Bias and hierarchical clustering

It is now well established that galaxies are biased tracers of the distribu tion of matter, although it is still not known what form this bias takes. I n local bias models, the propensity for a galaxy to form at a point depends only on the overall density of matter at that point. Hierarchical scaling arguments allow one to build a fully specified model of the underlying dist ribution of matter and to explore the effects of local bias in the regime o f strong clustering. Using a generating function method developed by Bernar deau & Schaeffer, we show that hierarchical models lead one directly to the conclusion that a local bias does not alter the shape of the galaxy correl ation function relative to the matter correlation function on large scales. This provides an elegant extension of a result first obtained by Coles for Gaussian underlying fields and confirms the conclusions of Scherrer & Wein berg obtained using a different approach. We also argue that particularly d ense regions in a hierarchical density field display a form of bias that is different from that obtained by selecting such peaks in Gaussian fields: t hey are themselves hierarchically distributed with scaling parameters S-p = p((p-2)). This kind of bias is also factorizable, thus in principle furnis hing a simple test of this class of models.