Relativistic numerical models for stationary superfluid Neutron Stars

TL;DR

This paper introduces a new numerical model for stationary rotating superfluid neutron stars in general relativity, allowing for different rotation rates of superfluid components and providing the first exact calculations of such models.

Contribution

The authors developed a comprehensive numerical code based on Carter's formalism for superfluid neutron stars, enabling exact modeling without approximations.

Findings

Confirmed existence of prolate-oblate configurations.

Analyzed how rotation rates affect the Kepler limit and mass-density relations.

Simulated neutron-star crusts by extending one fluid outward.

Abstract

We have developed a theoretical model and a numerical code for stationary rotating superfluid neutron stars in full general relativity. The underlying two-fluid model is based on Carter's covariant multi-fluid hydrodynamic formalism. The two fluids, representing the superfluid neutrons on one hand, and the protons and electrons on the other, are restricted to uniform rotation around a common axis, but are allowed to have different rotation rates. We have performed extensive tests of the numerical code, including quantitative comparisons to previous approximative results for these models. The results presented here are the first ``exact'' calculations of such models in the sense that no approximations (other than that inherent in a discretized numerical treatment) are used. Using this code we reconfirm the existence of prolate-oblate shaped configurations. We studied the dependency of the Kepler rotation limit and of the mass-density relation on the relative rotation rate. We further demonstrate how one can simulate a (albeit fluid) neutron-star ``crust'' by letting one fluid extend further outwards than the other, which results in interesting cases where the Kepler limit is actually determined by the outermost but slower fluid.