  We use a new set of cold dark matter simulations of the local universe to
investigate the distribution of fossils of primordial dwarf galaxies within,
and around the Milky Way. Throughout, we build upon previous results showing
agreement between the observed stellar properties of a subset of the
ultra-faint dwarfs and our simulated fossils. Here, we show that fossils of the
first galaxies have galactocentric distributions and cumulative luminosity
functions consistent with observations. In our model there are ~ 300 luminous
satellites orbiting the Milky Way, ~50-70% of which are well preserved fossils,
with this fraction decreasing with galactocentric distance. Within the Milky
Way virial radius, the majority of these fossils have luminosities L_V<10^5
L_solar. This work produces an overabundance of bright dwarf satellites (L_V >
10^4 L_solar) with respect to observations where observations are nearly
complete. The "bright satellite problem" is most evident in the outer parts of
the Milky Way. We estimate that, although relatively bright, the primordial
stellar populations are very diffuse, producing a population with surface
brightnesses below surveys` detection limits and are easily stripped by tidal
forces. Although we cannot yet present unmistakable evidence for the existence
of the fossils of first galaxies in the Local Group, the results of our studies
suggest observational strategies that may demonstrate their existence.
Primarily, the detection of "ghost halos" of primordial stars around isolated
dwarfs would prove that stars formed in minihalos (M<10^8 M_solar) before
reionization, and strongly suggest that at least a fraction of the ultra-faint
dwarfs are fossils of the first galaxies.
