Relaxation of structures resulting from head-on mergers of ultralight bosonic dark matter cores

In this work, we study some features of head-on mergers of equilibrium solutions of the Gross-Pitaevskii-Poisson system that rules the dynamics of the ultralight bosonic dark matter model. The importance of equilibrium solutions is that they play the role of halo cores in structure formation simulations. We consider a given range of initial conditions in order to sample the parameter space in terms of mass ratio and head-on momentum. In each case, we analyze the relaxation process induced by gravitational cooling in the high and low momentum regimes and estimate the relaxation timescales in each case. We detect a low frequency mode in the whole parameters space and it is found that the resulting configuration oscillates under this mode with amplitude that depends on the mass ratio and head-on momentum. In some cases, the resulting configuration oscillates with changes in density of 2 orders of magnitude and with a matter distribution that is far from isotropic. These results could contribute to the collection of possible mass distributions considered in the reconstruction of mass profiles obtained in structure formation simulations.