Analysis of galaxy morphology and evolution using the pointwise dimension

In this paper we explore the application of the pointwise dimension (PD) analysis as a large-scale structure descriptor to the Third Reference Catalog of Bright Galaxies (RC3). This technique, which originated in the field of fractal geometry (Mandelbrot 1983) and found many applications in nonlinear dynamics, is particularly illuminating in the study of correlations between morphology and environment. To our knowledge the technique is being applied for the first time to the study of galaxy morphology and evolution. The PD is the slope of the curve representing the number of galaxies within some radius, determined separately for each galaxy in the catalog. Thus the distributions of PDs can be compared for subsamples based on morphological type or luminosity. The conclusions of this analysis of RC3 are as follows: (1) The PD elucidates the tendency for early-type galaxies to cluster more than late-type galaxies; however, there is considerable overlap between these populations. (2) The PD statistic does not find a significant relationship between luminosity and clustering in RC3, but it could be an effective diagnostic in larger two-dimensional catalogs. (3) The majority of galaxies in RC3 (excluding clusters) are spread out in space much like a random distribution. A population of objects that traces the distribution of galaxies, but avoids clusters, would have only small correlations. It is worthwhile to pursue application of the PD to larger catalogs with a wider range of luminosities. Subject headings: galaxies: clusters: general - galaxies: structure - large-scale structure of universe -methods: analytical