Core Overshoot Constrained by the Absence of a Solar Convective Core and Some Solar-Like Stars

Convective-core overshoot mixing is a significant uncertainty in stellar evolution. Because numerical simulations and turbulent convection models predict exponentially decreasing radial rms turbulent velocity, a popular treatment of the overshoot mixing is to apply a diffusion process with exponentially decreasing diffusion coefficient. It is important to investigate the parameters of the diffusion coefficient because they determine the efficiency of the mixing in the overshoot region. In this paper, we have investigated the effects of the core overshoot mixing on the properties of the core in solar models and have constrained the parameters of the overshoot model by using helioseismic inferences and the observation of the solar 8B neutrino flux. For solar-mass stars, the core overshoot mixing helps to prolong the lifetime of the convective core developed at the ZAMS. If the strength of the mixing is sufficiently high, the convective core in a solar model could survive till the present solar age, leading to large deviations of the sound-speed and density profiles comparing with the helioseismic inferences. The 8B neutrino flux also favours a radiative solar core. Those provide a constraint on the parameters of the exponential diffusion model of the convective overshoot mixing. A limited asteroseismic investigation of 13 Kepler low-mass stars with 1.0 < M < 1.5 shows a mass-dependent range of the overshoot parameter. The overshoot mixing processes for different elements are analyzed in detail. It is found that the exponential diffusion overshoot model leads to different effective overshoot mixing lengths for elements with different nuclear equilibrium timescale.