Quantitative Comparison of Two-point Correlation Functions from Real and Mock SDSS Galaxy Catalogs

Abstract

We present a simple closed-form bandwidth selection method to obtain the optimal bin size for estimating the two-point correlation function (2PCF). To demonstrate its effectiveness, we apply this procedure in a numerical study using a theoretical point process model to 10 mock Sloan Digital Sky Survey (SDSS) catalogs with the same cosmology, and to a real SDSS catalog. With a point process model, the real 2PCF is known and ratios of the mean square errors of estimates can be computed. The standard deviation of 2PCF estimates, obtained from the 10 mock catalogs, provides information about the uncertainty of estimates. With the SDSS catalog, we use subsampling to assess uncertainty. In each case, we find that our procedure performs better than the commonly used procedure of equal bandwidths on the log-scale.