Characterization of the inner edge of the neutron star crust

TL;DR

This paper investigates the inner edge of neutron star crusts using Monte Carlo simulations and theoretical models to understand its equation of state, structure, and potential astrophysical implications.

Contribution

It introduces a semi-classical Monte Carlo approach combined with Kirkwood--Buff theory and a geometrical model to characterize the neutron star crust's inner edge and its equation of state.

Findings

Maximum isothermal compressibility at dilute neutron gas with non-symmetric clusters

Power-law behavior of nuclear energy in beta-equilibrium with baryon density

Refinement of neutron star mass-radius relation potential

Abstract

The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Using semi-classical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron-star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood--Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated non-symmetric clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in beta-equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron-star crust.