Self-gravitating Vector Dark Matter

TL;DR

This paper derives the non-relativistic limit of a massive vector field, revealing that its self-gravitating solitons behave similarly to scalar field solitons, with unique hedgehog solutions and implications for fuzzy vector dark matter models.

Contribution

It introduces the non-relativistic limit of massive vector fields, characterizes self-gravitating vector solitons, and identifies novel hedgehog solutions not present in scalar theories.

Findings

Vector solitons depend only on total mass and particle mass.

Ground-state vector solitons are indistinguishable from scalar solitons.

Hedgehog vector solitons are a new class with weaker gravitational binding.

Abstract

We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$\mathrm{-}$the gravitational potential and density field$\mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribution of energy across the vector field components, and are indistinguishable from their scalar-field counterparts. Fuzzy Vector Dark Matter models can therefore give rise to halo cores with identical observational properties to the ones in scalar Fuzzy Dark Matter models. We also provide novel hedgehog vector soliton solutions, which cannot be observed in scalar-field theories. The gravitational binding of the lowest-energy hedgehog halo is about three times weaker than the ground-state vector soliton. Finally, we show that no spherically symmetric solitons exist with a divergence-free vector field.