High-Order Correlations of Peaks and Halos: a Step toward Understanding Galaxy Biasing

Abstract

We develop an analytic model for the hierarchical correlation amplitudes S_j(R)= \bxi_j(R)/\bxi_2^{j-1}(R) of density peaks and dark matter halos in the quasi-linear regime. The statistical distribution of density peaks and dark matter halos within the initial density field are determined by the peak formalism and by an extension of the Press-Schechter formalism, respectively. Modifications of these distributions caused by gravitationally induced motions are treated using a spherical collapse model. We test our model against results from a variety of N-body simulations. The model works well for peaks and for halos that are identified earlier than the time when the moments are calculated. Because halos are spatially exclusive at the time of their identification, our model is only qualitatively correct for halos identified at the same time as the moments are calculated. The S_j depend only weakly on the bias parameter b for large b but increase rapidly with decreasing b at b\sim 1. Thus if galaxies are associated with peaks in the initial density field, or with dark halos formed at high redshifts, a measurement of S_j in the quasilinear regime should determine whether galaxies are significantly biased relative to the mass. We use our model to interpret the observed high order correlation functions of galaxies and clusters. We find that if the values of S_j for galaxies are as high as those given by the APM survey, then APM galaxies should not be significantly biased.