**Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 57, p. 10-15 (2018)**

**Gravitational microlensing of an elliptical source near a fold caustic**

**Alexandrov A.N., Ph. D.**

**Zhdanov V.I., Dr. Sci.**

Astronomical Observatory of Taras Shevchenko National University of Kyiv, Kyiv

**Kuybarov A.V., student**

Igor Sikorsky Polytechnic Institute, Kyiv

**Abstract**

We consider the amplification factor for the luminosity of an extended source near the fold caustic of the gravitational lens. It is assumed that the source has elliptical shape, and the brightness distribution along the radial directions is Gaussian. During the microlensing event the total brightness of all microimages is observed, which changes when the source moves relative to the caustic. The main contribution to the variable component is given by the so-called critical images that arise/disappear at the intersection of the caustic by the source. In the present paper we obtained an analogous formula for elliptical Gaussian source. The formula involves a dependence on the coordinates of the source centre, its geometric dimensions, and its orientation relative to the caustic. We show that in the linear caustic approximation the amplification of the circular and elliptical sources is described by the same (rescaled) formula. However, in the next approximations the differences are significant. We compare analytical calculations of the amplification curves for different orientations of an elliptical source and for a circular source with the same luminosity for the model example.

**Key words
**Gravitational lenses, fold caustic, microlensing, elliptical source, amplification factor, analytical formulas

**References
**

Schneider, P., Ehlers, J., Falco, E.E. 1992, Berlin

Alexandrov, A.N. 2007, Bull. Kyiv Nation. Taras Shevchenko Univ., Astronomiya, 44, 21

Alexandrov, A.N., Zhdanov, V.I. 2009, Bull. Kyiv Nation. Taras Shevchenko Univ., Astronomiya, 45, 4

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

Alexandrov, A.N., Zhdanov, V.I., Koval’, S.M. 2012, Bull. Kyiv Nation. Taras Shevchenko Univ., Astronomiya, 49, 17

Zhdanov, V.I., Alexandrov, A.N., Fedorova, E.V., Sliusar, V.M. 2012, ISRN Astronomy and Astrophysics., Article ID 906951, 21, doi:10.5402/2012/906951

Zhdanov, V.I., Alexandrov, A.N., Fedorova, E.V., Sliusar, V.M. 2014, Dark Matter. V. 2. Astrophysical Aspects of the Problem, 84

Alexandrov, A.N., Koval, S.M., Zhdanov, V.I. 2012, Advances in Astronomy and Space Physics, 2, 2, 184

Alexandrov, A.N., Zhdanov, V.I., Koval, S.M. 2013, Odessa Astronomical Publications, 26/2, 169

Heyrovskу, D., Loeb, A. 1997, Astrophys. J., 490, 38

Gaudi, B.S., Haiman, Z. arXiv:astro-ph/0401035

An, J.H., Evans, N.W. 2006, Mon. Not. Roy. Astron. Soc.,369(1), 317

Alexandrov, A.N. 2017, Bull. Kyiv Nation. Taras Shevchenko Univ., Astronomiya, 56 (2), 25