  Population-III (Pop-III) starformation (SF) is thought to be quenched when
the metallicity of the star-forming gas reaches a critical level. At high z,
when the general intergalactic medium (IGM) was enriched with metals, the
fraction of primordial gas already collapsed in minihalos was significantly
larger than the fraction of primordial gas that had already been involved in
Pop-III SF. We argue that this minihalo gas remained largely in a metal-free
state, until these minihalos merged into large systems and formed stars. As a
result, the era of Pop-III SF was significantly prolonged, leading to an
integrated Pop-III SF an order of magnitude larger than expected for an abrupt
transition redshift. The contribution of Pop-III SF to the reionization of
hydrogen could have been significant until z~10 and may have extended to z~6.
Our modeling allows for gradual enrichment of the IGM, feedback from
photo-ionization and screening of reionization by minihalos. Nevertheless,
extended Pop-III SF can result in complex, multi-peaked reionization histories.
The contribution of Pop-III stars to reionization will be tested by the
three-year WMAP results: (1) if Pop-III stars do not contribute to
reionization, tau_es<0.05-0.06 and a rapid reionization at z~6 is expected; (2)
if the product of star formation efficiency and escape fraction for Pop-III
stars is significantly larger than for Pop-II stars, then a maximum tau_es=0.21
is achievable; (3) in a scenario where the product of star formation efficiency
and escape fraction for Pop-III stars is comparable to that for Pop-II stars,
tau_es=0.09-0.12 would be observed, with reionization histories characterized
by an extended ionization plateau from z=7-12. This result holds regardless of
the redshift where the IGM becomes enriched with metals.
