Amplification of cluster correlations - The effect of sharp clipping

Statistics – Computation

Scientific paper

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Astronomical Catalogs, Galactic Clusters, Spatial Distribution, Computational Astrophysics, Correlation, Image Processing, Monte Carlo Method

Scientific paper

In this paper the method of generating functions is used to describe how cluster correlations arise from the galaxy correlations. As a model we use a 'sharp clipping' algorithm: we identify clusters as cells with density exceeding a certain threshold. We provide the generating function of the two- and three-point correlation functions of the resulting cumulative distribution, yielding the correlation functions for any threshold. The generating function can be expanded either with computer algebra or with analytic calculations. We evaluate two special cases which can be solved analytically and investigate their continuum limit properties. It is shown that the shape of the cluster correlation function is always identical to the galaxy correlation function, and we calculate the amplification for these special cases. The theoretical results agree reasonably well with known observations.

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