The authors examine the environmental impact of quasars and active nuclei on the intergalactic medium (IGM) and derive analytic and numerical results for ionization-front expansion as a function of redshift z in an expanding Friedmann cosmology. For an IGM of moderate density (ΩI ≈ 0.1) and a conservative estimate of QSO ionizing spectra, QSOs "turning on" at zon= 4 will not produce a fully ionized IGM until z ≈ 2.5. However, an IGM with ΩI = 0.03 - 0.10 could be ionized between z = 3.3 - 3.7. The authors also investigate the effects of I-fronts on the distribution of "Lyα forest" clouds. The photoionization of intergalactic clouds within ≡10 Mpc of a luminous QSO could explain the "inverse effect", an observed deficit in the distribution of Lyα absorption systems near zem.
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Donahue et al. (1987) studied this question.