Dark Matter Structure in Galaxies

我们研究了扩展源尺寸对引力透镜的影响，在引力透镜中，透镜由光滑势和小质量团组成(“子结构透镜”)。我们首先考虑一个透镜模型，该模型由一个被模拟为奇异等温球(SIS)的团块和一个被模拟为外部背景剪切和会聚的主透镜组成。对于这个简单的模型，我们推导了具有三种宇称的圆对称顶帽源的(去)放大系数的解析公式，它们的透镜像是正的、负的和双负的。假设源的大小足够大于SIS的爱因斯坦半径，我们发现，在正(双负)宇称情况下，与未扰动的微透镜系统相比，扩展的源总是被放大(去放大)，而在负奇偶的情况下，依赖于收敛减单位符号的(去)放大效应比在其他奇偶情况下弱。结果表明，如果相应的微透镜模型的透镜参数是根据多幅图像的位置和光通量确定的，那么测量多透镜图像中的失真图案能够打破块质量的透镜效应与块距离的透镜效应之间的简并关系。我们还表明，通过分析在爱因斯坦半径内的多重透镜图像中的“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.