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