Biased clustering in the cold dark matter cosmogony

Abstract

We have used the Press–Schechter approximation to calculate the abundance and large-scale clustering of dark haloes in the CDM cosmogony. Applying these results to quasars at z = 3−4, we find a wide range of haloes which are both sufficiently massive and sufficiently numerous to host quasars, and the prediction for the clustering strength is correspondingly uncertain. Current estimates of quasar clustering require that the parent haloes lie at the most massive end of the allowed range, with velocity dispersions in the range 550−900 km s−1, and that the quasar luminosity be quite tightly correlated with the parent halo properties. Another application is to the diffuse X-ray background. If this is generated by discrete sources associated with dark haloes then the upper limits on the X-ray angular correlation function constrain the halo masses to be |$\lt 10^{12} \enspace h^{-1} \enspace M_\odot$|⁠. We have considered two simple models for galaxy formation. In the first, which has some attractions for disc galaxies, we identify galaxies with dark haloes forming at the present epoch. We find that haloes with abundance like that of |$L_\ast$| galaxies have large-scale clustering which is nearly unbiased, and the smaller haloes are antibiased — quite a negative feature. In the second, the galaxies we see today are assumed to be a fossil remnant of haloes which formed earlier. The stellar and dark particle velocity dispersions are assumed to be equal, and the luminosity for each halo is adjusted to give a tight and universal L–V relation like that observed. We identify an epoch when the comoving number density of haloes with a given luminosity is maximized, and we calculate how this number density is biased by long wavelength modes. The results here are more encouraging: All of the ‘galaxies’ in this model are positively biased. The enhancement of the light-to-mass ratios for rich clusters is substantial, though dependent on the normalization. For a low normalization the bias is strong enough to reconcile virial estimates of M/L for clusters with Ω = 1.