High-order galaxy correlation functions in the APM Galaxy Survey

We estimate J-point galaxy averaged correlation functions ${\text{wbar}}_J(\theta )$ for $J=2,\mathrm{.}\mathrm{.}\mathrm{.},9$, in a sample of the APM Galaxy Survey with more than $1.3 \times 10^6$galaxiesandadepth$ \calD \sim 400 \Mpc$. The hierarchical amplitudes $s_J={\text{wbar}}_J\mathrm{/}{\text{wbar}}_2^{J-1}$ are roughly constant, up to $J=9$, between $0.5\text{Mpc}$ and $2\text{Mpc}$ and decrease slowly for larger scales. At scales larger than $7\text{Mpc}$ we find strong similarities between the statistical properties of the galaxy fluctuations and the theoretical properties of matter fluctuations evolving under the influence of gravity in an expanding universe on assumption that the initial fluctuations are small and Gaussian. This is most easily explained if at large scales there is no significant biasing between matter and galaxy fluctuations. The comparison of the skewness in the CfA and SSRS catalogues with comparable sub-samples of the APM indicates that the volume of a ``fair sample’’ has to be much larger that the one in the combined CfA/SSRS catalogues.