The virial mass distribution of ultra-diffuse galaxies in clusters and
  groups
  We use the observed abundances of ultra-diffuse galaxies (UDGs) in clusters
and groups and \Lambda CDM subhalo mass functions to put constraints on the
distribution {of present-day halo masses of satellite} UDGs. If all of the most
massive subhaloes in the cluster host a UDG, UDGs occupy all subhaloes with
\log M_{sub}/M_\odot\gtrsim11. For a model in which the efficiency of UDG
formation is higher around some characteristic halo mass, higher fractions of
massive UDGs require larger spreads in the UDG mass distribution. In a cluster
with a virial mass of 10^{15}M_\odot, the 90% upper limit for the fraction of
UDGs with \log M_{sub}/M_\odot>12 is 7%, occupying 70% of all cluster subhaloes
above the same mass. To reproduce the observed abundances, however, the mass
distribution of satellite UDGs has to be broad, with >30% having \log
M_{sub}/M_\odot<10.9. This strongly supports that UDGs are part of a continuous
distribution in which a majority are hosted by low mass haloes. The abundance
of satellite UDGs may fall short of the linear relation with the cluster/group
mass M_{host} in low-mass hosts, \log M_{host}/M_\odot\sim 12. Characterising
these deviations -- or the lack thereof -- will allow for stringent constraints
on the UDG virial mass distribution.
