The maximum contribution to reionization from metal-free stars
  We estimate the maximum contribution to reionization from the first generation of massive stars, with zero metallicity, under the assumption that one of these stars forms with a fixed mass in every collapsed halo in which metal-free gas is able to cool. We assume that any halo that has already had stars previously formed in one of their halo progenitors will form only stars with metals, which are assigned an emissivity of ionizing radiation equal to that determined at z=4 from the measured intensity of the ionizing background. We examine the impact of molecular hydrogen photodissociation (which tends to reduce cooling when a photodissociating background is produced by the first stars) and X-Ray photoheating (which heats the atomic medium, raising the entropy of the gas before it collapses into halos). We find that in the CDM$\Lambda$ model supported by present observations, and even assuming no negative feedbacks for the formation of metal-free stars, a reionized mass fraction of 50% is not reached until redshift $z\sim 12$. The combination of ordinary metal-enriched stars and early metal-free stars can yield a CMB optical depth to electron scattering of at most 0.13. The contribution of metal-free stars to the present Cosmic Infrarred Background is negligibly small. 
Jose M. Rozas, Jordi Miralda-Escude and Eduard Salvador-Sole