Asteroseismology of solar-type stars: signatures of convective and/or helium cores

Aims. Several frequency combinations are widely used in the analysis of stellar oscillations for comparisons between models and observations. In particular, the “small separations” can help constraining the stellar cores. We showed in a previous paper that they can change sign, in contradiction with the “asymptotic theory”, and that this behaviour could correspond to signatures of convective and/or helium cores. Here we analyse this behaviour in detail by systematic modelling during stellar evolution. Methods. We computed evolutionary tracks for models with various masses (from 1.05 to 1.25 $M_{\odot}$) and various chemical compositions, with and without overshooting. We computed the adiabatic oscillation frequencies of the models and analysed the evolution of their small separations along an evolutionary track. Results. We find that, for all cases, the stars go through a stage during their evolution, where the small separations computed between degrees $\ell=0$ and $\ell=2$ become negative in the observed range of frequencies. This behaviour is clearly related to the signature of a helium-rich core. We discuss the consequences for interpreting of the acoustic frequencies observed in solar-type stars