Dark Matter Structure in Galaxies

我们研究了扩展源尺寸对引力透镜的影响，其中透镜由光滑势和小质量团块组成（“子结构透镜”）。我们首先考虑一个透镜模型，它由一个模拟为奇异等温球（SIS）的团块和一个模拟为外部背景剪切和收敛的主透镜组成。对于这个简单的模型，我们导出了圆对称顶帽光源透镜图像的三种类型的奇偶，即正、负和双负奇偶的（去）放大的解析公式。如果源的大小足够大于SIS的爱因斯坦半径，我们发现在正（双负）宇称情况下，扩展源与无摄动的宏透镜系统相比总是被放大（消放大），而在负宇称情况下，依赖于收敛负单位符号的（消）放大效应要弱于其他宇称。结果表明，如果根据多透镜图像的位置和通量确定相应的大透镜模型的透镜参数，则测量多透镜图像中的畸变模式可以打破团块质量透镜效应和团块距离透镜效应之间的简并。我们还表明，通过分析在爱因斯坦半径内的多透镜图像中的“精细结构”，可以直接测量团块的实际密度分布。

We investigate the extended source size effects on gravitational lensing in which a lens consists of a smooth potential and small mass clumps ("substructure lensing"). We first consider a lens model that consists of a clump modeled as a singular isothermal sphere (SIS) and a primary lens modeled as an external background shear and convergence. For this simple model, we derive analytic formulae for (de)magnification of circularly symmetric top-hat sources with three types of parity for their lensed images, namely, positive, negative and doubly negative parities. Provided that the source size is sufficiently larger than the Einstein radius of an SIS, we find that in the positive (doubly-negative) parity case, an extended source is always magnified (demagnified) in comparison with an unperturbed macrolens system, whereas in the negative parity case, (de)magnification effect which depends on a sign of convergence minus unity is weaker than those in other parities. It is shown that a measurement of distortion pattern in a multiply lensed image enables us to break the degeneracy between the lensing effects of a clump mass and those of a clump distance if lensing parameters of the relevant macrolens model are determined from the position and flux of multiple images. We also show that an actual density profile of a clump can be directly measured by analyzing a "fine structure" in a multiply lensed image within the Einstein radius of a clump.