  The total number and luminosity function of the population of dwarf galaxies
of the Milky Way (MW) provide important constraints on the nature of the dark
matter and on the astrophysics of galaxy formation at low masses. However, only
a partial census of this population exists because of the flux limits and
restricted sky coverage of existing Galactic surveys. We combine the sample of
satellites recently discovered by the Dark Energy Survey (DES) with the
satellites found in Sloan Digital Sky Survey (SDSS) Data Release 9 (together
these surveys cover nearly half the sky) to estimate the total luminosity
function of satellites down to $M_{\rm V}=0$. We apply a new Bayesian inference
method in which we assume that the radial distribution of satellites
independently of absolute magnitude follows that of subhaloes selected
according to their peak maximum circular velocity. We find that there should be
at least $124^{+40}_{-27}$ (68 per cent CL, statistical error) satellites
brighter than $M_{\rm V}=0$ within $300$ kpc of the Sun. As a result of our use
of new data and better simulations, and a more robust statistical method, we
infer a much smaller population of satellites than reported in previous studies
using earlier SDSS data only; we also address an underestimation of the
uncertainties in earlier work by accounting for stochastic effects. We find
that the inferred number of faint satellites depends only weakly on the assumed
mass of the MW halo and we provide scaling relations to extend our results to
different assumed halo masses and outer radii. We predict that half of our
estimated total satellite population of the MW should be detected by the Large
Synoptic Survey Telescope. The code implementing our estimation method is
available online.
