A Global Descriptor of Spatial Pattern Interaction in the Galaxy Distribution

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Abstract
We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest-neighbor distribution and the void probability function. The J descriptor allows us to distinguish clustered (i.e., correlated) from regular (i.e., anticorrelated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matérn cluster process as an idealized model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (or in this case reject) viable models of cosmic structure formation.

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