Peakbagging the K2 KEYSTONE sample with PBjam: characterising the individual mode frequencies in solar-like oscillators

The availability of asteroseismic constraints for a large sample of stars from the missions CoRoT and Kepler paves the way for various statistical studies of the seismic properties of stellar populations. In this paper, we evaluate the impact of rotation-induced mixing and thermohaline instability on the global asteroseismic parameters at different stages of the stellar evolution from the Zero Age Main Sequence to the Thermally Pulsating Asymptotic Giant Branch to distinguish stellar populations. We present a grid of stellar evolutionary models for four metallicities (Z = 0.0001, 0.002, 0.004, and 0.014) in the mass range between 0.85 to 6.0 Msun. The models are computed either with standard prescriptions or including both thermohaline convection and rotation-induced mixing. For the whole grid we provide the usual stellar parameters (luminosity, effective temperature, lifetimes, ...), together with the global seismic parameters, i.e. the large frequency separation and asymptotic relations, the frequency corresponding to the maximum oscillation power {\nu}_{max}, the maximal amplitude A_{max}, the asymptotic period spacing of g-modes, and different acoustic radii. We discuss the signature of rotation-induced mixing on the global asteroseismic quantities, that can be detected observationally. Thermohaline mixing whose effects can be identified by spectroscopic studies cannot be caracterized with the global seismic parameters studied here. But it is not excluded that individual mode frequencies or other well chosen asteroseismic quantities might help constraining this mixing.

Since the advent of CoRoT, and NASA Kepler and K2, the number of low- and intermediate-mass stars classified as pulsators has increased very rapidly with time, now accounting for several $10^4$ targets. With the recent launch of NASA TESS space mission, we have confirmed our entrance to the era of all-sky observations of oscillating stars. TESS is currently releasing good quality datasets that already allow for the characterization and identification of individual oscillation modes even from single 27-days shots on some stars. When ESA PLATO will become operative by the next decade, we will face the observation of several more hundred thousands stars where identifying individual oscillation modes will be possible. However, estimating the individual frequency, amplitude, and lifetime of the oscillation modes is not an easy task. This is because solar-like oscillations and especially their evolved version, the red giant branch (RGB) oscillations, can vary significantly from one star to another depending on its specific stage of the evolution, mass, effective temperature, metallicity, as well as on its level of rotation and magnetism. In this perspective I will present a novel, fast, and powerful way to derive individual oscillation mode frequencies by building on previous results obtained with \diamonds. I will show that the oscillation frequencies obtained with this new approach can reach precisions of about 0.1 % and accuracies of about 0.01 % when compared to published literature values for the RGB star KIC~12008916.

Context. Metal-poor stars play a crucial role in understanding the nature and evolution of the first stellar generation in the Galaxy. Previously, asteroseismic characterisation of red-giant stars has relied on constraints from the global asteroseismic parameters and not the full spectrum of individual oscillation modes. Using the latter, we present for the first time the characterisation of two evolved very metal-poor stars including the detail-rich mixed-mode patterns. Aims. We will demonstrate that incorporating individual frequencies into grid-based modelling of red-giant stars enhances its precision, enabling detailed studies of these ancient stars and allowing us to infer the stellar properties of two very metal-poor [Fe/H] ∼ −2.5 dex Kepler stars: KIC 4671239 and KIC 7693833. Methods. Recent developments in both observational and theoretical asteroseismology have allowed for detailed studies of the complex oscillation pattern of evolved giants. In this work, we employ Kepler timeseries and surface properties from high-resolution spectroscopic data within a grid-based modelling approach to asteroseismically characterise KIC 4671239 and KIC 7693833 using the BAyesian STellar Algorithm, BASTA. Results. Both stars show agreement between constraints from seismic and classical observables, an overlap unrecoverable when purely considering the global asteroseismic parameters. KIC 4671239 and KIC 7693833 were determined to have masses of 0.78−0.03+0.04 and 0.83−0.01+0.03 M⊙ with ages of 12.1−1.5+1.6 and 10.3−1.4+0.6 Gyr, respectively. Particularly, for KIC 4671239 the rich spectrum of model frequencies closely matches the observed. Conclusions. A discrepancy between the observed and modelled νmax of ∼10% was found, indicating a metallicity dependence of the νmax scaling relation. For metal-poor populations, this results in overestimations of the stellar masses and wrongful age inferences. Utilising the full spectra of individual oscillation modes lets us circumvent the dependence on the asteroseismic scaling relations through direct constraints on the stars themselves. This allows us to push the boundaries of state-of-the-art detailed modelling of evolved stars at metallicities far different from solar.

Binary stars in which oscillations can be studied in either or both components can provide powerful constraints on our understanding of stellar physics. The bright binary 12 Boötis (12 Boo) is a particularly promising system because the primary is roughly 60 per cent brighter than the secondary despite being only a few per cent more massive. Both stars have substantial surface convection zones and are therefore, presumably, solar-like oscillators. We report here the first detection of solar-like oscillations and ellipsoidal variations in the TESS light curve of 12 Boo. Though the solar-like oscillations are not clear enough to unambiguously measure individual mode frequencies, we combine global asteroseismic parameters and a precise fit to the spectral energy distribution (SED) to provide new constraints on the properties of the system that are several times more precise than values in the literature. The SED fit alone provides new effective temperatures, luminosities, and radii of $6115\pm 45\, \mathrm{K}$, $7.531\pm 0.110\, \mathrm{L}_\odot$, and $2.450\pm 0.045\, \mathrm{R}_\odot$ for 12 Boo A and $6200\pm 60\, \mathrm{K}$, $4.692\pm 0.095\, \mathrm{L}_\odot$, and $1.901\pm 0.045\, \mathrm{R}_\odot$ for 12 Boo B. When combined with our asteroseismic constraints on 12 Boo A, we obtain an age of $2.67^{+0.12}_{-0.16}\, \mathrm{Gyr}$, which is consistent with that of 12 Boo B.

Individual mode frequencies have been detected in thousands of individual solar-like oscillators on the red giant branch (RGB). Fitting stellar models to these mode frequencies, however, is more difficult than in main-sequence stars. This is partly because of the uncertain magnitude of the surface effect: the systematic difference between observed and modelled frequencies caused by poor modelling of the near-surface layers. We aim to study the magnitude of the surface effect in RGB stars. Surface effect corrections used for main-sequence targets are potentially large enough to put the non-radial mixed modes in RGB stars out of order, which is unphysical. Unless this can be circumvented, model-fitting of evolved RGB stars is restricted to the radial modes, which reduces the number of available modes. Here, we present a method to suppress gravity modes (g-modes) in the cores of our stellar models, so that they have only pure pressure modes (p-modes). We show that the method gives unbiased results and apply it to three RGB solar-like oscillators in double-lined eclipsing binaries: KIC 8410637, KIC 9540226 and KIC 5640750. In all three stars, the surface effect decreases the model frequencies consistently by about 0.1--0.3 $\mu$Hz at the frequency of maximum oscillation power $\nu_\mathrm{max}$, which agrees with existing predictions from three-dimensional radiation hydrodynamics simulations. Though our method in essence discards information about the stellar cores, it provides a useful step forward in understanding the surface effect in RGB stars.

Aims.In this work, we determine the expected yield of detections of solar-like oscillations for the targets of the foreseen PLATO ESA mission. Our estimates are based on a study of the detection probability, which takes into account the properties of the target stars, using the information available in the PIC 1.1.0, including the current best estimate of the signal-to-noise ratio (S/N). The stellar samples, as defined for this mission, include those with the lowest noise level (P1 and P2 samples) and the P5 sample, which has a higher noise level. For the P1 and P2 samples, the S/N is high enough (by construction) that we can assume that the individual mode frequencies can be measured. For these stars, we estimate the expected uncertainties in mass, radius, and age due to statistical errors induced by uncertainties from the observations only.Methods.We used a formulation from the literature to calculate the detection probability. We validated this formulation and the underlying assumptions withKeplerdata. Once validated, we applied this approach to the PLATO samples. Using againKeplerdata as a calibration set, we also derived relations to estimate the uncertainties of seismically inferred stellar mass, radius, and age. We then applied those relations to the main sequence stars with masses equal to or below 1.2M⊙belonging to the PLATO P1 and P2 samples and for which we predict a positive seismic detection.Results.We found that we can expect positive detections of solar-like oscillations for more than 15 000 FGK stars in one single field after a two-year observation run. Among them, 1131 main sequence stars with masses of ≤1.2 M⊙satisfy the PLATO requirements for the uncertainties of the seismically inferred stellar masses, radii, and ages. The baseline observation programme of PLATO consists of observing two fields of similar size (one in the southern hemisphere and one in the northern hemisphere) for two years apiece. Accordingly, the expected seismic yields of the mission amount to over 30 000 FGK dwarfs and subgiants, with positive detections of solar-like oscillations. This sample of expected solar-like oscillating stars is large enough to enable the PLATO mission’s stellar objectives to be amply satisfied.Conclusions.The PLATO mission is expected to produce a catalog sample of extremely well seismically characterized stars of a quality that is equivalent to theKeplerLegacy sample, but containing a number that is about 80 times greater, when observing two PLATO fields for two years apiece. These stars are a gold mine that will make it possible to make significant advances in stellar modelling.

Asteroseismology provides a powerful way to constrain stellar parameters. Solar-like oscillations have been observed on subgiant stars with the \emph{Kepler\/} mission. The continuous and high-precision time series enables us to carry out a detailed asteroseismic study for these stars. We carry out data processing of two subgiants of spectral type G: KIC 6442183 and KIC 11137075 observed with the \emph{Kepler} mission, and perform seismic analysis for the two evolved stars. We estimate the values of global asteroseismic parameters: $\Delta\nu=64.9\pm 0.2 $ $\mu$Hz and $\nu_{\rm max}=1225 \pm 17$ $\mu$Hz for KIC 6442183, $\Delta\nu=65.5\pm 0.2 $ $\mu$Hz and $\nu_{\rm max}=1171 \pm 8$ $\mu$Hz for KIC 11137075, respectively. In addition, we extract the individual mode frequencies of the two stars. We compare stellar models and observations, including mode frequencies and mode inertias. The mode inertias of mixed modes, which are sensitive to the stellar interior, are used to constrain stellar models. We define a quantity $d\nu_{\rm m-p}$ that measures the difference between the mixed modes and the expected pure pressure modes, which is related to the inertia ratio of mixed modes to radial modes. Asteroseismic together with spectroscopic constraints provide the estimations of the stellar parameters: $M = 1.04_{-0.04}^{+0.01} M_{\odot}$, $R = 1.66_{-0.02}^{+0.01} R_{\odot}$ and $t=8.65_{-0.06}^{+1.12}$ Gyr for KIC 6442183, and $M = 1.00_{-0.01}^{+0.01} M_{\odot}$, $R = 1.63_{-0.01}^{+0.01} R_{\odot}$ and $t=10.36_{-0.20}^{+0.01}$ Gyr for KIC 11137075. Either mode inertias or $d\nu_{\rm m-p}$ could be used to constrain stellar models.

Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modeling error near the surface. This asteroseismic “surface term” must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit 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 description, they cannot be applied to subgiants directly. In Paper I, we generalized 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. Here, we apply those results, modeling 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. While these systematics are smaller than those resulting from other choices of model construction, they persist 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 modeling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from those of both main-sequence and red giant stars.

We present the asteroseismic analysis of 1948 F-, G- and K-type main-sequence and subgiant stars observed by the National Aeronautics and Space Administration Kepler mission. We detect and characterize 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 Catalogue and find a deficiency for stars with effective temperatures in the range 5300 ≲Teff≲ 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, νmax, the mean large frequency separation, Δν, and the maximum mode amplitude, Amax, 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.

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 benchmark 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 ± 11 pc, or mag, an average red giant mass of , in agreement with the dynamical mass from an eclipsing binary near the cluster turn-off, and ages of individual stars compatible with isochrone fitting. We see no evidence of strong mass loss on the red giant branch. We also determine seismic of all the cluster giants with a typical precision of dex. 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.

The preliminary results of an analysis of the red giant star KIC 5701829 observed for 29 days in short-cadence mode with theKeplersatellite are reported. The oscillation spectrum of this star is characterized by the presence of a well-defined solar-like oscillation pattern due to acoustic modes. The characterization of the power spectrum has been performed following three basics steps commonly used in the analysis of solar-like oscillations: fitting and correcting for the background, estimating the frequency of maximum power (νmax) and the large separation (Δν), and extracting individual frequencies. We have found that the frequency of maximum oscillation power, νmax, and the mean large frequency separation, Δν, are around, 143 and 12 μHz, respectively. The global asteroseismic parameters along with atmospheric parameters from the literature allow us to infer about evolutionary status of the star.

The Transiting Exoplanet Survey Satellite (TESS) is performing a near all-sky survey for planets that transit bright stars. In addition, its excellent photometric precision enables asteroseismology of solar-type and red-giant stars, which exhibit convection-driven, solar-like oscillations. Simulations predict that TESS will detect solar-like oscillations in nearly 100 stars already known to host planets. In this paper, we present an asteroseismic analysis of the known red-giant host stars HD 212771 and HD 203949, both systems having a long-period planet detected through radial velocities. These are the first detections of oscillations in previously known exoplanet-host stars by TESS, further showcasing the mission’s potential to conduct asteroseismology of red-giant stars. We estimate the fundamental properties of both stars through a grid-based modeling approach that uses global asteroseismic parameters as input. We discuss the evolutionary state of HD 203949 in depth and note the large discrepancy between its asteroseismic mass (M * = 1.23 ± 0.15 M ⊙ if on the red-giant branch or M * = 1.00 ± 0.16 M ⊙ if in the clump) and the mass quoted in the discovery paper (M * = 2.1 ± 0.1 M ⊙), implying a change >30% in the planet’s mass. Assuming HD 203949 to be in the clump, we investigate the planet’s past orbital evolution and discuss how it could have avoided engulfment at the tip of the red-giant branch. Finally, HD 212771 was observed by K2 during its Campaign 3, thus allowing for a preliminary comparison of the asteroseismic performances of TESS and K2. We estimate the ratio of the observed oscillation amplitudes for this star to be , consistent with the expected ratio of ∼0.85 due to the redder bandpass of TESS.

Asteroseismology of solar-like oscillators often relies on the comparisons between stellar models and stellar observations in order to determine the properties of stars. The values of the global seismic parameters, ν max (the frequency where the smoothed amplitude of the oscillations peak) and Δν (the large frequency separation), are frequently used in grid-based modeling searches. However, the methods by which Δν is calculated from observed data and how Δν is calculated from stellar models are not the same. Typically for observed stars, especially for those with low signal-to-noise data, Δν is calculated by taking the power spectrum of a power spectrum, or with autocorrelation techniques. However, for stellar models, the actual individual mode frequencies are calculated and the average spacing between them directly determined. In this work we try to determine the best way to combine model frequencies in order to obtain Δν that can be compared with observations. For this we use stars with high signal-to-noise observations from Kepler as well as simulated Transiting Exoplanet Survey Satellite data of Ball et al. We find that when determining Δν from individual mode frequencies the best method is to use the ℓ = 0 modes with either no weighting or with a Gaussian weighting around ν max.

Nearly all cool, evolved stars are solar-like oscillators, and fundamental stellar properties can be inferred from these oscillations with asteroseismology. Scaling relations are commonly used to relate global asteroseismic properties—the frequency of maximum power ν max and the large-frequency separation Δν—to stellar properties. Mass, radius, and age can then be inferred with the addition of stellar spectroscopy. There is excellent agreement between seismic radii and fundamental data on the lower red giant branch and red clump. However, the scaling relations appear to breakdown in luminous red-giant stars. We attempt to constrain the contributions of the asteroseismic parameters to the observed breakdown. We test the ν max and Δν scaling relations separately, by using stars of known mass and radius in star clusters and the Milky Way's high-α sequence. We find evidence that the Δν scaling relation contributes to the observed breakdown in luminous giants more than the ν max relation. We test different methods of mapping the observed Δν to the mean density via a correction factor, F Δν , and find a ≈ 1%–3% difference in the radii in the luminous giant regime, depending on the technique used to measure F Δν . The differences between the radii inferred by these two techniques are too small on the luminous giant branch to account for the inflated seismic radii observed in evolved giant stars. Finally, we find that the F Δν correction is insensitive to the adopted mixing length, chosen by calibrating the models to observations of T eff .

Space-based observations of solar-like oscillations present an opportunity to constrain stellar models using individual mode frequencies. However, current stellar models are inaccurate near the surface, which introduces a systematic difference that must be corrected. We introduce and evaluate two parametrizations of the surface corrections based on formulae given by Gough (1990). The first we call a cubic term proportional to $\nu^3/\mathcal{I}$ and the second has an additional inverse term proportional to $\nu^{-1}/\mathcal{I}$, where $\nu$ and $\mathcal{I}$ are the frequency and inertia of an oscillation mode. We first show that these formulae accurately correct model frequencies of two different solar models ... We then incorporate the parametrizations into a modelling pipeline that simultaneously fits the surface effects and the underlying stellar model parameters. We apply this pipeline to synthetic observations of a Sun-like stellar model, solar observations degraded to typical asteroseismic uncertainties, and observations of the well-studied CoRoT target HD52265. For comparison, we also run the pipeline with the scaled power-law correction proposed by Kjeldsen et al. (2008). The fits to synthetic and degraded solar data show that the method is unbiased and produces best-fit parameters that are consistent with the input models and known parameters of the Sun. Our results for HD52265 are consistent with previous modelling efforts and the magnitude of the surface correction is similar to that of the Sun. The fit using a scaled power-law correction is significantly worse but yields consistent parameters ... We find that the cubic term alone is suitable for asteroseismic applications and it is easy to implement in an existing pipeline. ... This parametrization is thus a useful new way to correct model frequencies so that observations of individual mode frequencies can be exploited.