The Tolman surface brightness test for the reality of the expansion. I. Calibration of the necessary local parameters

The extensive CCD photometry by Postman & Lauer in the Cape/Cousins R photometric band for first-ranked cluster elliptical and S0 galaxies in 118 low redshift ([z] = 0.037) clusters is analyzed for the correlations between average surface brightness, linear radius, and absolute magnitude. The purpose is to calibrate the correlations between these three parameters in the limit of zero redshift. The Postman-Lauer cluster galaxies at low redshift approximate this limit. We apply small corrections for the finite mean redshift of the sample in order to define the zero-redshift correlations. These local correlations provide the comparisons to be made in Paper IV with the sample of early-type galaxies at high redshift in search of the Tolman surface brightness signal of (1 + z)(4) if the expansion is real. Surface brightness averages are calculated at various metric radii in each galaxy in the sample. The definition of such radii by Petrosian uses ratios of observed surface photometric data. Petrosian radii have important properties for the Tolman test which are reviewed in this paper. The observed surface brightnesses are listed for 118 first-ranked cluster galaxies at Petrosian eta radii of 1.0, 1.3, 1.5, 1.7, 2.0, and 2.5 mag. The three local diagnostic correlation diagrams are defined and discussed. We review the Tolman test and show that, although recipes from the standard cosmological model that already have the Tolman signal incorporated are required to calculate linear radii and absolute magnitudes from the observed data, the test is nevertheless free from the hermeneutical circularity dilemma occasionally claimed in the literature. The reasons are the observed mean surface brightness (1) is independent of any assumptions of cosmological model, (2) does not depend on the existence of a Tolman signal because it is calculated directly from the data using only angular radii and apparent magnitudes, and (3) can be used to search for the Tolman signal because it carries the bulk of that signal.