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 virial masses of UDG hosting haloes. If all of the most massive subhaloes in clusters host a UDG, UDGs occupy all subhaloes with $\log M_h/M_\odot\gtrsim11$. 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 virial mass distribution. The 90% upper limit for the fraction of UDGs with $\log M_h/M_\odot>12$ is 7%, occupying 70% of all cluster subhaloes above the same mass. To reproduce the high observed abundances, however, the UDG mass distribution has to be broad, with >30% of all UDGs having $\log M_h/M_\odot<10.9$. This strongly supports that UDGs are part of a continuos distribution in which a majority are hosted by low mass haloes. Deviations from linearity in the relation between the UDG abundance and the cluster/group mass $M_c$ are expected in low mass hosts, $\log M_c/M_\odot\sim 12$, where abundances may fall short of the linear relation. Characterizing these deviations — or the lack thereof — will allow for stringent constraints on the UDG virial mass distribution.
Thu, 7 Dec 17
Comments: submitted to MNRAS Letters, comments welcome