Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 53, p. 6-11 (2016)

Time delay of critical images of a point source near the gravitational lens fold-caustic

A. N. Alexandrov, Ph. D.,
V. I. Zhdanov, Dr. Sci.
Astronomical Observatory of Taras Shevchenko National University of Kyiv

Abstract
Within the framework of the analytical theory of the gravitational lensing we derive asymptotic formula for the time delay of critical images of apoint source, which is situated near a fold-caustic. We found corrections of the first and second order in powers of a parameter, which describescloseness of the source to the caustic. Our formula modifies earlier result by Congdon, Keeton &Nordgren (MNRAS, 2008) obtained in zero-orderapproximation. We have proved the hypothesis put forward by these authors that the first-order correction to the relative time delay of two criticalmages is identically zero. The contribution of the corrections is illustrated in model example by comparison with exact expression.

Keywords
The gravitational lens fold-caustic

References
Congdon, A.B., Keeton, C.R., Nordgren, C.E. 2008, Mon. Not. Roy. Astron.,389, 398
Chang, K., Refsdal, S. 1979, Nature, 282, 561
Schneider, P., Ehlers, J., Falco, E. E. 1992, Berlin: Springer
Congdon, A.B., Keeton, C.R., Nordgren, C.E. 2010, Astrophys. J., 709, 552
Aleksandrov, O.M., Zhdanov, V.I., Fedorova, O.V. 2003, VisnykKyiv. Un-tu. Astronomiia, 39–40,52
Keeton, C.R., Gaudi, B.S., Petters. A.O. Astrophys. J.,2005, 635, 35
Alexandrov, A.N., Zhdanov, V.I., Fedorova, Е.V. 2010,Astronomy Letters, 36, 5, 329
Alexandrov, A.N., Zhdanov, V.I. 2011,Mon. Not. Roy. Astron. Soc.,417, 541
Александров, О., Жданов, В., Коваль, С. 2012, ВісникКиїв.Ун-ту. Астрономія, 49, 17
Alexandrov, A.N., Koval, S.M., Zhdanov, V.I. 2012, Advances inAstronomy and Space Physics, 2, 2, 184

Full text PDF