Two-fluid models of superfluid neutron star cores

TL;DR

This paper develops and compares relativistic and non-relativistic two-fluid models of neutron star cores, incorporating superfluid neutrons, superconducting protons, and leptons, with a focus on entrainment effects and effective masses.

Contribution

It introduces a comprehensive formalism for modeling neutron star cores using variational principles and nuclear energy density functionals, bridging relativistic and non-relativistic approaches.

Findings

Entrainment effects are interpretable via dynamical effective masses.

Relativistic effective masses are larger than non-relativistic ones.

Neutron effective mass exceeds the bare neutron mass in the core.

Abstract

Both relativistic and non-relativistic two-fluid models of neutron star cores are constructed, using the constrained variational formalism developed by Brandon Carter and co-workers. We consider a mixture of superfluid neutrons and superconducting protons at zero temperature, taking into account mutual entrainment effects. Leptons, which affect the interior composition of the neutron star and contribute to the pressure, are also included. We provide the analytic expression of the Lagrangian density of the system, the so-called master function, from which the dynamical equations can be obtained. All the microscopic parameters of the models are calculated consistently using the non-relativistic nuclear energy density functional theory. For comparison, we have also considered relativistic mean field models. The correspondence between relativistic and non-relativistic hydrodynamical models is discussed in the framework of the recently developed 4D covariant formalism of Newtonian multi-fluid hydrodynamics. We have shown that entrainment effects can be interpreted in terms of dynamical effective masses that are larger in the relativistic case than in the Newtonian case. With the nuclear models considered in this work, we have found that the neutron relativistic effective mass is even greater than the bare neutron mass in the liquid core of neutron stars.