The Method of a Two-Point Conditional Column Density for Estimating the Fractal Dimension of the Galaxy Distribution

Abstract

We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies, the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for galaxies with known redshifts from the LEDA database. The fractal dimension of a sample of LEDA and EDR SDSS galaxies has been estimated to be D = 2.1 for cylinder lengths of 200 Mpc. Amajor advantage of the suggested method is that it allows scales comparable to the catalog depth to be analyzed for galaxy surveys in the form of conical sectors and small fields in the sky.