A photometric and spectroscopic study of dwarf and giant galaxies in the Coma Cluster. IV. The luminosity function

A large spectroscopic survey is constructed of galaxies in the Coma Cluster. The survey covers a wide area (1 deg(2)) to deep magnitudes (R similar to 19.5), covering both the core ( high density) and outskirts ( intermediate to low density) of the cluster. The spectroscopic sample consists of a total of 1191 galaxies, of which 760 are confirmed members of the Coma Cluster. A statistical technique is developed to correct the spectroscopic sample for incompleteness. The corrected sample is then used to construct an R-band luminosity function (LF) spanning a range of 7 mag (-23 < M-R - 5 log h(65) < -16) at both the core and outskirts of the cluster. The R-band LF for the entire Coma Cluster, fitted to Schechter form, gives M-R* = -21.79(-0.09)(+0.08) + 5 log h(65) and alpha = -1.18(-0.02)(+0.04). Dependence of the LF on local environment in Coma is explored. The LFs are found to be the same, within the errors, between the inner and outer regions and close to those from recent measurements for field galaxies. This is remarkable given the variation in the spectral types of galaxies between field and cluster environments. The steep faint-end slope for the LFs, observed in previous studies using photometric surveys, is not found here. However, the LF in this study is only measured to M-R = -16, compared to much deeper limits (M-R similar to -12) achieved in photometric surveys. The total B-band LF for the Coma Cluster, fitted to a Schechter form, is M-B* = -19.95(-0.10)(+0.15) + 5 log h(65) and alpha = -0.96(-0.02)(+0.01) . This also shows a dip at M-B* = -18 mag, in agreement with previous studies. The implications of this feature are discussed. The LF is studied in B-R color intervals and shows a steep faint-end slope for red (B-R > 1.35) galaxies, at both the core and outskirts of the cluster. This population of low-luminosity red galaxies has a higher surface density than the blue (B-R < 1.35) star-forming population and dominates the faint end of the Coma Cluster LF. It is found that the relative number of high surface brightness galaxies is larger at the cluster core, implying the destruction of low surface brightness galaxies in the dense core environment.