We show that numerical simulations of reionization that resolve the Lyman limit systems (and, thus, correctly count absorptions of ionizing photons) have converged to about a 10% level for 5 z 6.2 and are in reasonable agreement (within 10%) with the SDSS data in this redshift interval. The SDSS data thus constrain the redshift of overlap of cosmic H II regions to zOVL = 6.1 ± 0.15. At higher redshifts, the simulations are far from convergence on the mean Gunn-Peterson optical depth but achieve good convergence for the mean neutral hydrogen fraction. The simulations that fit the SDSS data, however, do not have nearly enough resolution to resolve the earliest episodes of star formation and are very far from converging on the precise value of the optical depth to Thomson scattering—any value between 6% and 10% is possible, depending on the convergence rate of the simulations and the fractional contribution of Population III stars. This is generally consistent with the third-year WMAP results, but much higher resolution simulations are required to come up with the sufficiently precise value for the Thomson optical depth that can be statistically compared with the WMAP data.
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