Self-similarity relations for cooling superfluid neutron stars

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, $T_{\mathrm{C}}$, 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 $0.6T_{\mathrm{C}}\lesssim T\le T_{\mathrm{C}}$ 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 $T_{\mathrm{C}}$. 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.

arXiv comment10 pages, 14 figures, 2 tables; published in MNRAS. In version 2, typos and references corrected

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• Analyzing Neutron Star in HESS J1731-347 from Thermal Emission and Cooling Theory
• Model-independent constraints on superfluidity from the cooling neutron star in Cassiopeia A
• Constraints on neutron star superfluidity from the cooling neutron star in Cassiopeia A using all Chandra ACIS-S observations
• Cooling compact stars and phase transitions in dense QCD
• Neutrino luminosities and heat capacities of neutron stars in analytic form
• Cooling of neutron stars with diffusive envelopes
• Hybrid cooling of the Cassiopeia A neutron star
• Exploring phases of dense QCD with compact stars
• Neutrino emission from Cooper pairs at finite temperatures
• Cooling of the Cassiopeia A neutron star and the effect of diffusive nuclear burning