Classification of the multiple deflection two point-mass gravitational lens models and application of catastrophe theory in lensing

Details Classification of the multiple deflection two point-mass gravitational lens models and application of catastrophe theory in lensing Classification of the multiple deflection two point-mass gravitational lens models and application of catastrophe theory in lensing

Feb 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...268..453e&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 268, no. 2, p. 453-471.

Statistics

Computation

54

Astronomical Models, Catastrophe Theory, Cosmology, Gravitational Lenses, Caustics (Optics), Computational Astrophysics, Image Analysis

Scientific paper

A two-point mass lens is used here as a specific gravitational lens model to illustrate the detailed properties of a two-lens plane situation and the use of catastrophe theory in gravitational lensing. For the former, it is shown that the lens equation in this case admits a fairly simple representation of the critical curves, amenable to analytical investigation. This is used to derive the possible topologies of the critical curves, dependent on the model parameters, as well as the transition between these topologies. Catastrophe theory is introduced by relating the conditions for transitions between topologies of critical curves to the corresponding singularities described by catastrophe theory. A full classification of the topologies of critical curves is achieved. All bifurcations are beak-to-beak singularities except for an elliptic umbilic. A full classification of the caustic topology is obtained for a special three-parameter family of lens models.

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