A stochastic model of the chemical enrichment of metal-poor systems by core-collapse ( Type II ) supernovae is presented , allowing for large-scale mixing of the enriched material by turbulent motions and cloud collisions in the interstellar medium .
Infall of pristine material is taken into account by following the evolution of the gas density in the medium .
Analytical expressions were derived for the number of stars enriched by a given number of supernovae , as well as for the amount of mass with which the ejected material from a supernova is mixed before being locked up in a subsequently formed star .
It is shown that for reasonable values of the gas density ( \sim 0.1 cm ^ { -3 } ) and of the supernova rate ( \sim 0.25 kpc ^ { -3 } Myr ^ { -1 } ) of the Galactic halo , the resulting metallicity distributions of the extreme Population II stars show a distinct cut-off at [ \mathrm { Fe } / \mathrm { H } ] \simeq - 4 .
In fact , by assuming no low-mass Population III stars were able to form out of the primordial interstellar medium , the derived fraction of stars below [ \mathrm { Fe } / \mathrm { H } ] = -4 is in agreement with observations .
Moreover , the probability is high that even the most metal-poor stars observed to date have been enriched by several contributing supernovae .
This partly explains the relatively small star-to-star scatter in many chemical-abundance ratios for stars down to [ \mathrm { Fe } / \mathrm { H } ] = -4 , as recently found in several observational studies .
Contribution from the thermonuclear ( Type Ia ) supernovae is found to be negligible over almost the entire extremely metal-poor regime .
Although the fraction of contaminated stars may increase rapidly towards [ \mathrm { Fe } / \mathrm { H } ] = -2.5 , the fraction of stars with iron primarily from Type Ia supernovae remains small .
The stars that are heavily polluted by Type Ia supernovae are pushed towards higher metallicities , creating a hole/bump in the metallicity distribution .
Such features could be used to reveal the possible presence of subpopulations of Galactic halo stars that have been enriched by Type Ia supernovae .