  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 time scales in each case. We
detect a low frequency mode in the whole parameters space and it was 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 two 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.
