Chemical evolution of the Galactic halo through supernova-induced star formation and its implication for population III stars

A model for Galactic chemical evolution, driven by supernova-induced star formation, is formulated and used to examine the nature of the Galactic halo at early epochs. In this model, new stars are formed following each supernova event; thus, their abundance pattern is determined by the combination of heavy elements ejected from the supernova itself and those elements that are already present in the interstellar gas swept up by the supernova remnant. The end result is a prediction of large scatter in the abundance ratios among low-metallicity stars, reflecting a different nucleosynthesis yield for each Type II supernova with a different progenitor mass. Formation of new stars is terminated when supernova remnants sweep up too little gas to form shells. We show from calculations based on the above scenario that (1) the observed [Fe/H] distribution for the Galactic halo field stars can be reproduced without effectively decreasing the heavy-element yields from Type II supernovae by some manipulation required by previous models (e.g., via mass loss from the early Galaxy or later mixing with "pristine" hydrogen clouds), (2) the large observed scatter in the abundance ratio [Eu/Fe] for the most metal-poor stars can also be reproduced, and (3) the frequency distribution of stars in the [Eu/Fe]-[Fe/H] plane can be predicted. Our model suggests that the probability of identifying essentially metal-free stars (Population III) in the local halo is around one in 10(3)-10(4), provided that star formation in the halo is confined to individual gas clouds with a mass of 10(6)-10(7) M. and that the initial mass function of metal-free stars is not significantly different from the Salpeter mass function.