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The extensive CCD photometry by Postman & Lauer (1995, ApJ, 440, 28) in the Cape/Cousins R photometric band for first ranked cluster elliptical and S0 galaxies in 118 low redshift clusters is analyzed for the correlations between average surface brightness, linear radius, and absolute magnitude. The purpose is to calibrate the correlations between these three parameters in the limit of zero redshift. These local correlations provide the comparisons to be made in Paper IV with the sample of early-type galaxies at high redshift in search of the Tolman surface brightness signal of (1 + z)^4 if the expansion is real. Surface brightness averages are calculated at various metric radii in each galaxy in the sample. The definition of such radii by Petrosian (1976, ApJ, 209, L1) uses ratios of observed surface photometric data. The observed surface brightnesses are listed for 118 first ranked cluster galaxies at Petrosian eta radii of 1.0, 1.3, 1.5, 1.7, 2.0, and 2.5 mag. The three local diagnostic correlation diagrams are defined and discussed. We review the Tolman test and show that, although recipes from the standard cosmological model that already have the Tolman signal incorporated are required to calculate linear radii and absolute magnitudes from the observed data, the test is nevertheless free from the hermeneutical circularity dilemma occasionally claimed in the literature. The reasons are the observed mean surface brightness (1) is independent of any assumptions of cosmological model, (2) does not depend on the existence of a Tolman signal because it is calculated directly from the data using only angular radii and apparent magnitudes, and (3) can be used to search for the Tolman signal because it carries the bulk of that signal.
We review a sample of the early literature in which the reality of the expansion is discussed, explain Hubbles reticence to accept the expansion as real, and contrast the Tolman surface brightness test with three other modern tests. We search for the
To complete the Tolman surface brightness test on the reality of the expansion of the Universe, we need to measure accurately the surface brightness profiles of the high-redshift galaxy sample. We, therefore, investigate the effects of various sizes
Photometric data for 34 early-type galaxies in the three high-redshift clusters Cl 1324+3011 (z = 0.76), Cl 1604+4304 (z = 0.90), and Cl 1604+4321 (z = 0.92), observed with the Hubble Space Telescope (HST) and with the Keck 10-meter telescopes by Oke
Redshifts of an astronomical body measured at multiple epochs (e.g., separated by 10 years) are different due to the cosmic expansion. This so-called Sandage-Loeb test offers a direct measurement of the expansion rate of the Universe. However, accele
The nature of the dwarf galaxy population as a function of location in the cluster and within different environments is investigated. We have previously described the results of a search for low surface brightness objects in data drawn from an East-W