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

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 $ρ_b$. The exploration of the energy surface in the $(Z,ρ_b)$ 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.