Cluster correlations from N-point correlation amplitudes

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Correlation, Galactic Clusters, Galactic Mass, Mass Distribution, Algorithms, Astronomical Catalogs, Cosmology, Galactic Evolution, Galaxies, Mathematical Models

Scientific paper

It is shown, by using a new technique, how the much debated cluster correlation function is directly related to the higher order galaxy correlations. Mathematical techniques from biased galaxy formation are adopted: the biasing simulates the detection of the clusters, rather than their dynamic formation. A simple, analytical example is given. As a practical application of the simplified model, a novel method to determine the amplitudes of the irreducible N point correlation functions in the gravitational clustering hierarchy is presented. The corrected Lick catalog is used to obtain values of qN up to N = 8, considerably beyond previous attempts. The catalog, obtained from the Lick sample, has amplifications similar to the rich clusters, and the galaxy 'cluster' cross correlation is close to the geometric mean of the galaxy and cluster autocorrelations.

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