Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory

TL;DR

This paper compares neutron star models derived from the full BPS Skyrme field theory with those from a mean-field approximation, revealing significant differences and emphasizing the importance of full field calculations.

Contribution

It demonstrates that the full BPS Skyrme model lacks a universal equation of state, unlike the mean-field approach, and quantifies the impact on neutron star properties.

Findings

Full field theory shows non-constant energy density at equilibrium.

Differences between mean-field and full theory can be substantial.

Model results align with some theoretical and observational constraints.

Abstract

Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable. Further, we compare both exact and mean-field results with some theoretical and phenomenological constraints on neutron star properties, demonstrating thus the relevance of our model even in its most simple version.