N-point correlation functions in the CfA and SSRS redshift distribution of galaxies

Using counts in cells, we estimate the volume-average N-point galaxy correlation functions ξN_ (R) for N = 2, 3, and 4, in redshift samples of the CfA and SSRS catalogs. Volume-limited samples of different sizes are used to study the uncertainties at different scales the shot noise, and the problem with the boundaries. For each sample, a power law is obtained for the density contrast in a spherical cell of radius R: ξ₂_ (R) = (R₀_/R) gamma, in agreement with previous estimations. For higher order correlations we found in all samples a good agreement with the hierarchical symmetry: ξN_ = SNxiN-1^₂_, for scales R between 2 and 22 Mpc, which included both mildly linear, ξ₂_ > 1, and nonlinear, ξ₂_ < 1, scales. The hierarchical constants S₃_ and S₄_ agree well in all samples In CfA and SSRS, with average S₃_ = 1. 94 +/- 0. 07 and S₄_ = 4. 56 +/- 0. 53. We compare these results with estimates obtained from angular catalogs and recent analysis over IRAS samples. The amplitudes SJ_ seem larger in real space than in redshift space, although the values from the angular analysis correspond to smaller scales, where we might expect larger nonperturbative effects. It is also found that S₃_ and S₄_ are smaller for IRAS than for optical galaxies. This, together with the fact that IRAS galaxies have smaller amplitude for ξ₂_ (R), indicates that the density fluctuations of IRAS galaxies cannot be simply proportional to the density fluctuations of optical galaxies, i. e. , biasing has to be nonlinear between them.