THE DISTRIBUTION OF MINIHALOES IN COLD DARK-MATTER COSMOGONY

According to the minihalo model for the Ly alpha forest, the absorptio n lines arise from photoionized gas gravitationally confined in dark m atter haloes of low circular velocity. Using the Press-Schechter forma lism, we find that, in the CDM model, the number of Ly alpha clouds an d their evolution with redshift are in agreement with observations if we assume a constant intensity for the ionizing background and a const ant temperature for the gas in the minihaloes against changes in redsh ift. This is a generic consequence of the shape and the amplitude of t he CDM spectrum on subgalactic scales; the evolution is due to the dis appearance of the minihaloes as they merge into larger systems, althou gh other effects may also modify the evolution rate. The stringent upp er limits on the Gunn-Peterson absorption currently available are not a serious problem for the model, since the space between haloes produc ing absorption lines is mostly filled by highly underdense voids. If t he minihaloes giving rise to the absorption lines were as clustered as the mass, their autocorrelation should be about three times larger th an the upper limits found by Rauch et al. (depending on the bias param eter). Most minihaloes, however, would have already merged into larger structures at the epoch when the Ly alpha forest is observed, the sur viving ones being preferentially in low-density regions. In fact, usin g an analytical model based on the Press-Schechter formalism, we find that the cross-correlation between minihaloes and mass can be much sma ller than the autocorrelation of mass. We also discuss the amplitude o f the autocorrelation function of minihaloes.