Slowly Rotating General Relativistic Superfluid Neutron Stars with Relativistic Entrainment

TL;DR

This paper presents the first fully relativistic model of slowly rotating superfluid neutron stars with entrainment, analyzing how relative rotation affects their mass, shape, and stability.

Contribution

It introduces a second-order relativistic model of superfluid neutron stars with entrainment, including the effects of differential rotation between neutrons and protons.

Findings

Relative rotation influences star mass and shape.

Entrainment affects the star's rotational dynamics.

Model predicts Kepler and mass-shedding limits for superfluid stars.

Abstract

Neutron stars that are cold enough should have two or more superfluids/supercondutors in their inner crusts and cores. The implication of superfluidity/superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect, i.e. the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modelling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic $\sigma$ - $\omega$ mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit.