High-order galaxy correlation functions in the APM Galaxy Survey

We estimate J-point galaxy-averaged correlation functions $$\bar{\omega}_J(\theta)$$ for J = 2,...,9, in a sample of the APM Galaxy Survey with more than 1.3 × 10⁶ galaxies and a depth D ∼ 400 h^-1 Mpc. The hierarchical amplitudes $$s_J=\bar{\omega}_J/\bar{\omega}_2^{J-1}$$ are roughly constant, up to J = 9, between θD ∼ 0.5 h^-1 Mpc and θD ∼ 2 h^-1 Mpc, and decrease slowly for larger scales. At scales θD > 7 h^-1 Mpc, we find strong similarities between the statistical properties of the galaxy fluctuations δ_g and the theoretical properties of matter fluctuations δ_m evolving under the influence of gravity in a expanding universe on the 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, i.e. δ_g ≃ δ_m. The comparison of the skewness in the CfA and SSRS catalogues with comparable subsamples of the APM indicates that the volume of a ‘fair sample’ has to be much larger than the one in the combined CfA/SSRS catalogues.