20 CM VLA Survey of Abell Clusters of Galaxies. VI. Radio/Optical Luminosity Functions

From a statistically complete sample of 188 radio galaxies in Abell clusters, we examine the radio/optical correlations, the FR I/II division, and the univariate and bivariate luminosity functions. As suggested by Owen [Jets in Extragalactic Radio Sources, edited by H.-J. Roser and K. Meisenheimer (Springer, New York, 1993), p. 273], the FR I/II division is shown to be a strong function of the optical luminosity of the host galaxy ( is proportional to L^2^_opt_). This dependence is also seen in the bivariate luminosity function, which suggests that the evolutionary tracks of radio sources and/or the initial conditions in the source are governed by the host galaxy properties. The probability for detecting radio emission increases with optical luminosity. The optical dependence is clearly separated in the integral luminosity functions which can be used as a constraint to models of FR I radio power evolution. Additionally, the source counts from the integrated univariate radio luminosity function (RLF) are consistent with our suggestion in Paper V that radio sources may be a transient phenomenon which occurs in all elliptical galaxies at some time (or several times) over their lifetime. We find no statistically significant differences in the luminosity functions between rich cluster samples and radio sources not selected to reside in clusters. These results suggest that all radio galaxies live in similar environments in that the optical luminosity and the properties of the host galaxy are the most important parameters which affect radio source formation and evolution.