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

Abstract

We study the impact of star-forming mini-haloes, 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 mini-haloes, including the poor sampling of the Pop III IMF. We find that only when star-forming mini-haloes are included the low-Fe tail of the MDF is correctly reproduced, showing a plateau that is built up by C-enhanced metal-poor (CEMP) stars imprinted by primordial faint supernovae. The incomplete sampling of the Pop III IMF in inefficiently star-forming mini-haloes (< $10^{-3}$ $M_{\odot }$/yr) strongly limits the formation of Pair Instability Supernovae (PISNe), with progenitor masses $m_{\mathrm{popIII}}$=[140-260] $M_{\odot }$, even when a flat Pop III IMF is assumed. Second-generation stars formed in environments polluted at >50% level by PISNe are thus extremely rare, corresponding to $\approx$ 0.25% 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 $m_{\mathrm{popIII}}$=[10-300] $M_{\odot }$ is disfavoured by observations. We present testable predictions for Pop III stars extending down to lower masses, with $m_{\mathrm{popIII}}$=[0.1-300] $M_{\odot }$.

15 pages, 11 figures. Accepted for publication in MNRAS. The only change is the correction of a mistake in the list of authors

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