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 photo metric band for first-ranked cluster elliptical and S0 galaxies in 118 low redshift ([z] = 0.037) clusters is analyzed for the correlations between av erage surface brightness, linear radius, and absolute magnitude. The purpos e is to calibrate the correlations between these three parameters in the li mit of zero redshift. The Postman-Lauer cluster galaxies at low redshift ap proximate this limit. We apply small corrections for the finite mean redshi ft of the sample in order to define the zero-redshift correlations. These l ocal correlations provide the comparisons to be made in Paper IV with the s ample of early-type galaxies at high redshift in search of the Tolman surfa ce 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 prope rties for the Tolman test which are reviewed in this paper. The observed su rface brightnesses are listed for 118 first-ranked cluster galaxies at Petr osian eta radii of 1.0, 1.3, 1.5, 1.7, 2.0, and 2.5 mag. The three local di agnostic correlation diagrams are defined and discussed. We review the Tolm an test and show that, although recipes from the standard cosmological mode l that already have the Tolman signal incorporated are required to calculat e linear radii and absolute magnitudes from the observed data, the test is nevertheless free from the hermeneutical circularity dilemma occasionally c laimed in the literature. The reasons are the observed mean surface brightn ess (1) is independent of any assumptions of cosmological model, (2) does n ot depend on the existence of a Tolman signal because it is calculated dire ctly 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 o f that signal.