On the Dependence of the X-Ray Burst Rate on Accretion and Spin Rate

Nuclear burning and its dependence on the mass accretion rate are fundamental ingredients for describing the complicated observational phenomenology of neutron stars (NSs) in binary systems. Motivated by high-quality burst rate data emerging from large statistical studies, we report general calculations relating the bursting rate to the mass accretion rate and NS rotation frequency. In this first work, we ignore general relativistic effects and accretion topology, although we discuss where their inclusion should play a role. The relations we derive are suitable for different burning regimes and provide a direct link between parameters predicted by theory and what is to be expected in observations. We illustrate this for analytical relations of different unstable burning regimes that operate on the surface of an accreting NS. We also use the observed behavior of the burst rate to suggest new constraints on burning parameters. We are able to provide an explanation for the long-standing problem of the observed decrease of the burst rate with increasing mass accretion that follows naturally from these calculations: when the accretion rate crosses a certain threshold, ignition moves away from its initially preferred site, and this can cause a net reduction of the burst rate due to the effects of local conditions that set local differences in both the burst rate and stabilization criteria. We show under which conditions this can happen even if locally the burst rate keeps increasing with accretion.