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 -18 to -21 in M ( b _ { j } ) , for a composite sample of 22 of the richer clusters that has M ( b _ { j } ) ^ { * } = -20.16 \pm 0.02 and \alpha = -1.22 \pm 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 \leq 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 ^ { * } , as might be expected from the known tight correlation between M ^ { * } and \alpha .
By considering two parameter fits , the results of Monte-Carlo simulations and direct two-sample \chi ^ { 2 } 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 .
However , 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 .