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 <−16.3 is 3.6 mag. (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.