THE SURFACE BRIGHTNESS TEST FOR THE EXPANSION OF THE UNIVERSE .3. REDUCTION OF DATA FOR THE SEVERAL BRIGHTEST GALAXIES IN CLUSTERS TO STANDARD CONDITIONS AND A 1ST INDICATION THAT THE EXPANSION IS REAL

Petrosian radii, effective radii, apparent magnitudes, and average surface brightnesses are obtained for the first few ranked galaxies in 56 nearby clusters and groups using data from the literature. The radii of first-ranked galaxies continue to increase faster than Hubble's constant surface brightness scaling law of M approximately -5 log R, steepening the variation of <SB> with M calibrated in Paper II. The strong correlation of <SB> with M (and consequently with R) makes the correction of <SB> data to "standard conditions" for the first few ranked cluster galaxies even more important than discussed in Paper II in a search for the Tolman SB effect to test the reality of the expansion. A Scott-like selection bias is present in the data we have used, causing the first-ranked galaxies in our sample to have brighter absolute magnitudes at larger redshifts. This creates an artificial correlation of <SB> with log (1 + z) that imitates the Tolman cosmological surface brightness dimming with redshift but with a 4 times larger amplitude than is expected from theory if the universe expands. The correlation is shown to be an artifact of the selection biases in the sample. It is demonstrated that biases of this kind can always be removed by reducing the <SB> values to a "standard condition" of either fixed M or fixed R by using the correlations calibrated here. We apply these reduction procedures to data on distant clusters obtained by Djorgovski and Spinrad and show that a strong Tolman-like signal is present that matches the required slope of <SB>/d log (1 + z) approximately 10 for an expanding manifold. Reasons are given to be cautious of the result despite its importance in justifying the standard model of cosmology by proving that the expansion is real. The conclusion from the present result, if confirmed, is that the conventional interpretation of the redshifts as a change of the cosmological metric scale factor with time is correct.