The Tolman Surface Brightness Test for the Reality of the Expansion. V. Provenance of the Test and a New Representation of the Data for Three Remote Hubble Space Telescope Galaxy Clusters

Abstract

A new reduction is made of the Hubble Space Telescope (HST) photometric data for E galaxies in three remote clusters at redshifts near z = 0.85 in search for the Tolman surface brightness (SB) signal for the reality of the expansion. Because of the strong variation of SB of such galaxies with intrinsic size, and because the Tolman test is about SB, we must account for the variation. In an earlier version of the test, Lubin & Sandage calibrated the variation out. In contrast, the test is made here using fixed radius bins for both the local and remote samples. Homologous positions in the galaxy image at which to compare the SB values are defined by radii at five Petrosian η values ranging from 1.0 to 2.0. Sérsic luminosity profiles are used to generate two diagnostic diagrams that define the mean SB distribution across the galaxy image. A Sérsic exponent, defined by the rⁿ family of Sérsic profiles, of n = 0.46 fits both the local and remote samples, on average, with only a small spread from 0.4 to 0.6. Diagrams of the dimming of the langSBrang with redshift over the range of Petrosian η radii shows a highly significant Tolman signal but degraded by luminosity evolution in the look-back time. The expansion is real and a luminosity evolution exists at the mean redshift of the HST clusters of 0.8 mag in R _cape and 0.4 mag in the I _cape photometric rest-frame bands, consistent with the evolution models of Bruzual & Charlot.