The gravitational lens equation near cusps

Details The gravitational lens equation near cusps The gravitational lens equation near cusps

Jul 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992a%26a...260....1s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 260, no. 1-2, p. 1-13.

Statistics

Computation

65

Catastrophe Theory, Gravitation Theory, Gravitational Lenses, Point Sources, Computational Astrophysics, Polar Cusps

Scientific paper

The behavior of the gravitational lens mapping near cusps is studied, both analytically and numerically, paying particular attention to magnification probabilities. We demonstrate that the three images of a point source inside a cusp satisfy the relation that the sum of the magnifications of the two images with the same parity equals, up to a sign, the magnification of the third image (of opposite parity). This property will then be used to show that the asymptotic magnification cross section for point sources, in the limit mus approaching infinity, derived previously for folds only, is also valid in the presence of cusps. The next order term of such an expansion, which is due to sources just outside of cusps, is derived. We apply these relations to a special gravitational lens models and show that these asymptotic relations are indeed very good approximations for the large-mus cross sections. For the study of the magnification of extended sources near cusps, we generalize the ray-shooting method to allow for very small sources. The magnification cross-sections for extended sources are then compared to those for point sources. A magnification contour plot for extended sources near a cusp is obtained.

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