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Received 20 April 1998 / Accepted 4 June 1998
We define here a standard candle to determine the distance of clusters of galaxies and to investigate their peculiar velocities by using the nth rank galaxy (magnitude mn). We address the question of the universality of the luminosity function for a sample of 28 rich clusters of galaxies (cz20000 km.s-1) in order to model the influence on mn of cluster richness. This luminosity function is found to be universal and the fit of a Schechter profile gives =-1.500.11 and in the range [-21,-17]. The uncorrected distance indicator mn is more efficient for the first ranks n. With n=5, we have a dispersion of 0.61 magnitude for the (mn,5log(cz)) relation. When we correct for the richness effect and subtract the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15. Simulations show that a large part of this dispersion originates from the intrinsic scatter of the standard candle itself. These provide upper bounds on the amplitude of cluster radial peculiar motions. At a confidence level of 90 , the dispersion is 0.13 magnitude and is limited to 1200 km.s-1 for our sample of clusters.
Key words: cosmology: distance scale cosmology: large-scale structure of Universe galaxies: clusters galaxies: luminosity function
* Based on observations collected at the European Southern Observatory (La Silla, Chile)
Send offprint requests to: C. Adami
Online publication: August 6, 1998