Vortices and rotating solitons in ultralight dark matter

TL;DR

This paper investigates the formation and stability of rotating solitons with vortex lattices in ultralight dark matter, revealing wave-like effects and stable vortex structures through analytical and numerical methods.

Contribution

It demonstrates the emergence of stable rotating solitons with vortex lattices in ultralight dark matter within the Thomas-Fermi regime, combining analytical derivations and 2D simulations.

Findings

Rotating solitons form within a few dynamical times.

Vortices create a solid-body rotation pattern.

The configuration is a stable energy minimum at fixed angular momentum.

Abstract

The dynamics of ultralight dark matter with non-negligible self-interactions are determined by a nonlinear Schr\"odinger equation rather than by the Vlasov equation of collisionless particles. This leads to wave-like effects, such as interferences, the formation of solitons, and a velocity field that is locally curl-free, implying that vorticity is carried by singularities associated with vortices. Using analytical derivations and numerical simulations in 2D, we study the evolution of such a system from stochastic initial conditions with nonzero angular momentum. Focusing on the Thomas-Fermi regime, where the de Broglie wavelength of the system is smaller than its size, we show that a rotating soliton forms in a few dynamical times. The rotation is not associated with a large orbital quantum number of the wave function. Instead, it is generated by a regular lattice of vortices that gives rise to a solid-body rotation in the continuum limit. Such rotating solitons have a maximal radius and rotation rate for a given central density, while the vortices follow the matter flow on circular orbits. We show that this configuration is a stable minimum of the energy at fixed angular momentum and we check that the numerical results agree with the analytical derivations. We expect most of these properties to extend to the 3D case where point vortices would be replaced by vortex rings.