Gravitational Lensing of the X-Ray Background by Clusters of Galaxies
  Gravitational lensing by clusters of galaxies affects the cosmic X-ray background (XRB) by altering the observed density and flux distribution of background X-ray sources. At faint detection flux thresholds, the resolved X-ray sources appear brighter and diluted, while the unresolved component of the XRB appears dimmer and more anisotropic, due to lensing. The diffuse X-ray intensity in the outer halos of clusters might be lower than the sky-averaged XRB, after the subtraction of resolved sources. Detection of the lensing signal with a wide-field X-ray telescope could probe the mass distribution of a cluster out to its virialization boundary. In particular, we show that the lensing signature imprinted on the resolved component of the XRB by the cluster A1689, should be difficult but possible to detect out to 8' at the 2-4 sigma level, after 10^6 seconds of observation with the forthcoming AXAF satellite. The lensing signal is fairly insensitive to the lens redshift in the range 0.1<z<0.6. The amplitude of the lensing signal is however sensitive to the faint end slope of the number-flux relation for unresolved X-ray sources, and can thus help constrain models of the XRB. A search for X-ray arcs or arclets could identify the fraction of all faint sources which originate from extended emission of distant galaxies. The probability for a 3 sigma detection of an arclet which is stretched by a factor of about 3 after a 10^6 seconds observation of A1689 with AXAF, is roughly comparable to the fraction of all background X-ray sources that have an intrinsic size of order 1''. 
Alexandre Refregier (1) and Abraham Loeb (2) ((1) Columbia University,   (2) Harvard)