Decoding the stellar fossils of the dusty Milky Way progenitors
  We investigate the metallicity distribution function (MDF) in the Galactic
halo and the relative fraction of Carbon-normal and Carbon-rich stars. To this
aim, we use an improved version of the semi-analytical code GAlaxy MErger Tree
and Evolution (GAMETE), that reconstructs the hierarchical merger tree of the
MW, following the star formation history and the metal and dust evolution in
individual progenitors. The predicted scaling relations between the dust, metal
and gas masses for MW progenitors show a good agreement with observational data
of local galaxies and of Gamma Ray Burst (GRB) host galaxies at 0.1 < z < 6.3.
We find that in order to reproduce the observed tail of the MDF at [Fe/H] < -4,
faint SN explosions have to dominate the metal yields produced by Pop III
stars, disfavoring a Pop III IMF that extends to stellar masses > 140 M_{sun},
into the Pair-Instability SN progenitor mass range. The relative contribution
of C-normal and C-enhanced stars to the MDF and its dependence on [Fe/H] points
to a scenario where the Pop III/II transition is driven by dust-cooling and the
first low-mass stars form when the dust-to-gas ratio in their parent clouds
exceeds a critical value of D_crit = 4.4 x 10^{-9}.
