  We have re-examined the nature of the cluster galaxy luminosity function
using the data from the Edinburgh-Durham Southern Galaxy Catalogue and the
Edinburgh-Milano Redshift Survey. We derive a best fit luminosity function over
the range M(bj)=-18 to -21, for a composite sample of 22 of the richer clusters
that has M*=-20.16+/-0.02 and alpha=-1.22+/-0.04. The dominant error in these
values results from the choice of background subtraction method. From extensive
simulations we can show that when the LF is fitted over this narrow range, it
is difficult to discriminate against bright values of M*in the single cluster
fits, but that faint values provide a strong test of the universality of the
luminosity function. We find that all the individual cluster data are well fit
by a Schechter function with alpha fixed at -1.25, and that <=10% of these have
fitted values of M* that disagree from the average at the 99% confidence level.
We further show that fitting only a single parameter Schechter function to
composite subsets of the data can give erroneous results for the derived M*. By
considering two parameter fits, the results of Monte-Carlo simulations and
direct two-sample chi-squared tests we conclude that there is only weak
evidence for differences between the data when broken down into subsets based
on physical properties (Bautz-Morgan class, richness, velocity dispersion):
from our simulations, only the evidence for a difference between subsets based
on velocity dispersion may in fact be significant. We find no evidence at all
that a Schechter function is not a good model for the intrinsic cluster
luminosity function over this absolute magnitude range. Models that invoke
strong evolution of galaxy luminosity of all galaxies within clusters are
inconsistent with our results.
