Asteroseismic modelling of intermediate-mass stars

Many fields of astrophysical research rely on our understanding of stellar structure and evolution, as stars drive the chemical evolution of the Universe. The current theory of stellar structure and evolution falls short when it comes to predicting the efficiency of transport of angular momentum and chemical elements, as the underlying mechanisms responsible are not fully known. The recent advent of long-term photometric space- borne missions has boosted the field of asteroseismology, the study and interpretation of pulsations excited in stars. Pulsators of the γ Doradus type, are intermediate-mass stars that burn hydrogen into helium in a convective core. These stars exhibit gravity mode pulsations that allow for scrutiny of the deep stellar interior. The periods of these gravity modes detected in stars show regular patterns that depend on the internal mixing and rotation, making γ Doradus stars powerful laboratories to empirically constrain the efficiencies of angular momentum transport and chemical mixing. Only recently it has become possible to detect gravity modes with ultra-high frequency precision has become possible thanks to the NASA Kepler space telescope.

This thesis relies on detected frequencies of gravity modes excited in γ Doradus stars to perform the most detailed and largest asteroseismic modelling effort of this type of pulsators. Firstly, an asteroseismic diagnostic called the buoyancy travel time is combined with the effective temperature and surface gravity from spectroscopy, to infer stellar masses, ages, and core masses. To this end, a new forward modelling method has been developed, taking the underlying correlation structure of the observables into account, which is often neglected in the conventionally used merit functions. Moreover, multivariate linear models have been devised, which related these observables to the fundamental stellar parameters.

Secondly, a comparison has been made between the predicted pulsation periods from models with and without atomic diffusion (including radiative levitation) for two slowly-rotating γ Doradus pulsators. The effect of atomic diffusion alters the predicted frequencies of gravity modes in these stars significantly. For one star, a statistically significant improvement of the predicted mode frequencies is observed, while for the other star the models with atomic diffusion are not able to explain the data as well as the models without it.

Thirdly, the buoyancy travel time is replaced by the individual periods of the pulsation modes to study if this improves the prediction of the stellar parameters. As this is a high-dimensional problem, an artificial neural network has been trained on a grid of stellar structure and pulsation models. The neural network for Computing Pulsation Periods and Photospheric Observables, C-3PO, allows to predict the pulsation periods, effective temperature, surface gravity, and luminosity for any given set of stellar parameters within the typical values of γ Doradus stars. Using the C-3PO neural network, efficiencies of convective core overshoot, and thus precise stellar ages, have been inferred for a sample of 37 stars. The observed pulsation periods for some stars in the sample revealed that the prescription of chemical mixing in the radiative regions used in this study is missing physics.

Fourthly, predictions for the gravity-mode period spacing patterns and the evolution of the surface abundances are made, using models with microscopic diffusion (i.e. atomic diffusion and radiative levitation) and rotational mixing deduced from self-consistent two-dimensional stellar structure models. With the profile of the mixing efficiency that is obtained with the novel implementation presented in this thesis, it is possible to reproduce dips in the period spacing pattern, which are observed for some stars in the sample. This new generation of models makes it possible to include the observed surface abundances as additional constraints on the chemical mixing, provided that these abundances can be inferred with a precision on [X/H] less than about 0.1 dex.

The work presented in this thesis provides new methods for the asteroseismic modelling of intermediate-mass stars, as well as observational constraints on the chemical mixing and transport of angular momentum during the hydrogen-burning phase