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 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 constraint the redshift of overlap of cosmic H ii regions to z _ { OVL } = 6.1 \pm 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 Thompson scattering - any value between 6 and 10 % is possible , depending on the convergence rate of the simulations and the fractional contribution of PopIII stars .
This is generally consistent with the third-year WMAP results , but much higher resolution simulation are required to come up with the sufficiently precise value for the Thompson optical depth that can be statistically compared with the WMAP data .