THE SURFACE BRIGHTNESS TEST FOR THE EXPANSION OF THE UNIVERSE .2. RADII, SURFACE BRIGHTNESS, AND ABSOLUTE MAGNITUDE CORRELATIONS FOR NEARBY E-GALAXIES

The correlation between absolute magnitude and surface brightness, averaged over a series of areas defined by metric (rather than isophotal) radii, is studied using E galaxies in the Virgo, Fornax, and Coma clusters, and in four additional samples of bright nearby field galaxies. The work is a calibration step in preparation for the Tolman (1 + z)4 surface brightness test for the reality of the expansion. As known before, and as is seen in the present data, the average surface brightness is strongly correlated with absolute brightness for giant galaxies. Galaxies brighter than MB ∼ -20 have fainter average surface brightness values as the total galaxy luminosity increases. The lack of a constant average surface brightness with changing absolute magnitude for bright E galaxies shows that Hubble's m ∼ -5 log r″ scaling law is not correct over the first few brightest magnitudes of the E luminosity function. Therefore measurements will be required of the 〈SB〉 over a range of MT in distant clusters so as to reduce the 〈SB〉 data to "standard conditions" before searching for the Tolman (1 + z)4 cosmological test signal. The purpose of the present paper is to calibrate the correlation between MT and 〈SB〉 using local samples. In the samples studied here the dispersion in the 〈SB〉 distributions, after reducing the data to absolute magnitude MB = -22 is ∼0.5 mag. This value is smaller than the 1.8 mag Tolman (1 + z)4 factor, even at the modest redshift of z = 0.5, showing that the Tolman test is feasible in practice as well as in principle.