The dynamics of rich clusters - II. Luminosity functions

This is the second paper in an observational survey of the dynamical properties of 14 rich clusters of galaxies. Paper I in the series outlined the strategy of the survey and presented the radial velocities and stellar velocity dispersions obtained from multiplex spectroscopy of the clusters. This paper presents photographic photometry for the clusters and examines (heir luminosity functions (LFs). The individual cluster LFs are found to be well fitted by Schechter functions with $$\alpha \equiv -1.25$$. The mean characteristic magnitude $$M^\ast$$ is −20.12 in B_J$$(H_0=100 \enspace\text {km}\enspace \text s^{-1})$$ in good agreement with previous determinations. The composite LF formed from all 14 clusters is best fitted by a Schechter function with $$M^\ast = -20.04$$ and $$\alpha = -1.21$$, Various statistical tests provide no evidence that, over the range $$M^\ast -1 \enspace \text {to} \enspace M^\ast +2$$ examined here, individual cluster LFs are not all drawn from a universal cluster LF having approximately Schechter form and parameters $$M^\ast \approx -20.1 \enspace \text {and} \enspace \alpha \approx -1.25$$. Simulations show, however, that the small number of galaxies in the bright end of cluster LFs limits the statistical discrimination between differing LFs to a level greater than the smallest differences of physical interest. Comparisons of composite LFs formed by grouping rich and poor clusters, and clusters of Bautz–Morgan (B–M) types I and I–II and B–M type III, reveal no variation of cluster LFs with either richness or B–M type. A similar comparison, however, marginally suggests that the composite LF of the high velocity dispersion clusters has a fainter $$M^\ast$$ than that of the low velocity dispersion clusters. No evidence for mass segregation in the form of LF differences between the centres and peripheries of the clusters is found. Simulations to assess the power of the statistical tests imply thai variations of more than 0.4 mag in $$M^\ast$$ or 0.15 in α are ruled out by these comparisons. However, the reliable detection of smaller variations, such as those of the size expected due to differing morphological mixes, will require an increase by a factor of at least 4 in the size of the sample of cluster LFs.