Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

TL;DR

This paper introduces surface corrections to the TOV equations for neutron stars using a macroscopic liquid drop model, providing analytical solutions that improve understanding of nuclear effects on stellar structure.

Contribution

It extends the TOV equations by incorporating surface gradient terms within the effective surface approximation, offering a more accurate macroscopic model of neutron star structure.

Findings

Derived modified TOV equations with surface corrections.

Analytical solutions to the MTOV equations at first order.

Comparison shows improvements over standard TOV results.

Abstract

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation $a/R<<1$, where $a$ is the NS effective-surface (ES) thickness, and $R$ is the effective NS radius. The energy density $\mathcal{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $\Phi(\rho)$ of the energy density is taken into account in the simplest form as expansion in powers of $\rho-\overline{\rho} $, where $\overline{\rho}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions $\rho$ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. The MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.