An examination of the large-scale clustering of the Las Campanas Redshift Survey

Following the point of view of K. Falconer, a set referred to as fractal can be defined as a set with fine structure, some form of approximate or statistical self-similarity, and too irregular a structure to describe via traditional geometric language. The renewed modern interest in fractals has found as one of its applications the study of large-scale structure, giving a quantitative descriptive scheme to ideas that had been expressed qualitatively as early as the 1920s. This paper presents the results of an analysis of the structure of the Las Campanas Redshift Survey (LCRS). The LCRS is a galaxy survey of approximately 26,000 galaxies tin six declination slices) that has been studied extensively over the past few years with an eye toward understanding large-scale structure. For this analysis, I have used the pointwise dimension, an easy-to-apply fractal statistic that has previously been used to study cluster interiors, galactic distributions, and cluster distributions. The present analysis has been performed to serve as a guide for the study of future large redshift surveys. I find that the LCRS slices show statistical differences from homogeneous distributions out to a scale of 200 Mpc. More specifically, using Kolmogorov-Smirnov tests to compare the environments (quantified by the pointwise dimension) of individual galaxies within slices of LCRS to environments of galaxies in homogeneous slices show statistically significant differences, to the 99% level, out to fits of 200 Mpc. While this differs from some analyses that show a trend toward homogeneity at smaller regimes, it is consistent with other galaxy catalog analyses that show no trends toward homogeneity on even larger scales.