Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 54, p. 41-46 (2016)

Time delay of critical images in the vicinity of cusp point of gravitational-lens systems

A. Alexandrov, Ph.D., sen. researcher
V. Zhdanov, Dr. Sci., Prof.
Astronomical Obseravtory of Taras Shevchenko National University of Kyiv

We consider approximate analytical formulas for time-delays of critical images of a point source in the neighborhood of a cusp-caustic. We discuss zero, first and second approximations in powers of a parameter that defines the proximity of the source to the cusp. These formulas link the time delay with characteristics of the lens potential. The formula of zero approximation was obtained by Congdon, Keeton & Nordgren (MNRAS, 2008). In case of a general lens potential we derived first order correction thereto. If the potential is symmetric with respect to the cusp axis, then this correction is identically equal to zero. For this case, we obtained second order correction. The relations found are illustrated by a simple model example.

Gravitational-lens systems

Congdon, A.B., Keeton, C.R., Nordgren, C.E. 2010, Astrophys. J., 709, 552
Koopmans, L. V. E., Auger, M., Barnabe, M., arXiv:0902.3186.
Treu, T., Marshall, P. J., Cyr-Racine, F. Y., arXiv:1306.1272.
Suyu, S. H., Treu, T., Hilbert, S. 2014, The Astrophys. J. Let., 788, 35, 6
Aleksandrov, O., Zhdanov, V. 2016, Visnyk Kyiv. un-tu. Astronomiia, 53, 1, 6
Congdon, A.B., Keeton, C.R., Nordgren, C.E. 2008, Mon. Not. Roy. Astron. Soc., 389, 398
Alexandrov, A.N., Koval, S.M., Zhdanov, V.I. 2012, Advances in Astronomy and Space Physics, 2, 2, 184
Aleksandrov, O., Zhdanov, V., Koval, S. 2013, Visnyk Kyiv. un-tu. Astronomiia, 1, 50, 5
Chang, K., Refsdal, S. 1979, Nature, 282, 561
Schneider, P., Ehlers, J., Falco, E. E. 1992, Gravitational Lenses. Berlin: Springer

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