Abundance and Clustering of QSOs in Cosmic Structure Formation Models

Combining the observations of spatial abundance and two-point correlation function of QSOs, we can effectively set constraints on models of cosmic structure formation. Both the abundance of gravitationally confined halos and their two-point correlation functions can be calculated in the conventional Press-Schechter formalism. We apply this method to examine the properties of possible host halos of QSOs in three popular models: the standard cold dark matter (SCDM) model, the low density flat cold dark matter (LCDM) model and the cold-plus-hot dark matter (CHDM) model. The LCDM and CHDM models are normalized to the COBE-DMR observations, and the SCDM is normalized to $\sigma = 0.58$. We find that the SCDM and LCDM models can pass the abundance-plus-correlation test for QSOs. However, the CHDM are difficult to produce host halos to fit with the number density of high redshift QSOs and their clustering on large scales (10 h^{-1} Mpc) simultaneously. We studied various mechanisms, originated both gravitationally and non-gravitationally, which may lead to a biasing of the halo clustering. We conclude that these effects are too weak in order to release the trouble of the CHDM models.