A comparison of the filling factor in hydrodynamic simulations of pre-main-sequence stars

To interpret high-quality data produced from recent space missions such as Kepler and TESS, it is necessary to develop theoretical and computational modeling of convection under realistic stellar conditions. A major open question surrounding convection in stars is the amount of convective overshooting that takes place and how this affects stellar evolution. Overshooting depth has been theoretically linked to the filling factor, the fraction of horizontal area occupied by overshooting plumes at the edge of the unstable zone. Using the stratification in density, temperature, and luminosity from the stellar evolution code MESA (Paxton et al. 2010), we produce global multi-dimensional hydrodynamic simulations of a series of realistic pre-main-sequence stars with the MUltidimensional Stellar Implicit Code (MUSIC). Following the theoretical work of Zahn (1991), we directly calculate the filling factor from our simulations.  We relate the filling factor to the stellar mass, gravitational acceleration, convective velocity, and overshooting depth of these stars.