Studies of Rich Clusters of Galaxies-I: 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 0.13 to 0.20 have been made on V plates taken with the Palomar 48-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 β characterizing the radius of the cluster core. The mean distance of galaxies from the line of sight through the cluster centre, $$\bar r$$ , 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. where N_SH is the cluster population. This equation is used to define a new measure of angular radius $$\bar r_\text c$$ by reducing the observed value of $$\bar r$$ to that which would be observed for a cluster of standard radius on the assumption that R _{3 β} and N_SH uniquely determine $$R_\bar r$$ . A plot of $$\bar r_\text c$$ against z is given which shows a standard deviation of the residuals of $$\bar r_\text c$$ from a mean line with q₀ = +1 of only 18 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.