Proton superconductivity and the masses of neutron stars

The unexpected temperature evolution of the neutron star in the Cassiopeia A supernova remnant (Cas A, for short) has renewed tremendous interest in the cooling mechanisms of neutron stars. In particular, the formation of superconducting protons and superfluid neutrons deep inside the cores of neutron stars have become focal points of the discussion. The purpose of this letter is to add a new aspect to this discussion, which focuses on the connection between proton superconductivity and the masses of neutron stars. Assuming (as is currently the case) that the temperature evolution of Cas A is largely controlled by superconducting protons, we study a series of phenomenological proton-pairing models to determine how deep into the stellar core superconducting protons actually penetrate. This allows us to establish a heretofore unknown relationship between the mass of the neutron star in Cas A and the penetration depth of the superconducting proton phase. This relationship can be used to either predict the depth of the superconducting proton phase, or, conversely, determine the mass of Cas A from a reliable calculation of the size of the proton superconducting phase in superdense neutron star matter. We emphasize that the strategy outlined in this paper can be applied to any other neutron star of similar age, whose temperature might be reliably monitored over a several years period. High-mass neutron stars, such as the recently discovered neutron stars J1614-2230 ($1.97 \pm 0.04\, \msun$) and J0348+0432 ($2.01 \pm 0.04 \, \msun$), appear particularly appealing as a significant fraction of the protons in their cores may be superconducting.