the mean large frequency separation, $\Delta \nu$, are around 106 and 9.4 $\mu$Hz respectively. A regular pattern of radial and non-radial oscillation modes is identified by stacking the power spectra in an échelle diagram. We use the scaling relations of $\Delta \nu$ and $\nu_{\rm max}$ to estimate the preliminary asteroseismic mass, which is confirmed with the modelling result (M = 1.43 $\pm$ 0.02 $M_{\sun}$) using the Yale Rotating stellar Evolution Code (YREC7). In addition, we constrain the effective temperature, luminosity and radius from comparisons between observational constraints and models. A number of mixed $l = 1$ modes are also detected and taken into account in our model comparisons. We find a mean observational period spacing for these mixed modes of about 58 sec, suggesting that this red giant branch star is in the shell hydrogen-burning phase.
Granulation in Red Giants: Observations by the Kepler Mission and Three-dimensional Convection Simulations
The granulation pattern that we observe on the surface of the Sun is due to hot plasma from the interior rising to the photosphere where it cools down, and descends back into the interior at the edges of granules. This is the visible manifestation of convection taking place in the outer part of the solar convection zone. Because red giants have deeper convection zones and more extended atmospheres than the Sun, we cannot a priori assume that granulation in red giants is a scaled version of solar granulation. Until now, neither observations nor 1D analytical convection models could put constraints on granulation in red giants. However, thanks to asteroseismology, this study can now be performed. The resulting parameters yield physical information about the granulation. We analyze $\sim$ 1000 red giants that have been observed by Kepler during 13 months. We fit the power spectra with Harvey-like profiles to retrieve the characteristics of the granulation (time scale $\tau_{\rm gran}$ and power $P_{\rm gran}$). We also introduce a new time scale, $\tau_{\rm eff}$, which takes into account that different slopes are used in the Harvey functions. We search for a correlation between these parameters and the global acoustic-mode parameter (the position of maximum power, $\nu_{\rm max}$) as well as with stellar parameters (mass, radius, surface gravity (log $g$) and effective temperature ($T_{\rm eff}$)). We show that $\tau_{\rm eff} \propto \nu_{\rm max}^{-0.89}$ and $P_{\rm gran} \propto \nu_{\rm max}^{-1.90}$, which is consistent with the theoretical predictions. We find that the granulation time scales of stars that belong to the red clump have similar values while the time scales of stars in the red-giant branch are spread in a wider range. Finally, we show that realistic 3D simulations of the surface convection in stars, spanning the ($T_{\rm eff}$, log $g$)-range of our sample of red giants, match the Kepler observations well in terms of trends.
Asteroseismic Diagrams from a Survey of Solar-like Oscillations with Kepler
Photometric observations made by the NASA Kepler Mission have led to a dramatic increase in the number of main-sequence and subgiant stars with detected solar-like oscillations. We present an ensemble asteroseismic analysis of 78 solar-type stars. Using frequencies determined from the Kepler time-series photometry, we have measured three asteroseismic parameters that characterize the oscillations: the large frequency separation ($\Delta\nu$), the small frequency separation between modes of $l=0$ and $l=2$ ($\delta\nu_{02}$), and the dimensionless offset ($\epsilon$). These measurements allow us to construct asteroseismic diagrams, namely the so-called C-D diagram of $\delta\nu_{02}$ versus $\Delta\nu$, and the recently introduced $\epsilon$ diagram. We compare the Kepler results with previously observed solar-type stars and with theoretical models. The positions of stars in these diagrams places constraints on their masses and ages.
The Kepler characterization of the variability amongst A- and F-type stars I. General overview
Context. The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars.
Aims. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars, and observationally investigate the relation between $\gamma$ Doradus ($\gamma$ Dor), $\delta$ Scuti ($\delta$ Sct), and hybrid stars.
Methods. We compile a database of physical parameters for the sample stars from the literature and new ground-based observations. We analyse the Kepler light curve of each star and extract the pulsational frequencies using different frequency analysis methods. We construct two new observables, 'energy' and 'efficiency', related to the driving energy of the pulsation mode and the convective efficiency of the outer convective zone, respectively.
Results. We propose three main groups to describe the observed variety in pulsating A-F type stars: $\gamma$ Dor, $\delta$ Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars with a different spectral type than A or F, or stars that show no clear periodic variability. 23% of the stars (172 stars) are hybrid stars, which is a much larger fraction than what has been observed before. We characterize for the first time a large number of A-F type stars (475 stars) in terms of number of detected frequencies, frequency range, and typical pulsation amplitudes. The majority of hybrid stars show frequencies with all kinds of periodicities within the $\gamma$ Dor and $\delta$ Sct range, also between 5 and 10 d$^{-1}$, which is a challenge for the current models. The location of gdor and dsct classes in the (Teff, logg)-diagram has been extended. We find indications for the existence of $\delta$ Sct and $\gamma$ Dor stars beyond the edges of the current observational instability strips. The hybrid stars occupy the entire region within the $\delta$ Sct, and $\gamma$ Dor instability strips and beyond. Non-variable stars seem to exist within the instability strips. We investigate two newly constructed variables 'efficiency' and 'energy' as a means to explore the relation between $\gamma$ Dor and $\delta$ Sct stars.
Conclusions. Our results suggest a revision of the current observational instability strips of $\delta$ Sct and $\gamma$ Dor stars, and imply an investigation of pulsation mechanisms to supplement the $\kappa$ mechanism and convective blocking effect to drive hybrid pulsations. Accurate physical parameters for all stars are needed to confirm these findings.
Constructing a one-solar-mass evolutionary sequence using asteroseismic data from Kepler
Asteroseismology of solar-type stars has entered a new era of large surveys with the success of the NASA Kepler mission, which is providing exquisite data on oscillations of stars across the Hertzprung-Russell (HR) diagram. From the time-series photometry, the two seismic parameters that can be most readily extracted are the large frequency separation ($\Delta\nu$) and the frequency of maximum oscillation power ($\nu_\mathrm{max}$). After the survey phase, these quantities are available for hundreds of solar-type stars. By considering scaling relations from solar values, we use these two asteroseismic observables to identify for the first time an evolutionary sequence of 1-M$_\odot$ field stars, without the need of further information from stellar models. Comparison of our determinations with the few available spectroscopic results shows an excellent level of agreement. We discuss the potential of the method for differential analysis throughout the main-sequence evolution, and the possibility of detecting twins of very well-known stars.
Asteroseismology from multi-month Kepler photometry: the evolved Sun-like stars KIC 10273246 and KIC 10920273
The evolved main-sequence Sun-like stars KIC 10273246 (F-type) and KIC 10920273 (G-type) were observed with the NASA Kepler satellite for approximately ten months with a duty cycle in excess of 90%. Such continuous and long observations are unprecedented for solar-type stars other than the Sun.
We aimed mainly at extracting estimates of p-mode frequencies – as well as of other individual mode parameters – from the power spectra of the light curves of both stars, thus providing scope for a full seismic characterization.
The light curves were corrected for instrumental effects in a manner independent of the Kepler science pipeline. Estimation of individual mode parameters was based both on the maximization of the likelihood of a model describing the power spectrum and on a classic prewhitening method. Finally, we employed a procedure for selecting frequency lists to be used in stellar modeling.
A total of 30 and 21 modes of degree $l=0,1,2$ – spanning at least eight radial orders – have been identified for KIC 10273246 and KIC 10920273, respectively. Two avoided crossings ($l=1$ ridge) have been identified for KIC 10273246, whereas one avoided crossing plus another likely one have been identified for KIC 10920273. Good agreement is found between observed and predicted mode amplitudes for the F-type star KIC 10273246, based on a revised scaling relation. Estimates are given of the rotational periods, the parameters describing stellar granulation and the global asteroseismic parameters $\Delta\nu$ and $\nu_{\rm{max}}$.
Solar-like oscillations in KIC 11395018 and KIC 11234888 from 8 months of Kepler data
We analyze the photometric short-cadence data obtained with the Kepler Mission during the first eight months of observations of two solar-type stars of spectral types G and F: KIC 11395018 and KIC 11234888 respectively, the latter having a lower signal-to-noise ratio compared to KIC 11395018. We estimate global parameters of the acoustic (p) modes such as the average large and small frequency separations, the frequency of the maximum of the p-mode envelope and the average linewidth of the acoustic modes. We were able to identify and to measure 22 p-mode frequencies for the first star and 16 for the second one even though the signal-to-noise ratios of these stars are rather low. We also derive some information about the stellar rotation periods from the analyses of the low-frequency parts of the power spectral densities. We emphasize the importance of continued observations for the stars with low signal-to-noise ratio for an improved characterization of the oscillation modes. Our results offer a preview of what will be possible for many stars with the long data sets obtained during the remainder of the mission.
Amplitudes of solar-like oscillations: constraints from red giants in open clusters observed by Kepler
Scaling relations that link asteroseismic quantities to global stellar properties are important for gaining understanding of the intricate physics that underpins stellar pulsation. The common notion that all stars in an open cluster have essentially the same distance, age, and initial composition, implies that the stellar parameters can be measured to much higher precision than what is usually achievable for single stars. This makes clusters ideal for exploring how quantities of solar-like oscillations such as the mode amplitude depend on the global stellar properties. We have analyzed data obtained with NASA's Kepler space telescope to study solar-like oscillations in 100 red giant stars located in either of the three open clusters, NGC 6791, NGC 6819, and NGC 6811. By fitting the measured amplitudes to predictions from simple scaling relations that depend on luminosity, mass, and effective temperature, we find that the data cannot be described by any power of the luminosity-to-mass ratio as previously assumed. As a result we provide a new improved empirical relation which treats luminosity and mass separately. This relation turns out to also work remarkably well for main-sequence and subgiant stars. In addition, the measured amplitudes reveal the presence of a number of previously unknown unresolved binaries in the red clump in NGC 6791 and NGC 6819, pointing to an interesting new application for asteroseismology as a probe into the formation history of open clusters.
An Asteroseismic Membership Study of the Red Giants in Three Open Clusters Observed by Kepler: NGC 6791, NGC 6819, and NGC 6811
Studying star clusters offers significant advances in stellar astrophysics due to the combined power of having many stars with essentially the same distance, age, and initial composition. This makes clusters excellent test benches for verification of stellar evolution theory. To fully exploit this potential, it is vital that the star sample is uncontaminated by stars that are not members of the cluster. Techniques for determining cluster membership therefore play a key role in the investigation of clusters. We present results on three clusters in the Kepler field of view based on a newly established technique that uses asteroseismology to identify fore- or background stars in the field. Four previously identified seismic non-members in NGC 6819 are confirmed in this study, and three additional non-members are found – two in NGC 6819 and one in NGC6791. We further highlight which stars are, or might be, affected by blending, which needs to be taken into account when analysing these Kepler data.
Verification of the Kepler Input Catalog from asteroseismology of solar-type stars
We calculate precise stellar radii and surface gravities from the asteroseismic analysis of over 500 solar-type pulsating stars observed by the Kepler space telescope. These physical stellar properties are compared with those given in the Kepler Input Catalog (KIC), determined from ground-based multi-colour photometry. For the stars in our sample, we find general agreement but we detect an average overestimation bias of 0.23 dex in the KIC determination of $\log(g)$ for stars with $\log(g)_\mathrm{KIC}>4.0$ dex, and a resultant underestimation bias of up to 50 % in the KIC radii estimates for stars with $R_\mathrm{KIC}<2$ $R_\odot$. Part of the difference may arise from selection bias in the asteroseismic sample; nevertheless, this result implies there may be fewer stars characterised in the KIC with $R\sim 1$ $R_\odot$ than is suggested by the physical properties in the KIC. Furthermore, if the radius estimates are taken from the KIC for these affected stars and then used to calculate the size of transiting planets, a similar underestimation bias will be applied to the planetary radii.
Variable turbulent convection as the cause of the Blazhko effect - testing the Stothers model
The amplitude and phase modulation observed in a significant fraction of the RR Lyrae variables - the Blazhko effect - represents a long-standing enigma in stellar pulsation theory. No satisfactory explanation for the Blazhko effect has been proposed so far. In this paper we focus on the Stothers (2006) idea, in which modulation is caused by changes in the structure of the outer convective zone, caused by a quasi-periodically changing magnetic field. However, up to this date no quantitative estimates were made to investigate whether such a mechanism can be operational and whether it is capable of reproducing the light variation we observe in Blazhko variables. We address the latter problem. We use a simplified model, in which the variation of turbulent convection is introduced into the non-linear hydrodynamic models in an ad hoc way, neglecting interaction with the magnetic field. We study the light curve variation through the modulation cycle and properties of the resulting frequency spectra. Our results are compared with Kepler observations of RR Lyr. We find that reproducing the light curve variation, as is observed in RR Lyr, requires a huge modulation of the mixing length, of the order of $\pm$50 per cent, on a relatively short time-scale of less than 40 days. Even then, we are not able to reproduce all the observed relations between modulation components present in the frequency spectrum and the relations between Fourier parameters describing the shape of the instantaneous light curves.
Global asteroseismic properties of solar-like oscillations observed by Kepler: Comparison of complementary analysis methods
We present the asteroseismic analysis of 1948 F-, G- and K-type main-sequence and subgiant stars observed by the NASA Kepler Mission. We detect and characterise solar-like oscillations in 642 of these stars. This represents the largest cohort of main-sequence and subgiant solar-like oscillators observed to date. The photometric observations are analysed using the methods developed by nine independent research teams. The results are combined to validate the determined global asteroseismic parameters and calculate the relative precision by which the parameters can be obtained. We correlate the relative number of detected solar-like oscillators with stellar parameters from the Kepler Input Catalog and find a deficiency for stars with effective temperatures in the range $5300 \lesssim T_\mathrm{eff} \lesssim 5700$ K and a drop-off in detected oscillations in stars approaching the red edge of the classical instability strip. We compare the power-law relationships between the frequency of peak power, $\nu_\mathrm{max}$, the mean large frequency separation, $\Delta\nu$, and the maximum mode amplitude, $A_\mathrm{max}$, and show that there are significant method-dependent differences in the results obtained. This illustrates the need for multiple complementary analysis methods to be used to assess the robustness and reproducibility of results derived from global asteroseismic parameters.
Cepheid investigations using the Kepler space telescope
We report results of initial work done on selected candidate Cepheids to be observed with the Kepler space telescope. Prior to the launch 40 candidates were selected from previous surveys and databases. The analysis of the first 322 days of Kepler photometry, and recent follow-up ground-based multicolour photometry and spectroscopy allowed us to confirm that one of these stars, V1154 Cyg (KIC 7548061), is indeed a 4.9-d Cepheid. Using the phase lag method we show that this star pulsates in the fundamental mode. New radial velocity data are consistent with previous measurements, suggesting that a long-period binary component is unlikely. No evidence is seen in the ultra-precise, nearly uninterrupted Kepler photometry for nonradial or stochastically excited modes at the micromagnitude level. The other candidates are not Cepheids but an interesting mix of possible spotted stars, eclipsing systems and flare stars.
Ensemble asteroseismology of solar-type stars with the NASA Kepler Mission
In addition to its search for extrasolar planets, the NASA Kepler mission provides exquisite data on stellar oscillations. We report the detections of oscillations in 500 solar-type stars in the Kepler field of view, an ensemble that is large enough to allow statistical studies of intrinsic stellar properties (such as mass, radius, and age) and to test theories of stellar evolution. We find that the distribution of observed masses of these stars shows intriguing differences to predictions from models of synthetic stellar populations in the Galaxy.
Predicting the detectability of oscillations in solar-type stars observed by Kepler
Asteroseismology of solar-type stars has an important part to play in the exoplanet program of the NASA Kepler Mission. Precise and accurate inferences on the stellar properties that are made possible by the seismic data allow very tight constraints to be placed on the exoplanetary systems. Here, we outline how to make an estimate of the detectability of solar-like oscillations in any given Kepler target, using rough estimates of the temperature and radius, and the Kepler apparent magnitude.
The impact of stellar activity on the detectability of solar-like oscillations observed by Kepler
We use photometric observations of solar-type stars, made by the NASA Kepler Mission, to conduct a statistical study of the impact of stellar surface activity on the detectability of solar-like oscillations. We find that the number of stars with detected oscillations fall significantly with increasing levels of activity. The results present strong evidence for the impact of magnetic activity on the properties of near-surface convection in the stars, which appears to inhibit the amplitudes of the stochastically excited, intrinsically damped solar-like oscillations.
HD 181068: A Red Giant in a Triply Eclipsing Compact Hierarchical Triple System
Hierarchical triple systems comprise a close binary and a more distant component. They are important for testing theories of star formation and of stellar evolution in the presence of nearby companions. We obtained 218 days of Kepler photometry of HD 181068 (magnitude of 7.1), supplemented by ground-based spectroscopy and interferometry, which show it to be a hierarchical triple with two types of mutual eclipses. The primary is a red giant that is in a 45-day orbit with a pair of red dwarfs in a close 0.9-day orbit. The red giant shows evidence for tidally induced oscillations that are driven by the orbital motion of the close pair. HD 181068 is an ideal target for studies of dynamical evolution and testing tidal friction theories in hierarchical triple systems.
Kepler-Detected Gravity-Mode Period Spacings in a Red Giant Star
Stellar interiors are inaccessible through direct observations. For this reason, helioseismologists made use of the Sun's acoustic oscillation modes to tune models of its structure. The quest to detect modes which probe the solar core has been ongoing for decades. We report the detection of mixed modes penetrating all the way to the core of an evolved star from 320 days of observations with the Kepler satellite. The period spacings of these mixed modes are directly dependent on the density gradient between the core region and the convective envelope
Atmospheric parameters and pulsational properties for a sample of $\delta$ Scuti, $\gamma$ Doradus, and hybrid Kepler targets
We report spectroscopic observations for 19 $\delta$ Scuti (Sct) candidates observed by the Kepler satellite in both long and short cadence mode. For all these stars, by using spectral synthesis, we derive the effective temperature, the surface gravity and the projected rotational velocity. An equivalent spectral type classification has been also performed for all stars in the sample. These determinations are fundamental for modelling the frequency spectra that will be extracted from the Kepler data for asteroseismic inference. For all the 19 stars, we present also periodograms obtained from Kepler data. We find that all stars show peaks in both low- ($\gamma$ Dor; g mode) and high-frequency ($\delta$ Sct; p mode) ranges. Using the amplitudes and considering 5 c/d as a boundary frequency, we classified 3 stars as pure $\gamma$ Dor, 4 as $\gamma$ Dor - $\delta$ Sct hybrid, 5 as $\delta$ Sct - $\gamma$ Dor hybrid, and 6 as pure $\delta$ Sct. The only exception is the star KIC 05296877 which we suggest could be a binary.
Kepler observations of Am stars
We present an analysis of high-resolution spectra for two pulsating Am stars
in the Kepler field. The stellar parameters derived in this way are
important because parameters derived from narrow-band photometry may be
affected by the strong metal lines in these stars. We analyse the Kepler
time series of ten known Am stars and find that six of them clearly show
$\delta$ Scuti pulsations. The other four appear to be non-pulsating. We
derive fundamental parameters for all known pulsating Am stars from ground-based
observations and also for the Kepler Am stars to investigate the location
of the instability strip for pulsating Am stars. We find that there is not much
difference between the Am-star instability strip and the $\delta$ Scuti
instability strip. We find that the observed location of pulsating Am
stars in the HR diagram does not agree with the location predicted from
recent diffusion calculations.
Kepler observations of variability in B-type stars
The analysis of the light curves of 48 B-type stars observed by Kepler is presented. Among these are 15 pulsating stars, all of which show low frequencies characteristic of SPB stars. Seven of these stars also show a few weak, isolated high frequencies and they could be considered as SPB/$\beta$ Cep hybrids. In all cases the frequency spectra are quite different from what is seen from ground-based observations. We suggest that this is because most of the low frequencies are modes of high degree which are predicted to be unstable in models of mid-B stars. We find that there are non-pulsating stars within the $\beta$ Cep and SPB instability strips. Apart from the pulsating stars, we can identify stars with frequency groupings similar to what is seen in Be stars but which are not Be stars. The origin of the groupings is not clear but may be related to rotation. We find periodic variations in other stars which we attribute to proximity effects in binary systems. The variations in other stars can be understood as proximity effects in a binary system or possibly rotational modulation. We find no evidence for pulsating stars between the cool edge of the SPB and the hot edge of the $\delta$ Sct instability strips. None of the stars show the broad features which can be attributed to stochastically-excited modes as recently proposed. Among our sample of B stars are two chemically peculiar stars, one of which is a HgMn star showing rotational modulation in the light curve.
Rotation and oblique pulsation in Kepler observations of the roAp star KIC 10483436
Photometry of KIC 10483436 was obtained continuously with 1-min exposures over a 27-d period from the Kepler satellite. The light curve shows rotational variations from surface spots with a period of $4.303 \pm 0.002$ d, an amplitude of about 6 mmag, and eight pulsation frequencies typical of roAp stars. The high frequency pattern consists of a quintuplet of equally spaced peaks where the frequency of the dominant central peak (68 $\mu$mag amplitude) is 1353.00 $\mu$Hz ($P = 12.32$ min). A second set of three peaks of lower amplitude is also visible. These appear to form part of a quintuplet centered on 1511.6 $\mu$Hz with the central peak and one side peak missing. The equidistant frequency spacing is 2.69 $\mu$Hz, which corresponds to the 4.303 d rotation period. However, the amplitudes (12 $\mu$mag) of these peaks are too close to the detection level to allow definite identification of the multiplets. Although no spectrum is available, the character of the pulsations shows that this is a roAp star with two high frequency modes modulated in amplitude in accordance with the oblique pulsator model. The 4.303-d variation in the light curve, which is interpreted as rotational modulation, shows harmonics as high as the 26$^{\rm th}$. These harmonics are probably a result of many patches of varying surface brightness associated with surface abundance variations characteristic of Ap stars.
The first evidence for multiple pulsation axes: a new roAp star in the Kepler field, KIC 10195926
We have discovered a new rapidly oscillating Ap star among the Kepler Mission target stars, KIC 10195926. This star shows two pulsation modes with periods that are amongst the longest known for roAp stars at 17.1 min and 18.1 min, indicating that the star is near the terminal age main sequence. The principal pulsation mode is an oblique dipole mode that shows a rotationally split frequency septuplet that provides information on the geometry of the mode. The secondary mode also appears to be a dipole mode with a rotationally split triplet, but we are able to show within the improved oblique pulsator model that these two modes cannot have the same axis of pulsation. This is the first time for any pulsating star that evidence has been found for separate pulsation axes for different modes. The two modes are separated in frequency by 55 $\mu$Hz, which we model as the large separation. The star is an $\alpha^2$ CVn spotted magnetic variable that shows a complex rotational light variation with a period of $P_{\rm rot} = 5.68459$ d. For the first time for any spotted magnetic star of the upper main sequence, we find clear evidence of light variation with a period of twice the rotation period; i.e. a subharmonic frequency of $\nu_{\rm rot}/2$. We propose that this and other subharmonics are the first observed manifestation of torsional modes in an roAp star. From high resolution spectra we determine $T_{\rm eff} = 7400$ K, $\log g = 3.6$ and $v \sin i = 21$ km s$^{-1}$. We have found a magnetic pulsation model with fundamental parameters close to these values that reproduces the rotational variations of the two obliquely pulsating modes with different pulsation axes. The star shows overabundances of the rare earth elements, but these are not as extreme as most other roAp stars. The spectrum is variable with rotation, indicating surface abundance patches.
Sounding open clusters: asteroseismic constraints from Kepler on the properties of NGC 6791 and NGC 6819
We present initial results on some of the properties of open clusters NGC 6791 and NGC 6819 derived from asteroseismic data obtained by NASA's Kepler mission. In addition to estimating the mass, radius and ogg of stars on the red-giant branch of these clusters, we estimate the distance to the clusters and their ages. Our model-independent estimate of the distance modulus of NGC 6791 is $(m-M)_0= 13.11\pm 0.06$. We find $(m-M)_0= 11.85\pm 0.05$ for NGC 6819. The average mass of stars on the red-giant branch of NGC 6791 is $1.20 \pm 0.01 M_\odot$, while that of NGC 6819 is $1.68\pm 0.03M_\odot$. It should be noted that we do not have data that cover the entire red-giant branch and the actual mass will be somewhat lower. We have determined model-dependent estimates of ages of these clusters. We find ages between 6.8 and 8.6 Gyr for NGC 6791, however, most sets of models give ages around 7Gyr. We obtain ages between 2 and 2.4 Gyr for NGC 6819.
Kepler observations of a roAp star: $\delta$ Scuti and $\gamma$ Doradus pulsations in Ap stars
Observations of the A5p star KIC 8677585 obtained during the Kepler 10-d commissioning run with 1-min time resolution show that it is a roAp star with several frequencies with periods near 10 min. In addition, a low frequency at $3.142 d^{-1}$ is also clearly present. Multiperiodic $\gamma$ Dor and $\delta$ Sct pulsations, never before seen in any Ap star, are present in Kepler observations of at least three other Ap stars. Since $\gamma$ Dor pulsations are seen in Ap stars, it is likely that the low-frequency in KIC 8677585 is also a $\gamma$ Dor pulsation. The simultaneous presence of both $\gamma$ Dor and roAp pulsations and the unexpected detection of $\delta$ Sct and $\gamma$ Dor pulsations in Ap stars present new opportunities and challenges for the interpretation of these stars.
Does Kepler unveil the mystery of the Blazhko effect? First detection of period doubling in Kepler Blazhko RR Lyrae stars
The first detection of the period doubling phenomenon is reported in the Kepler RR Lyrae stars RR Lyr, V808 Cyg and V355 Lyr. Interestingly, all these pulsating stars show Blazhko modulation. The period doubling manifests itself as alternating maxima and minima of the pulsational cycles in the light curve, as well as through the appearance of half-integer frequencies located halfway between the main pulsation period and its harmonics in the frequency spectrum. The effect was found to be stronger during certain phases of the modulation cycle. We were able to reproduce the period doubling bifurcation in our nonlinear RR Lyrae models computed by the Florida-Budapest hydrocode. This enabled us to trace the origin of this instability in RR Lyrae stars to a resonance, namely a 9:2 resonance between the fundamental mode and a high-order (9th) radial overtone showing strange mode characteristics. We discuss the connection of this new type of variation to the mysterious Blazhko effect and argue that it may give us fresh insights to solve this century-old enigma.
Asteroseismology of Red Giants from the first four months of Kepler data: Global oscillation parameters for 800 stars
We studied solar-like oscillations in $\sim$800 red-giant stars using Kepler long-cadence photometry. The sample includes stars ranging in evolution from the lower part of the red-giant branch to the Helium main sequence. We investigate the relation between the large frequency separation ($\Delta\nu$) and the frequency of maximum power ($\nu_\mathrm{max}$) and show that it is different for red giants than for main-sequence stars, which is consistent with evolutionary models and scaling relations. The distributions of $\nu_\mathrm{max}$ and $\Delta\nu$ are in qualitative agreement with a simple stellar population model of the Kepler field, including first evidence for a secondary clump population characterized by $M\gtrsim2\,M_{\odot}$ and $\nu_\mathrm{max}\simeq40-110\,\mu\mathrm{Hz}$. We measured the small frequency separations $\delta\nu_{02}$ and $\delta\nu_{01}$ in over 400 red giants and $\delta\nu_{03}$ in over 40 stars. We present C-D diagrams for $l=1$, 2 and 3 and show that the frequency separation ratios $\delta\nu_{02}/\Delta\nu$ and $\delta\nu_{01}/\Delta\nu$ have opposite trends as a function of $\Delta\nu$. The data show a narrowing of the $l=1$ ridge towards lower $\nu_\mathrm{max}$, in agreement with models predicting more efficient mode trapping in stars with higher luminosity. We investigate the offset $\epsilon$ in the asymptotic relation and find a clear correlation with $\Delta\nu$, demonstrating that it is related to fundamental stellar parameters. Finally, we present first results for the amplitude-$\nu_\mathrm{max}$ relation for Kepler red giants. We observe a lack of low amplitude stars for $\nu_\mathrm{max}\gtrsim110\,\mu\mathrm{Hz}$, and find that for a given $\nu_\mathrm{max}$ between $40-110\,\mu\mathrm{Hz}$ stars with lower $\Delta\nu$ (and consequently higher mass) tend to show lower amplitudes than stars with higher $\Delta\nu$.
A precise asteroseismic age and radius for the evolved Sun-like star KIC 11026764
The primary science goal of the Kepler Mission is to provide a census of exoplanets in the solar neighborhood, including the identification and characterization of habitable Earth-like planets. The asteroseismic capabilities of the mission are being used to determine precise radii and ages for the target stars from their solar-like oscillations. Chaplin et al. (2010) published observations of three bright G-type stars, which were monitored during the first 33.5 d of science operations. One of these stars, the subgiant KIC 11026764, exhibits a characteristic pattern of oscillation frequencies suggesting that it has evolved significantly. We have derived asteroseismic estimates of the properties of KIC 11026764 from Kepler photometry combined with ground-based spectroscopic data. We present the results of detailed modeling for this star, employing a variety of independent codes and analyses that attempt to match the asteroseismic and spectroscopic constraints simultaneously. We determine both the radius and the age of KIC 11026764 with a precision near 1%, and an accuracy near 2% for the radius and 15% for the age. Continued observations of this star promise to reveal additional oscillation frequencies that will further improve the determination of its fundamental properties.
Asteroseismology of red giants from the first four months of Kepler data: Fundamental stellar parameters
Context: Clear power excess in a frequency range typical for solar-type oscillations in red giants has been detected in more than 1000 stars, which have been observed during the first 138 days of science operation of the NASA Kepler satellite. The sample includes stars in a large mass and radius range with spectral type G and K, extending in luminosity from the bottom of the giant branch up to high-luminous red giants including the red bump and clump. The high-precision asteroseismic observations with Kepler provide a perfect source for testing stellar structure and evolutionary models as well as investigating the stellar population in our Galaxy.
Aims: We aim to extract accurate seismic parameters from the Kepler time series and use them to infer asteroseismic fundamental parameters from scaling relations and a comparison with red-giant models.
Methods: We fit a global model to the observed power density spectra which allows us to accurately estimate the granulation background signal and the global oscillation parameters, such as the frequency of maximum oscillation power. We find regular patterns of radial and non-radial oscillation modes and use a new technique to automatically identify the mode degree and the characteristic frequency separations between consecutive modes of the same spherical degree. In most cases we can also measure the small separation between $\ell$ = 0, 1, and 2 modes. Subsequently, the seismic parameters are used to estimate stellar masses and radii and to place the
stars in a H-R diagram by using an extensive grid of stellar models that covers a large parameter range. Using Bayesian techniques throughout our entire analysis allows us to determine reliable uncertainties for all parameters.
Results: We provide accurate seismic parameters and their uncertainties for a large sample of red giants and determine their asteroseismic fundamental parameters. We investigate the influence of the stars’ metallicities on their positions in the H-R diagram. Finally, we study the red-giant populations in the red clump and bump and compare them to a synthetic population. We find a mass and metallicity gradient in the red clump and clear evidence for a secondary-clump population.
Flavours of variability: 29 RR Lyrae stars observed with Kepler
We present our analysis of Kepler observations of 29 RR Lyrae stars, based on 138-d of observation. We report precise pulsation periods for all stars. Nine of these stars had incorrect or unknown periods in the literature. Fourteen of the stars exhibit both amplitude and phase Blazhko modulations, with Blazhko periods ranging from 27.7 to more than 200 days. For V445 Lyr, a longer secondary variation is also observed in addition to its 53.2-d Blazhko period. The unprecedented precision of the Kepler photometry has led to the discovery of the the smallest modulations detected so far. Moreover, additional frequencies beyond the well-known harmonics and Blazhko multiplets have been found. These frequencies are located around the half-integer multiples of the main pulsation frequency for at least three stars. In four stars, these frequencies are close to the first and/or second overtone modes. The amplitudes of these periodicities seem to vary over the Blazhko cycle. V350 Lyr, a non-Blazhko star in our sample, is the first example of a double mode RR Lyrae star that pulsates in its fundamental and second overtone modes.
Detection of Solar-like Oscillations from Kepler Photometry of the Open Cluster NGC 6819
Asteroseismology of stars in clusters has been a long-sought goal because the assumption of a common age, distance, and initial chemical composition allows strong tests of the theory of stellar evolution. We report results from the first 34 days of science data from the Kepler Mission for the open cluster NGC 6819 - one of the four clusters in the field of view. We obtain the first clear detections of solar-like oscillations in the cluster red giants and are able to measure the large frequency separation, $\Delta\nu$, and the frequency of maximum oscillation power, $\nu_\mathrm{max}$. We find that the asteroseismic parameters allow us to test cluster membership of the stars, and even with the limited seismic data in hand, we can already identify four possible non-members despite their having a better than 80% membership probability from radial velocity measurements. We are also able to determine the oscillation amplitudes for stars that span about 2 orders of magnitude in luminosity and find good agreement with the prediction that oscillation amplitudes scale as the luminosity to the power of 0.7. These early results demonstrate the unique potential of asteroseismology of the stellar clusters observed by Kepler.
First Kepler results on RR Lyrae stars
We present the first results of our analyses of selected RR Lyrae stars for which data have been obtained by the Kepler Mission. As expected, we find a significant fraction of the RRab stars to show the Blazhko effect, a still unexplained phenomenon that manifests itself as periodic amplitude and phase modulations of the light curve, on timescales of typically tens to hundreds of days. The long time span of the Kepler Mission of 3.5 yr and the unprecedentedly high precision of its data provide a unique opportunity for the study of RR Lyrae stars. Using data of a modulated star observed in the first roll as a showcase, we discuss the data, our analyses, findings, and their implications for our understanding of RR Lyrae stars and the Blazhko effect. With at least 40% of the RR Lyrae stars in our sample showing modulation, we confirm the high incidence rate that was only found in recent high-precision studies. Moreover, we report the occurrence of additional frequencies, beyond the main pulsation mode and its modulation components. Their half-integer ratio to the main frequency is reminiscent of a period doubling effect caused by resonances, observed for the first time in RR Lyrae stars.
Solar-like oscillations in low-luminosity red giants: first results from Kepler
We have measured solar-like oscillations in red giants using time-series photometry from the first 34 days of science operations of the Kepler Mission. The light curves, obtained with 30-minute sampling, reveal clear oscillations in a large sample of G and K giants, extending in luminosity from the red clump down to the bottom of the giant branch. We confirm a strong correlation between the large separation of the oscillations ($\Delta \nu$) and the frequency of maximum power ($\nu_{\rm max}$). We focus on a sample of 50 low-luminosity stars ($\nu_{\rm max} > 100\,\mu$Hz, $L \lesssim 30\,L_\odot$) having high signal-to-noise ratios and showing the unambiguous signature of solar-like oscillations. These are H-shell-burning stars, whose oscillations should be valuable for testing models of stellar evolution and for constraining the star-formation rate in the local disk. We use a new technique to compare stars on a single échelle diagram by scaling their frequencies and find well-defined ridges corresponding to radial and non-radial oscillations, including clear evidence for modes with angular degree $l=3$. Measuring the small separation between $l=0$ and $l=2$ allows us to plot the so-called C-D diagram of $\delta\nu_{02}$ versus $\Delta \nu$. The small separation $\delta\nu_{01}$ of $l=1$ from the midpoint of adjacent $l=0$ modes is negative, contrary to the Sun and solar-type stars. The ridge for $l=1$ is notably broadened, which we attribute to mixed modes, confirming theoretical predictions for low-luminosity giants. Overall, the results demonstrate the tremendous potential of Kepler data for asteroseismology of red giants.
Hybrid γ Doradus-δ Scuti Pulsators: New Insights into the Physics of the Oscillations from Kepler Observations
Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main-sequence γ Doradus (Dor) and δ Scuti (Sct) stars with masses 1.2-2.5 M sun are particularly useful for these studies. The γ Dor stars pulsate in high-order g-modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The δ Sct stars pulsate in low-order g- and p-modes with periods of order 2 hr, driven by the κ mechanism operating in the He II ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where "hybrid" stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known γ Dor and δ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure δ Sct or γ Dor pulsators, i.e., essentially all of the stars show frequencies in both the δ Sct and the γ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency and is applied to categorize 234 stars as δ Sct, γ Dor, δ Sct/γ Dor or γ Dor/δ Sct hybrids.
The asteroseismic potential of Kepler: first results for solar-type stars
We present preliminary asteroseismic results from Kepler on three G-type stars. The observations, made at one-minute cadence during the first 33.5 d of science operations, reveal high signal-to-noise solar-like oscillation spectra in all three stars: About 20 modes of oscillation may be clearly distinguished in each star. We discuss the appearance of the oscillation spectra, use the frequencies and frequency separations to provide first results on the radii, masses and ages of the stars, and comment in the light of these results on prospects for inference on other solar-type stars that Kepler will observe.