Heat capacity of low density neutron matter: from quantum to classical regimes

TL;DR

This paper investigates the heat capacity of neutron matter across different densities and temperatures relevant to neutron-star crusts, incorporating superfluid transitions and classical limits, and proposes a simple parametrization for use in astrophysical models.

Contribution

It introduces a non-perturbative interpolation method for the heat capacity of neutron matter, bridging quantum and classical regimes, and validates approximate formulas against detailed calculations.

Findings

Levenfish and Yakovlev formula accurately reproduces numerical results below T_sf.

Linear approximation is only valid at temperatures much lower than Fermi temperature.

A simple parametrization of heat capacity is proposed for neutron-star cooling simulations.

Abstract

The heat capacity of neutron matter is studied over the range of densities and temperatures prevailing in neutron-star crusts, allowing for the transition to a superfluid phase at temperatures below some critical temperature $T_{sf}$ and including the transition to the classical limit. Finite temperature Hartree-Fock-Bogoliubov equations (FTHFB) are solved and compared to existing approximate expressions. In particular, the formula given by Levenfish and Yakovlev is found to reproduce the numerical results with a high degree of accuracy for temperatures $T\leq T_{sf}$. In the non-superfluid phase, $T\geq T_{sf}$, the linear approximation is valid only at temperature $T\ll T_{{\rm F} n}$ ($T_{{\rm F} n}$ being the Fermi temperature of the neutron gas) which is rarely the case in the shallow layers of the neutron star's crust. A non-perturbative interpolation between the quantal and the classical regimes is proposed here. The heat capacity, conveniently parametrized solely in terms of $T_{sf}$, $T_{{\rm F} n}$, and the neutron number density $n_n$, can be easily implemented in neutron-star cooling simulations.