Limits on Population III star formation with the most iron-poor stars

Abstract

We study the impact of star-forming minihaloes, and the initial mass function (IMF) of Population III (Pop III) stars, on the Galactic halo metallicity distribution function (MDF) and on the properties of C-enhanced and C-normal stars at [Fe/H] < −3. For our investigation we use a data-constrained merger tree model for the Milky Way formation, which has been improved to self-consistently describe the physical processes regulating star formation in minihaloes, including the poor sampling of the Pop III IMF. We find that only when star-forming minihaloes are included the low-Fe tail of the MDF is correctly reproduced, showing a plateau that is built up by C-enhanced metal-poor stars imprinted by primordial faint supernovae. The incomplete sampling of the Pop III IMF in inefficiently star-forming minihaloes (<10−3 M<inf>⊙</inf> yr−1) strongly limits the formation of pair-instability supernovae (PISNe), with progenitor masses <it>m</it><inf>PopIII</inf> = [140–260] M<inf>⊙</inf>, even when a flat Pop III IMF is assumed. Second-generation stars formed in environments polluted at >50 per cent level by PISNe are thus extremely rare, corresponding to ≈0.25 per cent of the total stellar population at [Fe/H] < −2, which is consistent with recent observations. The low-Fe tail of the MDF strongly depends on the Pop III IMF shape and mass range. Given the current statistics, we find that a flat Pop III IMF model with <it>m</it><inf>PopIII</inf> = [10–300] M<inf>⊙</inf> is disfavoured by observations. We present testable predictions for Pop III stars extending down to lower masses, with <it>m</it><inf>PopIII</inf> = [0.1–300] M<inf>⊙</inf>.