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

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 (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 mPopIII = [10-300] M⊙ is disfavoured by observations. We present testable predictions for Pop III stars extending down to lower masses, with mPopIII = [0.1-300] M⊙.