A polytropic model for the helium shell flash

Abstract

A model consisting of two polytropes is constructed, to represent a helium core of a star during the helium shell flash occurring at the onset of helium burning in a degenerate core. The maximum temperature reached during the flash can be predicted as a function of core mass and mass inside the helium burning shell. This temperature will generally be too low for the production of neutrons out of 14N. Some additional results on the helium shell flash in a star of 1.3 M| are also presented. Since the first numerical results on stellar evolution through the helium flash were published by Schwarzschild and H~irm (1962), this part of stellar evolution computa- tions has been known for its numerical difficulties. These are caused by a short evo- lutionary timescale in the central part of the star in contrast to slow changes in the rest of the star. Following the evolution timestep by timestep one has to choose a certain chemical composition and mass for the stellar model and for another set of these parameters the computations must be repeated. This was done by Schwarz- schild and Hfirm in several papers (H/irm and Schwarzschild, 1964, 1966). A com- pletely different approach, which avoids these time-consuming computations, is the use of polytropic models. These were used by Sugimoto (1964), to calculate models for the helium flash as a function of core mass. Including the weak interaction neutrino processes leads to a different kind of helium flash, burning in a shell around the center (Thomas, 1965). This introduces the mass inside this shell as a new parameter, which enters the helium flash computations. The polytropic model presented here provides an answer to the question, how changes in this mass value change the behavior of the flash. But first some results using corrected neutrino rates are given, as obtained with the method described in Thomas (1967) (referred to as paper I). These cover the phase from the beginning of the flash until shortly after the top of the flash, which is defined by the maximum rate of nuclear energy generation. Because energy generation depends on density, too, this is not identical with the maximum temperature reached during the flash. The stellar model has a total mass of 1.3 M@ and a chemical composition, X=0.9, Z=0.001, the sequence leading to the flash models started at model 303 of paper I, the plasma neutrino rates being decreased by a factor of 4.