Gravitationally lensed X-ray sources towards galaxy clusters

Foreground massive galaxy clusters are expected to gravitationally lens bac kground sources. Here, we calculate the expected number of gravitationally lensed X-ray sources on the sky owing to foreground galaxy clusters for dif ferent cosmological models. We describe the background sources using flux a nd redshift distribution observed in the ROSAT Deep Survey towards the 'Loc kman' hole, and model the foreground galaxy clusters as isothermal spheres. We account for the redshift evolution of lensing clusters using a Press-Sc hechter analysis with normalizations based on the observed cluster temperat ure function. For a flat cosmology with Omega(m) = 0.3 and Omega(Lambda) = 0.7, we predict similar to 10(3) lensed sources with fluxes larger than sim ilar to 5 x 10(-15) erg cm(-2) s(-1) and similar to 10(4) sources with flux es larger than similar to 10(-16) erg cm(-2) s(-1) in the 0.5-2.5 keV band. We discuss the possibility of detecting lensed X-ray sources towards clust ers in deep AXAF observations. The planned AXAF guaranteed time observation of A370 with an exposure of 90 ks is likely to recover at least two lensed active galactic nuclei (AGNs) above the 3 sigma level. Aided by amplificat ion owing to gravitational lensing, the search for lensed X-ray sources tow ards clusters is likely to recover AGNs at redshifts of 1-4.