On the dark matter content of ultra-diffuse galaxies

I compare the dark matter content within stellar half-mass radius expected in a $\Lambda$CDM-based galaxy formation model with existing observational estimates for the observed dwarf satellites of the Milky Way and ultra-diffuse galaxies (UDGs). The model reproduces the main properties and scaling relations of dwarf galaxies, in particular their stellar mass-size relation. I show that the model also reproduces the relation between the dark matter mass within the half-mass radius, $M_{\rm dm}(<r_{1/2})$, and stellar mass exhibited by the observed dwarf galaxies. The scatter in the $M_{\rm dm}(<r_{1/2})-M_\star$ relation is driven primarily by the broad range of sizes of galaxies of a given stellar mass. I also show the $M_{\rm dm}(<r_{1/2})$ of UDGs are within the range expected in the model for their stellar mass, but they tend to lie above the median relation due to their large sizes. The upper limits on $M_{\rm dm}(<r_{1/2})$ for the dark matter deficient UDGs are also consistent with the range of dark matter masses expected in the model. The most dark matter-deficient galaxies of a given size correspond to halos with the smallest concentrations and the largest ratios of $M_\star/M_{\rm 200c}$. Conversely, the most dark matter-dominated galaxies are hosted by the highest concentration halos with the smallest $M_\star/M_{\rm 200c}$ ratios. Results presented in this paper indicate that dark matter content of observed UDGs may represent a tail of the expected dark matter profiles, especially if the effect of feedback on these profiles is taken into account. Nevertheless, the unusually rich GC populations in some UDG galaxies do indicate unusual evolution. Our results simply indicate that with the current accuracy of the velocity dispersion measurements their $M_{\rm dm}(<r_{1/2})$ are consistent with the range expected in the $\Lambda$CDM model.