Self-similarity relations for cooling superfluid neutron stars

TL;DR

This paper develops analytic self-similar relations to model the cooling of superfluid neutron stars, enabling the reconstruction of their thermal history and neutrino emission based on surface temperature observations.

Contribution

It introduces a novel analytic framework for describing neutron star cooling during superfluid transition, linking surface temperature data to internal superfluid properties.

Findings

Cooling within 0.6 T_C to T_C is described by self-similar relations.

Models can reconstruct the star's cooling history and neutrino emission levels.

Application to Cassiopeia A provides insights into its superfluid properties.

Abstract

We consider models of cooling neutron stars with nucleon cores which possess moderately strong triplet-state superfluidity of neutrons. When the internal temperature drops below the maximum of the critical temperature over the core, $T_{\rm C}$, this superfluidity sets in. It produces a neutrino outburst due to Cooper pairing of neutrons which greatly accelerates the cooling. We show that the cooling of the star with internal temperature $T$ within $0.6\,T_{\rm C} \lesssim T \leq T_{\rm C}$ is described by analytic self-similar relations. A measurement of the effective surface temperature of the star and its decline, supplemented by assumptions on star's mass, radius and composition of heat-blanketing envelope, allows one to construct a family of cooling models parametrized by the value of $T_{\rm C}$. Each model reconstructs cooling history of the star including its neutrino emission level before neutron superfluidity onset and the intensity of Cooper pairing neutrinos. The results are applied to interpret the observations of the neutron star in the Cassiopeia A supernova remnant.