Cosmological H II regions and the photoionization of the intergalactic medium

The generalization of the classical H II region problem to the case of a point source of ionizing radiation in a cosmologically expanding gas in a Friedmann-Robertson-Walker universe is described. We derive the cosmological generalization of the static Stromgren radius and solve analytically for the time dependence of the radius and peculiar velocity of the ionization front which surrounds each source. An application of this work is described in which is tested the hypothesis that quasars photoionize the IGM to the degree implied by the well-known absence of a Gunn-Peterson effect. Recent studies of faint quasars at high redshift, which suggest a decline in the number density of quasars for z > 3, imply that the H II regions of high-redshift quasars cannot overlap early enough to satisfy the Gunn-Peterson test. This suggests that either the observations are failing to detect the true number density of high-redshift quasars or else something else must ionize the IGM at high redshift. An interpretation of the "Lyman-alpha forest" in quasar absorption spectra as caused by intergalactic clouds which are highly photoionized by the quasar background radiation leads to a similar conclusion.