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Gravitationally Lensed muJy Radio Sources towards Galaxy Clusters

Galaxy clusters are expected to gravitationally lens background radio sources. However, due to the smaller surface density of radio sources, when compared to optical galaxies, such lensed events are rare. For an example, it is expected that there is no lensed radio source due to foreground galaxy clusters in the 1.4 GHz VLA FIRST survey. However, at the $μ$Jy level, the surface density of radio sources increases. Using the radio properties of the Hubble Deep Field (HDF) galaxies, we calculate the expected number of gravitationally lensed $μ$Jy rad io sources on the sky due to foreground galaxy clusters for different cosmological models. For a flat cosmology with $Ω_m=0.3$ and $Ω_Λ=0.7$, we predict $\sim$ 1500 lensed radio sources with flux densities $\sim$ 10 to 1000 muJy at 1.4 GHz. We discuss the possibility of detecting lensed muJy radio sources towards clusters with deep radio surveys. Given the recent detection of a sub-mm selected lensed muJy radio source towards A370, it is suggested that deep radio observations of clusters should already contain such lensed sources. Aided by amplification due to gravitational lensing, the search for lensed \muJy radio sources towards clusters are likely to recover star-forming galaxies at redshifts of 1 to 3.