Gravitationally bound BCS state as dark matter

TL;DR

This paper investigates the formation of a superfluid BCS state in fermionic dark matter halos induced by torsion, proposing a novel model for dark matter structure with potential vortex features.

Contribution

It introduces a mechanism for fermionic dark matter to form a superfluid via torsion-induced attraction, modeling self-gravitating halos with the Bogoliubov-de Gennes formalism.

Findings

Superfluid dark matter halos can form with particle masses around 200 eV.

There is a maximum attractive coupling strength before halo instability occurs.

Dark matter halos may contain vortex lines if they have a superfluid component.

Abstract

We explore the possibility that fermionic dark matter undergoes a BCS transition to form a superfluid. This requires an attractive interaction between fermions and we describe a possible source of this interaction induced by torsion. We describe the gravitating fermion system with the Bogoliubov-de Gennes formalism in the local density approximation. We solve the Poisson equation along with the equations for the density and gap energy of the fermions to find a self-gravitating, superfluid solution for dark matter halos. In order to produce halos the size of dwarf galaxies, we require a particle mass of $\sim 200\mathrm{eV}$. We find a maximum attractive coupling strength before the halo becomes unstable. If dark matter halos do have a superfluid component, this raises the possibility that they contain vortex lines.