Asteroseismic Scaling Relations Research Articles

Flow-based Generative Emulation of Grids of Stellar Evolutionary Models

We present a flow-based generative approach to emulate grids of stellar evolutionary models. By interpreting the input parameters and output properties of these models as multidimensional probability distributions, we train conditional normalizing flows to learn and predict the complex relationships between grid inputs and outputs in the form of conditional joint distributions. Leveraging the expressive power and versatility of these flows, we showcase their ability to emulate a variety of evolutionary tracks and isochrones across a continuous range of input parameters. In addition, we describe a simple Bayesian approach for estimating stellar parameters using these flows and demonstrate its application to asteroseismic data sets of red giants observed by the Kepler mission. By applying this approach to red giants in open clusters NGC 6791 and NGC 6819, we illustrate how large age uncertainties can arise when fitting only to global asteroseismic and spectroscopic parameters without prior information on initial helium abundances and mixing length parameter values. We also conduct inference using the flow at a large scale by determining revised estimates of masses and radii for 15,388 field red giants. These estimates show improved agreement with results from existing grid-based modeling, reveal distinct population-level features in the red clump, and suggest that the masses of Kepler red giants previously determined using the corrected asteroseismic scaling relations have been overestimated by 5%–10%.

Benchmarking the spectroscopic masses of 249 evolved stars using asteroseismology with TESS

Abstract One way to understand planet formation is through studying the correlations between planet occurrence rates and stellar mass. However, measuring stellar mass in the red giant regime is very difficult. In particular, the spectroscopic masses of certain evolved stars, often referred to as ”retired A-stars”, have been questioned in the literature. Efforts to resolve this mass controversy using spectroscopy, interferometry and asteroseismology have so far been inconclusive. A recent ensemble study found a mass-dependent mass offset, but the result was based on only 16 stars. With NASA’s Transiting Exoplanet Survey Satellite (TESS), we expand the investigation of the mass discrepancy to a total of 92 low-luminosity stars, synonymous with the retired A-stars. We measure their characteristic oscillation frequency, νmax, and the large frequency separation, Δν, from their TESS photometric time series. Using these measurements and asteroseismic scaling relations, we derive asteroseismic masses and compare them with spectroscopic masses from five surveys, to comprehensively study the alleged mass-dependent mass offset. We find a mass offset between spectroscopy and seismology that increases with stellar mass. However, we note that adopting the seismic mass scale does not have a significant effect on the planet occurrence-mass-metallicity correlation for the so-called retired A-stars. We also report seismic measurements and masses for 157 higher luminosity giants (mostly helium-core-burning) from the spectroscopic surveys.

Testing the asteroseismic estimates of stellar radii with surface brightness-colour relations and Gaia DR3 parallaxes. Red giants and red clump stars

We compared stellar radii derived from asteroseismic scaling relations with those estimated using two independent surface brightness-colour relations (SBCRs) combined with Gaia DR3 parallaxes. We cross-matched asteroseismic and astrometric data for over 6,400 red giant branch (RGB) and red clump (RC) stars from the APO-K2 catalogue with the TESS Input Catalogue v8.2 to obtain precise $V$ band magnitudes and $E(B-V)$ colour excesses. We then adopted two different SBCRs from the literature to derive stellar radius estimates, denoted as $R^a$ and $R^b$, respectively. We analysed the ratio of these SBCR-derived radii to the asteroseismic radius estimates, $R,$ provided in the APO-K2 catalogue. Both SBCRs exhibited good agreement with asteroseismic radius estimates. On average, $R^a$ was overestimated by 1.2<!PCT!> with respect to $R$, while $R^b$ was underestimated by 2.5<!PCT!>. For stars larger than 20 $R_ sun $, SBCR radii are systematically lower than asteroseismic ones. The dispersion in the radius ratio was similar for the two methods (around 10<!PCT!>). The agreement with asteroseismic radii shows a strong dependence on the parallax. The dispersion is halved for stars with a parallax greater than 2.5 mas. In this subsample, $R^b$ showed perfect agreement with $R$, while $R^a$ remained slightly overestimated, by 3<!PCT!>. A trend with Fe/H was found at a level of 4<!PCT!> to 6<!PCT!> per dex. Additionally, a clear trend with asteroseismic mass is found. For stars less massive than about 0.95 $M_ sun $, SBCR radii were significantly higher than asteroseismic ones, by about 6<!PCT!>. This overestimation correlated with the presence of extended helium cores in these stars' structures relative to their envelopes. Furthermore, radius ratios showed a dichotomous behaviour at higher masses, mainly due to the presence of several RC stars with SBCR radii significantly lower with respect to asteroseismology. This behaviour originates from a different response of asteroseismic scaling relations and SBCR to alpha /Fe abundance ratios for massive stars, both in RGB and RC phases, which is reported here for the first time.

Asteroseismology of evolved stars in six star clusters observed by Kepler/K2

In this study, we have explored the frequency separations, Δν and δν02, the height and width of the oscillation power excess, HGauss and δνenv, as a function of the frequency of maximum power νmax by analyzing 187 evolved stars in six star clusters observed by the Kepler/K2 missions. We have also examined the asteroseismic relation in the Christensen-Dalsgaard diagram. Given the importance of scaling relations, the dependency of asteroseismic scaling relations on physical quantities must be verified to reduce systematic errors through the exploration of observational data obtained from various sources. In this context, the star cluster provides a valuable means to assess the age and metallicity. Focusing on evolved stars with 30μHz<νmax<220μHz, we have exploited the mass effect without the need for deriving the individual stellar mass. We have found that the considered relations appear to be associated with the age of star clusters, thereby the mass of the stars in a given evolutionary status for star clusters with different ages. By separately considering red giant branch stars and red clump stars, we have found that red clump stars appear more sensitive to the cluster age compared with red giant branch stars. It has been suggested that conclusions regarding the dependency of metallicity should be drawn with due care as outcomes are subject to how to treat metallicity. Finally, we conclude by briefly pointing out implications of our findings on asteroseismic inferences.

Stellar population astrophysics with the TNG

Context. Asteroseismology, a powerful approach for obtaining internal structure and stellar properties, requires surface temperature and chemical composition information to determine mass and age. High-resolution spectroscopy is a valuable technique for precise stellar parameters (including surface temperature) and for an analysis of the chemical composition. Aims. We combine spectroscopic parameters with asteroseismology to test stellar models. Methods. Using high-resolution optical and near-IR spectra from GIARPS at the Telescopio Nazionale Galileo, we conducted a detailed spectroscopic analysis of 16 stars that were photometrically selected to be on the red giant and red clump branch. Stellar parameters and chemical abundances for light elements (Li, C, N, and F), Fe peak, α and n-capture elements were derived using a combination of equivalent widths and spectral synthesis techniques based on atomic and molecular features. Ages were determined through asteroseismic scaling relations and were compared with ages based on chemical clocks, [Y/Mg] and [C/N]. Results. The spectroscopic parameters confirmed that the stars are part of the red giant branch and red clump. Two objects, HD 22045 and HD 24680, exhibit relatively high Li abundances, and HD 24680 might be a Li-rich giant resulting from mass transfer with an intermediate-mass companion that already underwent its asymptotic giant branch phase. The stellar parameters derived from scaling different sets of relations were consistent with each other. The values based on asteroseismology for the ages agree excellently with those derived from theoretical evolutionary tracks, but they disagree with ages derived from the chemical clocks [Y/Mg] and [C/N].

Does the νmax Scaling Relation Depend on Metallicity? Insights from 3D Convection Simulations

Solar-like oscillations have been detected in thousands of stars thanks to modern space missions. These oscillations have been used to measure stellar masses and ages, which have been widely applied in Galactic archeology. One of the pillars of such applications is the νmax scaling relation: the frequency of maximum power νmax , assumed to be proportional to the acoustic cutoff frequency, ν ac, scales with effective temperature and surface gravity. However, the theoretical basis of the νmax scaling relation is uncertain, and there is an ongoing debate about whether it can be applied to metal-poor stars. We investigate the metallicity dependence of the νmax scaling relation by carrying out 3D near-surface convection simulations for solar-type stars with [Fe/H] between −3 and 0.5 dex. First, we found a negative correlation between ν ac and metallicity from the 3D models. This is in tension with the positive correlation identified by studies using 1D models. Second, we estimated theoretical νmax values using velocity amplitudes determined from first principles, by quantifying the mode excitation and damping rates with methods validated in our previous works. We found that νmax does not show correlation with metallicity at solar effective temperature and surface gravity. This study opens an exciting prospect of testing the asteroseismic scaling relations against realistic 3D hydrodynamical stellar models.

The effect of the adiabatic assumption on asteroseismic scaling relations for luminous red giants

ABSTRACT Although stellar radii from asteroseismic scaling relations agree at the per cent level with independent estimates for main sequence and most first-ascent red giant branch (RGB) stars, the scaling relations over-predict radii at the tens of per cent level for the most luminous stars ($R \gtrsim 30 \, \mathrm{R}_{\odot }$). These evolved stars have significantly superadiabatic envelopes, and the extent of these regions increase with increasing radius. However, adiabaticity is assumed in the theoretical derivation of the scaling relations as well as in corrections to the large frequency separation. Here, we show that a part of the scaling relation radius inflation may arise from this assumption of adiabaticity. With a new reduction of Kepler asteroseismic data, we find that scaling relation radii and Gaia radii agree to within at least 2 per cent for stars with $R \lesssim 30\, \mathrm{R}_{\odot }$, when treated under the adiabatic assumption. The accuracy of scaling relation radii for stars with $50\, \mathrm{R}_{\odot }\lesssim R \lesssim 100\, \mathrm{R}_{\odot }$, however, is not better than $10~{{\ \rm per \, cent}}-15~{{\ \rm per \, cent}}$ using adiabatic large frequency separation corrections. We find that up to one third of this disagreement for stars with $R \approx 100\, \mathrm{R}_{\odot }$ could be caused by the adiabatic assumption, and that this adiabatic error increases with radius to reach 10 per cent at the tip of the RGB. We demonstrate that, unlike the solar case, the superadiabatic gradient remains large very deep in luminous stars. A large fraction of the acoustic cavity is also in the optically thin atmosphere. The observed discrepancies may therefore reflect the simplified treatment of convection and atmospheres.

A prescription for the asteroseismic surface correction

ABSTRACT In asteroseismology, the surface effect refers to a disparity between the observed and the modelled frequencies in stars with solar-like oscillations. It originates from improper modelling of the surface layers. Correcting the surface effect usually requires using functions with free parameters, which are conventionally fitted to the observed frequencies. On the basis that the correction should vary smoothly across the H–R diagram, we parameterize it as a simple function of surface gravity, effective temperature, and metallicity. We determine this function by fitting a wide range of stars. The absolute amount of the surface correction decreases with luminosity, but the ratio between it and νmax increases, suggesting the surface effect is more important for red giants than dwarfs. Applying the prescription can eliminate unrealistic surface correction, which improves parameter estimations with stellar modelling. Using two open clusters, we found a reduction of scatter in the model-derived ages for each star in the same cluster. As an important application, we provide a new revision for the Δν scaling relation that, for the first time, accounts for the surface correction. The values of the correction factor, fΔν, are up to 2 per cent smaller than those determined without the surface effect considered, suggesting decreases of up to 4 per cent in radii and up to 8 per cent in masses when using the asteroseismic scaling relations. This revision brings the asteroseismic properties into an agreement with those determined from eclipsing binaries. The new correction factor and the stellar models with the corrected frequencies are available at https://www.github.com/parallelpro/surface.

Establishing the accuracy of asteroseismic mass and radius estimates of giant stars

Context. Eclipsing binary stars with an oscillating giant component allow accurate stellar parameters to be derived and asteroseismic methods to be tested and calibrated. To this aim, suitable systems need to be firstly identified and secondly measured precisely and accurately. KIC 4054905 is one such system, which has been identified, but with measurements of a relatively low precision and with some confusion regarding its parameters and evolutionary state. Aims. Our aim is to provide a detailed and precise characterisation of the system and to test asteroseismic scaling relations. Methods. Dynamical and asteroseismic parameters of KIC 4054905 were determined from Kepler time-series photometry and multi-epoch high-resolution spectra from FIES at the Nordic Optical Telescope. Results. KIC 4054905 was found to belong to the thick disk and consist of two lower red giant branch (RGB) components with nearly identical masses of 0.95 M⊙ and an age of 9.9 ± 0.6 Gyr. The most evolved star with R ≃ 8.4 R⊙ displays solar-like oscillations. These oscillations suggest that the star belongs to the RGB, supported also by the radius, which is significantly smaller than the red clump phase for this mass and metallicity. Masses and radii from corrected asteroseismic scaling relations can be brought into full agreement with the dynamical values if the RGB phase is assumed, but a best scaling method could not be identified. Conclusions. The dynamical masses and radii were measured with a precision better than 1.0%. We firmly establish the evolutionary nature of the system to be that of two early RGB stars with an age close to 10 Gyr, unlike previous findings. The metallicity and Galactic velocity suggest that the system belongs to the thick disk of the Milky Way. We investigate the agreement between dynamical and asteroseismic parameters for KIC 4054905 measured in various ways. This suggests that consistent solutions exist, but the need to analyse more of these systems continues in order to establish the accuracy of asteroseismic methods.

Fundamental properties of red giants from Kepler and Gaia DR3 data: diagnostic potential of the mass–metallicity diagram

ABSTRACT For solar-like oscillators, the asteroseismic relations connect the stellar mean density and surface gravity to observable properties of the oscillations. Since the space missions CoRoT and Kepler, the asteroseismic relations have been massively employed out of their theoretical domain of validity, that is the main-sequence solar-type stars, in particular for red giant stars. However, despite a surprisingly good performance of the asteroseismic relation with red giant stars, they are biased and attempts to parametrize the departure of the relations for evolved stars have been the subject of many recent efforts. In this study, we propose a new parametrization of the asteroseismic relations for red giants of radii up to ${\sim } 50\, \mathrm{R}_\odot$, based on a calibration performed with Gaia parallax data. We find that the asteroseismic scaling relations depend on metallicity and effective temperature. For this solution, we obtain a parallax offset of about −0.026 ± 0.001 mas, and radius ranges from 3.8 to 53.2 R⊙. Most stars have masses that range from 0.9 to 1.7 M⊙, with the star count peaking around 1.2 M⊙. We also use data of the eclipsing binaries with solar-like oscillating components for calibration and discuss the diagnostic potential of the mass–metallicity diagram for our understanding of the evolution of red giants and the chemodynamics of the Galactic disc. Using this diagram, we identify stars that lost and gained mass and estimate the minimum change in mass.

Detection of p-mode Oscillations in HD 35833 with NEID and TESS

We report the results of observations of p-mode oscillations in the G0 subgiant star HD 35833 in both radial velocities and photometry with NEID and TESS, respectively. We achieve separate, robust detections of the oscillation signal with both instruments (radial velocity amplitude A RV = 1.11 ± 0.09 m s−1, photometric amplitude A phot = 6.42 ± 0.60 ppm, frequency of maximum power μHz, and mode spacing Δν = 36.65 ± 0.96 μHz) as well as a nondetection in a TESS sector concurrent with the NEID observations. These data shed light on our ability to mitigate the correlated noise impact of oscillations with radial velocities alone and on the robustness of commonly used asteroseismic scaling relations. The NEID data are used to validate models for the attenuation of oscillation signals for exposure times , and we compare our results to predictions from theoretical scaling relations and find that the observed amplitudes are weaker than expected by >4σ, hinting at gaps in the underlying physical models.

Establishing the accuracy of asteroseismic mass and radius estimates of giant stars – II. Revised stellar masses and radii for KIC 8430105

ABSTRACT Asteroseismic scaling relations can provide high-precision measurements of mass and radius for red giant (RG) stars displaying solar-like oscillations. Their accuracy can be validated and potentially improved using independent and accurate observations of mass, radius, effective temperature and metallicity. We seek to achieve this using long period SB2 eclipsing binaries hosting oscillating RGs. We explore KIC 8430105, for which a previous study found significant asteroseismic overestimation of mass and radius when compared with eclipsing binary measurements. We measured dynamical masses and radii for both components to be significantly lower than previously established, increasing the discrepancy between asteroseismic and dynamical measurements. Our dynamical measurements of the RG component were compared to corresponding measurements of mass and radius using asteroseismic scaling relations. Uncorrected scaling relations overestimated the mass of the RG by $26{{\ \rm per\ cent}}$, the radius by $11{{\ \rm per\ cent}}$, and the average density by $7{{\ \rm per\ cent}}$, in agreement with studies for other systems. However, using a theoretical correction to Δν, we managed to obtain an asteroseismic average density that is 1σ consistent with our dynamical result. We obtained several measurements of νmax that are not fully consistent. With νmax = 76.78 ± 0.81 $\mu$Hz, the Δν correction provided 2σ consistent mass and radius for the giant. The age of the system was estimated to be 3.7 ± 0.4 Gyr.

HD-TESS: An Asteroseismic Catalog of Bright Red Giants within TESS Continuous Viewing Zones

We present HD-TESS, a catalog of 1709 bright (V ∼ 3–10) red giants from the Henry Draper (HD) Catalog with asteroseismic measurements based on photometry from NASA’s Transiting Exoplanet Survey Satellite (TESS). Using light curves spanning at least 6 months across a single TESS observing cycle, we provide measurements of global asteroseismic parameters ( and Δν) and the evolutionary state for each star in the catalog. We adopt literature values of atmospheric stellar parameters to estimate the masses and radii of the giants in our catalog using asteroseismic scaling relations, and observe that HD-TESS giants on average have larger masses compared to Kepler red giants. Additionally, we present the discovery of oscillations in 99 red giants in astrometric binary systems, including those with subdwarf or white dwarf companions. Finally, we benchmark radii from asteroseismic scaling relations against those measured using long-baseline interferometry for 18 red giants and find that correction factors to the scaling relations improve the agreement between asteroseismic and interferometric radii to approximately 3%.

Spectroscopic and seismic analysis of red giants in eclipsing binaries discovered byKepler

Eclipsing binaries (EBs) are unique targets for measuring accurate 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 verify the ability of ensemble asteroseismology to derive stellar properties. On the other hand, the oscillations and surface activity 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) in EBs; so far 20 known systems have been discovered by the NASAKeplermission. We report the discovery of 16 RGs in EBs, which are also from theKeplerdata, leading to a total of 36 confirmed RG stars in EBs from the originalKeplermission. This new sample includes three SB2-EBs with oscillations, resulting in a total of 14 known SB2-EBs with an oscillating RG component. This sample also includes six close systems in which the RG display a clear surface activity and complete oscillation suppression. Based on dedicated high-resolution spectroscopic observations (Apache Point Observatory, Observatoire de Haute Provence), we focus on three main aspects. Firstly, from the extended sample of 14 SB2-EBs, we confirm that the simple application of the asteroseismic scaling relations to RGs overestimates masses and radii of RGs by about 15% and 5%. This bias can be reduced by employing either new asteroseismic reference values for RGs or model-based corrections of the asteroseismic parameters. Secondly, we confirm that close binarity leads to a high level of photometric modulation (up to 10%) 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 complement previous observational studies that aimed to constrain tidal dissipation in interacting binaries. We confirm the important role of the equilibrium tide in binary evolution, but we also identify systems with circular orbits despite relatively young ages, which suggests the need to explore complementary tidal dissipation mechanisms in the future. Finally, as a by-product, we report the measurements of mass, radius, and age of three M-dwarf companion stars.

Lithium abundances and asteroseismology of red giants: understanding the evolution of lithium in giants based on asteroseismic parameters

In this study, we explore the evolution of lithium in giant stars based on data assembled from the literature on asteroseismology and Li abundances for giants. Our final sample of 187 giants consists of 44 red giant branch (RGB), 140 core He-burning (CHeB) and three giants with an unclassified evolutionary phase. For all 187 stars, the seismic parameters $\nu\rm_{max}$ (frequency of maximum oscillation power) and $\Delta \nu$ (large frequency spacing) are available, while $\Delta \Pi\rm_{1}$ (the asymptotic gravity-mode period spacing) is available for a subset of 64. For some of the CHeB giants, mass estimates from the asteroseismic scaling relations are found to be underestimated when compared with mass estimates from isochrones based on seismic data. Whilst most of the Li-rich giants in the sample have masses less than 1.5 $M_\odot$, they are also present up to and beyond the maximum mass expected to have suffered a core He-flash, i.e. $M$ $\leq$ 2.25 $M_\odot$: this suggests contributions from other processes towards Li enrichment. To understand the evolution of giants in the $\Delta \Pi\rm_{1}$ $-$ $\Delta \nu$ plane, we use the {\it Modules for Experiments in Stellar Astrophysics} models which show the presence of mini He-flashes following the initial strong core He-flash. From the distribution of A(Li) as a function of $\Delta \nu$, which is similar to the distribution of A(Li) as a function of luminosity, we find no indication of Li enrichment near the luminosity bump. Also, A(Li) trends to $\sim$ -1.5 dex near the RGB tip. The data also suggest a decrease in A(Li) with an increase in $\Delta \Pi\rm_{1}$ for CHeB giants.

Testing the intrinsic scatter of the asteroseismic scaling relations with Kepler red giants

ABSTRACT Asteroseismic scaling relations are often used to derive stellar masses and radii, particularly 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 Δν and νmax, 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 Δν and νmax provide the dominating scatter that blurs the features. As a consequence, we conclude that the scaling relations have intrinsic scatter of $\sim 0.5$ (Δν), $\sim 1.1$ (νmax), $\sim 1.7$ (M), and $\sim 0.4{{\ \rm per\ cent}}$ (R), for the SYD pipeline measured Δν and νmax. 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.

Spectroscopic and Asteroseismic Analysis of the Secondary Clump Red Giant HD 226808*

Abstract In order to clarify the properties of the secondary clump star HD 226808 (KIC 5307747), we combined four years of data from Kepler space photometry with high-resolution spectroscopy of the High Efficiency and Resolution Mercator Échelle Spectrograph mounted on the Mercator telescope. The fundamental atmospheric parameters, radial velocities, rotation velocities, and elemental abundance for Fe and Li were determined by analyzing line strengths and fitting-line profiles, based on a 1D local thermodynamic equilibrium model atmosphere. Second, we analyzed a photometric light curve obtained by Kepler and we extracted asteroseismic data of this target using Lets Analysis, Use and Report of Asteroseismology, a new seismic tool developed for the study of evolved FGK solar-like stars. We determined the evolutionary status and effective temperature, surface gravity, metallicity, microturbulence, and chemical abundances for Li, Ti, Fe, and Ni for HD 226808, by employing spectroscopy, asteroseismic scaling relations, and evolutionary structure models built in order to match observed data. Our results also show that an accurate synergy between good spectroscopic analysis and asteroseismology can provide a jump toward understanding evolved stars.

Solar cycle variation of νmax in helioseismic data and its implications for asteroseismology

ABSTRACT The frequency, νmax, at which the envelope of pulsation power peaks for solar-like oscillators is an important quantity in asteroseismology. We measure νmax for the Sun using 25 yr of Sun-as-a-star Doppler velocity observations with the Birmingham Solar-Oscillations Network (BiSON), by fitting a simple model to binned power spectra of the data. We also apply the fit to Sun-as-a-star Doppler velocity data from Global Oscillation Network Group and Global Oscillations at Low Frequency, and photometry data from VIRGO/SPM on the ESA/NASA SOHO spacecraft. We discover a weak but nevertheless significant positive correlation of the solar νmax with solar activity. The uncovered shift between low and high activity, of $\simeq 25\, \rm \mu Hz$, translates to an uncertainty of 0.8 per cent in radius and 2.4 per cent in mass, based on direct use of asteroseismic scaling relations calibrated to the Sun. The mean νmax in the different data sets is also clearly offset in frequency. Our results flag the need for caution when using νmax in asteroseismology.

Testing the Radius Scaling Relation with Gaia DR2 in the Kepler Field

Abstract We compare radii based on Gaia parallaxes to radii based on asteroseismic scaling relations for ∼300 dwarfs and subgiants and ∼3600 first-ascent giants from the Kepler mission. Systematics due to temperature, bolometric correction, extinction, asteroseismic radius, and the spatially correlated Gaia parallax zero-point contribute to a 2% systematic uncertainty on the agreement in Gaia–asteroseismic radius. We find that dwarf and giant scaling radii are on a parallactic scale at the level of −2.1% ± 0.5% (rand.) ± 2.0% (syst.) (dwarfs) and +1.7% ± 0.3% (rand.) ± 2.0% (syst.) (giants), supporting the accuracy and precision of scaling relations. In total, the 2% agreement that we find holds for stars spanning radii between 0.8 R ⊙ and 30 R ⊙ . We do, however, see evidence for relative errors in scaling radii between dwarfs and giants at the level of 4% ± 0.6%, and find evidence of departures from simple scaling relations for radii above 30 R ⊙ . Asteroseismic masses for very metal-poor stars are still overestimated relative to astrophysical priors, but at a reduced level. We see no trend with metallicity in radius agreement for stars with −0.5 &lt; [Fe/H] &lt; +0.5. We quantify the spatially correlated parallax errors in the Kepler field, which globally agree with the Gaia team’s published covariance model. We provide Gaia radii, corrected for extinction and the Gaia parallax zero-point, for our full sample of ∼3900 stars, including dwarfs, subgiants, and first-ascent giants.

The K2-HERMES Survey: age and metallicity of the thick disc

ABSTRACT Asteroseismology is a promising tool to study Galactic structure and evolution because it can probe the ages of stars. Earlier attempts comparing seismic data from the Kepler satellite with predictions from Galaxy models found that the models predicted more low-mass stars compared to the observed distribution of masses. It was unclear if the mismatch was due to inaccuracies in the Galactic models, or the unknown aspects of the selection function of the stars. Using new data from the K2 mission, which has a well-defined selection function, we find that an old metal-poor thick disc, as used in previous Galactic models, is incompatible with the asteroseismic information. We use an importance-sampling framework, which takes the selection function into account, to fit for the metallicities of a population synthesis model using spectroscopic data. We show that spectroscopic measurements of [Fe/H] and [α/Fe] elemental abundances from the GALAH survey indicate a mean metallicity of log (Z/Z⊙) = −0.16 for the thick disc. Here Z is the effective solar-scaled metallicity, which is a function of [Fe/H] and [α/Fe]. With the revised disc metallicities, for the first time, the theoretically predicted distribution of seismic masses show excellent agreement with the observed distribution of masses. This indirectly verifies that the asteroseismic mass scaling relation is good to within five per cent. Assuming the asteroseismic scaling relations are correct, we estimate the mean age of the thick disc to be about 10 Gyr, in agreement with the traditional idea of an old α-enhanced thick disc.