On the evolution of slowly accreting neutron stars

In the light of recent calculations of pycnonuclear reaction rates for light elements, we reconsider the problem of slow interstellar accretion onto old, possibly magnetized neutron stars. We argue that accretion will occur at the Hoyle-Lyttleton rate after the star has spun down in < 109 yr. A deep ocean of liquid hydrogen and helium, extending down to depths ∼ 100 m, will cover the surface of the star once it has accreted ∼ 1025 g of gas. Beneath the ocean will be a layer of almost pure solid 16O which undergoes two-stage electron capture to 16C above a pressure 2.7 × 1028 dyne cm-2, corresponding to an accreted mass of ∼ 1027 g. The accreted material will then be potentially vulnerable to elastic Rayleigh-Taylor instability with the old underlying crust below. Taking into account the presence of multiple layers of distinct chemical composition, we conclude that the crust will be stable to small perturbations under the conditions envisaged for instellar accretion. A thick layer of up to 1027 g of metastable 16C will then accumulate. Seismic waves could possibly be released if finite amplitude perturbations are applied or by some other unspecified quake mechanism. They will generally transfer energy into the magnetosphere in the form of relativistic shear Alfvén waves, in spite of the presence of the deep ocean. We discuss the implications of these results to old Galactic neutron stars as sources of gamma-ray bursts. We find that any planar distribution of sources with any luminosity function produces a unique relationship between the source counts and the sky distribution, which is inconsistent with the BATSE data. Wide LMXBs and neutron stars in molecular clouds may also accrete under the circumstances described.