Near-infrared luminosity function and colours of dwarf galaxies in the Coma cluster

We present K -band observations of the low-luminosity galaxies in the Coma cluster, which are responsible for the steep upturn in the optical luminosity function at M _R～?16, discovered recently. The main results of this study are as follows.
(i) The optical–near-infrared colours of these galaxies imply that they are dwarf spheroidal galaxies. The median B ? K colour for galaxies with ?19.3< M_K (ii) The K -band luminosity function in the Coma cluster is not well constrained, because of the uncertainties due to the field-to-field variance of the background. However, within the estimated large errors, this is consistent with the R -band luminosity function, shifted by ～3 mag.
(iii) Many of the cluster dwarfs lie in a region of the B ? K versus B ? R colour–colour diagram where background galaxies are rare ( B ? K <5; 1.2< B ? R <1.6). Local dwarf spheroidal galaxies lie in this region too. This suggests that a better measurement of the K -band cluster luminosity can be made if the field-to-field variance of the background can be measured as a function of colour, even if it is large.
(iv) If we assume that none of the galaxies in the region of the B ? K versus B ? R plane given in (iii) in our cluster fields are background, and that all the cluster galaxies with 15.5< K <18.5 lie in this region of the plane, then we measure α=?1.41^+0.34_?0.37 for ?19.3< M_K ?16.3, where α is the logarithmic slope of the luminosity function. The uncertainties in this number come from counting statistics.