Annu. Rev. Astron. Astrophys. 1988. 26: 561-630
Copyright © 1988 by . All rights reserved

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8.2. Diameters of First-Ranked Cluster Galaxies at Low Redshift

To test the z-1 dependence of Equation 45 at low redshift requires only a crude experiment. Furthermore, in this regime, isophotal and metric diameters are nearly the same. A photographic test made in 1970-71 using eye estimates of the angular diameters from Palomar Schmidt and 200-inch plates (Sandage 1972a) was sufficient to show that the dependence on z is z-1, as in Equation 55. The data, set out in Figure 12, range in redshift from z = 0.0023 for the Leo group to z = 0.46 for 3C 295. Over this range, the isophotal diameters (to an isophote of ~ 23 mag arcsec-2) range from ~ 250 arcsec to ~ 2 arcsec.

Figure 12

Figure 12. The observed theta(z) relation for low-redshift, first-ranked E cluster galaxies obtained by eye estimates from a homogeneous set of photographic plates. The line is the theta ~ z-1 Euclidean expectation (from Sandage 1972a).

This test of the linearity of the redshift-distance relation is independent of the m(z) test of Section 4, although it is related to m(z) under the assumption that all first-ranked E galaxies have only a small dispersion in surface brightness about a mean value. In the quoted paper, I called this premise the "constant" surface brightness condition, to which Gudehus (1975) pointed out the more proper statement now given - to wit, that a stable mean surface brightness with small dispersion exists that is independent of redshift at low redshift.

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