3D Vortices and rotating solitons in ultralight dark matter

Abstract: We study the formation and the dynamics of vortex lines in rotating scalar dark matter halos, focusing on models with quartic repulsive self-interactions. In the nonrelativistic regime, vortex lines and their lattices arise from the Gross-Pitaevskii equation of motion, as for superfluids and Bose-Einstein condensates studied in laboratory experiments. Indeed, in such systems vorticity is supported by the singularities of the phase of the scalar field, which leads to a discrete set of quantized vortices amid a curl-free velocity background. In the continuum limit where the number of vortex lines becomes very large, we find that the equilibrium solution is a rotating soliton that obeys a solid-body rotation, with an oblate density profile aligned with the direction of the total spin. This configuration is dynamically stable provided the rotational energy is smaller than the self-interaction and gravitational energies. Using numerical simulations in the Thomas-Fermi regime, with stochastic initial conditions for a spherical halo with a specific averaged density profile and angular momentum, we find that a rotating soliton always emerges dynamically, within a few dynamical times, and that a network of vortex lines aligned with the total spin fills its oblate profile. These vertical vortex lines form a regular lattice in the equatorial plane, in agreement with the analytical predictions of uniform vortex density and solid-body rotation. These vortex lines might further extend between halos to form the backbone of spinning cosmic filaments.