We derive the galaxy luminosity function in the K _ { s } band for galaxies in 24 clusters to provide a local reference for higher redshift studies and to analyse how and if the luminosity function varies according to environment and cluster properties .
We use new , deep K band imaging and match the photometry to available redshift information and to optical photometry from the SDSS or the UKST/POSS : > 80 \% of the galaxies to K \sim 14.5 have measured redshifts .
We derive composite luminosity functions , for the entire sample and for cluster subsamples .
We consider the luminosity functions for red sequence and blue cloud galaxies .
The full composite luminosity function has K ^ { * } = 12.79 \pm 0.14 ( M _ { K } = -24.81 ) and \alpha = -1.41 \pm 0.10 .
We find that K ^ { * } is largely unaffected by the environment but that the slope \alpha increases towards lower mass clusters and clusters with Bautz-Morgan type < II .
The red sequence luminosity function seems to be approximately universal ( within errors ) in all environments : it has parameters K ^ { * } = 13.16 \pm 0.15 ( M _ { K } = -24.44 ) and \alpha = -1.00 \pm 0.12 ( for all galaxies ) .
Blue galaxies do not show a good fit to a Schechter function , but the best values for its parameters are K ^ { * } = 13.51 \pm 0.41 ( M _ { K } = -24.09 ) and \alpha = -1.60 \pm 0.29 : we do not have enough statistics to consider environmental variations for these galaxies .
We find some evidence that K ^ { * } in clusters is brighter than in the field and \alpha is steeper , but note this comparison is based ( for the field ) on 2MASS photometry , while our data are considerably deeper .