Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance

TL;DR

This paper develops a relativistic superfluid model for neutron star crusts, incorporating the Iordanskii force and addressing gauge ambiguities, to improve understanding of superfluid dynamics in extreme astrophysical environments.

Contribution

It introduces a gauge-covariant hydrodynamic model for neutron star crust superfluids, including the Iordanskii force, extending existing mutual friction models for better physical accuracy.

Findings

The model accounts for the Iordanskii force in neutron star superfluids.

Chemical gauge covariance is achieved in the relativistic hydrodynamics.

Different dynamical regimes may explain conflicting results on the Iordanskii force.

Abstract

We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.