Perturbative Approach to the Gravitational Lensing by a Non-spherically Distorted Compact Object

TL;DR

This paper develops a perturbative method to analyze gravitational lensing by non-spherical compact objects with quadrupole moments, revealing that small distortions can significantly affect flux ratios.

Contribution

It introduces a perturbative approach to model gravitational lensing by non-spherical objects, focusing on quadrupole effects on image positions and fluxes.

Findings

Separation angle of images is minimally affected by quadrupole.

Flux ratios can be significantly altered by small non-spherical distortions.

Tiny deviations in lens shape can cause observable flux anomalies.

Abstract

We investigate the gravitational lens effect caused by a non-spherically distorted compact object. The non-spherical property of the gravitational potential is modeled by a quadrupole moment. Under the assumption that the quadrupole contribution is small, we solve perturbatively the lens equation and obtain the image positions and the amplification factors. We show that the separation angle of two major images is only slightly changed by the existence of the quadrupole contribution, whereas the difference of the amplification factors may be significantly modified. Our results indicate that even a tiny non-spherical distortion of the lens potential may cause significant amount of flux anomalies in the lensed images.