The Luminosity Function of the Coma Cluster Core for -25<M_R<-11

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/dL\propto L^\alpha, with \alpha=-1.42\pm0.05, over the range -19.4<M_R<-11.4; faintward of this range, the galaxies are unresolved and indistinguishable from globular clusters, but the data are consistent with an extrapolation of the power law. Surface brightness biases are minimized since galaxies are not subjected to morphological selection, and the limiting detection isophote is 27.6 R mag~arcsec$^{-2}$. We find the typical $M_R\approx-12$ Coma cluster galaxy to have an exponential scale length $\approx200$~pc, similar to Local Group galaxies of comparable magnitude. These extreme dwarf galaxies show a surface density increasing towards the giant elliptical NGC~4874 as $r^{-1.3}$, similar to the diffuse light and globular cluster distributions. The luminosity in the detected dwarf galaxies is at most a few percent of the total diffuse light of the giant galaxies in the cluster, and the contribution of the dwarfs to the mass of the cluster is likely negligible as well.