# Vortex buoyancy in superfluid and superconducting neutron stars

## TL;DR

This paper revises the understanding of vortex buoyancy forces in neutron stars, providing corrected expressions for proton and neutron vortices and discussing implications for magnetic field dynamics.

## Contribution

It derives the correct buoyancy force expressions for neutron and proton vortices, correcting previous assumptions and integrating them into existing hydrodynamic frameworks.

## Key findings

- Corrected buoyancy force expressions for vortices.
- Identification of the force's presence in Bekarevich & Khalatnikov's hydrodynamics.
- Discussion of buoyancy effects on neutron star magnetic fields.

## Abstract

Buoyancy of proton vortices is considered as one of the important mechanisms of magnetic field expulsion from the superconducting interiors of neutron stars. Here we show that the generally accepted expression for the buoyancy force is not correct and should be modified. The correct expression is derived for both neutron and proton vortices. It is argued that this force is already contained in the coarse-grained hydrodynamics of Bekarevich & Khalatnikov and its various multifluid extensions, but is absent in the hydrodynamics of Hall. Some potentially interesting buoyancy-related effects are briefly discussed.