We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of lowdegree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used χ 2 statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.

Context. While rotation has a major impact on stellar structure and evolution, its effects are not well understood. Thanks to highquality and long timebase photometric observations obtained with recent space missions, we are now able to study stellar rotation more precisely. Aims. We aim to constrain radial differential rotation profiles in γ Doradus (γ Dor) stars, and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation. Methods. We derive a new asymptotic description which accounts for the impact of weak differential near-core rotation on gravitymode period spacings. The theoretical predictions are illustrated from pulsation computations with the code GYRE and compared with observations of γ Dor stars. When possible, we also derive the surface rotation rates in these stars by detecting and analysing signatures of rotational modulation, and compute the core-to-surface rotation ratios. Results. Stellar rotation has to be strongly differential before its effects on period spacing patterns can be detected, unless multiple period spacing patterns can be compared. Six stars in our sample exhibit a single unexplained period spacing pattern of retrograde modes. We hypothesise that these are Yanai modes. Finally, we find signatures of rotational spot modulation in the photometric data of eight targets.Conclusions. If only one period spacing pattern is detected and analysed for a star, it is difficult to detect differential rotation. A rigidly rotating model will often provide the best solution. Differential rotation can only be detected when multiple period spacing patterns have been found for a single star or its surface rotation rate is known as well. This is the case for eight stars in our sample, revealing surface-to-core rotation ratios between 0.95 and 1.05.

The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring Π 0 ), in combination with the effective temperature (T eff ) and surface gravity (log g) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 γ Doradus (γ Dor) stars whose rotation frequency has been derived from Kepler photometry. We make use of two 6D grids of stellar models, one with step core overshooting and one with exponential core overshooting, to evaluate correlations between the three observables Π 0 , T eff , and log g and the mass, age, core overshooting, metallicity, initial hydrogen mass fraction and envelope mixing. We provide multivariate linear model recipes relating the stellar parameters to be estimated to the three observables (Π 0 , T eff , log g). We estimate the (core) mass, age, core overshooting and metallicity of γ Dor stars from an ensemble analysis and achieve relative uncertainties of ∼ 10 per cent for the parameters. The asteroseismic age determination allows us to conclude that efficient angular momentum transport occurs already early on during the main sequence. We find that the nine stars with observed Rossby modes occur across almost the entire main-sequence phase, except close to core-hydrogen exhaustion. Future improvements of our work will come from the inclusion of more types of detected modes per star, larger samples, and modelling of individual mode frequencies.

We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). The new auto_diff module implements automatic differentiation in MESA, an enabling capability that alleviates the need for hard-coded analytic expressions or finite-difference approximations. We significantly enhance the treatment of the growth and decay of convection in MESA with a new model for time-dependent convection, which is particularly important during late-stage nuclear burning in massive stars and electron-degenerate ignition events. We strengthen MESA’s implementation of the equation of state, and we quantify continued improvements to energy accounting and solver accuracy through a discussion of different energy equation features and enhancements. To improve the modeling of stars in MESA, we describe key updates to the treatment of stellar atmospheres, molecular opacities, Compton opacities, conductive opacities, element diffusion coefficients, and nuclear reaction rates. We introduce treatments of starspots, an important consideration for low-mass stars, and modifications for superadiabatic convection in radiation-dominated regions. We describe new approaches for increasing the efficiency of calculating monochromatic opacities and radiative levitation, and for increasing the efficiency of evolving the late stages of massive stars with a new operator-split nuclear burning mode. We close by discussing major updates to MESA’s software infrastructure that enhance source code development and community engagement.

It has been known for several decades that transport of chemical elements is induced by the process of microscopic atomic diffusion. Yet the effect of atomic diffusion, including radiative levitation, has hardly been studied in the context of gravity-mode pulsations of core hydrogen burning stars. In this paper we study the difference in the properties of such modes for models with and without atomic diffusion. We perform asteroseismic modeling of two slowly rotating A-and F-type pulsators, KIC 11145123 ( f rot » -0.010 day 1 ) and KIC 9751996 ( f rot » -0.0696 day 1 ), respectively, based on the periods of individual gravity modes. For both stars, we find models whose g-mode periods are in very good agreement with the Kepler asteroseismic data, keeping in mind that the theoretical/numerical precision of present-day stellar evolution models is typically about two orders of magnitude lower than the measurement errors. Using the Akaike Information Criterion, we have made a comparison between our best models with and without diffusion and found very strong evidence for signatures of atomic diffusion in the pulsations of KIC 11145123. In the case of KIC 9751996 the models with atomic diffusion are not able to explain the data as well as the models without it. Furthermore, we compare the observed surface abundances with those predicted by the best-fitting models. The observed abundances are inconclusive for KIC 9751996, while those of KIC 11145123 from the literature can better be explained by a model with atomic diffusion.

Context. The Kepler and Transiting Exoplanet Survey Satellite (TESS) space telescopes delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars, revealing their numerous gravito-inertial (g) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation, a framework to evaluate the effect of the Coriolis acceleration on g modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far have mostly been neglected in asteroseismology. This extension of the traditional approximation was conceived by re-deriving the traditional approximation in a centrifugally-deformed, spheroidal coordinate system. Aims. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometric observations. Methods. We implemented the new theoretical framework to calculate the centrifugal deformation of pre-computed 1D spherical stellar structure models and computed the corresponding g-mode frequencies, assuming uniform rotation. The framework was evaluated for a grid of stellar structure models covering a relevant parameter space for observed g-mode pulsators. Results. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties of the measured period spacing values in Kepler and TESS data. Conclusions. The effect of the centrifugal acceleration on g modes is formally detectable in modern space photometry. The implementation of the used theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars in order to assess its effect on mode excitation, trapping, and damping.

Context. The efficiency of the transport of angular momentum and chemical elements inside intermediate-mass stars lacks proper calibration, thereby introducing uncertainties on a star’s evolutionary pathway. Improvements require better estimation of stellar masses, evolutionary stages, and internal mixing properties. Aims. Our aim was to develop a neural network approach for asteroseismic modelling, and test its capacity to provide stellar masses, ages, and overshooting parameter for a sample of 37 γ Doradus stars; these parameters were previously determined from their effective temperature, surface gravity, near-core rotation frequency, and buoyancy travel time Π0. Here our goal is to perform the parameter estimation from modelling of individual periods measured for dipole modes with consecutive radial order rather than from Π0. We assess whether fitting these individual mode periods increases the capacity of the parameter estimation. Methods. We trained neural networks to predict theoretical pulsation periods of high-order gravity modes (n ∈ [15, 91]), and to predict the luminosity, effective temperature, and surface gravity for a given mass, age, overshooting parameter, diffusive envelope mixing, metallicity, and near-core rotation frequency. We applied our neural networks for Computing Pulsation Periods and Photospheric Observables (C-3PO) to our sample and compute grids of stellar pulsation models for the estimated parameters. Results. We present the near-core rotation rates (from the literature) as a function of the inferred stellar age and critical rotation rate. We assessed the rotation rates of the sample near the start of the main sequence assuming rigid rotation. Furthermore, we measured the extent of the core overshoot region and find no correlation with mass, age, or rotation. Finally, for one star in our sample, KIC 12066947, we find indications of mode coupling in the period spacing pattern which we cannot reproduce with mode trapping. Conclusions. The neural network approach developed in this study allows the derivation of stellar properties dominant for stellar evolution, such as mass, age, and extent of core-boundary mixing. It also opens a path for future estimation of mixing profiles throughout the radiative envelope, with the aim of inferring these profiles for large samples of γ Doradus stars.

Context. Asteroseismic modelling of the internal structure of main-sequence stars born with a convective core has so far been based on homogeneous analyses of space photometric Kepler light curves of four years in duration, to which most often incomplete inhomogeneously-deduced spectroscopic information was added to break degeneracies. Aims. Our goal is twofold: (1) to compose an optimal sample of gravity-mode pulsators observed by the Kepler space telescope for joint asteroseismic and spectroscopic stellar modelling, and (2) to provide spectroscopic parameters for its members, deduced in a homogeneous way. Methods. We assembled HERMES high-resolution optical spectroscopy at the 1.2 m Mercator telescope for 111 dwarfs, whose Kepler light curves allowed for the determination of their near-core rotation rates. Our spectroscopic information offers additional observational input to also model the envelope layers of these non-radially pulsating dwarfs. Results. We determined stellar parameters and surface abundances from atmospheric analysis with spectrum normalisation based on a new machine-learning tool. Our results suggest a systematic overestimation of metallicity ([M/H]) in the literature for the studied F-type dwarfs, presumably due to normalisation limitations caused by the dense line spectrum of these rotating stars. CNO surface abundances were found to be uncorrelated with the rotation properties of the F-type stars. For the B-type stars, we find a hint of deep mixing from C and O abundance ratios; N abundance uncertainties are too great to reveal a correlation of N with the rotation of the stars. Conclusions. Our spectroscopic stellar parameters and abundance determinations allow for the future joint spectroscopic, astrometric (Gaia), and asteroseismic modelling of this legacy sample of gravity-mode pulsators, with the aim of improving our understanding of transport processes in the core-hydrogen burning phase of stellar evolution.