Slowly Accreting Neutron Stars and the Origin of Gamma-Ray Bursts

Old, isolated neutron stars accrete interstellar gas at a rate of about 10 to the 10th g/s. 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-alpha and (alpha, gamma) 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. 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 percent, depending upon the composition of the two layers. If the star has a magnetosphere, then this will be excited as well, producing a gamma-ray burst. If a substantial amount of the energy released is converted into heat locally, then the resulting temperature, roughly one billion K, may be hot enough to trigger thermonuclear reactions and raise the total energy release by a factor of about 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.