A Tolman Surface Brightness Test for Universal Expansion and the Evolution of Elliptical Galaxies in Distant Clusters

Abstract

We use the intercept of the elliptical galaxy radius-surface brightness (SB) relation at a fixed metric radius as the standard condition for the Tolman SB test of the universal expansion. We use surface photometry in the optical and near-infrared of elliptical galaxies in Abell 2390 (z = 0.23) and Abell 851 (z = 0.41) and compare them to the Coma Cluster at z ≈ 0. The photometric data for each cluster are well described by the Kormendy relation r -->e -->∑eA, where A = -0.9 in the optical and A = -1.0 in the near-infrared. The scatter about this near-infrared relation is only 0.076 in log re at the highest redshift, which is much smaller than at low redshifts, suggesting a remarkable homogeneity of the cluster elliptical population at z = 0.41. We use the intercept of these fixed-slope correlations at Re = 1 kpc (assuming H0 = 75 km s-1 Mpc-1, Ω0 = 0.2, and Λ0 = 0, where the results are only weakly dependent on the cosmology) to construct the Tolman SB test for these three clusters. The data are fully consistent with universal expansion if we assume simple models of passive evolution for elliptical galaxies but are inconsistent with a nonexpanding geometry (the tired-light cosmology) at the 5 σ confidence level at z = 0.41. These results suggest luminosity evolution in the rest-frame K band of 0.36 ± 0.14 mag from z = 0.41 to the present and are consistent with the elliptical galaxies' having formed at high redshift. The SB intercept in elliptical galaxy correlations is thus a powerful tool for investigating models of their evolution for significant look-back times.