arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1012.0070astro-ph.COgr-qc
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用质量比表示的多平面透镜效应的微扰理论:两个透镜平面透镜像位置的近似表达式

Perturbation theory of multi-plane lens effects in terms of mass ratios: Approximate expressions of lensed-image positions for two lens planes

Koji Izumi, Hideki Asada

摘要:

继续在早期出版物(浅田,MNRAS。394(2009)818),我们进行了系统的尝试,以确定作为透镜和源参数的函数的多平面引力透镜的图像的位置。在单平面透镜方程的基础上,本文提出了一种泰勒级数展开法求解除焦散线邻域外的质量比的多平面透镜方程。这种方法的优点是,它允许系统的迭代分析,并阐明了透镜和源参数的依赖性。与多平面透镜图像计数定理一致,图像数量的下限是$2^N$ N个平面上的一个单质点,我们的迭代结果显示如何实现$2^N$图像。数值试验进行调查,如果泰勒展开方法是强大的。小质量比的方法对于改变平面间距效果很好,而在焦散线附近的内域中它会崩溃。

英文摘要:

Continuing work initiated in an earlier publication (Asada, MNRAS. 394 (2009) 818), we make a systematic attempt to determine, as a function of lens and source parameters, the positions of images by multi-plane gravitational lenses. By extending the previous single-plane work, we present a method of Taylor-series expansion to solve the multi-plane lens equation in terms of mass ratios except for the neighborhood of the caustics. The advantage of this method is that it allows a systematic iterative analysis and clarifies the dependence on lens and source parameters. In concordance with the multi-plane lensed-image counting theorem that the lower bound on the image number is $2^N$ for N planes with a single point mass on each plane, our iterative results show how $2^N$ images are realized. Numerical tests are done to investigate if the Taylor expansion method is robust. The method with a small mass ratio works well for changing a plane separation, whereas it breaks down in the inner domain near the caustics.

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