Soliton formation and the core-halo mass relation: An eigenstate perspective

Ultralight dark matter (ULDM) is an axion-like dark matter candidate with an extremely small particle mass. ULDM halos consist of a spherically symmetric solitonic core and an NFW-like skirt. We simulate halo creation via soliton mergers and use these results to explore the core-halo mass relation. We calculate the eigenstates of the merged halos and use these to isolate the solitonic core and calculate its relative contribution to the halo mass. We compare this approach to using a fitting function to isolate the core and find a difference in masses up to 8. 2%. We analyze three families of simulations---equal-mass mergers, unequal mass mergers, and halos with a two-step merger history. Setting the halo mass to the initial mass in the simulation does not yield a consistent core-halo relationship. Excluding material ``ejected'' by the collision yields a core-halo relationship with a slope of 1/3 for simultaneous mergers and roughly 0. 4 for two-step mergers. Our findings suggest there is no universal core-halo mass relationship for ULDM and shed light on the differing results for the core-halo relationship previously reported in the literature.