The most metal-poor , high redshift damped Lyman \alpha systems ( DLAs ) provide a window to study some of the first few generations of stars .
In this paper , we present a novel model to investigate the chemical enrichment of the near-pristine DLA population .
This model accounts for the mass distribution of the enriching stellar population , the typical explosion energy of their supernovae , and the average number of stars that contribute to the enrichment of these DLAs .
We conduct a maximum likelihood analysis of these model parameters using the observed relative element abundances ( [ C/O ] , [ Si/O ] , and [ Fe/O ] ) of the 11 most metal-poor DLAs currently known .
We find that the mass distribution of the stars that have enriched this sample of metal-poor DLAs can be well-described by a Salpeter-like IMF slope at M > 10 ~ { } { M } _ { \odot } and that a typical metal-poor DLA has been enriched by \lesssim 72 massive stars ( 95 per cent confidence ) , with masses \lesssim 40 ~ { } { M _ { \odot } } .
The inferred typical explosion energy ( \hat { E } _ { exp } = 1.8 ^ { +0.3 } _ { -0.2 } \times 10 ^ { 51 } ~ { } { erg } ) is somewhat lower than that found by recent works that model the enrichment of metal-poor halo stars .
These constraints suggest that some of the metal-poor DLAs in our sample may have been enriched by Population II stars .
Using our enrichment model , we also infer some of the typical physical properties of the most metal-poor DLAs .
We estimate that the total stellar mass content is \log _ { 10 } ( M _ { \star } / { M _ { \odot } } ) = 3.5 ^ { +0.3 } _ { -0.4 } and the total gas mass is \log _ { 10 } ( { M _ { gas } } / ~ { } { M _ { \odot } } ) = 7.0 ^ { +0.3 } _ { -0.4 } for systems with a relative oxygen abundance [ O/H ] \approx - 3.0 .