Slowly accreting neutron stars and the origin of gamma-ray bursts

Old, isolated neutron stars accrete interstellar gas at a rate ∼10¹⁰ g s^-1. At this slow accretion rate, the interior temperature is too low for thermonuclear reactions to proceed, and the hydrogen burns by pycnonuclear reactions. The resulting helium then burns through pycnonuclear triple-α and (α, γ) channels until it is exhausted. As the pressure increases under the weight of the accreted gas, the electron Fermi energy becomes large enough for electron capture to increase the neutron fraction in the nuclei. The layer of accreted gas can then become denser than the underlying crust, and the interface is susceptible to elastic Rayleigh-Taylor instability. We find that a crust supported by relativistic electron degeneracy pressure is unstable when the fractional density decrease at the interface exceeds a critical value between 3% and 8% depending upon the composition of the two layers. The internal and gravitational energy released during the overturn of an unstable interface is typically between 10²⁸ and 10³⁰ ergs cm^-2. This occurs sufficiently deep below the surface that its effects are communicated to the surface seismically. If the star has a magnetosphere, then this will be excited as well, producing a γ-ray burst. If a substantial amount of the energy released is converted into heat locally, then the resulting temperature, roughly 10⁹ K, may be hot enough to trigger thermonuclear reactions and raise the total energy release by a factor ∼30. Energetic and statistical implications of the model are critically examined, and some observable consequences are described. The model's sensitive dependence on poorly known pycnonuclear and thermonuclear reaction rates is emphasized.