Constraining stellar evolution theory with asteroseismology of γ Doradus stars using deep learning

Abstract

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.

Predictions for gravity-mode periods and surface abundances in intermediate-mass dwarfs from shear mixing and radiative levitation

“…The periods of the quadrupole modes exhibit clear recurring dips, indicative of trapped modes. Therefore, we use this star to find a reasonable value for η, that produces dips in the period spacing pattern for a model with the parameters found by Mombarg et al (2021). We use a scaling of α ov ≈ 10f ov (Claret & Torres 2017), as in this work, we model the CBM with convective penetration.…”

“…One difference between the setup used in this work and the aforementioned ones, is that here we describe the CBM by convective penetration, following the results from Pedersen et al (2021). It should be noted, however, that no clear distinction between an exponential and step overshoot profile 2 has yet been made for γ Dor stars (Mombarg et al 2019(Mombarg et al , 2021. Our focus is on the prograde dipole modes and radial orders n ∈ [−100, −10], as these are most commonly observed mode geometry in γ Dor and SPB pulsators (e.g.…”

“…Although for a large part of the sample this simple prescription seems sufficient, there are also several stars which show signatures of mode trapping, such that modes are confined in a narrow cavity due to wave reflection caused by a gradient in the local mean molecular weight. The clearest example of a γ Dor star with trapped modes is KIC 11294808, which shows pronounced 'dips' in the period spacing pattern (Van Reeth et al 2015) that could not be explained with the physics used in the models of Mombarg et al (2021). These authors find that similar amplitudes of the dips, compared to those observed in KIC 11294808, are only reproduced at a level of D macro = 0.05 cm 2 s −1 for the macroscopic mix-ing.Yet, such low diffusion coefficients throughout the radiative envelope is four to six orders of magnitude lower than typical values assumed for macroscopic mixing induced by turbulent diffusion in stellar models (Miglio et al 2008;Christophe et al 2018;Ouazzani et al 2019).…”

“…Their work shows a REM profile based on vertical shear is preferred for the majority of the sample containing 26 stars. Similarly, Mombarg et al (2021) measured the value of f ov , the parameter defining the extent of the CBM region (Freytag et al 1996), for a sample of 37 γ Doradus (γ Dor) stars. In their work, a constant value D macro = 1 cm 2 s −1 for the macroscopic mixing in the radiative envelope was chosen.…”

Five young $δ$ Scuti stars in the Pleiades seen with Kepler/K2

“…When 𝑣 sin 𝑖 is available, the stellar inclination is then calculable under the assumption of solid-body rotation, and that assumption is testable (Dziembowski & Goode 1992;Nielsen et al 2015;Benomar et al 2018;Van Reeth et al 2018;Hatta et al 2019). Moreover, the stellar pulsation frequencies place strong constraints on the stellar density and internal structure (Rodríguez-Martín et al 2020;Dhouib et al 2021;Michielsen et al 2021), including on angular momentum transport and chemical mixing (Mombarg et al 2019(Mombarg et al , 2021, provided that the oscillation modes can be identified. Since the observational constraints can come directly from the seismology, the effects of gravity darkening on the observed temper-ature and luminosity become less problematic.…”