2021MNRAS.503.6026R

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: Bootes 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 Bootes 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 ( i < 19) in the UFDs represented by our model, we demonstrate that m_ ch_ > 1\: M_☉ or m_ min_ > 0.8 \: M_☉ 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\: M_☉ independent of the PopIII IMF shape by targeting the four UFDs Bootes I, Hercules, Leo IV, and Eridanus II with future generation instruments, such as ELT/MOSAIC ( i < 25), which can provide samples of >10 000 stars.