Mathematics
Scientific paper
May 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979phdt.........3f&link_type=abstract
Ph.D. Thesis Princeton Univ., NJ.
Mathematics
1
Cross Correlation, Functions (Mathematics), Galactic Clusters, Approximation, Astronomical Catalogs, Asymptotes
Scientific paper
A simple model is presented for the form of the three-point function in terms of products of two-point functions, and the assumed form for the spatial functions is shown to give in projection the observed angular functions. The amplitude coefficient is interpreted as a measure of the dispersion in cluster sizes. A theoretical description of the development of a rich cluster comes from the BBGKY hierarchy of equations for the correlation functions. The model suggested by the catalogs and supported by the N-body results permits the truncation of the hierarchy and results in a closed set of equations for the cluster-galaxy two-point function and auxiliary velocity moments. The asymptotic form the solution far from the cluster center is fixed by the initial power spectrum of irregularities, and a scaling assumption relates this to the solution for small separation.
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