Abundance matching with the mean star formation rate: there is no missing satellites problem in the Milky Way above $\mathbf{M_{200} \sim 10^9\,{\rm \bf M}_\odot}$

Abstract

We introduce a novel abundance matching technique that produces a more accurate estimate of the pre-infall halo mass, $M_{200}$, for satellite galaxies. To achieve this, we abundance match with the mean star formation rate, averaged over the time when a galaxy was forming stars, $\langle {\rm SFR}\rangle$, instead of the stellar mass, $M_*$. Using data from the Sloan Digital Sky Survey, the GAMA survey and the Bolshoi simulation, we obtain a statistical $\langle {\rm SFR}\rangle-{\rm M}_{200}$ relation in $\Lambda{\rm CDM}$. We then compare the pre-infall halo mass, $M^{\rm abund}_{200}$, derived from this relation with the pre-infall dynamical mass, $M^{\rm dyn}_{200}$, for 21 nearby dSph and dIrr galaxies, finding a good agreement between the two. As a first application, we use our new $\langle {\rm SFR}\rangle-{\rm M}_{200}$ relation to empirically measure the cumulative mass function of a volume-complete sample of bright Milky Way satellites within 280 kpc of the Galactic centre. Comparing this with a suite of cosmological 'zoom' simulations of Milky Way-mass halos that account for subhalo depletion by the Milky Way disc, we find no missing satellites problem above $M_{200} \sim 10^9\,{\rm M}_\odot$ in the Milky Way. We discuss how this empirical method can be applied to a larger sample of nearby spiral galaxies.