The heat capacity of the neutron star inner crust within an extended NSE model

TL;DR

This study investigates how the distribution of nuclear species in the neutron star inner crust affects heat capacity calculations, highlighting the importance of cluster distributions and temperature-dependent proton fractions for accurate modeling.

Contribution

It introduces an extended NSE model incorporating cluster degrees of freedom and pairing correlations to improve heat capacity estimations in neutron star crusts.

Findings

Cluster distribution impacts heat capacity near the crust and core.

Temperature evolution of proton fraction is crucial for accurate results.

Accounting for nuclear species distribution refines neutron star cooling models.

Abstract

Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasi-particle mean-field Hartree-Fock-Bogoliubov theory with temperature dependent occupation numbers for the quasi-particle states. Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust. Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons. The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity.