A one-zone model for shell flashes on accreting compact stars

Abstract

A one-zone model is developed for analysis of properties of nuclear shell flashes on accreting degenerate dwarfs and neutron stars. The model provides a description of a steady-state nuclear burning and a linear stability analysis with a small number of algebraic equations. Time evolution of the accreted layer is described with two first order ordinary differential equations: one for the heat balance, the second for the mass balance. A very small computing power is required for the analysis. This makes the model attractive for pilot studies, for a simple analysis of many properties of compact stars accreting nuclear fuel, and for teaching purposes. When the accretion rate is either very low or very high, then column density increases with the accretion rate and the models with a steady state nuclear burning are stable. For intermediate rates, the surface mass density decreases with increasing accretion rate and the models are thermally unstable. Near the transition from stability to instability the eigenvalues of the problem are always complex. The models are stable for any value of the accretion rate when either the heat flux from the core exceeds some critical value, or the accreted matter is rich in hydrogen but has nomore » metals, so that nuclear burning may proceed through the proton-proton chain only. Large-amplitude shell flashes develop for all unstable models provided that heat flux from the core is below a certain value. The time interval between the flashes decreases with increasing surface gravity, accretion rate and heat flux from the core. The shortest periods for accreting degenerate dwarfs are just 1 month for hydrogen-rich matter and 1 year for helium-rich matter. The shortest interflash period for a neutron star accreting helium is only 10 s. The values of these periods may be incorrect by a factor of 2 or so, because of simplifications inherent in the one-zone model.« less