Semiconvection: theory

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
e-mail: henk@mpa-garching.mpg.de

Received: 16 October 2012
Accepted: 16 February 2013

Abstract

A model is developed for the transport of heat and solute in a system of double-diffusive layers under astrophysical conditions (where viscosity and solute diffusivity are low compared with the thermal diffusivity). The process of formation of the layers is not part of the model but, as observed in geophysical and laboratory settings, is assumed to be faster than the life time of the semiconvective zone. The thickness of the layers is a free parameter of the model. When the energy flux of the star is specified, the effective semiconvective diffusivities are only weakly dependent on this parameter. An estimate is given of the evolution of layer thickness with time in a semiconvective zone. The model predicts that the density ratio has a maximum for which a stationary layered state can exist, R_ρ ≲ Le^−1/2. Comparison of the model predictions with a grid of numerical simulations is presented in a companion paper.