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

Abstract

ABSTRACT 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 (mmin), and the characteristic mass (mch). 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 mmin. 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.