Reionization in a cold dark matter universe: The feedback of galaxy formation on the intergalactic medium

We study the coupled evolution of the intergalactic medium (IGM) and the emerging structure in the universe in the context of the cold dark matter (CDM) model, with a special focus on the consequences of imposing reionization and the Gunn-Peterson constraint as a boundary condition on the model. We have calculated the time-varying density of the IGM by coupling our detailed, numerical calculations of the thermal and ionization balance and radiative transfer in a uniform, spatially averaged IGM of H and He, including the mean opacity of an evolving distribution of gas clumps which correspond to quasar absorption line clouds, to the linearized equations for the growth of density fluctuations in both the gaseous and dark matter components in a CDM universe. We use the linear growth equations to identify the fraction of the gas which must have collapsed out at each epoch, an approach similar in spirit to the so-called Press-Schechter formalism. We identify the IGM density with the uncollapsed baryon fraction. The collapsed fraction is postulated to be a source of energy injection into the IGM, by radiation or bulk hydrodynamical heating (e. g. , via shocks) or both, at a rate which is marginally enough to satisfy the Gunn-Peterson constraint at z 3, depending on the nature of the sources of IGM reionization. (4) We find, moreover, that a CDM model with high bias parameter b (ie. , b ~> 2) cannot account for the baryon content of the universe at z ~ 3 observed in quasar absorption line gas unless OMEGAB_ significantly exceeds the maximum value allowed by big bang nucleosynthesis. (5) For a CDM model with bias parameter within the allowed range of (lower) values, the lower limit to OMEGAB_ imposed by big bang nucleosynthesis (OMEGABₕ²^ >= 0. 01) combines with our results to yield the minimum IGM density for the CDM model For CDM with b = 1 (COBE normalization), we find OMEGAIGM_ᵐin^ (z ~ 4) = 0. 02- 0. 03, and OMEGAIGM_ᵐin^ (z ~ 0) ~0. 005-0. 03, depending upon the nature of the sources of IGM reionization. (6) In general, we find that self- consistent reionization of the IGM by the collapsed baryon fraction has a strong effect on the rate of collapse. (7) As a further example, we show that the feedback effect on the IGM of energy release by the collapsed baryon fraction may explain the slow evolution of the observed comoving QSO number density between z = 5 and z = 2, followed by the sharp decline after z = 2.