The Angular Fractal Dimension in Galaxy’s Distributions

Abstract

The study of large scale structure (LSS) of the Universe has entered a precision era due to all-sky surveys and numerical simulations. The new data has provided a way to bring new methods to bear to analyze the cosmology as probed by large scale structure. We use wavelet packets to investigate fractal point-processes on galactic scales. In particular, we develop a method to calculate the angular fractal dimension of galaxy distributions as a function of cosmological comoving distance. Taking advantage of the self-similarity and localization properties of discrete wavelets, we compute the angular fractal dimension of galaxies in narrow redshift bins. The narrow bins assure that dynamical evolution in the range being studied has not occurred to a significant extent. We use both real and simulated data from the Baryon Oscillation Spectroscopic Survey (BOSS) and the Mock Galaxy Catalogs produced by the Sloan Digital Sky Survey (SDSS). Using the wavelet packet power spectrum, we find areas in the galaxy distribution which have power law like behavior indicating fractal processes are present. The exponent of the power law is the Hurst exponent H, which is directly related to the fractal dimension of spatial point processes. We find the fractal dimension ranges from D = 1.1 to D = 1.4 for BOSS Galaxies while it ranges from D = 1.4 to D = 1.8 for Mock Galaxy Catalogs. The results are mildly dependent on the number of galaxies present in each redshift bin and less so on the resolution at which the data is binned. We conclude that this method can be used to characterize large scale structure and its evolution as a function of redshift. There are hints that the galaxy distribution may be fractal at higher redshifts than previously reported, however more data is necessary before a firmer conclusion is reached.