Crystallization of the inner crust of a neutron star and the influence of shell effects

T Carreau,F Gulminelli,N Chamel,J M Pearson,A F Fantina

doi:10.1051/0004-6361/201937236

Abstract

Context. In the cooling process of a non-accreting neutron star, the composition and properties of the crust are thought to be fixed at the finite temperature where nuclear reactions fall out of equilibrium. A lower estimate for this temperature is given by the crystallization temperature, which can be as high as ≈7 × 109 K in the inner crust, potentially leading to sizeable differences with respect to the simplifying cold-catalyzed matter hypothesis. Aims. We extend a recent work on the outer crust to the study of the crystallization of the inner crust and the associated composition in the one-component plasma approximation. Methods. The finite temperature variational equations for non-uniform matter in both the liquid and the solid phases are solved using a compressible liquid-drop approach with parameters optimized on four different microscopic models that cover current uncertainties in nuclear modeling. Results. We consider the effect of the different nuclear ingredients with their associated uncertainties separately: the nuclear equation of state, the surface properties in the presence of a uniform gas of dripped neutrons, and the proton shell effects arising from the ion single-particle structure. Our results suggest that the highest source of model dependence comes from the smooth part of the nuclear functional. Conclusions. We show that shell effects play an important role at the lowest densities close to the outer crust, but the most important physical ingredient to be settled for a quantitative prediction of the inner crust properties is the surface tension at extreme isospin values.

Highlights

The essential input determining the composition of the outer crust of a cold non-accreting neutron star (NS) under the cold-catalyzed matter hypothesis is given by the masses of the atomic nuclei, which are confined to the crystalline ion sites
A study of the temperature dependence of shell effects within the finite-temperature extended Thomas–Fermi plus Strutinsky integral approach (TETFSI) using the BSk14 functional was performed in Onsi et al (2008), where it was shown that proton shell corrections decrease substantially around kBT = 1 MeV
We fixed T0, which represents the temperature at which shell effects vanish, and x(T0) to reproduce the TETFSI results of Onsi et al (2008; see Fig. 3), yielding kBT0 = 1 MeV and x(T0) = 0.02. This is a very rough treatment of the temperature dependence of shell effects, but we show that the difference in the results obtained with or without this temperature dependence is smaller than the uncertainty due to our imperfect knowledge of the smooth part of the nuclear functional

Summary

Introduction

The essential input determining the composition of the outer crust of a cold non-accreting neutron star (NS) under the cold-catalyzed matter hypothesis is given by the masses of the atomic nuclei, which are confined to the crystalline ion sites. We here extend the work of Pearson et al (2018) and Fantina et al (2020) by calculating the crystallization temperature and the associated composition in the inner crust in the OCP approximation To this end, we solve the variational equations for non-uniform matter within the compressible liquid-drop (CLD) approach presented in Carreau et al (2019). Our formalism can be extended to account for this distribution of nuclei, following an approach similar to that of Fantina et al (2020) for the outer crust This extension allows a microscopic evaluation of the nuclear distribution and the associated impurity factor.

Model of the inner crust

Inclusion of shell effects

Numerical results

Findings

Conclusions