Improved constraints on the neutral intergalactic hydrogen surrounding quasars at redshifts z > 6

We analyze the evolution of H II regions around the seven known SDSS quasars at z > 6. The comparison between the observed and model radii of the H II regions generated by these quasars individually suggests that the surrounding intergalactic hydrogen is significantly neutral. When all constraints are combined, the existing quasar sample implies a volume-averaged neutral fraction that is larger than 10% at z > 6. This limited sample permits a preliminary analysis of the correlations between the quasar parameters, the sizes of their H II regions, and the associated constraints on the neutral hydrogen fraction. We find no evidence in these correlations to contradict the interpretation that the red side of the Gunn-Peterson trough corresponds to the boundary between an H II region and a partially neutral IGM.