Substructure of fuzzy dark matter haloes

Abstract

We derive the halo mass function (HMF) for fuzzy dark matter (FDM) by solving\nthe excursion set problem explicitly with a mass-dependent barrier function,\nwhich has not been done before. We find that compared to the naive approach of\nthe Sheth--Tormen HMF for FDM, our approach has a higher cut off mass and the\ncut off mass changes less strongly with redshifts. Using merger trees\nconstructed with a modified version of the Lacey & Cole formalism that accounts\nfor suppressed small scale power and the scale-dependent growth of FDM haloes\nand the semi-analytic GALACTICUS code, we study the statistics of halo\nsubstructure including the effects from dynamical friction and tidal stripping.\nWe find that if the dark matter is a mixture of cold dark matter (CDM) and FDM,\nthere will be a suppression on the halo substructure on small scales which may\nbe able to solve the Missing Satellites Problem faced by the pure CDM model.\nThe suppression becomes stronger with increasing FDM fraction or decreasing FDM\nmass. Thus, it may be used to constrain the FDM model.\n