Tully-Fisher Scalings and Boundary Conditions for Wave Dark Matter

TL;DR

This paper explores how specific boundary conditions in wave dark matter models lead to Tully-Fisher-like relations, connecting galaxy rotation speeds with dark matter halo properties.

Contribution

It introduces two boundary conditions that produce Tully-Fisher relations within wave dark matter halos, linking theoretical models to observed galaxy dynamics.

Findings

Boundary condition fixing halo edge length yields $M/v^4=const$.

Boundary condition fixing halo edge density yields $M/v^{3.4}=const$.

These relations resemble the empirical Tully-Fisher relation.

Abstract

We investigate a theory of dark matter called wave dark matter, also known as scalar field dark matter (SFDM) and boson star dark matter or Bose-Einstein condensate (BEC) dark matter (also see axion dark matter), and its relation to the Tully-Fisher relation. We exhibit two boundary conditions that give rise to Tully-Fisher-like relations for spherically symmetric static wave dark matter halos: (BC1) Fixing a length scale at the outer edge of wave dark matter halos gives rise to a Tully-Fisher-like relation of the form $M/v^4=\text{constant}$. (BC2) Fixing the density of dark matter at the outer edge of wave dark matter halos gives rise to a Tully-Fisher-like relation of the form $M/v^{3.4}=\text{const}$.