THE MASS MIXING LENGTH IN CONVECTIVE STELLAR ENVELOPES

The scale length over which convection mixes mass in a star can be calculated as the inverse of the vertical derivative of the unidirectional (up or down) mass flux. This is related to the mixing length in the mixing length theory of stellar convection. We give the ratio of mass mixing length to pressure scale height for a grid of three-dimensional surface convection simulations, covering from 4300 K to 6900 K on the main sequence, and up to giants at log g = 2.2, all for solar composition. These simulations also confirm what is already known from solar simulations that convection does not proceed by discrete convective elements, but rather as a continuous, slow, smooth, warm upflow and turbulent, entropy deficient, fast down drafts. This convective topology also results in mixing on a scale comparable to the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.