  Using three-dimensional simulations, we study the dynamics and final
structure of merging solitonic cores predicted to form in ultra-light axion
dark matter halos. The classical, Newtonian equations of motion of a
self-gravitating scalar field are described by the Schr\"odinger-Poisson
equations. We investigate mergers of ground state (boson star) configurations
with varying mass ratios, relative phases, orbital angular momenta and initial
separation with the primary goal to understand the mass loss of the emerging
core by gravitational cooling. Previous results showing that the final density
profiles have solitonic cores and NFW-like tails are confirmed. In binary
mergers, the final core mass does not depend on initial phase difference or
angular momentum and only depends on mass ratio, total initial mass, and total
energy of the system. For non-zero angular momenta, the otherwise spherical
cores become rotating ellipsoids. The results for mergers of multiple cores are
qualitatively identical.
