Perturbation Theory of MultiPlane Lens Effects in Terms of Mass Ratios  Approximate Expressions of LensedImage Positions for Two Lens Planes 
Abstract
Continuing work initiated in an earlier publication (H. Asada, Mon. Not. R. Astron. Soc. 394 (2009), 818), we make a systematic attempt to determine, as a function of lens and source parameters, the positions of images by multiplane gravitational lenses. By extending the previous singleplane work, we present a method of Taylorseries expansion to solve the multiplane lens equation in terms of mass ratios except for the neighborhood of the caustics. The advantage of this method is that it allows a systematic iterative analysis and clarifies the dependence on lens and source parameters. In concordance with the multiplane lensedimage counting theorem that the lower bound on the image number is 2^N for N planes with a single point mass on each plane, our iterative results show how 2^N images are realized. Numerical tests are done to investigate if the Taylor expansion method is robust. The method with a small mass ratio works well for changing a plane separation, whereas it breaks down in the inner domain near the caustics.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 February 2012
 DOI:
 10.1143/PTP.127.355
 arXiv:
 arXiv:1012.0070
 Bibcode:
 2012PThPh.127..355I
 Keywords:

 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 13 pages, 2 figures