The chemical abundance patterns observed in metal-poor Galactic halo stars contain the signature of the first supernovae , and thus allows us to probe the first stars that formed in the universe .
We construct a theoretical model for the early chemical enrichment history of the Milky Way , aiming in particular at the contribution from pair-instability supernovae ( PISNe ) .
These are a natural consequence of current theoretical models for primordial star formation at the highest masses .
However , no metal-poor star displaying the distinct PISN signature has yet been observed .
We here argue that this apparent absence of any PISN signature is due to an observational selection effect .
Whereas most surveys traditionally focus on the most metal-poor stars , we predict that early PISN enrichment tends to ‘ overshoot ’ , reaching enrichment levels of [ \mathrm { Ca } / \mathrm { H } ] \simeq - 2.5 that would be missed by current searches .
We utilize existing observational data to place constraints on the primordial initial mass function ( IMF ) .
The number fraction of PISNe in the primordial stellar population is estimated to be < 0.07 , or \lesssim 40 \% by mass , assuming that metal-free stars have masses in excess of 10 ~ { } \mathcal { M _ { \odot } } .
We further predict , based on theoretical estimates for the relative number of PISNe , that the expected fraction of second generation stars below [ \mathrm { Ca } / \mathrm { H } ] = -2 with a dominant ( i.e. , > 90 \% ) contribution from PISNe is merely \sim 10 ^ { -4 } -5 \times 10 ^ { -4 } .
The corresponding fraction of stars formed from gas exclusively enriched by PISNe is a factor of \sim 4 smaller .
With the advent of next generation telescopes and new , deeper surveys , we should be able to test these predictions .