We examine the significance of the first metal-free stars ( Pop III ) for the cosmological reionization of H I and He II .
These stars have unusually hard spectra , with the integrated ionizing photon rates from a Pop III stellar cluster for H I and He II being 1.6 and 10 ^ { 5 } times stronger respectively than those from a Pop II cluster .
For the currently favored cosmology , we find that Pop III stars alone can reionize H I and He II at redshifts , z \simeq 9 ( 4.7 ) and 5.1 ( 0.7 ) for continuous ( instantaneous ) modes of star formation .
More realistic scenarios involving combinations of Pop III and Pop II stellar spectra yield similar results for hydrogen .
Helium never reionizes completely in these cases ; the ionization fraction of He III reaches a maximum of about 60 % at z \sim 5.6 if Pop III star formation lasts for 10 ^ { 9 } yr. Future data on H I reionization can test the amount of small-scale power available to the formation of the first objects , and provide a constraint on values of \sigma _ { 8 } \lesssim 0.7 .
Since current UV observations indicate an epoch of reionization for He II at z \sim 3 , He II may reionize more than once .
Measurements of the He II Gunn-Peterson effect in the intergalactic medium at redshifts z \gtrsim 3 may reveal the significance of Pop III stars for He II reionization , particularly in void regions that may contain relic ionization from early Pop III stellar activity .