Galaxy correlations, matter correlations and biasing
Abstract
From the simple assumption that the manybody matter correlation functions behave as a product of twobody correlation functions, that is expected to hold at the scales (0.1 to 10 h^1^ Mpc) where the universe in nonlinear, we derive the expression of the two and threebody correlation functions of condensed objects. We demonstrate that the galaxy and the matter correlations are proportional. Their ratio is shown to be a product of two bias factors that depend only on the intrinsic properties of the two objects that are correlated. Each factor obeys a scaling relation in the sense that it depends on a unique physical parameter X is proportional to M/R^3γ, where M is the mass of the considered object, R its size and γ is the powerlaw index of the twobody correlation function. The calculated bias appears to be a growing function of X and hence of luminosity. An apparent magnitude limited sample of galaxies is shown to have a bias who has a universal value, independent of depth, that can be estimated to be between 1.5 and 3. We however find that the galaxy distribution as a whole is not biased since the massweighted average over all galaxies of the bias factor is unity. The calculation of the galaxy threebody correlation is also presented. Our theory predicts in a natural way that the latter is given by the product of two twobody correlation functions. The normalization parameter Q is found to depend weakly on the model chosen for the matter correlations and to lie, under very general assumptions, between 0.7 and 1. Comparison is made with the observed galaxy and cluster correlations. Our model which allows the calculation of the bias parameters is seen to agree with all currently known constraints.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1992
 Bibcode:
 1992A&A...255....1B
 Keywords:

 Astronomical Models;
 Correlation;
 Galactic Clusters;
 Galactic Structure;
 Mass Distribution;
 Bias;
 Scaling Laws;
 Three Body Problem;
 Trees (Mathematics);
 Two Body Problem;
 Astrophysics