Ultra-faint dwarf galaxies: unveiling the minimum mass of the first stars

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: Bo\"otes 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 Color Magnitude Diagram of Bo\"otes 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 ($\rm i < 19$) in the UFDs represented by our model, we demonstrate that: $m_{ch} > 1 \rm M_{\odot}$ or $m_{min} > 0.8 \rm M_{\odot}$ 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 $m_{min} > 0.8 \rm M_{\odot}$ independent of the PopIII IMF shape by targeting the four UFDs Bo\"otes I, Hercules, Leo IV and Eridanus II with future generation instruments, such as ELT/MOSAIC ($\rm i < 25$), which can provide samples of >10\,000 stars.