多极引力透镜与四极透镜的高阶微扰
Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens
摘要：
任意表面质量密度的引力透镜都可以分解成多极分量。在解析计算出的偏转角的基础上，模拟了广义SIS（奇异等温球）模型多极质量分布的射线追踪。然后用反射技术求出源平面上的放大率图形。如已经发现的，对于某些透镜模型，奇模透镜的焦散线由两个重叠层组成。当点源遍历此类重叠焦散时，图像编号将更改为\pm 4，而不是\pm 2。焦散有两种图像。一个是临界曲线，另一个是过渡轨迹。发现褶皱的像数恰好是褶皱两侧像数的平均值，而尖点的像数等于较小的一个。我们还研究了m = 2的四极透镜在m = 3，4和5模扰动下的放大模式，发现分别可以产生一个，2个和3个蝶形或燕尾形奇点。随着高阶微扰强度的增加，奇异点逐渐增大，形成六倍像区。如果这些扰动大到足以让两个或三个蝴蝶或燕尾接触，也可以产生八倍或十倍的图像区域。讨论了可能的天文应用。
英文摘要：
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.
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