6.4. Scale dependence of bias
The Poisson clustering hypothesis would propose that galaxies are simply a dilute sampling of the mass field. If this were a correct hypothesis, no CDM universe would be acceptable, since the correlation functions for these models differ from the observed galaxy correlations in a complicated scale-dependent fashion (e.g. Klypin, Primack & Holtzman 1996; Peacock 1997; Jenkins et al. 1998).
For a few years, this failure of CDM models to match the shape of the galaxy power spectrum was seen as a serious problem, but this was eventually resolved by more detailed theoretical predictions for galaxy clustering. Two approaches are being followed in this regard. The brute-force method is to perform N-body simulations in which the evolution of both collisionless dark matter and dissipative gas is followed, with the physical state of the gas (i.e. its ability to cool) being used as a cue to insert star formation. The stars in turn are allowed to feed energy back into the gas, simulating the effects of mass loss and supernovae. This determines the star formation history of a given halo, and its appearance can be predicted using spectral synthesis codes. This is challenging, but starting to be feasible with current computing power (Pearce et al. 2001). The alternative is `semianalytic' modelling, in which the merging history of dark-matter haloes is treated via the extended Press-Schechter theory (Bond et al. 1991), and the location of galaxies within haloes is estimated using dynamical-friction arguments (e.g. Kauffmann et al. 1993, 1999; Cole et al. 1994, 2000; Somerville & Primack 1999; van Kampen, Jimenez & Peacock 1999; Benson et al. 2000a, b).
Both these approaches have yielded similar conclusions, and shown how CDM models can match the galaxy data: specifically, the low-density flat CDM model that is favoured on other grounds can yield a correlation function that is close to a single power law over 1000 1, even though the mass correlations show a marked curvature over this range (Pearce et al. 1999; 2001; Benson et al. 2000a; see figure 11). These results are impressive, yet it is frustrating to have a result of such fundamental importance emerge from a complicated calculational apparatus. There is thus some motivation for constructing a simpler heuristic model that captures the main processes at work in the full semianalytic models. The following section describes an approach of this sort (Peacock & Smith 2000; Seljak 2000; Cooray & Sheth 2002).
Figure 11. The correlation function of galaxies in the semianalytical simulation of an LCDM universe by Benson et al. (2000a). Although the nonlinear correlations of the mass show a characteristic convex bulge at separations around 1 Mpc, the galaxy data follow a power law which thus is antibiased on these small scales. The simulation is successful at reproducing this trend.