A new 1-D core convection zone model including the penetration region

We have been studying convection, mass entrainment, and mixing processes in the convective boundary region as well as the radiative envelope for a model star of 25 solar masses using the 3-D stellar hydrodynamics code PPMstar. We will report on the portion of this work that focuses on the effects of radiation pressure in the equation of state and especially on radiative diffusion. We will show the general features of core convection for this star from a high-resolution simulation on a grid of 2688³ cells using volume rendered movies. The convection flow is dominated by a global-scale dipole circulation pattern, which strongly suggests that no local model of convection will be adequate. Through very long duration simulations in 3D on grids of 896³ cells, we have followed the steady formation of a penetrative convection region. The results of 3 such simulations have guided us in the construction of a new 1-D model for the core convection zone that includes a penetrative convection region and that is in thermal and dynamical equilibrium. There are no adjustable parameters of this model. However, a knowledge of the turbulent dissipation rate of kinetic energy in the convection zone is needed. We will show that this can be obtained in a short 3-D simulation on a modest grid. Alternatively, if a set of such simulations are tabulated, in the manner of a tabular equation of state, the turbulent dissipation rate can be interpolated. The dissipation rate is important, but plays only a quantitatively minor role in the final equilibrium. Therefore the equilibrium model is not unduly sensitive to small errors in this dissipation estimate. Results of our simulations will be shown along with the equilibrium convection zone models that they imply, and the method for working with the new model will be described.