A numerical test of the quasi-equilibrium approximation for stellar silicon burning

Abstract

A measure of the range of the validity of the nuclear quasi-equilibrium approximation, employed byBodansky, Clayton andFowler (1968) for the treatment of stellar silicon burning, is obtained by comparison of the predicted abundances with the results of a numerical solution of the equations for the time rates of change of the nuclear abundances. The results of these calculations, performed for a temperatureT=3×10⁹K, are compared with those obtained by Bodanskyet al. for a temperatureT=5×10⁹K. The time required for the realization of the quasi-equilibrium condition at high temperatures is found to comprise a more substantial fraction of the silicon burning lifetime. This behavior is found to be attributable to the relative temperature sensitivities of the nuclear photodisintegration rates which determine the silicon burning lifetime and the charged particle reaction rates (largely Ti⁴⁴(α,p) V⁴⁷) which determine the rate of buildup of iron peak nuclei.