Testing the cores of first ascent red-giant stars using the period spacing of g modes

In the context of the determination of stellar properties using asteroseismology, we study the influence of rotation and convective-core overshooting on the properties of red-giant stars. We used models in order to investigate the effects of these mechanisms on the asymptotic period spacing of gravity modes ($\Delta \Pi_1$) of red-giant stars that ignite He burning in degenerate conditions (M$\lesssim$2.0 M$_{\odot}$). We also compare the predictions of these models with Kepler observations. For a given $\Delta\nu$, $\Delta \Pi_1$ depends not only on the stellar mass, but also on mixing processes that can affect the structure of the core. We find that in the case of more evolved red-giant-branch (RGB) stars and regardless of the transport processes occurring in their interiors, the observed $\Delta \Pi_1$ can provide information as to their stellar luminosity, within ~10-20%. In general, the trends of $\Delta \Pi_1$ with respect to mass and metallicity that are observed in Kepler red-giant stars are well reproduced by the models.