Limits on Energy Storage in the Crusts of Accreting Neutron Stars

Abstract

We have carried out a systematic study of the storage of nuclear and gravitational energy in the crusts of old neutron stars that are slowly accreting matter from the interstellar medium or distant binary companion stars. We considered neutron-star masses, radii, and accretion rates in the ranges 0.1-2.8 M☉, 7-150 km, and 1010-1016 g s-1, respectively. We also investigated the effects of variations in resulting from periodic passages of the neutron star through the Galactic midplane and/or occasional encounters with molecular clouds. We found, consistent with earlier work, that pycnonuclear reactions lead to the development of density inversions in the crust; the strongest inversions (of order 2% in density), which occur at the interface between 16C and heavier nuclei, store ~1041 ergs of gravitational potential energy. If an instability can trigger the overturn of such an inversion, the released energy would ignite a powerful thermonuclear flash, and the resulting starquake might result in magnetospheric effects that lead to the emission of a γ-ray burst or other energetic astrophysical phenomenon. Although the isotropy of the distribution of γ-ray burst sources, as determined by the BATSE experiment, precludes the possibility that all γ-ray bursts are associated with neutron stars in the Galactic disk, it remains possible that a subset of the observed bursts have their origin in events of this type. From our calculations, we determined that the total nuclear energy that can be stored in the crust of a neutron star is limited by the 16C +16C pycnonuclear reaction, which converts the accreted material at a density of ~5 × 1010 g cm-3 into nuclei substantially closer to nuclear equilibrium. As a result, the total (nuclear plus gravitational) energy, Etot, that can be stored is quite generally limited to less than ~1046 ergs, irrespective of neutron-star mass, radius, mean , or variations in . For =1010 g s-1, it takes ~1010 yr for maximum energy storage to be achieved; for higher accretion rates, the required time decreases very nearly as −1. For 3×1015 g s-1, thermonuclear flashes in the helium shell greatly reduce Etot. Irrespective of the γ-ray burst emission mechanism, the upper limit that we have obtained on Etot places a strong constraint on any model that ascribes a subset of γ-ray bursts to the emission of energy stored in the crusts of neutron stars. Our results are also relevant to any other energetic celestial phenomenon that might be associated with a Galactic-disk population of isolated neutron stars.