Bias and Hierarchical Clustering

It is now well established that galaxies are biased tracers of thedistribution of matter, although it is still not known what form this biastakes. In local bias models the propensity for a galaxy to form at a pointdepends only on the overall density of matter at that point. Hierarchicalscaling arguments allow one to build a fully-specified model of the underlyingdistribution of matter and to explore the effects of local bias in the regimeof strong clustering. Using a generating-function method developed byBernardeau & Schaeffer (1992), we show that hierarchical models lead onedirectly to the conclusion that a local bias does not alter the shape of thegalaxy correlation function relative to the matter correlation function onlarge scales. This provides an elegant extension of a result first obtained byColes (1993) for Gaussian underlying fields and confirms the conclusions ofScherrer & Weinberg (1998) obtained using a different approach. We also arguethat particularly dense regions in a hierarchical density field display a formof bias that is different from that obtained by selecting such peaks inGaussian fields: they are themselves hierarchically distributed with scalingparameters $S_p=p^{(p-2)}$. This kind of bias is also factorizable, thus inprinciple furnishing a simple test of this class of models.Comment: Latex, accepted for publication in ApJL; moderate revision