Constraining mixing processes in stellar cores using asteroseismology Impact of semiconvection in low-mass stars

Context. The overall evolution of low-mass stars is heavily influenced by the processes occurring in the stellar interior. In particular, mixing processes in convectively unstable zones and overshooting regions affect the resulting observables and main sequence lifetime. Aims. We aim to study the effects of different convective boundary definitions and mixing prescriptions in convective cores of low-mass stars and to distinguish the existence, size, and evolutionary stage of the central mixed zone by means of asteroseismology. Methods. We implemented the Ledoux criterion for convection in our stellar evolution code, together with a time-dependent diffusive approach for mixing of elements when semiconvective zones are present. We compared models with masses ranging from 1.1 M-circle dot to 2 M-circle dot computed with two different criteria for convective boundary definition and included different mixing prescriptions within and beyond the formal limits of the convective regions. Using calculations of adiabatic oscillations frequencies for a large set of models, we developed an asteroseismic diagnosis using only l = 0 and l = 1 modes based on the ratios of small to large separations r(01) and r(10) defined by Roxburgh & Vorontsov (2003, A&A, 411, 215). We analyzed the sensitivity of this seismic tool to the central conditions of the star during the main sequence evolution. Results. The seismic variables r(01) and r(10) are almost linear in the expected observable frequency range, and we show that their slope depends simultaneously on the central hydrogen content, the extent of the convective core, and the amplitude of the sound-speed discontinuity at the core boundary. By considering about 25 modes and an accuracy in the frequency determinations as expected from the CoRoT and Kepler missions, the technique we propose allows us to detect the presence of a convective core and to discriminate the different sizes of the homogeneously mixed central region without the need for a strong prior knowledge on the stellar mass.