Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

TL;DR

This paper investigates the effects of multipole mass distributions on gravitational lensing, revealing complex caustic structures and high-order image multiplicities through simulations of generalized SIS models.

Contribution

It introduces a detailed simulation approach for multipolar gravitational lenses, analyzing high-order perturbations and their impact on caustic structures and image multiplicities.

Findings

Odd mode lenses have overlapping caustic layers causing  image changes.

Fold caustics have image numbers equal to the average of sides; cusp caustics equal the smaller side.

High-order perturbations produce multiple butterfly and swallowtail singularities, increasing image regions.

Abstract

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.