Studies of rich clusters of galaxies-1. Galaxy counts for nine clusters of intermediate redshift and the angular diameter-redshift relation

Counts of galaxies in the fields of nine rich clusters with z ranging from to have been made on V plates taken with the Palomar 8-in. Schmidt telescope. The surface density of galaxies as a function of distance from the cluster centre is discussed in the context of three previously suggested approaches to a definition of angular size. Least-squares fits of the data to the projected isothermal gas sphere lead to a parameter fl characterizing the radius of the cluster core. The mean distance of galaxies from the line of sight through the cluster centre, r, is a measure characterizing the size of the cluster as a whole. The use of secondary maxima in the density distribution is considered and dismissed. Rr and R3fl, the intrinsic cluster and core radii in Mpc, are found to be related through the empirical equation Rr = (031 i0oz) R3fl s'+( x I0- ) NsH-( +009) where NsH is the cluster population. This equation is used to define a new measure of angular radius r% by reducing the observed value of r to that which would be observed for a cluster of standard radius on the assumption that R3fl and NsH uniquely determine Rr. A plot of r% against z is given which shows a standard deviation of the residuals of r% from a mean line with qo = + I of only i8 per cent. We suggest that the use of this parameter as a measure of angular size makes the angular diameter-redshift test using clusters of galaxies competitive with the apparent magnitude-redshift test using brightest cluster galaxies.