Higher Order Clustering in the Durham/UKST and Stromlo-APM Galaxy Redshift Surveys

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Abstract
We present a counts-in-cells analysis of clustering in the optically selected Durham/UKST and Stromlo-APM Galaxy Redshift Surveys. Minimum variance estimates of the second moment, skewness (S_3) and kurtosis (S_4) of the count probability distribution are extracted from a series of volume limited samples of varying radial depth. The corresponding theoretical error calculation takes into account all sources of statistical error on the measurement of the moments, and is in good agreement with the dispersion over mock redshift catalogues. The errors that we find on S_3 and S_4 are larger than those quoted in previous studies, in spite of the fact that the surveys we consider cover larger volumes. S_3 varies little with cell size, with values in the range 1.8-2.2 and errors ~20%, for cubical cells of side 3-20 h^{-1}Mpc. Direct measurements of S_3 are possible out to ~35 h^{-1}Mpc, though with larger errors. A significant determination of S_4 is only possible for one scale, l=6 h^{-1}Mpc, with S_4~5. We compare our results with theoretical predictions from N-body simulations of cold dark matter universes. Qualitatively, the skewness of the dark matter has the same form as that of the galaxies. However, 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 of a simple model in which initially Gaussian fluctuations in the dark matter evolve gravitationally, if a second order bias term is specified, in addition to the traditional linear bias, in order to describe the relation between the distribution of galaxies and dark matter.

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