Biasing and high-order statistics from the SSRS2

Abstract

We analyze different volume-limited samples extracted from the Southern Sky Redshift Survey (SSRS2), using counts-in-cells to compute the Count Probability Distribution Function (CPDF).From the CPDF we derive volume-averaged correlation functions to fourth order and the normalized skewness and kurtosis $S_3 = \bar{ξ_3}/\bar{ξ_2}^2$ and $S_4=\bar{ξ_4}/\bar{ξ_2}^3$. We find that the data satisfies the hierarchical relations in the range $0.3 \lsim \bar{ξ_2} \lsim 10$. In this range, we find $S_3$ to be scale-independent with a value of $\sim 1.8$, in good agreement with the values measured from other optical redshift surveys probing different volumes, but significantly smaller than that inferred from the APM angular catalog. In addition, the measured values of $S_3$ do not show a significant dependence on the luminosity of the galaxies considered. This result is supported by several tests of systematic errors that could affect our measures and estimates of the cosmic variance determined from mock catalogs extracted from N-body simulations. This result is in marked contrast to what would be expected from the strong dependence of the two-point correlation function on luminosity in the framework of a linear biasing model. We discuss the implications of our results and compare them to some recent models of the galaxy distribution which address the problem of bias.