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 Milky Way (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. Comparing the simulated and the observed MDF, we find that in order to predict the formation of hyper-iron-poor stars at [Fe/H] < -4, faint supernova (SN) explosions have to dominate the metal yields produced by Population III (Pop III) stars, disfavouring a Pop III initial mass function that extends to stellar masses >140 M_⊙, 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 {\cal D}_crit = 4.4 × 10^{-9}. Other transition criteria do not predict any C-normal stars below [Fe/H] < -4, at odds with observations.