CLUSTER LUMINOSITY FUNCTION AND N(TH) RANKED MAGNITUDE AS A DISTANCE INDICATOR

We define here a standard candle to determine the distance of clusters of galaxies and to investigate their peculiar velocities by using the n(th) rank galaxy (magnitude m(n)). We address the question of the un iversality of the luminosity function for a sample of 28 rich clusters of galaxies (cz similar or equal to 20000 km.s(-1)) in order to model the influence on m(n) of cluster richness. This luminosity function i s found to be universal and the fit of a Schechter profile gives alpha =- 1.50+/-0.11 and M-bj =-19.91 +/-0.21 in the range [-21,-17]. The u ncorrected distance indicator m(n) is more efficient for the first ran ks n. With n=5, we have a dispersion of 0.61 magnitude for the (m(n),5 log(cz)) relation. When we correct for the richness effect and subtrac t the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15. Simulations show that a large part of this dispersion origi nates from the intrinsic scatter of the standard candle itself. These provide upper bounds on the amplitude a, of cluster radial peculiar mo tions. At a confidence level of 90%, the dispersion is 0.13 magnitude and sigma(v) is limited to 1200 km.s(-1) for our sample of clusters.