Matching the mass function of Milky Way satellites in competing dark matter models

Any successful model of dark matter must explain the diversity of observed Milky Way (MW) satellite density profiles, from very dense ultrafaints to low-density satellites so large that they could be larger than their inferred dark matter haloes. Predictions for these density profiles are complicated by the limitations of simulation resolution in the stripping of subhaloes by the MW system. We consider cold dark matter (CDM), warm dark matter (WDM, 3.3 keV thermal relic power spectrum), and a self-interacting dark matter model (SIDM) that induces gravothermal collapse in low-mass subhaloes. Using N-body simulations combined with a halo stripping algorithm, we find that most CDM and WDM subhaloes of mass > 10(8) M-? are large enough after stripping to fit most satellites; however, the required amount of stripping often requires a stronger tidal field than is available on the subhalo's orbit. The lower concentrations of WDM subhaloes enable more stripping to take place, even on orbits with large pericentres. SIDM cores offer the best fits to massive, low-density satellites at the expense of predicting > 10(9 )M(?) subhaloes to host low-density satellites with no observed analogue. The agreement of the total number of satellites with observations in CDM and WDM depends strongly on the assumptions made to draw the observational estimates. We conclude that an SIDM model must have a very high velocity-dependent cross-section in order to match all satellites, and that WDM offers a marginally better fit than CDM to the MW satellite mass function.