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, because of 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) s of observation with the forthcoming Advanced X-Ray Astrophysics Facility (AXAF) satellite. The lensing signal is fairly insensitive to the lens redshift in the range 0.1 less than or similar to z(l) less than or similar to 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 it can thus help constrain models of the XRB. A search for X-ray arcs or arclets could identify the fraction of all faint sources that originate from extended emission of distant galaxies. The probability for a 3 sigma detection of an arclet that is stretched by a factor of approximately 3 after a 10(6) s observation of A1689 with AXAF is roughly comparable to the fraction of all background X-ray sources that have an intrinsic size of approximately 1 ''.