Quasar H ii regions during cosmic reionization

Cosmic reionization progresses as H ii regions form around sources of ionizing radiation. Their average size grows continuously until they percolate and complete reionization. We demonstrate how this typical growth can be calculated around the largest, biased sources of UV emission, such as quasars, by further developing an analytical model based on the excursion set formalism. This approach allows us to calculate the sizes and growth of the H ii regions created by the progenitors of any dark matter halo of given mass and redshift with a minimum of free parameters. Statistical variations in the size of these pre-existing H ii regions are an additional source of uncertainty in the determination of very high redshift quasar properties from their observed H ii region sizes. We use this model to demonstrate that the transmission gaps seen in very high redshift quasars can be understood from the radiation of only their progenitors and associated clustered small galaxies. The fit sets a lower limit [Correction added after online publication 16 July 2007: the term ‘sets an upper limit’ has been corrected to ‘sets a lower limit’] on the redshift of overlap at z = 5.8 ± 0.1. This interpretation makes the transmission gaps independent of the age of the quasars observed. If this interpretation were correct it would raise the prospects of using radio interferometers currently under construction to detect the epoch of reionization.