On the galaxy luminosity function in the central regions of the Coma cluster
We have obtained new redshifts for 265 objects in the central 48~$\times$~25~arcmin$^2$ region of the Coma cluster. When supplemented with literature data, our redshift sample is 95~\% complete up to a magnitude b$_{26.5}$=18.0 (the magnitudes are taken from the photometric sample of Godwin et al. 1983). Using redshift-confirmed membership for 205 galaxies, and the location in the colour-magnitude diagram for another 91 galaxies, we have built a sample of cluster members which is complete up to b$_{26.5}$=20.0. We show that the Coma cluster luminosity function cannot be adequately fitted by a single Schechter (1976) function, because of a dip in the magnitude distribution at b$_{26.5}$$\sim$17. The superposition of an Erlang (or a Gauss) and a Schechter function provides a significantly better fit. We compare the luminosity function of Coma to those of other clusters, and of the field. Luminosity functions for rich clusters look similar, with a maximum at $M_{b} \simeq -19.5 + 5 \times \log h_{50}$, while the Virgo and the field luminosity functions show a nearly monotonic behaviour. These differences may be produced by physical processes related to the environment which affect the luminosities of a certain class of cluster galaxies.