The Luminosity Function of the Coma Cluster Core for -25<M/R<-9.4

Abstract
We determine the luminosity function (LF) of galaxies in the core of the Coma cluster for M_R<=-11.4 (assuming H_0=75 km/s/Mpc), a magnitude regime previously explored only in the Local Group. Objects are counted in a deep CCD image of Coma having RMS noise of 27.7 R mag~arcsec$^{-2}$. A correction for objects in the foreground or background of the Coma cluster---and the uncertainty in this correction---are determined from images of five other high-latitude fields, carefully matched to the Coma image in both resolution and noise level. Accurate counts of Coma cluster members are obtained as faint as R=25.5, or M_R=-9.4. The LF for galaxies is well fit by a power law dN/dLpropto L^alpha, with alpha=-1.42pm0.05, over the range -19.4