  In the context of structure formation with ultralight axion dark matter, we
offer an alternative explanation for the mass relation of solitonic cores and
their host halos observed in numerical simulations. Our argument is based
entirely on the mass gain that occurs during major mergers of binary cores and
largely independent of the initial core-halo mass relation assigned to hosts
that have just collapsed. We find a relation between the halo mass $M_h$ and
corresponding core mass $M_c$, $M_c\propto M_h^{2\beta-1}$, where $(1-\beta)$
is the core mass loss fraction. Following the evolution of core masses in
stochastic merger trees, we find empirical evidence for our model. Our results
are useful for statistically modeling the effects of dark matter cores on the
properties of galaxies and their substructures in axion dark matter
cosmologies.
