Self-Interaction Controls Vortex Scale in Soliton Mergers

TL;DR

Addressing how self-interactions affect turbulent vortex structure during soliton mergers in ultra-light dark matter, the study solves the nonrelativistic Gross-Pitaevskii-Poisson equations with a dimensionless coupling $g$ across multi-soliton mergers. The authors perform a fourth-order pseudospectral integration and analyze velocity correlations, kinetic-energy spectra, vorticity, and vortex-size distributions. They find that vortex formation is universal, but the vortex scale expands with repulsive $g>0$ and shrinks with attractive $g<0$, accompanied by longer velocity correlation lengths and a shift of $E(k)$ to lower $k$. These results link microphysical self-interactions to macroscopic flow organization in dark matter halos and suggest potential observational signatures in lensing substructure and halo dynamics.

Abstract

This study investigates the impact of self-interaction strength on the formation and scale of turbulent vortex structures during the merger of Bose stars, using numerical simulations of the Gross-Pitaevskii-Poisson (GPP) equations. We find that vortex formation is a universal outcome of soliton mergers, with the vortex size strongly dependent on the self-interaction coupling parameter $g$. Through analysis of velocity correlations, kinetic energy spectra, and vorticity distributions, we conclude that for repulsive self-interaction, the vortex region expands as self-interaction strength increases; conversely, for attractive self-interaction, the vortex region shrinks as self-interaction strength increases.

Figures (8)

• Figure 1: Snapshots of the density field at different time from simulations in a box of size $\widetilde{L}=18$ and total mass $\widetilde{N} = 157$. Upper row is $\widetilde{g} = 0$. Middle row is $\widetilde{g} = 0.01$. Lower row is $\widetilde{g} = -0.01$.
• Figure 2: Density profiles of the halos from simulations (colored dots) with $\widetilde{g} = 0$, $\widetilde{g} = 0.01$, $\widetilde{g} = -0.01$, compared with solitonic profiles (solid lines) as given by Schive:2014hzaPhysRevD.104.083022
• Figure 3: Velocity field snapshots at various self-interaction coupling strengths $\widetilde{g}$. The color map represents the magnitude of the velocity $|\bm{v}|$.
• Figure 4: The log-log plot of velocity correlation functions at different strengths $\widetilde{g}$.
• Figure 5: Normalized energy spectrum at $\widetilde{t}=20$ with different $\widetilde{g}$.