3.4 The `Breakthrough' Epoch
Quasar spectra tell us that the diffuse IGM is almost fully ionized back to z = 5, but we do not know when it in effect became an HII region. The IGM would already be inhomogeneous at the time when the ionization occurred. The traditional model of expanding HII regions that overlap at a well defined epoch when `breakthrough' occurs (dating back at least to Arons and McCray (1972)) is consequently rather unrealistic. By the time ionization occurs the gas is so inhomogeneous that half the mass (and far more than half of the recombinations) is within 10 percent of the volume. HII regions in the `voids' can overlap (in the sense that the IGM becomes ionized except for `islands' of high density) before even half the material has been ionized. Thereafter, the overdense regions would be `eroded away': Stromgren surfaces encroach into them; the neutral regions shrink and present a decreasing cross-section; the mean free path of ionizing photons (and consequently the UV background intensity J) goes up (Miralda-Escudé, Haehnelt and Rees 1999, Gnedin 1999).
The thermal history of the IGM beyond z = 5 is relevant to the modelling of the absorption spectra of quasars at lower redshifts. The recombination and cooling timescales are comparable to the cosmological expansion timescale. Therefore the `texture' and temperature of the filamentary structure responsible for the lines in the Lyman alpha `forest' yield fossil evidence of the thermal history at higher redshifts.