3D Vortices and rotating solitons in ultralight dark matter
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.