The redshift-distance relation. II. The Hubble diagram and its scatter for first-ranked cluster galaxies: a formal value for q0.

The Hubble diagram for first-ranked cluster galaxies is discussed on the basis of new photoelectric measurements of 41 clusters. Additional data by Westerlund and Wall and by Peterson, reduced by the same corrections, increase the sample to 84 clusters. The diagram has small scatter about a line of slope 5. Analysis of the scatter gives upper limits to the dispersions in redshift and in apparent magnitude, respectively. Treated as redshift residuals, the data show A log z to be independent of z; and because of this, most of the scatter must be due to residuals in magnitude. A limit of a(Acz) 100 km -1 for the distribution of random velocities of cluster centers in the present sample can be put from the analysis. From the magnitude residuals, the dispersion in absolute luminosities of first-ranked galaxies is (7(AMv) = 0.25 mag. For such galaxies in the present sample, the absolute magnitudes are independent of richness of the parent cluster over a richness range 5 <% N <% 500. There is no evidence for intergalactic absorption for galaxies in the present sample, either patchy at the a = 0.25 mag level, or general and selective at the aE(B - V) 0.05 mag level. If a strictly homogeneous Friedmann model universe is adopted, the deceleration parameter is calculated to be q0 = 0.96 + 0.4 (p.e.). To reduce this formal value to q0 = 0 requires a luminosity evolution at the rate dM/dt = 1.09 (1 + z)H0 mag yr -1, in the sense that E galaxies were brighter in the past. With q0 = +1 and H0 = 50 km 1 Mpc -1, the time to the Friedmann singularity is 11 x 10 years, which agrees with the age of globular clusters in our own Galaxy.