Semiconvection: theory

Abstract

A model is developed for the transport of heat and solute in a system of double-diffusive layers under astrophysical conditions (viscosity and solute diffusivity 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 fast compared to the life time of the semiconvective zone. The thickness of the layers is \tbf{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, $R_ρ\la \mr{Le}^{-1/2}$. Comparison of the model predictions with a grid of numerical simulations is presented in a companion paper.

Accepted for publication in Astronomy & Astrophysics

Cited by in corpus (26)

• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models
• The Compactness of Presupernova Stellar Cores
• Hydrodynamics of core-collapse supernovae and their progenitors
• On Variations Of Pre-Supernova Model Properties
• Beyond Mixing-length Theory: a step toward 321D
• Understanding Jupiter's Interior
• On Carbon Burning in Super Asymptotic Giant Branch Stars
• Evolution of ONeMg Core in Super-AGB Stars towards Electron-Capture Supernovae: Effects of Updated Electron-Capture Rate
• Matter Mixing in Aspherical Core-collapse Supernovae: Three-dimensional Simulations with Single Star and Binary Merger Progenitor Models for SN 1987A
• Double-diffusive erosion of the core of Jupiter
• The Impact of Nuclear Reaction Rate Uncertainties On The Evolution of Core-Collapse Supernova Progenitors
• Semiconvection: numerical simulations
• A New Model for Mixing By Double-Diffusive Convection (Semi-Convection). III. Thermal and Compositional Transport Through Non-Layered ODDC
• Main Sequence Evolution with Layered Semiconvection
• Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets
• The Properties of G-modes in Layered Semi-Convection
• Axisymmetric simulations of the convective overstability in protoplanetary discs
• Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number
• Layer formation in double-diffusive convection over resting and moving heated plates
• 3D Simulations of Semiconvection in Spheres: Turbulent Mixing and Layer Formation
• Overshooting in the core helium burning stage of a $30M_{\odot }$ star using the $k$-$\omega$ model
• The Evolution of Jupiter and Saturn as a function of the Parameter R${}_{\rho }$
• Overshooting by differential heating
• The effects of rotation on a double-diffusive layer in a rotating spherical shell
• Planetary dynamos driven by semiconvection in stably stratified layers