2023MNRAS.525..190K

The nature of the first Pop III stars is still a mystery and the energy distribution of the first supernovae is completely unexplored. For the first time we account simultaneously for the unknown initial mass function (IMF), stellar mixing, and energy distribution function (EDF) of Pop III stars in the context of a cosmological model for the formation of a MW-analogue. Our data-calibrated semi-analytic model is based on a N-body simulation and follows the formation and evolution of both Pop III and Pop II/I stars in their proper time-scales. We discover degeneracies between the adopted Pop III unknowns, in the predicted metallicity and carbonicity distribution functions and the fraction of C-enhanced stars. None the less, we are able to provide the first available constraints on the EDF, $dN/dE_\star \propto E_{\star }^{-\alpha _e}$ with 1 ≤ α_e ≤ 2.5. In addition, the characteristic mass of the Pop III IMF should be m_ch < 100 M_⊙, assuming a mass range consistent with hydrodynamical simulations (0.1-1000 M_⊙). Independent of the assumed Pop III properties, we find that all $\rm [C/Fe]\gt +0.7$ stars (with $\rm [Fe/H]\lt -2.8$) have been enriched by Pop III supernovae at a $\gt 20~{{\ \rm per\ cent}}$ level, and all $\rm [C/Fe]\gt +2$ stars at a $\gt 95~{{\ \rm per\ cent}}$ level. All very metal-poor stars with $\rm [C/Fe]\lt 0$ are predicted to be predominantly enriched by Pop III hypernovae and/or pair instability supernovae. To better constrain the primordial EDF, it is absolutely crucial to have a complete and accurate determination of the metallicity distribution function, and the properties of C-enhanced metal-poor stars (frequency and [C/Fe]) in the Galactic halo.