Proton superconductivity and the masses of neutron stars

TL;DR

This paper explores how the depth of proton superconductivity inside neutron stars relates to their mass, using models to connect observable temperature evolution with internal core properties, especially in the context of the Cas A neutron star.

Contribution

It introduces a novel relationship between neutron star mass and the penetration depth of superconducting protons, aiding in mass estimation from core superconductivity models.

Findings

Established a link between neutron star mass and proton superconductivity depth.

Provided a method to estimate neutron star mass from superconducting phase size.

Highlighted the relevance for high-mass neutron stars like J1614-2230 and J0348+0432.

Abstract

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.