Abstract
According to the minihalo model for the Ly α forest, the absorption lines arise from photoionized gas gravitationally confined in dark matter haloes of low circular velocity. Using the Press-Schechter formalism, we find that, in the CDM model, the number of Ly α clouds and their evolution with redshift are in agreement with observations if we assume a constant intensity for the ionizing background and a constant temperature for the gas in the minihaloes against changes in redshift. This is a generic consequence of the shape and the amplitude of the CDM spectrum on subgalactic scales; the evolution is due to the disappearance of the minihaloes as they merge into larger systems, although other effects may also modify the evolution rate
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