Reionization of Hydrogen and Helium by Early Stars and Quasars

We compute the reionization histories of hydrogen and helium due to theionizing radiation fields produced by stars and quasars. For the quasars we usea model based on halo-merger rates that reproduces all known properties of thequasar luminosity function at high redshifts. The less constrained propertiesof the ionizing radiation produced by stars are modeled with two freeparameters: (i) a transition redshift, z_tran, above which the stellarpopulation is dominated by massive, zero-metallicity stars and below which itis dominated by a Scalo mass function; (ii) the product of the escape fractionof stellar ionizing photons from their host galaxies and the star-formationefficiency, f_esc f_*. We constrain the allowed range of these free parametersat high redshifts based on the lack of the HI Gunn-Peterson trough at z<6 andthe upper limit on the total intergalactic optical depth for electronscattering, tau_es<0.18, from recent cosmic microwave background (CMB)experiments. We find that quasars ionize helium by a redshift z~4, but cannotreionize hydrogen by themselves before z~6. A major fraction of the allowedcombinations of f_esc f_* and z_tran lead to an early peak in the ionizedfraction due to metal-free stars at high redshifts. This sometimes results intwo reionization epochs, namely an early HII or HeIII overlap phase followed byrecombination and a second overlap phase. Even if early overlap is notachieved, the peak in the visibility function for scattering of the CMB oftencoincides with the early ionization phase rather than with the actualreionization epoch. Consequently, tau_es does not correspond directly to thereionization redshift. We generically find values of tau_es>7%, that should bedetectable by the MAP satellite.Comment: 33 pages, 10 figures, Accepted for publication in Ap