Numerical Simulations of Penetration and Overshoot in the Sun

We present numerical simulations of convective overshoot in a two-dimensional model of the solar equatorial plane. The model equations are solved in the anelastic approximation with enhanced thermal conductivity and viscosity for numerical stability. The simulated domain extends from 0.001 to 0.93 R_solar, spanning both convective and radiative regions. We show that convective penetration leads to a slightly extended, mildly subadiabatic temperature gradient beneath the convection zone, spanning approximately 0.05H_p, below which there is a rapid transition to a strongly subadiabatic region. A slightly higher temperature is maintained in the overshoot region by adiabatic heating from overshooting plumes. This enhanced temperature may partially account for the sound speed discrepancy between the standard solar model and helioseismology. Simulations conducted with tracer particles suggest that a fully mixed region exists down to at least 0.684 R_solar.