A fluctuation analysis for optical cluster galaxies - I. Theory

It is evident that considerable information exists in astronomical data below the threshold for the detection of individual sources (perhaps set for a '5 sigma' total detection, or for isophotal detection thresholds of '2 sigma' above the sky background), and that such information, if descriptive of an underlying population of objects characterized by a relatively small parameter set, could in principle be used to set constraints on these parameters. We therefore derive a general theoretical framework for fluctuation analysis (after the radio astronomers' 'P(D)' analysis) of optical imaging data on faint galaxy fields, in particular; on fields containing rich clusters of galaxies, in an attempt to determine the Schechter luminosity function of the dwarf galaxies that dominate the statistics at this magnitude range.