Angular Momentum and the Absence of Vortices in the Cores of Fuzzy Dark Matter Haloes

TL;DR

This paper demonstrates that solitonic cores in fuzzy dark matter halos do not form vortices due to angular momentum, as the angular momentum per particle is insufficient and vortex formation is energetically unfavorable.

Contribution

The study extends previous analysis to fuzzy dark matter, showing explicitly that vortices do not form in solitonic cores from angular momentum, contrasting with vortex formation outside cores.

Findings

Vortices are not expected to form in FDM cores from angular momentum.

Angular momentum per particle in typical halos is below the threshold for vortex formation.

Vortex formation is energetically disfavored even with higher angular momentum.

Abstract

Scalar Field Dark Matter (SFDM), comprised of ultralight ($\gtrsim 10^{-22}$ eV) bosons, is distinguished from massive ($\gtrsim$ GeV), collisionless Cold Dark Matter (CDM) by its novel structure-formation dynamics as Bose-Einstein condensate (BEC) and quantum superfluid with wave-like properties, described by the Gross-Pitaevski and Poisson (GPP) equations. In the free-field (fuzzy) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength $\lambda_{\text{deB}}$, but resembles CDM on larger scales. Virialized haloes have solitonic cores of radius $\sim \lambda_{\text{deB}}$ that follow the ground-state attractor solution of GPP, surrounded by CDM-like envelopes. As superfluid, SFDM is irrotational (vorticity-free) but can be unstable to vortex formation. We previously showed this can happen in halo cores, from angular momentum arising during structure formation, when repulsive self-interaction (SI) is present to support them out to a second length scale $\lambda_{\text{SI}}$ with $\lambda_{\text{SI}} > \lambda_{\text{deB}}$ (the Thomas-Fermi regime), but only if SI is strong enough. This suggested FDM cores (without SI) would not form vortices. FDM simulations later found vortices, but only outside halo cores, consistent with our previous suggestion based upon TF-regime analysis. We extend that analysis now to FDM, to show explicitly that vortices should not arise in solitonic cores from angular momentum, modelling them as either Gaussian spheres or compressible, ($n = 2$)-polytropic, irrotational Riemann-S ellipsoids. We find that, for typical halo spin parameters, angular momentum per particle is below $\hbar$, the minimum required even for one singly-quantized vortex in the centre. Even for larger angular momentum, however, vortex formation is not energetically favoured.