Measurement of dwarf galaxies in the rich clusters Abell 665 and 963 at z=0.2

We show that the luminosity functions of the distant rich clusters Abell 665 ( z =0.182) and Abell 963 ( z =0.206) are flat or gradually rising down to M_R =−14, with α≈−1.2±0.4 [here α is the logarithmic slope of the luminosity function: φ( L )∝ L ^α at the faint end]. We do not confirm the steep luminosity functions (α≤−1.8) that have been recently proposed for these two clusters.
Several technical points are discussed in detail. In particular, we compute the corrections to the background contamination caused by gravitational lensing from the cluster dark matter, and show that the corrections are small unless we wish to determine variations in the luminosity function on small scales.
Recent observations have also shown that the field galaxy luminosity function at z ≈0.2 is also shallow between M_B =−19 and M_B =−13. Abell 665 and 963 are two of the richest clusters known at that redshift. We therefore propose that the galaxy luminosity function might be universal in this magnitude range at z =0.2.
The dwarf galaxies that we see in Abell 665 have a colour distribution that is strongly peaked at B − R =1.9. We compute K -corrections based on the spectral energy distributions of local galaxies, and show that these are probably dwarf spheroidal galaxies. This might suggest that the dwarf spheroidal population observed in Virgo already existed at z =0.2.