The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies
We review a sample of the early literature in which the reality of the expansion is discussed. Hubble's reluctance, even as late as 1953, to accept the expansion as real is explained as due to his use of equations for distances and absolute magnitudes of redshifted galaxies that do not conform to the modern Mattig equations of the standard model. The Tolman surface brightness test, once the only known test for the reality of the expansion, is contrasted with three other modern tests. These are (1) the time dilation in Type Ia supernovae light curves, (2) the temperature of the relic radiation as a function of redshift, and (3) the surface brightness normalization of the Planckian shape of the relic radiation. We search for the Tolman surface brightness depression with redshift using the Hubble Space Telescope (HST) data from Paper III for 34 early-type galaxies from the three clusters Cl 1324+3011 (z=0.76), Cl 1604+4304 (z=0.90), and Cl 1604+4321 (z=0.92). Depressions of the surface brightness relative to the zero-redshift fiducial lines in the mean surface brightness-logarithm of the linear radius diagrams of Paper I are found for all three clusters. Expressed as the exponent, n, in 2.5log(1+z)n mag, the value of n averaged over Petrosian radii of η=1.7 and η=2.0 for all three clusters is n=2.59+/-0.17 in the R band and 3.37+/-0.13 in the I band for a q0=1/2 model. The sensitivity of the result to the assumed value of q0 is shown to be less than 23% between q=0 and +1. The conclusion is that the exponent on (1+z) varies from 2.28 to 2.81(+/-0.17) in the R band and 3.06 to 3.55(+/-0.13) in the I band, depending on the value of q0. For a true Tolman signal with n=4, the luminosity evolution in the look-back time, expressed as the exponent in 2.5log(1+z)4-n mag, must then be between 1.72 to 1.19(+/-0.17) in the R band and 0.94 to 0.45(+/-0.13) in the I band. We show that this is precisely the range expected from the evolutionary models of Bruzual and Charlot and other measurements of the luminosity evolution of early-type galaxies. We conclude that the Tolman surface brightness test is consistent with the reality of the expansion to within the combined errors of the observed <SB> depression and the theoretical correction for luminosity evolution. We have also used the high-redshift HST data to test the ``tired light'' speculation for a nonexpansion model for the redshift. The HST data rule out the tired light model at a significance level of better than 10 σ.