The last decade has seen a revolution in the field of asteroseismology – the study of stellar pulsations. It has become a powerful method to precisely characterize exoplanet host stars and as a consequence also the exoplanets themselves. This synergy between asteroseismology and exoplanet science has flourished in large part due to space missions such as Kepler, which have provided high-quality data that can be used for both types of studies. Perhaps the primary contribution from asteroseismology to the research on transiting exoplanets is the determination of very precise stellar radii that translate into precise planetary radii, but asteroseismology has also proven useful in constraining eccentricities of exoplanets as well as the dynamical architecture of planetary systems. In this chapter, we introduce some basic principles of asteroseismology and review current synergies between the two fields.

In the third APOKASC catalog, we present data for the complete sample of 15,808 evolved stars with APOGEE spectroscopic parameters and Kepler asteroseismology. We used 10 independent asteroseismic analysis techniques and anchor our system on fundamental radii derived from Gaia L and spectroscopic Teff. We provide evolutionary state, asteroseismic surface gravity, mass, radius, age, and the data used to derive them for 12,418 stars. This includes 10,036 exceptionally precise measurements, with median fractional uncertainties in nu max , Delta nu, mass, radius, and age of 0.6%, 0.6%, 3.8%, 1.8%, and 11.1%, respectively. We provide more limited data for 1624 additional stars that either have lower-quality data or are outside of our primary calibration domain. Using lower red giant branch (RGB) stars, we find a median age for the chemical thick disk of 9.14 +/- 0.05(ran) +/- 0.9(sys) Gyr with an age dispersion of 1.1 Gyr, consistent with our error model. We calibrate our red clump (RC) mass loss to derive an age consistent with the lower RGB and provide asymptotic GB and RGB ages for luminous stars. We also find a sharp upper-age boundary in the chemical thin disk. We find that scaling relations are precise and accurate on the lower RGB and RC, but they become more model dependent for more luminous giants and break down at the tip of the RGB. We recommend the use of multiple methods, calibration to a fundamental scale, and the use of stellar models to interpret frequency spacings.

We present results from fitting p-mode spectra derived from 7-d segments of Sun-as-a-star helioseismic observations from the Birmingham Solar Oscillations Network covering 32 yr. The results show a clear dependence of the mode frequencies on solar activity, and the frequency dependence of the sensitivity to activity can also be seen. Because we use data segments that cover less than half of a solar rotation, we are able to test for the effect of activity on the solar far side. By fitting with a model that takes into account activity on the far side of the Sun, we show that the frequency shifts are sensitive to activity from the whole Sun, not just the side facing the observer. Our results suggest that there is potential to investigate activity-related asteroseismic frequency shifts in solar-like oscillators using short time series of observations.

The European Space Agency has selected PLATO (PLAnetary Transits and Oscillations of stars) for its M3 launch which is scheduled for 2026. With its extremely large field of view, PLATO is designed to obtain photometric measurements over an extended period for bright stars in order to detect and characterise (primarily) rocky planets in the habitable zones of solar type stars. The PLATO measurements will have sufficient sensitivity to determine the mass, radius and age of the host stars with unprecedented accuracy. The PLATO planet database will provide the first large-scale catalogue of accurately and homogeneously characterised small planets at intermediate orbital periods, which will can be used to severely constraint planet formation theories. This would facilitate large scale comparative exo-planetology. In addition the bright PLATO host stars will be ideal targets for atmospheric study with next generation facilities such as the ELT. The PLATO sensitivity will be sufficient to detect pulsations from stars across the HR diagram allowing a deep understanding of stellar structure and evolution to be developed using parameters determined from asteroseismology.

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.

Fuelled by space photometry, asteroseismology is vastly benefitting the study of cool main-sequence stars, which exhibit convection-driven solar-like oscillations. Even so, the tiny oscillation amplitudes in K dwarfs continue to pose a challenge to space-based asteroseismology. A viable alternative is offered by the lower stellar noise over the oscillation timescales in Doppler observations. In this Letter we present the definite detection of solar-like oscillations in the bright K5 dwarf ϵ Indi based on time-intensive observations collected with the ESPRESSO spectrograph at the VLT, thus making it the coolest seismic dwarf ever observed. We measured the frequencies of a total of 19 modes of degree ℓ = 0–2 along with ν max = 5305 ± 176 μHz and Δ ν = 201.25 ± 0.16 μHz. The peak amplitude of radial modes is 2.6 ± 0.5 cm s −1 , or a mere ∼14% of the solar value. Measured mode amplitudes are ∼2 times lower than predicted from a nominal L / M scaling relation and favour a scaling closer to ( L / M ) 1.5 below ∼5500 K, carrying important implications for our understanding of the coupling efficiency between pulsations and near-surface convection in K dwarfs. This detection conclusively shows that precise asteroseismology of cool dwarfs is possible down to at least the mid-K regime using next-generation spectrographs on large-aperture telescopes, effectively opening up a new domain in observational asteroseismology.

Aims . The KEYSTONE project aims to enhance our understanding of solar-like oscillators by delivering a catalogue of global asteroseismic parameters (Δ v and v max ) for 173 stars, comprising mainly dwarfs and subgiants, observed by the K2 mission in its short-cadence mode during campaigns 6–19. Methods . We derive atmospheric parameters and luminosities using spectroscopic data from TRES, astrometric data from Gaia , and the infrared flux method (IRFM) for a comprehensive stellar characterisation. Asteroseismic parameters are robustly extracted using three independent methods, complemented by an iterative refinement of the spectroscopic analyses using seismic log g values to enhance parameter accuracy. Results . Our analysis identifies new detections of solar-like oscillations in 159 stars, providing an important complement to already published results from previous campaigns. The catalogue provides homogeneously derived atmospheric parameters and luminosities for the majority of the sample. Comparison between spectroscopic T eff and those obtained from the IRFM demonstrates excellent agreement. The iterative approach to spectroscopic analysis significantly enhances the accuracy of the stellar properties derived.

Red giant stars host solar-like oscillations which have mixed character, being sensitive to conditions both in the outer convection zone and deep within the interior. The properties of these modes are sensitive to both core rotation and magnetic fields. While asteroseismic studies of the former have been done on a large scale, studies of the latter are currently limited to tens of stars. We aim to produce the first large catalogue of both magnetic and rotational perturbations. We jointly constrain these parameters by devising an automated method for fitting the power spectra directly. We successfully apply the method to 302 low-luminosity red giants. We find a clear bimodality in core rotation rate. The primary peak is at delta nu(rot) = 0.32 mu Hz, and the secondary at delta nu(rot) = 0.47 mu Hz. Combining our results with literature values, we find that the percentage of stars rotating much more rapidly than the population average increases with evolutionary state. We measure magnetic splittings of 2 sigma significance in 23 stars. While the most extreme magnetic splitting values appear in stars with masses >1.1 M-circle dot, implying they formerly hosted a convective core, a small but statistically significant magnetic splitting is measured at lower masses. Asymmetry between the frequencies of a rotationally split multiplet has previously been used to diagnose the presence of a magnetic perturbation. We find that of the stars with a significant detection of magnetic perturbation, 43 per cent do not show strong asymmetry. We find no strong evidence of correlation between the rotation and magnetic parameters.

Context. The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may require several dozen parameters to accurately describe features in the spectra caused by the oscillation modes and surface granulation. Many of these parameters are often highly correlated, making the parameter space difficult to quickly and accurately sample. They are, however, all dependent on a much smaller set of parameters, namely the fundamental stellar properties. Aims. We aim to leverage this to develop a method for simplifying the process of sampling the model parameter space for the asteroseismic analysis of solar-like oscillators, with an emphasis on mode identification. Methods. Using a large set of previous observations, we applied principal component analysis to the sample covariance matrix to select a new basis on which to sample the model parameters. Selecting the subset of basis vectors that explains the majority of the sample variance, we then redefined the model parameter prior probability density distributions in terms of a smaller set of latent parameters. Results. We are able to reduce the dimensionality of the sampled parameter space by a factor of two to three. The number of latent parameters needed to accurately model the stellar oscillation spectra cannot be determined exactly but is likely only between four and six. Using two latent parameters, the method is able to produce models that describe the bulk features of the oscillation spectrum, while including more latent parameters allows for a frequency precision better than ≈10% of the small frequency separation for a given target. Conclusions. We find that sampling a lower-rank latent parameter space still allows for accurate mode identification and parameter estimation on solar-like oscillators over a wide range of evolutionary stages. This allows for the potential to increase the complexity of spectrum models without a corresponding increase in computational expense.

To detect Earth-mass planets using the Doppler method, a major obstacle is to differentiate the planetary signal from intrinsic stellar variability (e.g., pulsations, granulation, spots and plages). Convective blueshift, which results from small-scale convection at the surface of Sun-like stars, is relevant for Earth-twin detections as it exhibits Doppler noise on the order of 1 m/s. Here, we present a simple model for convective blueshift based on fundamental equations of stellar structure. Our model successfully matches observations of convective blueshift for FGK stars. Based on our model, we also compute the intrinsic noise floor for stellar granulation in the radial velocity observations. We find that for a given mass range, stars with higher metallicities display lower radial-velocity dispersion due to granulation, in agreement with MHD simulations. We also provide a set of formulae to predict the amplitude of radial-velocity dispersion due to granulation as a function of stellar parameters. Our work is vital in identifying the most amenable stellar targets for EPRV surveys and radial velocity follow-up programmes for TESS, CHEOPS, and the upcoming PLATO mission.

The Transiting Exoplanet Survey Satellite (TESS) mission searches for new exoplanets. The observing strategy of TESS results in high-precision photometry of millions of stars across the sky, allowing for detailed asteroseismic studies of individual systems. In this work, we present a detailed asteroseismic analysis of the giant star HD 76920 hosting a highly eccentric giant planet (e = 0.878) with an orbital period of 415 days, using five sectors of TESS light curve that cover around 140 days of data. Solar-like oscillations in HD 76920 are detected around 52 μHz by TESS for the first time. By utilizing asteroseismic modeling that takes classical observational parameters and stellar oscillation frequencies as constraints, we determine improved measurements of the stellar mass (1.22 ± 0.11 M ⊙), radius (8.68 ± 0.34 R ☉), and age (5.2 ± 1.4 Gyr). With the updated parameters of the host star, we update the semimajor axis and mass of the planet as a = 1.165 ± 0.035 au and Mpsini=3.57±0.22MJup . With an orbital pericenter of 0.142 ± 0.005 au, we confirm that the planet is currently far away enough from the star to experience negligible tidal decay until being engulfed in the stellar envelope. We also confirm that this event will occur within about 100 Myr, depending on the stellar model used.

The Birmingham Solar Oscillations Network (BiSON) observes acoustic oscillations of the Sun. The dominant noise source is caused by fluctuations of Earth's atmosphere, and BiSON seeks to mitigate this effect by combining multiple rapid observations in alternating polarisation states. Current instrumentation uses bespoke Pockels-effect cells to select the polarisation state. Here, we investigate an alternative off-the-shelf solution, a liquid crystal retarder, and discuss the potential impact of differences in performance. We show through electrical simulation of the photodiode-based detectors, and assessment of both types of polarisation device, that although the switching rate is slower the off-the-shelf LCD retarder is a viable replacement for a bespoke Pockels-effect cell. The simplifications arising from the use of off-the-shelf components allows easier and quicker instrumentation deployment.

ABSTRACT We present solar low-degree rotational splitting values based on a new analysis of Sun-as-a-star observations from the Birmingham Solar Oscillations Network, covering a 16 425-d period from 1976 December 31 to 2021 December 20 with a duty cycle of 57 per cent. The splitting values are estimated from the power spectrum using a Markov chain Monte Carlo sampling method, and we also present for comparison the results from an analysis of 100 realizations of synthetic data with the same resolution and gap structure. Comparison of the scatter in the results from the synthetic realizations with their estimated uncertainties suggests that for this data set the formal uncertainty estimates are about 30 per cent too small. An upward bias in the splittings at frequencies above 2200 μHz, where the components are not fully resolved, is seen in both the observed and synthetic data. When this bias is taken into account, our results are consistent with a frequency-independent synodic rotational splitting value of 400 nHz.

Photometric time series gathered by space telescopes such as CoRoT and Kepler allow to detect solar-like oscillations in red giant stars and to measure their global seismic constraints, which can be used to infer global stellar properties (e.g. masses, radii, and evolutionary states). Combining such precise constraints with photospheric abundances provides a means of testing mixing processes that occur inside red-giant stars. In this work, we conduct a detailed spectroscopic and seismic analysis of nine nearby (d < 200 pc) red giant stars observed by Kepler. Both seismic constraints and grid-based modelling approaches are used to determine precise fundamental parameters for those evolved stars. We compare distances and radii derived from Gaia Data Release 3 parallaxes with those inferred by a combination of seismic, spectroscopic, and photometric constraints. We find no deviations within errors bars, however the small sample size and the associated uncertainties are a limiting factor for such comparison. We use the period spacing of mixed modes to distinguish between ascending red-giants and red clump stars. Based on the evolutionary status, we apply corrections to the values of Delta nu for some stars, resulting in a slight improvement to the agreement between seismic and photometric distances. Finally, we couple constraints on detailed chemical abundances with the inferred masses, radii, and evolutionary states. Our results corroborate previous studies that show that observed abundances of lithium and carbon isotopic ratio are in contrast with predictions from standard models, giving robust evidence for the occurrence of additional mixing during the red-giant phase.

Context. The Transiting Exoplanet Survey Satellite (TESS) mission has provided photometric light curves for stars across nearly the entire sky. This allows for the application of asteroseismology to a pool of potential solar-like oscillators that is unprecedented in size. Aims. We aim to produce a catalogue of solar-like oscillators observed by TESS in the 120-s and 20-s cadence modes. The catalogue is intended to highlight stars oscillating at frequencies above the TESS 30-min cadence Nyquist frequency with the purpose of encompassing the main-sequence and subgiant evolutionary phases. We aim to provide estimates for the global asteroseismic parameters v max and ∆ v . Methods. We applied a new probabilistic detection algorithm to the 120-s and 20-s light curves of over 250 000 stars. This algorithm flags targets that show characteristic signatures of solar-like oscillations. We manually vetted the resulting list of targets to confirm the presence of solar-like oscillations. Using the probability densities computed by the algorithm, we measured the global asteroseismic parameters v max and ∆ v . Results. We produce a catalogue of 4177 solar-like oscillators, reporting ∆ v and v max for 98% of the total star count. The asteroseismic data reveal a vast coverage of the Hertzsprung-Russell diagram, populating the red giant branch, the subgiant regime, and extending towards the main sequence. Conclusions. A crossmatch with external catalogues shows that 25 of the detected solar-like oscillators are a component of a spectroscopic binary, and 28 are confirmed planet host stars. These results provide the potential for precise, independent asteroseismic constraints on these and any additional TESS targets of interest.

ABSTRACT The angle between the rotation and orbital axes of stars in binary systems – the obliquity – is an important indicator of how these systems form and evolve, but few such measurements exist. We combine the sample of astrometric orbital inclinations from Gaia Data Release 3 with a sample of solar-like oscillators in which rotational inclinations have been measured using asteroseismology. We supplement our sample with one binary whose visual orbit has been determined using speckle interferometry and present the projected spin–orbit alignments in five systems. We find that each system, and the overall sample, is consistent with alignment but there are important caveats. First, the asteroseismic rotational inclinations are fundamentally ambiguous and, secondly, we can only measure the projected (rather than true) obliquity. If rotational and orbital inclinations are independent and isotropically distributed, the likelihood of drawing our data by chance is less than a few per cent. Though small, our data set argues against uniformly random obliquities in binary systems. We speculate that dozens more measurements could be made using data from NASA’s Transiting Exoplanet Survey Satellite mission, mostly in red giants. ESA’s PLAnetary Transits and Oscillations mission will likely produce hundreds more spin–orbit measurements in systems with main-sequence and subgiant stars.

The asteroseismic analysis of stellar power density spectra is often computationally expensive. The models used in the analysis may use several dozen parameters to accurately describe features in the spectra caused by oscillation modes and surface granulation. Many parameters are often highly correlated, making the parameter space difficult to quickly and accurately sample. They are, however, all dependent on a smaller set of parameters, namely the fundamental stellar properties. We aim to leverage this to simplify the process of sampling the model parameter space for the asteroseismic analysis of solar-like oscillators, with an emphasis on mode identification. Using a large set of previous observations, we applied principal component analysis to the sample covariance matrix to select a new basis on which to sample the model parameters. Selecting the subset of basis vectors that explains the majority of the sample variance, we redefine the model parameter prior probability density distributions in terms of a smaller set of latent parameters. We are able to reduce the dimensionality of the sampled parameter space by a factor of two to three. The number of latent parameters needed to accurately model the stellar oscillation spectra cannot be determined exactly but is likely only between four and six. Using two latent parameters, the method is able to describe the bulk features of the oscillation spectrum, while including more latent parameters allows for a frequency precision better than $\approx10\%$ of the small frequency separation for a given target. We find that sampling a lower-rank latent parameter space still allows for accurate mode identification and parameter estimation on solar-like oscillators over a wide range of evolutionary stages. This allows for the potential to increase the complexity of spectrum models without a corresponding increase in computational expense.

Asteroseismology has transformed stellar astrophysics. Red giant asteroseismology is a prime example, with oscillation periods and amplitudes that are readily detectable with time-domain space-based telescopes. These oscillations can be used to infer masses, ages and radii for large numbers of stars, providing unique constraints on stellar populations in our galaxy. The cadence, duration, and spatial resolution of the Roman galactic bulge time-domain survey (GBTDS) are well-suited for asteroseismology and will probe an important population not studied by prior missions. We identify photometric precision as a key requirement for realizing the potential of asteroseismology with Roman. A precision of 1 mmag per 15-min cadence or better for saturated stars will enable detections of the populous red clump star population in the Galactic bulge. If the survey efficiency is better than expected, we argue for repeat observations of the same fields to improve photometric precision, or covering additional fields to expand the stellar population reach if the photometric precision for saturated stars is better than 1 mmag. Asteroseismology is relatively insensitive to the timing of the observations during the mission, and the prime red clump targets can be observed in a single 70 day campaign in any given field. Complementary stellar characterization, particularly astrometry tied to the Gaia system, will also dramatically expand the diagnostic power of asteroseismology. We also highlight synergies to Roman GBTDS exoplanet science using transits and microlensing.

Dating stars is a major challenge with a deep impact on many astrophysical fields. One of the most promising techniques for this is using chemical abundances. Recent space- and ground-based facilities have improved the quantity of stars with accurate observations. This has opened the door for using Bayesian inference tools to maximise the information we can extract from them. Our aim is to present accurate and reliable stellar age estimates of FGK stars using chemical abundances and stellar parameters. We used one of the most flexible Bayesian inference techniques (hierarchical Bayesian models) to exceed current possibilities in the use of chemical abundances for stellar dating. Our model is a data-driven model. We used a training set that has been presented in the literature with ages estimated with isochrones and accurate stellar abundances and general characteristics. The core of the model is a prescription of certain abundance ratios as linear combinations of stellar properties including age. We gathered four different testing sets to assess the accuracy, precision, and limits of our model. We also trained a model using chemical abundances alone. We found that our age estimates and those coming from asteroseismology, other accurate sources, and also with ten Gaia benchmark stars agree well. The mean absolute difference of our estimates compared with those used as reference is 0.9 Ga, with a mean difference of 0.01 Ga. When using open clusters, we reached a very good agreement for Hyades, NGC 2632, Ruprecht 147, and IC4651. We also found outliers that are a reflection of chemical peculiarities and/or stars at the limit of the validity ranges of the training set. The model that only uses chemical abundances shows slightly worse mean absolute difference (1.18 Ga) and mean difference (-0.12 Ga).