| Mexican Hat Gravitational Lenses (2007) | |||||||||||||
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| The mexican hat function is used to model a compensated (in density) gravitational lens. First we discuss the need for compensation. Then we integrate photon orbits to construct wavefronts. One consequence of underdensities is an off-axis caustic. We report the structure of the critical curves and caustics using the thin lens approximation, both for the mexican hat and for a perturbed mexican hat. We discuss the nonlocal effect of shear. 1 Introduction Gravitational lensing of distant galaxies by foreground clusters of galaxies is a recent and powerful new tool for observational cosmology. For example, the HST image of the Abell Cluster A2218 dramatically illustrates that images of background galaxies are distorted [8]. Lensing can be used either as a powerful telescope to observe very distant galaxies, or to investigate the distribution of matter around the lensing cluster. However, the current models for mass distribution of clusters are all uncompensated; for example, the most... | |||||||||||||
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