Gravitational Bose-Einstein condensation of vector or hidden photon dark matter

We study the gravitational Bose-Einstein condensation of a massive vector field in the kinetic regime and the nonrelativistic limit using nonlinear dynamical numerical methods. Gravitational condensation leads to the spontaneous formation of solitons. We measure the condensation time and growth rate, and compare to analytical models in analogy to the scalar case. We find that the condensation time of the vector field depends on the correlation between its different components. For fully correlated configurations, the condensation time is the same as that for a scalar field. On the other hand, uncorrelated or partially correlated configurations condense slower than the scalar case. As the vector soliton grows, it can acquire a net spin angular momentum even if the total spin angular momentum of the initial conditions is zero.