Theoretical Models of Superbursts on Accreting Neutron Stars

Abstract

We carry out a general relativistic global linear stability analysis of the amassed carbon fuel on the surface of an accreting neutron star to determine the conditions under which superbursts occur. We reproduce the general observational characteristics of superbursts, including burst fluences, recurrence times, and the absence of superbursts on stars with accretion rates 1044 ergs) superbursts that are inconsistent with observations, in agreement with previous investigations. Also, because of pycnonuclear burning of carbon, they do not have superbursts in the range of accretion rates at which superbursts are actually observed unless the crust is very impure. Stars with less efficient neutrino emission (due to modified Urca reactions, for example) produce bursts that agree better with observations. Stars with highly inefficient neutrino emission in their cores produce bursts that agree best with observations. Furthermore, we find that neutron stars with large radii (R ~ 16 km) produce very energetic superbursts that conflict with observations, even if the core neutrino emission mechanism is highly inefficient. Superburst characteristics are quite sensitive to several other parameters as well, most notably the composition of the accreted gas, concentration of carbon in the ignition region, and degree of crystallization of the crust. All systems that accrete primarily hydrogen and in which superbursts are observed show evidence of H- and He-burning delayed mixed bursts. We speculate that delayed mixed bursts provide sufficient amounts of carbon fuel for superbursts and are thus a prerequisite for having superbursts. We compare our global stability analysis to approximate one-zone criteria used by other authors and identify a particular set of approximations that give accurate results for most choices of parameters.