Are there binary galaxies in clusters?

We investigate a sample of 73 rich clusters containing in total 7754 galaxies and find, after a thorough assessment of the projection effects, that 6 per cent of the galaxies are part of a 'binary' system. Apparent 'binaries' are defined as nearest-neighbour pairs for which the velocity difference Delta V of the galaxies does not exceed 300 km s(-1) and the maximum separation Delta R is less than 0.1 h(-1) Mpc. This results in 1514 pairs. Monte Carlo simulations show that 1047 of these must be accidental, leaving 467 binaries. These binaries cannot be identified individually, but their properties can be studied statistically. The binaries found in this way are dynamically 'soft', i.e. Delta V is less than the global sigma(v) of the cluster. Despite this, they only seem to avoid the inner 0.4 h(-1) Mpc of clusters, suggesting that outside a radius of 0.4 h(-1) Mpc the velocity dispersion must locally be lower than the global value of sigma(v) that we measure in projection, or that many of the found pairs are unbound. There is a significant correlation between the presence of binaries and the detection of substructure with the Dressier & Shectman test. Binaries in binary-rich clusters seem to be directly associated with the low-sigma(v) subclusters for which the DS-test is sensitive. The fraction of binaries in the 19 binary-rich clusters is nearly as high (approximate to 12 per cent) as in the population of fore- and background galaxies ('interlopers') that is normally removed from the cluster surveys (approximate to 14.5 per cent). In the remaining 54 clusters the binary fraction is considerably lower (approximate to 3 per cent). Depending on the assumed form of the orbits of the galaxies in a binary, the average mass of the binaries lies in the range of 2-5 x 10(11) h(-1) M., while the average M/L-ratio lies in the range of 20-40 h M./L. for circular orbits to about 45-100 h M./L. for eccentric orbits, which is consistent with the results for field binaries. Monte Carlo models of the binaries suggest that the orbits are likely to have low eccentricities. Both the masses and the M/L-ratios of binaries are larger inside 1.2 h(-1) Mpc than outside, which argues against the tidal stripping of galaxy haloes in the central regions of clusters. We have compared our Monte Carlo methods with recent N-body models of clusters which incorporate galaxy formation in a crude way. These models reproduce the main statistical properties of the binaries. When applied to the models, our statistical method detects about 75 per cent of the bound pairs of galaxies that satisfy our selection criteria for binaries. In comparison with the binaries in the data, the masses of bound pairs in these models are systematically larger by a factor of 6. This prevents more detailed comparisons between the data and the models.