  We propose a heuristic model that displays the main features of realistic
theories for galaxy bias. We show that the low-order clustering statistics of
the dark-matter distribution depend almost entirely on the locations and
density profiles of dark-matter haloes. A hypothetical galaxy catalogue depends
on (i) the efficiency of galaxy formation, as manifested by the halo occupation
number -- the number of galaxies brighter than some sample limit contained in a
halo of a given mass; (ii) the location of these galaxies within their halo.
The first factor is constrained by the empirical luminosity function of groups.
For the second factor, we assume that one galaxy marks the halo centre, with
any remaining galaxies acting as satellites that trace the halo mass. These
simple assumptions amount to a recipe for non-local bias, in which the
probability of finding a galaxy is not a simple function of its local mass
density. We have applied this prescription to some CDM models of current
interest, and find that the predictions are close to the observed galaxy
correlations for a flat $\Omega=0.3$ model ($\Lambda$CDM), but not for an
$\Omega=1$ model with the same power spectrum ($\tau$CDM). This is an
inevitable consequence of cluster normalization for the power spectra:
cluster-scale haloes of given mass have smaller core radii for high $\Omega$,
and hence display enhanced small-scale clustering. Finally, the pairwise
velocity dispersion of galaxies in the $\Lambda$CDM model is lower than that of
the mass, allowing cluster-normalized models to yield a realistic Mach number
for the peculiar velocity field. This is largely due to the strong variation of
galaxy-formation efficiency with halo mass that is required in this model.

Astrophysics