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The metal-poor stars in the Galactic halo are thought to show the imprints of the first (Pop III) stars, and thus provide a glance at the first episodes of star formation. In this work, we aim at understanding whether all very metal-poor stars formed in environments polluted by Pop III supernovae (SNe) and at what level. With a general parametric model for early metal enrichment, we study the chemical abundances (from C to Zn) of an environment imprinted by a single Pop III SN. We investigate how these abundances depend on the initial mass and internal mixing of Pop III stars, as well as on their SN explosion energy. We then study how subsequent generations of normal (Pop II) SNe affect the Pop III chemical signatures. By comparing the observed chemical abundances with our model predictions, we show that stars with [C/Fe] > +2.5 form in environments polluted purely by low-energy Pop III SNe (E SN < 2 × 1051 erg). At lower [C/Fe], stars can be imprinted either by Pop III only, or also by normal Pop II SNe. The probability of being enriched by Pop II SNe increases as [C/Fe] decreases. When Pop II stars contribute more to the pollution, they wash out the diverse chemical peculiarities left by the different Pop III SNe, and the chemical dispersion between their descendants decreases. We conclude that C-normal stars (⁠|$\rm [C/Fe] \le +0.7$|⁠) have likely been enriched by Pop II SNe at a |$\ge 50~{{\ \rm per\ cent}}$| level and we identify in the abundance scatter a key diagnostic to pinpoint the signature of Pop III SNe. [ABSTRACT FROM AUTHOR]

The non-detection of zero-metallicity stars in ultra-faint dwarf galaxies (UFDs) can be used to constrain the initial mass function (IMF) of the first (PopIII) stars by means of a statistical comparison between available data and predictions from chemical evolution models. To this end we develop a model that follows the formation of isolated UFDs, calibrated to best reproduce the available data for the best studied system: Boötes I. Our statistical approach shows that UFDs are the best suitable systems to study the implications of the persisting non-detection of zero-metallicity stars on the PopIII IMF, i.e. its shape, the minimum mass (m min), and the characteristic mass (m ch). We show that accounting for the incomplete sampling of the IMF is essential to compute the expected number of long-lived PopIII stars in inefficiently star-forming UFDs. By simulating the colour–magnitude diagram of Boötes I, and thus take into account the mass-range of the observed stars, we can obtain even tighter constrains on m min. By exploiting the 96 stars with measured metallicities (⁠|$\rm i \lt 19$|⁠) in the UFDs represented by our model, we demonstrate that |$m_{\mathrm{ ch}} \gt 1\: \rm {M_{\odot }}$| or |$m_{\mathrm{ min}} \gt 0.8 \:\rm {M_{\odot }}$| at |$99\%$| confidence level. This means that a present-day IMF for PopIII stars is excluded by our model, and a top-heavy PopIII IMF is strongly favoured. We can limit |$m_{\mathrm{ min}} \gt 0.8\: \rm {M_{\odot }}$| independent of the PopIII IMF shape by targeting the four UFDs Boötes I, Hercules, Leo IV, and Eridanus II with future generation instruments, such as ELT/MOSAIC (⁠|$\rm i \lt 25$|⁠), which can provide samples of >10 000 stars. [ABSTRACT FROM AUTHOR]