Higher order clustering in the Durham/UKST and Stromlo-APM Galaxy RedshiftSurveys

We present a counts-in-cells analysis of clustering in the optically select ed Durham/UKST and Stromlo-APM Galaxy Redshift Surveys. Minimum variance es timates of the second moment, skewness (S-3) and kurtosis (S-4) Of the coun t probability distribution are extracted from a series of volume-limited sa mples of varying radial depth. The corresponding theoretical error calculat ion takes into account all sources of statistical error on the measurement of the moments, and is in good agreement with the dispersion over mock reds hift catalogues. The errors that we find on S-3 and S-4 are larger than tho se quoted in previous studies, in spite of the fact that the surveys we con sider cover larger volumes. S3 varies little with cell size, with values in the range 1.8-2.2 and errors less than or similar to 20per cent, for cubic al cells of side 3-20 h(-1) Mpc. Direct measurements of S3 are possible out to similar to 35 h(-1) MPc, though with larger errors. A significant deter mination of S-4 is only possible for one scale, l similar to 6 h(-1) Mpc, w ith S-4 approximate to 5. We compare our results with theoretical predictio ns from N-body simulations of cold dark matter universes. Qualitatively, th e skewness of the dark matter has the same form as that of the galaxies. Ho wever, the amplitude of the galaxy S-3 is lower than that predicted for the dark matter. Our measurements of S-3 are consistent with the predictions o f a simple model in which initially Gaussian fluctuations in the dark matte r evolve gravitationally, if a second-order bias term is specified, in addi tion to the traditional linear bias, in order to describe the relation betw een the distribution of galaxies and dark matter.