Moments of the Counts Distribution in the 1.2 Jy IRAS Redshift Survey

Abstract

We derive the volume-averaged 2, 3, 4, and 5-point correlation functions from the moments of the Count probability distribution function of a redshift survey of IRAS galaxies, and find them all to be reasonably well-described by power laws. Weak systematic effects with the sample size provide evidence for stronger clustering of galaxies of higher luminosity on small scales. Nevertheless, remarkably tight relationships hold between the correlation functions of different order. In particular, the ``normalized" skewness defined by the ratio $S_3\equiv \bar{ξ_3} / \bar{ξ_2}^2$ varies at most weakly with scale in the range $0.1 < \bar{ξ_2} < 10$. That is, $S_3$ is close to constant ($=1.5\pm 0.5$) from weakly to strongly non-linear scales. Furthermore, we find that the void probability function obeys a scaling relation with density to great precision, in accord with the scale-invariance hypothesis ($\bar{ξ_N}\propto\bar{ξ_2}^{N-1}$).