Mathematics – Logic
Scientific paper
Sep 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt........15k&link_type=abstract
Thesis (PHD). MICHIGAN STATE UNIVERSITY , Source DAI-B 58/09, p. 4871, Mar 1998, 207 pages.
Mathematics
Logic
Abell Clusters
Scientific paper
In this thesis I explore a procedure for the detection and quantification of substructure in the projected positions of galaxies in clusters. The method is first tested by application to the 56 well-studied galaxy clusters that make up the morphological sample of Dressler (1980). This method is then applied to a much larger, volume-limited sample of 119 Abell clusters originally identified of Hoessel, Gunn, & Thuan (1980). This sample includes all Abell clusters with distance class <=4 and richness class >=0 with | b|>30. Two tests for substructure, one parametric and one nonparametric, are applied to the galaxy positions and the results are compared. The KMM algorithm partitions the data into Gaussian sub-populations and estimates their statistical significance via a hypothesis test. The DEDICA algorithm is a nonparametric technique that identifies peaks in the projected galaxy density and determines their significance with respect to the background. After a K-S test is employed on the magnitude distributions to remove background/foreground groups, 64/%± 15/% of the large cluster sample is found to contain significant substructure. Nonparametric methods of density estimation are explored and applied to the construction of contour plots and the calculation of radial number-density profiles for each of the sample clusters. An average core radius of 150± 100 kpc (H0=75 km s-1) is obtained. This is however, likely to be an upper limit due to mis-specification of the cluster centers. Inside of 1 Mpc, the space density is found to vary as ρ∝r-1.9±0.3 after a correction is made for background galaxies. The large fraction of clusters with presently-detectable substructure, as well as the shallow space-density profiles, are used to argue that rich clusters of galaxies are still in the process of formation during the present epoch and are not well described by equilibrium models. If clusters are currently accreting large amounts of material, this implies a high-density Universe, with Ω ~>/ 0.4.
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