The detectability of the first stars and their cluster enrichment signatures

We conduct a comprehensive investigation of the detectability of the first stars and their enrichment signatures in galaxy clusters. As the initial mass function (IMF) of these Population III stars is unknown and likely to be biased to high masses, we base our study on analytical models that parameterize these uncertainties and allow us to make general statements. We show that the mean metallicity of outflows from Population III objects containing these stars is well above the critical transition metallicity (Z_cr ∼ 10 ^-4 Z_⊙) that marks the formation of normal stars. Thus, the fraction of Population III objects formed as a function of redshift is heavily dependent on the distribution of metals and fairly independent of the mean metallicity of the universe, or the precise value of Z_cr. Using an analytic model of inhomogeneous structure formation, we study the evolution of Population III objects as a function of the star formation efficiency, IMF, and efficiency of outflow generation. For all models, Population III objects tend to be in the 10^6.5-10^7.0 M_⊙ mass range, just large enough to cool within a Hubble time, but small enough that they are not clustered near areas of previous star formation. Although the mean metallicity exceeds Z_cr at z ∼ 15 in all models, the peak of Population III star formation occurs at z ∼ 10, and such stars continue to form well into the observable range. We discuss the observational properties of these objects, some of which may have already been detected in ongoing surveys of high-redshift Lyα emitters. Finally, we combine our Population III distributions with the yield models of Heger & Woosley to study their impact on the intracluster medium (ICM) in galaxy clusters. We find that Population III stars can contribute no more than 20% of the iron observed in the ICM, but if they form with characteristic masses ∼200-260 M_⊙, their peculiar elemental yields help to reconcile theoretical models with the observed Fe and Si/Fe abundances. However, these stars tend to overproduce S/Fe and can account only for the O/Fe ratio in the inner regions of poor clusters. Additionally, the associated supernova heating falls far short of the observed level of ∼1 keV per ICM gas particle. Thus, the properties of the first objects may be best determined by direct observation.