Core-halo mass relation of ultralight axion dark matter from merger history

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.