Radial cluster lensing: A simple differential equation describing arclet fields

Abstract

Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen as small ellipses. The orientation and axial ratio of the ellipses could then be used to trace the properties of the lens. We introduce and solve an ordinary homogeneous linear first order differential equation which describes completely the radial cluster lens. It can be used to reconstruct the lens mappeing from the measured axial ratios of lensed background galaxies.