The growth of helium burning cores

Helium burning in the convective cores of horizontal branch and `red clump' stars appears to involve a process of `ingestion' of unburnt helium into the core, the physics of which has not been identified yet. I show here that a limiting factor controlling the growth is the buoyancy of helium entering the denser C+O core. It yields a growth rate which scales directly with the convective luminosity of the core, and agrees with constraints on core size from current asteroseismology.Comment: Accepted for publication in A&

Semiconvection: theory

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_\rho\la \mr{Le}^{-1/2}. Comparison of the model predictions with a grid of numerical simulations is presented in a companion paper.Comment: Accepted for publication in Astronomy & Astrophysic