The Shape of Stellar Convection

Recent space missions such as Kepler, TESS, and soon PLATO have provided an abundance of high-quality stellar data, highlighting the need for more accurate models of stellar structure and evolution. A key challenge in this area is understanding how thermal convection contributes to fluid mixing processes in stellar interiors. Thermal convection is fundamentally a multi-dimensional, multi-scale, nonlinear fluid process; evaluating the accuracy of one-dimensional parameterizations of mixing that results from convection is a challenge for stellar structure and evolution. Using the Multi-dimensional Stellar Implicit Code (MUSIC), a time-implicit, fully compressible hydrodynamics code designed for global simulations of stars, we study convection in stars that have a wide range of properties. We apply existing diagnostics for evaluating stellar convection, including three versions of a filling factor for convection, and a non-dimensional parameter called the ``penetration parameter'' based on the convective flux. We also develop two new non-dimensional quantities that we call the plume interaction parameter and the plume merging parameter. We identify a radial shape for the number and the width of convective plumes, and the changing non-local structure of convection as a convection zone deepens. Although the filling factor quantifies the asymmetry of convection, it is not capable of predicting the depth of convective overshooting. Using three different sets of simulations, we confirm that the plume interaction parameter and the plume merging parameter can distinguish between 2D and 3D convection, predict the convective overshooting depth in stars of different masses, and to some extent predict the convective overshooting depth in stars evolving along the red giant branch that have different convection zone sizes.