Abstract
Abstract 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.
Highlights
When a compact object with a solid surface such as a neutron star (NS) is part of a binary system with a less evolved companion, accretion onto the compact object may start, which will lead to the burning of the fresh fuel accumulated on the surface of the neutron stars (NSs)
The effects of mixing should be stronger than those due to changes in effective gravity, making mixing a more plausible cause for the decreasing burst rate with accretion rate; the argument for the mechanism we suggest could be behind this phenomenon relies mostly only on the fact that there is a dependence of the burst rate on a function g, which is greater at the pole than at the equator
Finding the exact formulae is beyond the scope of this paper, even though it definitely warrants further work based on the conclusions of Section 5, where we suggest that they could provide an explanation for the decreasing burst rate
Summary
When a compact object with a solid surface such as a neutron star (NS) is part of a binary system with a less evolved companion, accretion onto the compact object may start, which will lead to the burning of the fresh fuel accumulated on the surface of the NS. Rotation opposes gravity, reducing the local effective gravity, which has a direct effect on the local accretion rate and on how the burning proceeds (for example, determining the most likely ignition colatitude; Cooper & Narayan 2007a; AlGendy & Morsink 2014 and see the sections) Another source of heat that might have significant importance for the burning processes is the heat released by some effective friction that is present at the boundary and the spreading layers between the accretion disk and the surface of the star (Inogamov & Sunyaev 1999, 2010; Kajava et al 2014; Philippov et al 2016). This paper is by necessity leaning toward the abstract side, but we hope it would offer a guide to the theoretical efforts and a bridge between theory and observations
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