弯曲弧基中的引力透镜形式主义：从弱到强透镜区的可观测量和简并性的连续描述
Gravitational lensing formalism in a curved arc basis: A continuous description of observables and degeneracies from the weak to the strong lensing regime
摘要：
引力透镜弯曲弧提供了大量关于潜在的透镜畸变的信息。从扩展源中提取精确的透镜信息是许多旨在回答宇宙基本问题的研究的关键组成部分。为了在提高精度的同时保持准确性，表征和理解透镜观测量中固有的简并性的影响至关重要。在这项工作中，我们提出了一种形式主义来描述的引力透镜失真的影响，导致弯曲的扩展弧的特征向量和特征值的局部透镜雅可比矩阵和他们的方向微分的基础上。我们确定了一个非本地和非线性扩展偏转器的基础上，继承这些本地属性。我们的参数化与扩展源中的可观察特征紧密相关，并且允许人们在不施加显式全局偏转器模型的情况下准确地提取扩展图像的透镜信息。我们量化什么样的退化可以被打破的基础上的本地透镜性质和假设的内在源形状的具体假设。我们的形式主义是适用于从弱线性政权，半线性政权的高度非线性政权的高度放大的多个图像的弧。在这项工作中提出的方法和实施提供了一个框架，以评估系统，指导推理工作的正确选择的复杂性的基础上，手头的数据，并量化的透镜信息提取的模型无关的方式。
英文摘要：
Gravitationally lensed curved arcs provide a wealth of information about the underlying lensing distortions. Extracting precise lensing information from extended sources is a key component in many studies aiming to answer fundamental questions about the Universe. To maintain accuracy with increased precision, it is of vital importance to characterize and understand the impact of degeneracies inherent in lensing observables. In this work, we present a formalism to describe the gravitational lensing distortion effects resulting in curved extended arcs based on the eigenvectors and eigenvalues of the local lensing Jacobian and their directional differentials. We identify a non-local and non-linear extended deflector basis that inherits these local properties. Our parameterization is tightly linked to observable features in extended sources and allows one to accurately extract the lensing information of extended images without imposing an explicit global deflector model. We quantify what degeneracies can be broken based on specific assumptions on the local lensing nature and assumed intrinsic source shape. Our formalism is applicable from the weak linear regime, the semi-linear regime all the way up to the highly non-linear regime of highly magnified arcs of multiple images. The methodology and implementation presented in this work provides a framework to assessing systematics, to guide inference efforts in the right choices in complexity based on the data at hand, and to quantify the lensing information extracted in a model-independent way.
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