Based on the gamma-ray burst (GRB) event rate at redshifts of $4 leq z leq 12$, which is assessed by the spectral peak energy-to-luminosity relation recently found by Yonetoku et al., we observationally derive the star formation rate (SFR) for Pop III stars in a high redshift universe. As a result, we find that Pop III stars could form continuously at $4 leq z leq 12$. Using the derived Pop III SFR, we attempt to estimate the ultraviolet (UV) photon emission rate at $7 leq z leq 12$ in which redshift range no observational information has been hitherto obtained on ionizing radiation intensity. We find that the UV emissivity at $7 leq z leq 12$ can make a noticeable contribution to the early reionization. The maximal emissivity is higher than the level required to keep ionizing the intergalactic matter at $7 leq z leq 12$. However, if the escape fraction of ionizing photons from Pop III objects is smaller than 10%, then the IGM can be neutralized at some redshift, which may lead to the double reionization. As for the enrichment, the ejection of all metals synthesized in Pop III objects is marginally consistent with the IGM metallicity, although the confinement of metals in Pop III objects can reduce the enrichment significantly.
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