Evolution of the Ionizing Background and the Epoch of Reionization from the Spectra of z~6 Quasars

We study the process of cosmic reionization and estimate the ionizing background in the IGM using the Lyman series absorption in the spectra of the four quasars at 5.7<z<6.3 discovered by the SDSS. We derive the evolution of the ionizing background at high redshifts, using both semi-analytic techniques and cosmological simulations to model the density fluctuations in the IGM. The existence of the complete Ly alpha Gunn-Peterson trough in the spectrum of the z=6.28 quasar SDSS 1030+0524 indicates a photoionization rate Gamma_{-12} at z~6 lower than 0.08, at least a factor of 6 smaller than the value at z~3. The Ly beta and Ly gamma Gunn-Peterson troughs give an even stronger limit Gamma_{-12}<0.02 due to their smaller oscillator strengths, indicating that the ionizing background in the IGM at z~6 is more than 20 times lower than that at z~3. Meanwhile, the volume-averaged neutral hydrogen fraction increases from 10^{-5} at z~3 to >10^{-3} at z~6. At this redshift, the mass-averaged neutral hydrogen fraction is larger than 1%; the mildly overdense regions (delta > 3) are still mostly neutral and the comoving mean free path of ionizing photons is shorter than 8 Mpc. Comparison with simulations of cosmological reionization shows that the observed properties of the IGM at z~6 are typical of those in the era at the end of the overlap stage of reionization when the individual HII regions merge. Thus, z~6 marks the end of the reionization epoch. The redshift of reionization constrains the small scale power of the mass density fluctuations and the star forming efficiency of the first generation of objects.