Luminosity functions of 10 nearby clusters of galaxies. II. Analysis of the luminosity function

We investigate the total luminosity function (LF) and the type-specific luminosity functions (TSLFs) of r(1/4)-like galaxies and exponential-like galaxies in 10 nearby clusters. The composite total LF of the 10 clusters is described well by the Schechter function with M-R* = -21.3 and alpha = -1.31 in the range -23.5 < M-R + 5 log h < -16. This value of is consistent with the previous results for cluster galaxies. An extensive comparison of the values of is made between clusters and fields. We find that the total LF of cluster galaxies has a steeper faint end slope than that of field galaxies. In contrast to the composite total LF, the individual total LFs of some clusters are not fitted well by the Schechter function. They show a hump around M(R)similar to-20 to -19 associated with a dip around M(R)similar to -19 to -18. The composite TSLFs of both r(1/4)-like galaxies and exponential-like galaxies are fitted well by the Schechter function. The best-fit parameters are ( M-R similar to -21.2, alpha = -1.08) for the former and (M(R)similar to -21.1, alpha = -1.49) for the latter. When seen on a cluster to cluster basis, however, the TSLFs of the two types of galaxies show different behaviors. The TSLF of r(1/4)-like galaxies shows a considerable diversity among the clusters, while the TSLF of exponential-like galaxies is similar in all the clusters. We demonstrate that the dip at MR 19 to 18 seen in the total LFs of some clusters is almost entirely due to r(1/4)-like galaxies, rather than exponential-like galaxies. We find that the dip of the TSLF of r(1/4)-like galaxies is correlated with the velocity dispersion of the cluster in the sense that clusters with larger velocity dispersion show more distinct dips.