The zero-crossing scale and the problem of galaxy bias

Abstract

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.