A revised formalism for slowly-rotating superfluid neutron stars in general relativity

TL;DR

This paper develops a corrected formalism for modeling slowly-rotating superfluid neutron stars in general relativity, extending previous single-fluid models to account for non-vanishing energy densities at the star's surface.

Contribution

It introduces a new second-order perturbation framework for superfluid neutron stars, correcting previous formalisms to handle non-zero surface energy densities.

Findings

Corrected the original two-fluid formalism for non-zero surface energy density.

Demonstrated significant impact of corrections on stellar structure models.

Compared models showing improved accuracy in mass and deformation calculations.

Abstract

We discuss slowly-rotating, general relativistic, superfluid neutron stars in the Hartle-Thorne formulation. The composition of the stars is described by a simple two-fluid model which accounts for superfluid neutrons and all other constituents. We apply a perturbed matching framework to derive a new formalism for slowly-rotating superfluid neutron stars, valid up to second-order perturbation theory, building on the original formulation reported by Andersson and Comer in 2001. The present study constitutes an extension of previous work in the single-fluid case where it was shown that the Hartle-Thorne formalism needs to be amended since it does not provide the correct results when the energy density does not vanish at the surface of the star. We discuss in detail the corrections that need to be applied to the original two-fluid formalism in order to account for non vanishing energy densities at the boundary. In the process, we also find a correction needed in the computation of the deformation of the stellar surface in the original two-fluid model in all cases (irrespective of the value of the energy density at the surface). The discrepancies found between the two formalisms are illustrated by building numerical stellar models, focusing on the comparison in the calculation of the stellar mass, the deformation of the star, and in the Kepler limit of rotation. In particular, using a toy-model equation of state for which the energy density does not vanish at the boundary of the star we demonstrate that the corrections to the formalism we find impact the structure of slowly-rotating superfluid neutron stars in a significant way.