A Numerical Treatment of Double Shell Source Stars

A technique for computing the evolution of stars with a narrow hydrogen-burning shell source, described by Eggleton, has been applied to a model which developed narrow hydrogen and helium burning shells. The technique allows time steps to be taken which are substantially longer than the growth time of the helium shell instability (Schwarzschild & Härm), and we find that this physical instability is numerically suppressed. The test model, a Population I star of 4 $$M_\odot$$ , was followed from the main sequence until it had developed a carbon core of 1.28 $$M_\odot$$ .