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The standard cosmological scenario predicts a hierarchical formation for galaxies. Many substructures were found in the Galactic halo, identified as clumps in kinematic spaces, like the energy-angular momentum one (E-Lz), under the hypothesis of the conservation of these quantities. If these clumps also feature different chemical properties, e.g. metallicity distribution functions (MDF), they are often associated to independent merger debris. The aim of this study is to explore to what extent we can couple kinematics and metallicities of stars in the Galactic halo to reconstruct the accretion history of the Milky Way. In particular, we want to understand whether different clumps in the E-Lz space with different MDF should be associated to distinct merger debris. We analysed dissipationless, self-consistent high-resolution N-body simulations of a MW-type galaxy accreting a satellite with mass ratio 1:10, with different orbital parameters and metallicity gradients (assigned a posteriori). We confirm that accreted stars from a ~1:10 satellite redistribute in a wide range of E and Lz, due to the dynamical friction, thus not being associated to a single clump. Because satellite stars with different metallicities can be deposited in different regions of the E-Lz space (on average the more metal-rich ones end up more gravitationally bound to the MW), this implies that a single ~1:10 accretion can manifest with different MDFs, in different regions of the E-Lz space. Groups of stars with different E, Lz and metallicities may be interpreted as originating from different satellites, but our analysis shows that these interpretations are not physically motivated. In fact, the coupling of kinematics with MDFs to reconstruct the accretion history of the MW can bias the reconstructed merger tree towards increasing the number of past accretions and decreasing the masses of the progenitor galaxies., Comment: Submitted to A&A. Comments are welcome

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 timescales. We discover degeneracies between the adopted Pop III unknowns, in the predicted metallicity and carbonicity distribution functions and the fraction of C-enhanced stars. Nonetheless, we are able to provide the first available constraints on the EDF, $dN/dE_\star \propto E_{\star}^{-\alpha_e}$ with $1\leq \alpha_e \leq2.5$. In addition, the characteristic mass of the Pop III IMF should be $m_{\rm ch}<100\:{\rm M_\odot}$, assuming a mass range consistent with hydrodynamical simulations (0.1-1000$\:{\rm M_\odot}$). Independent of the assumed Pop III properties, we find that all [C/Fe]>+0.7 stars (with [Fe/H]<-2.8) have been enriched by Pop III supernovae at a $>20\%$ level, and all [C/Fe]>+2 stars at a $>95\%$ level. All very metal-poor stars with $\rm [C/Fe]<0$ are predicted to be predominantly enriched by Pop III hypernovae and/or pair instabillity 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., Comment: 22 pages, 13 figures