A new statistical method for the structure of the inner crust of neutron stars

TL;DR

This paper introduces a statistical Gaussian Process Emulator to efficiently explore the energy surface of neutron star crusts, achieving high precision in HFB calculations and revealing the crust's structure as a function of density.

Contribution

The work presents a novel statistical approach that accelerates HFB calculations by tenfold and improves energy precision to distinguish local minima in neutron star crust modeling.

Findings

Gaussian Process Emulator speeds up energy surface exploration

Achieved energy uncertainty of approximately 4 keV per particle

Provided detailed predictions of proton content in neutron star crusts

Abstract

We investigated the structure of the low density regions of the inner crust of neutron stars using the Hartree-Fock-Bogoliubov (HFB) model to predict the proton content $Z$ of the nuclear clusters and, together with the lattice spacing, the proton content of the crust as a function of the total baryonic density $\rho_b$. The exploration of the energy surface in the $(Z,\rho_b)$ configuration space and the search for the local minima require thousands of calculations. Each of them implies an HFB calculation in a box with a large number of particles, thus making the whole process very demanding. In this work, we apply a statistical model based on a Gaussian Process Emulator that makes the exploration of the energy surface ten times faster. We also present a novel treatment of the HFB equations that leads to an uncertainty on the total energy of $\approx 4$ keV per particle. Such a high precision is necessary to distinguish neighbour configurations around the energy minima.