Shape, shear and flexion II - Quantifying the flexion formalism for extended sources with the ray-bundle method

Flexion-based weak gravitational lensing analysis is proving to be a useful adjunct to traditional shear-based techniques. As flexion arises from gradients across an image, analytic and numerical techniques are required to investigate flexion predictions for extended image/source pairs. Using the Schwarzschild lens model, we demonstrate that the ray-bundle method for gravitational lensing can be used to accurately recover second flexion, and is consistent with recovery of zero first flexion. Using lens plane to source plane bundle propagation, we find that second flexion can be recovered with an error no worse than 1% for bundle radii smaller than {\Delta}{\theta} = 0.01 {\theta}_E and lens plane impact pararameters greater than {\theta}_E + {\Delta}{\theta}, where {\theta}_E is the angular Einstein radius. Using source plane to lens plane bundle propagation, we demonstrate the existence of a preferred flexion zone. For images at radii closer to the lens than the inner boundary of this zone, indicative of the true strong lensing regime, the flexion formalism should be used with caution (errors greater than 5% for extended image/source pairs). We also define a shear zone boundary, beyond which image shapes are essentially indistinguishable from ellipses (1% error in ellipticity). While suggestive that a traditional weak lensing analysis is satisfactory beyond this boundary, a potentially detectable non-zero flexion signal remains.Comment: 14 pages, 13 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Gravitational Lensing in Astronomy

Deflection of light by gravity was predicted by General Relativity and observationaly confirmed in 1919. In the following decades various aspects of the gravitational lens effect were explored theoretically, among them the possibility of multiple or ring-like images of background sources, the use of lensing as a gravitational telescope on very faint and distant objects, and the possibility to determine Hubble's constant with lensing. Only relatively recently gravitational lensing became an observational science after the discovery of the first doubly imaged quasar in 1979. Today lensing is a booming part of astrophysics. In addition to multiply-imaged quasars, a number of other aspects of lensing have been discovered since, e.g. giant luminous arcs, quasar microlensing, Einstein rings, galactic microlensing events, arclets, or weak gravitational lensing. By now literally hundreds of individual gravitational lens phenomena are known. Although still in its childhood, lensing has established itself as a very useful astrophysical tool with some remarkable successes. It has contributed significant new results in areas as different as the cosmological distance scale, the large scale matter distribution in the universe, mass and mass distribution of galaxy clusters, physics of quasars, dark matter in galaxy halos, or galaxy structure.Comment: Review article for "Living Reviews in Relativity", see http://www.livingreviews.org . 41 pages, latex, 22 figures (partly in GIF format due to size constraints). High quality postscript files can be obtained electronically at http://www.aip.de:8080/~jkw/review_figures.htm