Axion Emission from Proton Cooper Pairs in Neutron Stars

We investigate axion emission from singlet proton Cooper pairs in neutron stars, a process that dominates axion emission in young neutron stars in the KSVZ model. By re-deriving its emissivity, we confirm consistency with most existing literature, except for a recent study that exhibits a different dependence on the effective mass. This discrepancy results in more than an order-of-magnitude deviation in emissivity, significantly impacting constraints on the KSVZ axion from the cooling observations of the Cassiopeia A neutron star. Furthermore, we examine uncertainties arising from neutron-star equations of state and their role in the discrepancy, finding that the large deviation persists regardless of the choice of equations of state.