Gravitational lensing by clusters of galaxies in the millimetre/submillimetre waveband

Rich clusters of galaxies are observed to produce strongly magnified arcs and multiple images of background galaxies in the optical waveband. Here the properties of the equivalent images in the submillimetre waveband are discussed. Carefully designed submillimetre-wave surveys preferentially select galaxies at large redshifts, because the flux density-redshift relations for distant dusty star-forming galaxies are expected to be flat in this waveband, and so distant galaxies are much brighter as compared with observations in the optical waveband. For the same reason, submillimetre-wave observations are also ideally suited to detect the lensed images of very distant galaxies in clusters. Here we combine a model of a lensing cluster with predicted source counts of distant galaxies in the submillimetre waveband in order to investigate the form of the magnification bias introduced into the population of faint galaxies by lensing. A positive magnification bias corresponds to an increase in the surface density of galaxies. In the submillimetre waveband magnification biases can be large and positive, and depend strongly on the form of evolution of distant galaxies. New submillimetre-wave instruments and telescopes will allow galaxies at redshifts z similar to 10 to be observed in as much detail as galaxies at z similar or equal to 0.5, and we assess the practicality of detecting a useful sample of lensed images in the fields of clusters using both single-antenna telescopes and large interferometer arrays. The surface and flux densities of the lensed images in the submillimetre waveband are expected to exceed those of galaxies within the lensing cluster, and their values can be used to infer the form of evolution of star-forming galaxies since redshifts of about 10.