The Tolman surface brightness test for the reality of the expansion. IV. Ameasurement 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 expa nsion is discussed. Hubble's reluctance, even as late as 1953, to accept th e expansion as real is explained as due to his use of equations for distanc es and absolute magnitudes of redshifted galaxies that do not conform to th e modern Mattig equations of the standard model. The Tolman surface brightn ess test, once the only known test for the reality of the expansion, is con trasted with three other modern tests. These are (1) the time dilation in T ype 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 surfac e 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 fiduc ial lines in the mean surface brightness-logarithm of the linear radius dia grams of Paper I are found for all three clusters. Expressed as the exponen t, n, in 2.5 log (1+z)(n) mag, the value of n averaged over Petrosian radii of eta = 1.7 and eta = 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 q(o) = 1/2 model. The sens itivity of the result to the assumed value of is shown to be less than 23% between q = 0 and +1. The conclusion is that the exponent on (1+z) varies f rom 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 q(o). For a true Tolman signal with n = 4, the luminosity evolution in the look-back time, q 0. expressed as the ex ponent in 2.5 log (1+z)(4-n) mag, must then be between 1.72 to 1.19 (+/-0.1 7) in the R band and 0.94 to 0.45 (+/-0.13) in the I band. We show that thi s is precisely the range expected from the evolutionary models of Bruzual a nd Charlot and other measurements of the luminosity evolution of early-type galaxies. We conclude that the Tolman surface brightness test is consisten t with the reality of the expansion to within the combined errors of the ob served [SB] depression and the theoretical correction for luminosity evolut ion. 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 o ut the tired light model at a significance level of better than 10 sigma.