Luminosity distributions within rich clusters — II. Demonstration and verification via simulation

We present detailed simulations of long-exposure CCD images. The simulations are used to explore the validity of the statistical method for reconstructing the luminosity distribution of galaxies within a rich cluster, i.e., by the subtraction of field number-counts from those of a sight-line through the cluster. In particular, we use the simulations to establish the reliability of our observational data to be presented in Paper III. Based on our intended CCD field-of-view (6.5 × 6.5 arcmin²) and a 1σ detection limit of 26 mag arcsec⁻², we conclude that the luminosity distribution can be robustly determined over a wide range of absolute magnitude (−23 > M R > −16) provided: the cluster has an Abell richness 1.5 or greater; the redshift of the cluster lies in the range 0.1 > z > 0.3; the seeing is better than FWHM 1.25 arcsec, and the photometric zero-points are accurate to within Δm = ± 0.12. If these conditions are not met, then the recovered luminosity distribution is unreliable. Finally, although the method clearly has limitations, within these limitations the technique represents an extremely promising probe of galaxy evolution and environmental dependences.