Thermal relaxation oscillations in a two-zone model

We simulate the behavior of stars in those advanced evolutionary phases in which thermal cycles have been reported. To this end we consider a two-zone stellar model in hydrostatic equilibrium, consisting of a thin energy-generating shell and a buffer zone on top of it with the rest of the star acting as boundary conditions. Under the conditions apposite to thin-shell helium burning we show that this model can exhibit rigorous thermal limit cycle oscillations. By the same token our result implies that the two-time asymptotic method may be used to bridge such otherwise inaccessible evolutionary phases