The Relative Neighborhood Graph for Estimating Two-Dimensional Voids in the Cold Dark Matter Universe

Abstract

A new technique based on a graph-theoretical approach is proposed for identifying and estimating voids in two-dimensional galaxy distributions. A relative neighborhood graph is utilized for identifying two-dimensional voids. The loop angle that characterizes the size of the voids is defined, and the distribution function as well as the average of loop angles are used for estimating the voids statistically. We applied our new technique to two-dimensional voids in Cold Dark Matter (CDM) simulations. Low-density, middle-density, and high-density CDM models were adopted for examining the nature of two-dimensional voids. From our analyses, we found that the average of the loop angle in the low-density CDM model is apparently larger than that in the middle-density or the high-density CDM models. However, the difference between the middle-density and the high-density CDM models is subtle. We also analyzed the observational two-dimensional galaxy distributions and compared the two-dimensional mock samples that are constructed from CDM simulations. From our analyses, we succeeded to restrict the density parameter of our universe.