Model-independent constraints on superfluidity from the cooling neutron star in Cassiopeia A

TL;DR

This paper develops a model-independent method to analyze neutron star cooling, specifically focusing on neutrino emission due to neutron superfluidity, and applies it to the neutron star in Cassiopeia A to constrain superfluid properties.

Contribution

It introduces a model-independent analytical framework for neutrino emissivity from neutron superfluidity, enabling analysis of neutron star cooling without specific interior models.

Findings

Constrained the maximum critical temperature of neutron pairing to (5-10)×10^8 K.

Derived analytical formulas for neutrino luminosity applicable across various equations of state.

Provided constraints on the efficiency of the Cooper Pair Formation neutrino process.

Abstract

We present a new model-independent (applicable for a broad range of equations of state) analysis of the neutrino emissivity due to triplet neutron pairing in neutron star cores. We find that the integrated neutrino luminosity of the Cooper Pair Formation (CPF) process can be written as a product of two factors. The first factor depends on the neutron star mass, radius and maximal critical temperature of neutron pairing in the core, $T_{Cn \mathrm{max}}$, but not on the particular superfluidity model; it can be expressed by an analytical formula valid for many nucleon equations of state. The second factor depends on the shape of the critical temperature profile within the star, the ratio of the temperature $T$ to $T_{Cn \mathrm{max}}$, but not on the maximal critical temperature itself. While this second factor depends on the superfluidity model, it obeys several model-independent constraints. This property allows one to analyse the thermal evolution of neutron stars with superfluid cores without relying on a specific model of their interiors. The constructed expressions allow us to perform a self-consistent analysis of spectral data and neutron star cooling theory. We apply these findings to the cooling neutron star in the Cassiopeia A supernova remnant using 14 sets of observations taken over 19 years. We constrain $T_{Cn\mathrm{max}}$ to the range of $ (5-10)\times 10^8$ K. This value depends weakly on the equation of state and superfluidity model, and will not change much if cooling is slower than the current data suggest. We also constrain the overall efficiency of the CPF neutrino luminosity.