Analysis of the Spatial Distribution of Galaxies in the Numerical Galaxy Catalog

Abstract

Abstract We examine the spatial distribution of galaxies in the Numerical Galaxy Catalog, which is based on a hierarchical clustering framework. This catalog is constructed from a semianalytic model of galaxy formation combined with high-resolution $N$-body simulations in a $\Lambda$-dominated flat cold dark-matter cosmological model. To quantify the spatial distribution of galaxies, we use a graph-theoretical approach, because it is one of the most powerful statistical ways of estimating spatial data. In particular, three types of graphs are adopted: the Delaunay graph, the minimal spanning tree, and the constellation graph. To quantify the galaxy distributions, we apply statistical measures suitable for each type. The mass distributions in the cold dark-matter universe are also examined to clarify differences in the spatial distribution of dark matter and galaxies. The spatial distribution of galaxies in the two-degree field (2dF) galaxy redshift survey is finally compared with that in the Numerical Galaxy Catalog. From our analysis, we definitely show that galaxy distributions in the Numerical Galaxy Catalog are different from the dark-matter distributions. We also find that the Numerical Galaxy Catalog considerably improves the theoretical prediction of spatial galaxy distributions, although it does not do enough to reproduce the 2dF galaxy redshift survey. Finally, we show that the constellation graph and the minimal spanning tree are convenient for quantifing the galaxy distributions in an objective manner.