Reionization of hydrogen and helium by early stars and quasars

We compute the reionization histories of hydrogen and helium caused by the ionizing radiation fields produced by stars and quasars. For the quasars we use a model based on halo-merger rates that reproduces all known properties of the quasar luminosity function at high redshifts. The less constrained properties of the ionizing radiation produced by stars are modeled with two free parameters: ( i) a transition redshift, z(tran), above which the stellar population is dominated by massive, zero-metallicity stars and below which it is dominated by a Scalo mass function; and (ii) the product of the escape fraction of stellar ionizing photons from their host galaxies and the star formation efficiency, f(esc) f*. We constrain the allowed range of these free parameters at high redshifts on the basis of the lack of the H I Gunn-Peterson trough at z less than or similar to 6 and the upper limit on the total intergalactic optical depth for electron scattering, tau(es) < 0.18, from recent cosmic microwave background (CMB) experiments. We find that quasars ionize helium by a redshift z similar to 4, but cannot reionize hydrogen by themselves before z similar to 6. A major fraction of the allowed combinations of f(esc) f* and z(tran) leads to an early peak in the ionized fraction because of the presence of metal-free stars at high redshifts. This sometimes results in two reionization epochs, namely, an early H ii or He III overlap phase followed by recombination and a second overlap phase. Even if early overlap is not achieved, the peak in the visibility function for scattering of the CMB often coincides with the early ionization phase rather than with the actual reionization epoch. Consequently, tau(es) does not correspond directly to the reionization redshift. We generically find values of tau(es) greater than or similar to 7%, which should be detectable by the MAP satellite.