Deep optical imaging of the field of PC 1643+4631A&B - II. Estimating the colours and redshifts of faint galaxies

In an investigation of the cause of the cosmic microwave background decrement in the field of the z=3.8 quasar pair PC 1643+4631, we have developed techniques for making photometric estimates of galaxy redshifts in deep multicolour optical images of the field taken with the William Herschel Telescope (WHT). Using a combination of low-redshift observed spectra and high-redshift model spectra, we find that we can assign well-constrained redshift estimates for z<1 and z >2. The lack of strong spectral features at intermediate redshifts means that the estimates are poorly constrained, and galaxies are typically misassigned to lower or higher redshifts. We find that such ambiguous redshifts can be reliably flagged by calculating both the mode and mean of the photometric redshift likelihood distribution. To examine the possibility that a massive cluster of galaxies lies in the field, we have attempted to recover simulated galaxies with intrinsic colours matching those of the model galaxies used in the photometric redshift estimation. We find that a model cluster at z >1 can easily remain undetected in the images. We further find that when model galaxies are recovered from the images, there is considerable scatter of the recovered galaxy redshifts away from the model value; this scatter is larger than that expected from photometric errors and is the result of confusion, simply due to ground-based seeing, between objects in the field. Lastly we have carried out a simulation to test the efficiency of the selection of z greater than or similar to3 Lyman-break galaxies (LBGs). We find that the number of LBGs recovered from our images by the standard UGR technique is several times smaller than the number of test galaxies in our simulations. A significant contribution to this inefficiency is due to confusion between the high-redshift galaxies and other objects near the line of sight. We argue that the actual surface density of z approximate to3 galaxies may be several times greater than that recovered from typical 4-m class ground-based imaging, and note that this conclusion is consistent with the surface density of high-redshift objects found in the Hubble Deep Field (HDF).