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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 Omega_m=0.4 and Omega_Lambda =0.6, we predict roughly 1.5 \times 10^4 lensed sub-mm sources with flux densities greater than 4 mJy at 850 microns, and with amplifications due to lensing greater than 2, towards galaxy clusters with X-ray luminosities greater than 8 x 10^44 h^-2 ergs s^-1 (0.3 to 3.5 keV band). We compare our predictions with observations from the SCUBA instrument, and briefly consider the possibility of using the South Pole 10-m sub-mm 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.