Asteroseismology of hybrid $\delta$ Scuti--$\gamma$ Doradus pulsating stars

Hybrid $\delta$ Scuti-$\gamma$ Doradus pulsating stars show acoustic ($p$) oscillation modes typical of $\delta$ Scuti variable stars, and gravity ($g$) pulsation modes characteristic of $\gamma$ Doradus variable stars simultaneously excited. Observations from space missions like MOST, CoRoT, and \emph{Kepler} have revealed a large number of hybrid $\delta$ Scuti-$\gamma$ Doradus pulsators, thus paving the way for a exciting new channel for asteroseismic studies. We perform a detailed asteroseismological modeling of five hybrid $\delta$ Scuti-$\gamma$ Doradus stars. We employ a grid-based modeling approach to sound the internal structure of the target stars by employing a huge grid of stellar models from the zero-age main sequence to the terminal-age main sequence, varying parameters like stellar mass, effective temperature, metallicity and core overshooting. We compute their adiabatic radial ($\ell= 0$) and non-radial ($\ell= 1, 2, 3$) $p$ and $g$ mode periods. We employ two model-fitting procedures to searching for the models that best reproduce the observed pulsation spectra of each target star, that is, the asteroseismological models. We derive the fundamental parameters and the evolutionary status of five hybrid $\delta$ Scuti-$\gamma$ Doradus variable stars recently observed with the CoRoT and \emph{Kepler} space missions: CoRoT 105733033, CoRoT 100866999, KIC 11145123, KIC 9244992, and HD 49434. The asteroseismological model for each star results from different criteria of model selection, in which we take full advantage of the richness of periods that characterizes the pulsation spectra of this kind of stars.