# Mutual Interference And Structural Properties of Object Images in the Vicinity of the Gravitational Lens Cusp Point

Chapter

## Abstract

Gravitational lens system could form multiple images of the same radiating surface of a cosmic object. The radiation fluxes of these images interfere to one another (Refsdal, 1964). The practical importance of this effect is seems to be as follows: (i) it is the only direct test of microlensing (Schneider et. al. 1985); (ii) this effect may say about fine structure of a lensed object; (iii) it must be allowed for simulations of microlensing process. The maximum effect is expected in the case when a cusp point of the microlensing caustic is projected on the lensed object. To investigate the interference effect in this case, the exact solution of the lens equation in the vicinity of the cusp point was obtained (Mandzhos,1993): were ξη are dimensionless coordinates of a radiating element on the object plane; x,y are coordinates of the point at which the lens plane is intersected by light beam; furthermore: Where \(u = {\partial ^4}\psi /\partial {x^4};v = {\partial ^3}\psi /\partial {x^2}\partial y,\psi\) is the lens scalar potential.

$${x_{1,2}} = 2|A|.\cos \{{\Phi _0} + \left[{1 \pm sign\left(\xi \right)} \right]\frac{\pi}{3}.sign\left(\xi \right),$$

$${{x}_{3}} = 2|A| \cdot \cos \{ {{\Phi }_{0}} + \frac{4}{3}\pi \} \cdot sign\left( \xi \right),y = \frac{1}{2}\eta - \frac{1}{4}v{{x}^{2}}$$

(1)

$${{\Phi }_{0}} = \frac{1}{3}Arc\tan \sqrt {{h\frac{{{{\eta }^{3}}}}{{{{\xi }^{2}}}} - 1,|A| = k{{\eta }^{{1/2}}}}}$$

$$h = \frac{2}{9}\frac{{{v^3}}}{{3{v^2} - 2u}},k = \sqrt {\left| {\left. {\frac{{2v}}{{3{v^2} - 2u}}} \right|} \right.}.$$

(2)

## Keywords

Object Plane Mutual Interference Magellan Cloud Cusp Point Gravitational Lens
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Reference

- Mandzhos A.V. 1993 Mutual interference and structural properties of object images in the vicinity of the gravitational lens cusp point. SAO RAS prepr. No. 98Google Scholar
- Refsdal S. 1964
*Mon. Not. Roy. Astron. Soc.*128 295MathSciNetADSzbMATHGoogle Scholar - 3.Schneider P. and Schmid-Burgk J. 1985
*Astron. Astrophys.*2 369ADSGoogle Scholar

## Copyright information

© International Astronomical Union 1996