Gravitationally Lensed Sub-mm Sources towards Galaxy Clusters

Recent observations of galaxy clusters with the SCUBA instrument on the James Clarke Maxwell Telescope have revealed a sample of gravitationally lensed sources at sub-mm wavelengths. We extend our previous calculation on the expected number of lensed optical arcs and radio sources to study the sub-mm lensed source statistics due to foreground massive clusters. For a flat cosmology with Ωm = 0.4 and ΩΛ = 0.6, we predict ∼ 1.5×10 lensed sub-mm sources with flux densities greater than ∼ 4 mJy at 850 μm, and with amplifications due to lensing greater than 2, towards galaxy clusters with X-ray luminosities greater than 8× 10 h ergs s (0.3 to 3.5 keV band). We compare our predictions with the observations from the SCUBA instrument, and briefly consider the possibility of using the South Pole 10-m submm telescope and the Planck surveyor to identify lensed sub-mm sources. A catalog of around 100 gravitationally lensed sources at 353 GHz may be a useful by-product of Planck.