  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.
