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