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arXiv 2007.11588astro-ph.GA
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来自强透镜III的星系质量分布：二维破缺幂律模型

Galaxy mass profiles from strong lensing III: The two-dimensional broken power-law model

Conor M. O'Riordan, Stephen J. Warren, Daniel J. Mortlock

备注：
8 pages, 3 figures, accepted to MNRAS
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摘要：

当模拟强引力透镜时，即，在同一个源有多个图像的情况下，透镜星系质量分布最广泛使用的参数化是奇异幂律模型$ρ(r)\propto r^{-γ}$。该模型对于非常精确的工作可能不够灵活，例如基于多个图像之间的时间延迟测量哈勃常数。在这里，我们推导出一个更具适应性的模型，其中投影质量表面密度参数化为连续的二维破幂律（2DBPL）的透镜性质-偏转角，剪切和放大率。该椭圆2DBPL模型的特征在于断裂半径$θ_\mathrm{B}$两侧的幂律斜率$t_1$、$t_2$。2DBPL模型的关键是截断幂律（TPL）模型的透镜性质的推导，其中表面密度是截断半径$θ_\mathrm{T}$和零以外的幂律。这种TPL模式本身也很有用。我们通过TPL轮廓创建透镜效应的模拟观测，其中图像形成在截断半径之外，因此图像覆盖的环中没有质量。然后，我们表明，内部的图像的轮廓的斜率可以准确地恢复为中等椭圆度的透镜。这表明，广泛持有的概念，即透镜测量图像的环形中的质量分布的斜率，并且对图像内部半径处的质量分布不敏感，是不正确的。

英文摘要：

When modelling strong gravitational lenses, i.e., where there are multiple images of the same source, the most widely used parameterisation for the mass profile in the lens galaxy is the singular power-law model $ρ(r)\propto r^{-γ}$. This model may be insufficiently flexible for very accurate work, for example measuring the Hubble constant based on time delays between multiple images. Here we derive the lensing properties - deflection angle, shear, and magnification - of a more adaptable model where the projected mass surface density is parameterised as a continuous two-dimensional broken power-law (2DBPL). This elliptical 2DBPL model is characterised by power-law slopes $t_1$, $t_2$ either side of the break radius $θ_\mathrm{B}$. The key to the 2DBPL model is the derivation of the lensing properties of the truncated power law (TPL) model, where the surface density is a power law out to the truncation radius $θ_\mathrm{T}$ and zero beyond. This TPL model is also useful by itself. We create mock observations of lensing by a TPL profile where the images form outside the truncation radius, so there is no mass in the annulus covered by the images. We then show that the slope of the profile interior to the images may be accurately recovered for lenses of moderate ellipticity. This demonstrates that the widely-held notion that lensing measures the slope of the mass profile in the annulus of the images, and is insensitive to the mass distribution at radii interior to the images, is incorrect.

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