Semiconvection: numerical simulations

TL;DR

This paper presents numerical simulations of double-diffusive convection in stellar interiors, validating theoretical models and estimating mixing timescales relevant for astrophysical semiconvection.

Contribution

It provides the first detailed numerical validation of semiconvective mixing theories under astrophysical conditions, including the effects of low viscosity and diffusivity.

Findings

Effective He-diffusion coefficient nearly independent of layering thickness

Predicted mixing timescale around 10^10 years for a 15 solar mass star

Secular increase of layer thickness can reach a significant fraction of a pressure scale height

Abstract

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As in laboratory and geophysical cases convection takes place in a layered form. The proper translation between subsonic flows in a stellar interior and an incompressible (Boussinesq) fluid is given, and the validity of the Boussinesq approximation for the semiconvection problem is checked by comparison with fully compressible simulations. The predictions of a simplified theory of mixing in semiconvection given in a companion paper are tested against the numerical results, and used to extrapolate these to astrophysical conditions. The predicted effective He-diffusion coefficient is nearly independent of the double-diffusive layering thickness $d$. For a fiducial main sequence model (15 $M_\odot$) the inferred mixing time scale is of the order $10^{10}$ yr. An estimate for the secular increase of $d$ during the semiconvective phase is given. It can potentially reach a significant fraction of a pressure scale height.