EDP Sciences
Free access
Volume 397, Number 3, January III 2003
Page(s) 825 - 829
Section Extragalactic astronomy
DOI http://dx.doi.org/10.1051/0004-6361:20021599

A&A 397, 825-829 (2003)
DOI: 10.1051/0004-6361:20021599

Images for an isothermal ellipsoidal gravitational lens from a single real algebraic equation

H. Asada1, 2, T. Hamana3 and M. Kasai1

1  Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan
2  Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
3  National Astronomical Observatory, Mitaka 181-8588, Japan

(Received 30 September 2002 / Accepted 4 November 2002 )

We present explicit expressions for the lens equation for a cored isothermal ellipsoidal gravitational lens as a single real sixth-order algebraic equation in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar ones. We find a condition for physical solutions which correspond to at most five images. For a singular isothermal ellipsoid, the sixth-order equation is reduced to fourth-order one for which analytic solutions are well-known. Furthermore, we derive analytic criteria for determining the number of images for the singular lens, which give us simple expressions for the caustics and critical curves. The present formulation offers a useful way for studying galaxy lenses frequently modeled as isothermal ellipsoids.

Key words: gravitational lensing -- galaxies: general -- cosmology: theory

Offprint request: H. Asada, asada@phys.hirosaki-u.ac.jp

© ESO 2003