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

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. We study the effects of different convective boundary definitions and mixing prescriptions in convective cores of low-mass stars, to discriminate the existence, size, and evolutionary stage of the central mixed zone by means of asteroseismology. 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 M* to 2 M* computed with two different criteria for convective boundary definition and including 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 r01 and r10 defined by Roxburgh & Vorontsov (2003). These variables 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 of a strong a priori for the stellar mass.