Constraining stellar evolution theory with asteroseismology of γ Doradus stars using deep learning: Stellar masses, ages, and core-boundary mixing

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 gamma Doradus stars; these parameters were previously determined from their effective temperature, surface gravity, near-core rotation frequency, and buoyancy travel time Pi (0). 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 Pi (0). 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 is an element of [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 gamma Doradus stars.

Automated summary

The neural network approach developed in this study allows for the derivation of important stellar properties for evolution, such as mass, age, and extent of core-boundary mixing. It also paves the way for inferring mixing profiles throughout the radiative envelope for large samples of gamma Doradus stars in the future.