The Mass Mixing Length in Convective Stellar Envelopes

TL;DR

This paper calculates the mass mixing length in stellar convection zones using 3D simulations, confirming it aligns with the classical mixing length theory and describing the nature of convective flows.

Contribution

It provides the ratio of mass mixing length to pressure scale height across various stellar types and confirms the continuous nature of stellar convection flows.

Findings

Mass mixing length ratios are consistent with classical mixing length theory.

Convection occurs as a continuous, slow upflow and turbulent downflows.

Convective topology results from mass conservation in stratified atmospheres.

Abstract

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 3D 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 doesn't 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 as that of the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.