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Prog. Theor. Phys. Vol. 108 No. 6 (2002) pp. 1031-1037

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Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

Hideki Asada,1,2,* Taketoshi Kasai1 and Masumi Kasai1,**

1Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
2Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany

(Received September 13, 2002)

Abstract:

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.


URL : http://ptp.ipap.jp/link?PTP/108/1031/
DOI : 10.1143/PTP.108.1031


*E-mail: asada@phys.hirosaki-u.ac.jp
**E-mail: kasai@phys.hirosaki-u.ac.jp

[ Full Text PDF : FREE ACCESS (105K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 112 No. 2 (2004) pp. 241-248 :
    Euclidean Algorithm for a Gravitational Lens in a Polynomial Equation
    Hideki Asada, Taketoshi Kasai and Masumi Kasai

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