Fast Neutrino Cooling in the Accreting Neutron Star MXB 1659-29

Modeling of crust heating and cooling across multiple accretion outbursts of the low mass X-ray binary MXB 1659-29 indicates that the neutrino luminosity of the neutron star core is consistent with direct Urca (dUrca) reactions occurring in similar to 1% of the core volume. We investigate this scenario with neutron star models that include a detailed equation of state parametrized by the slope of the nuclear symmetry energy L, and a range of neutron and proton superfluid gaps. We find that the predicted neutron star mass depends sensitively on L and the assumed gaps. We discuss which combinations of superfluid gaps reproduce the inferred neutrino luminosity. Larger values of L greater than or similar to 80 MeV require superfluidity to suppress dUrca reactions in low mass neutron stars, i.e., the proton or neutron gap is sufficiently strong and extends to high enough density. However, the largest gaps give masses near the maximum mass, making it difficult to accommodate colder neutron stars. The heat capacities of our models span the range from fully paired to fully unpaired nucleons meaning that long-term observations of core cooling could distinguish between models. As a route to solutions with a larger emitting volume, which could provide a more natural explanation for the inferred neutrino luminosity, we discuss the possibility of alternative, less efficient, fast cooling processes in exotic cores. To be consistent with the inferred neutrino luminosity, such processes must be within a factor of similar to 1000 of dUrca. We discuss the impact of future constraints on neutron star mass, radius, and the density dependence of the symmetry energy.