Improved mixed dark matter halo model for ultralight axions

We present a complete halo model for mixed dark matter composed of cold (CDM) and ultralight axion-like particles (ULAs). Our treats ULAs as biased tracer CDM, in analogy to treatments massive neutrinos neutral hydrogen. The accounts clustering around CDM host halos, fully models the cross correlations both components. inputs include ULA Jeans scale, soliton density profile. can be used predict power spectrum, $P(k)$, on non-linear scales sub-populations across mass range $10^{-33}\text{ eV}\leq m\leq 10^{-21}\text{ eV}$, calibrated against future DM simulations improve its accuracy. also allows us assess importance various approximations.