Despite a growing sample of precisely measured stellar rotation periods and ages, the strength of magnetic braking and the degree of departure from standard (Skumanich-like) spin-down have remained persistent questions, particularly for stars more evolved than the Sun. Rotation periods can be measured for stars older than the Sun by leveraging asteroseismology, enabling models to be tested against a larger sample of old field stars. Because asteroseismic measurements of rotation do not depend on starspot modulation, they avoid potential biases introduced by the need for a stellar dynamo to drive starspot production. Using a neural network trained on a grid of stellar evolution models and a hierarchical model-fitting approach, we constrain the onset of weakened magnetic braking (WMB). We find that a sample of stars with asteroseismically measured rotation periods and ages is consistent with models that depart from standard spin-down prior to reaching the evolutionary stage of the Sun. We test our approach using neural networks trained on model grids produced by separate stellar evolution codes with differing physical assumptions and find that the choices of grid physics can influence the inferred properties of the braking law. We identify the normalized critical Rossby number Ro _crit /Ro _⊙ = 0.91 ± 0.03 as the threshold for the departure from standard rotational evolution. This suggests that WMB poses challenges to gyrochronology for roughly half of the main-sequence lifetime of Sun-like stars.

The radial metallicity distribution of the Milky Way's disc is an important observational constraint for models of the formation and evolution of our Galaxy. It informs our understanding of the chemical enrichment of the Galactic disc and the dynamical processes therein, particularly radial migration. We investigate how the metallicity changes with guiding radius in the thin disc using a sample of red-giant stars with robust astrometric, spectroscopic and asteroseismic parameters. Our sample contains $668$ stars with guiding radii $4$ kpc < $R_\mathrm{g}$ < $11$ kpc and asteroseismic ages covering the whole history of the thin disc with precision $\approx 25\%$. We use MCMC analysis to measure the gradient and its intrinsic spread in bins of age and construct a hierarchical Bayesian model to investigate the evolution of these parameters independently of the bins. We find a smooth evolution of the gradient from $\approx -0.07$ dex/kpc in the youngest stars to $\approx -0.04$ dex/kpc in stars older than $10$ Gyr, with no break at intermediate ages. Our results are consistent with those based on asteroseismic ages from CoRoT, with that found in Cepheid variables for stars younger than $1$ Gyr, and with open clusters for stars younger than $6$ Gyr. For older stars we find a significantly lower metallicity in our sample than in the clusters, suggesting a survival bias favouring more metal-rich clusters. We also find that the chemical evolution model of Chiappini (2009) is too metal-poor in the early stages of disc formation. Our results provide strong new constraints for the growth and enrichment of the thin disc and radial migration, which will facilitate new tests of model conditions and physics.

Young $\delta$ Scuti stars have proven to be valuable asteroseismic targets but obtaining robust uncertainties on their inferred properties is challenging. We aim to quantify the random uncertainties in grid-based modelling of $\delta$ Sct stars. We apply Bayesian inference using nested sampling and a neural network emulator of stellar models, testing our method on both simulated and real stars. Based on results from simulated stars we demonstrate that our method can recover plausible posterior probability density estimates while accounting for both the random uncertainty from the observations and neural network emulation. We find that the posterior distributions of the fundamental parameters can be significantly non-Gaussian, multi-modal, and have strong covariance. We conclude that our method reliably estimates the random uncertainty in the modelling of $\delta$ Sct stars and paves the way for the investigation and quantification of the systematic uncertainty.

The detailed modelling of stellar oscillations is a powerful approach to characterising stars. However, poor treatment of systematics in theoretical models leads to misinterpretations of stars. Here we propose a more principled statistical treatment for the systematics to be applied to fitting individual mode frequencies with a typical stellar model grid. We introduce a correlated noise model based on a Gaussian Process (GP) kernel to describe the systematics given that mode frequency systematics are expected to be highly correlated. We show that tuning the GP kernel can reproduce general features of frequency variations for changing model input physics and fundamental parameters. Fits with the correlated noise model better recover stellar parameters than traditional methods which either ignore the systematics or treat them as uncorrelated noise.

Grid-based modelling is widely used for estimating stellar parameters. However, stellar model grid is sparse because of the computational cost. This paper demonstrates an application of a machine-learning algorithm using the Gaussian Process (GP) Regression that turns a sparse model grid onto a continuous function. We train GP models to map five fundamental inputs (mass, equivalent evolutionary phase, initial metallicity, initial helium fraction, and the mixing-length parameter) to observable outputs (effective temperature, surface gravity, radius, surface metallicity, and stellar age). We test the GP predictions for the five outputs using off-grid stellar models and find no obvious systematic offsets, indicating good accuracy in predictions.As a further validation, we apply these GP models to characterise 1,000 fake stars. Inferred masses and ages determined with GP models well recover true values within one standard deviation. An important consequence of using GP-based interpolation is that stellar ages are more precise than those estimated with the original sparse grid because of the full sampling of fundamental inputs.

The advent of asteroseismology as the golden path to precisely characterize single stars naturally led to synergies with the field of exoplanetology. Today, the precise determination of stellar masses, radii and ages for exoplanet-host stars is a driving force in the development of dedicated software and techniques to achieve this goal. However, as various approaches exist, it is clear that they all have advantages and inconveniences and that there is a trade-off between accuracy, efficiency, and robustness of the techniques. We aim to compare and discuss various modelling techniques for exoplanet-host red giant stars for which TESS data are available. The results of the seismic modelling are then used to study the dynamical evolution and atmospheric evaporation of the planetary systems. We study, in detail, the robustness, accuracy and precision of various seismic modelling techniques when applied to four exoplanet-host red giants observed by TESS. We discuss the use of global seismic indexes, the use of individual radial frequencies and that of non-radial oscillations. In each case, we discuss the advantages and inconveniences of the modelling technique. We determine precise and accurate masses of exoplanet-host red giant stars orbited by long-period Jupiter-like planets using various modelling techniques. For each target, we also provide a model-independent estimate of the mass from a mean density inversion combined with radii values from Gaia and spectroscopic data. We show that no engulfment or migration is observed for these targets, even if their evolution is extended beyond their estimated seismic ages up the red giant branch.

With recent advances in modelling stars using high-precision asteroseismology, the systematic effects associated with our assumptions of stellar helium abundance (Y) and the mixing-length theory parameter (αMLT) are becoming more important. We apply a new method to improve the inference of stellar parameters for a sample of Kepler dwarfs and subgiants across a narrow mass range ($0.8 \lt M \lt 1.2\, \rm M_\odot$). In this method, we include a statistical treatment of Y and the αMLT. We develop a hierarchical Bayesian model to encode information about the distribution of Y and αMLT in the population, fitting a linear helium enrichment law including an intrinsic spread around this relation and normal distribution in αMLT. We test various levels of pooling parameters, with and without solar data as a calibrator. When including the Sun as a star, we find the gradient for the enrichment law, $\Delta Y / \Delta Z = 1.05\substack{+0.28\\-0.25}$ and the mean αMLT in the population, $\mu _\alpha = 1.90\substack{+0.10\\-0.09}$. While accounting for the uncertainty in Y and αMLT, we are still able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Our method can also be applied to larger samples that will lead to improved constraints on both the population level inference and the star-by-star fundamental parameters.

Asteroseismology is an exceptional tool for studying stars using the properties of observed modes of oscillation. So far the process of performing an asteroseismic analysis of a star has remained somewhat esoteric and inaccessible to nonexperts. In this software paper we describe PBjam, an open-source Python package for analyzing the frequency spectra of solar-like oscillators in a simple but principled and automated way. The aim of PBjam is to provide a set of easy-to-use tools to extract information about the radial and quadropole oscillations in stars that oscillate like the Sun, which may then be used to infer bulk properties such as stellar mass, radius, age, or even structure. Asteroseismology and its data analysis methods are becoming increasingly important as space-based photometric observatories are producing a wealth of new data, allowing asteroseismology to be applied in a wide range of contexts such as exoplanet, stellar structure and evolution, and Galactic population studies.

ABSTRACT We report the discovery of a warm sub-Saturn, TOI-257b (HD 19916b), based on data from NASA’s Transiting Exoplanet Survey Satellite (TESS). The transit signal was detected by TESS and confirmed to be of planetary origin based on radial velocity observations. An analysis of the TESS photometry, the Minerva-Australis, FEROS, and HARPS radial velocities, and the asteroseismic data of the stellar oscillations reveals that TOI-257b has a mass of MP = 0.138 ± 0.023 $\rm {M_J}$ (43.9 ± 7.3 $\, M_{\rm \oplus}$), a radius of RP = 0.639 ± 0.013 $\rm {R_J}$ (7.16 ± 0.15 $\, \mathrm{ R}_{\rm \oplus}$), bulk density of $0.65^{+0.12}_{-0.11}$ (cgs), and period $18.38818^{+0.00085}_{-0.00084}$ $\rm {days}$. TOI-257b orbits a bright (V = 7.612 mag) somewhat evolved late F-type star with M* = 1.390 ± 0.046 $\rm {M_{sun}}$, R* = 1.888 ± 0.033 $\rm {R_{sun}}$, Teff = 6075 ± 90 $\rm {K}$, and vsin i = 11.3 ± 0.5 km s−1. Additionally, we find hints for a second non-transiting sub-Saturn mass planet on a ∼71 day orbit using the radial velocity data. This system joins the ranks of a small number of exoplanet host stars (∼100) that have been characterized with asteroseismology. Warm sub-Saturns are rare in the known sample of exoplanets, and thus the discovery of TOI-257b is important in the context of future work studying the formation and migration history of similar planetary systems.