The Rapid Proton Process Ashes from Stable Nuclear Burning on an Accreting Neutron Star

The temperature and nuclear composition of the crust and ocean of an accreting neutron star depend on the mix of material (the ashes) that is produced at lower densities by fusion of the accreting hydrogen and helium. The hydrogen/helium burning is thermally stable at high accretion rates, a situation encountered in weakly magnetic (B ≪ 1011 G) neutron stars accreting at rates > 10-8 M☉ yr-1 and in most accreting X-ray pulsars, where the focusing of matter onto the magnetic poles results in local accretion rates high enough for stable burning. For a neutron star accreting at these high rates, we calculate the steady state burning of hydrogen and helium in the upper atmosphere (ρ < 2 × 106 g cm-3), where T ≈ (5-15) × 108 K. Since the breakout from the "hot" CNO cycle occurs at a temperature comparable to that of stable helium burning (T ≳ 5 × 108 K), the hydrogen is always burned via the rapid proton capture (rp) process of Wallace & Woosley. The rp-process makes nuclei far beyond the iron group, always leading to a mixture of elements with masses A ~ 60-100. The average nuclear mass of the ashes is set by the extent of helium burning via (α, p) reactions and, because these reactions are temperature sensitive, depends on the local accretion rate. Nuclear statistical equilibrium, leading to a composition of mostly iron, occurs only for very high local accretion rates in excess of 50 times the Eddington rate. We briefly discuss the consequences of our results for the properties of the neutron star. The wide range of nuclei made at a fixed accretion rate and the sensitivity of the ash composition to the local accretion rate makes it inevitable that accreting neutron stars have an ocean and crust made up of a large variety of nuclei. This has repercussions for the thermal and electrical properties and structural properties (the shear modulus and viscosity) of the neutron star crust. A crustal lattice as impure as implied by our results will have the conductivity throughout most of its mass set by impurity scattering, allowing for more rapid Ohmic diffusion of magnetic fields than previously estimated for mononuclear mixes.