The zero-crossing scale and the problem of galaxy bias
Abstract
Description
One of the main problems in the studies of large scale galaxy structures concerns the relation of the correlation properties of a certain population of objects with those of a selected subsample of it, when the selection is performed by considering physical quantities like luminosity or mass. I consider the case where the sampling is defined as in the simplest thresholding selection scheme of the peaks of a Gaussian random field as well as the case of the extraction of point distributions in high density regions from gravitational N-body simulations. I show that an invariant scale under sampling is represented by the zero-crossing scale of ξ(r). By considering recent measurements in the 2dF and SDSS galaxy surveys I note that the zero-point crossing length has not yet been clearly identified, while a dependence on the finite sample size related to the integral constraint is manifest. I show that this implies that other length scales derived from ξ(r) are also affected by finite size effects. I discuss the theoretical implications of these results, when considering the comparison of structures formed in N-body simulations and observed in galaxy samples, and different tests to study this problem.
8 pages, 6 .eps figures
8 pages, 6 .eps figures