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 f ormation, is formulated and used to examine the nature of the Galactic halo at early epochs. In this model, new stars are formed following each supern ova event; thus, their abundance pattern is determined by the combination o f heavy elements ejected from the supernova itself and those elements that are already present in the interstellar gas swept up by the supernova remna nt. 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 n ew stars is terminated when supernova remnants sweep up too little gas to f orm 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 r eproduced 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 cl ouds), (2) the large observed scatter in the abundance ratio [Eu/Fe] for th e most metal-poor stars can also be reproduced, and (3) the frequency distr ibution of stars in the [Eu/Fe]-[Fe/H] plane can be predicted. Our model su ggests that the probability of identifying essentially metal-free stars (Po pulation 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 mas s 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.