Model-independent characterisation and model selection of gravitational lenses

到目前为止，关于引力束缚物体中暗物质的性质、分布和凝聚的信息是通过将引力透镜模型与特定观测结果相拟合，从对强引力透镜区星系扭曲图像的观测中得出的。然而，模型拟合是繁琐的（手动）微调工作，并且它不是唯一的，因为多个图像的相同集合可以由许多不同的透镜模型产生。为了克服这些问题，我们提出了一种与模型无关的方法来计算透镜，这种方法是基于对多重成像源的观测和引力透镜形式主义的一般性质。我们的方法产生了一组简单的方程来计算临界曲线处的透镜势导数（比率），临界曲线从观察到的形状，方向和附近多个图像的相对距离确定其在天空中的位置和方向角。另外，多个图像之间的给定时间延迟确定局部表面质量密度和剪切以及由于透镜效应引起的图像的放大率。原理证明的结果表明，我们的方程组具有足够高的准确性和精度是有用的星系团的中心部分的重建。由于我们的方法不需要手动特设添加质量，或耗时的参数优化算法，它是一个很有前途的工具，完全自动分析大量的多个图像来描述星系团中的局部暗物质分布。这个建议的目标是把我们的原型变成一个工作系统，并测试精度和准确性的改善，它实现时，被集成到一个无网格的自由形式的全球集群潜力重建算法。

So far, information about the nature, distribution and agglomeration of dark matter in gravitationally bound objects was drawn from observations of distorted images of galaxies in the strong gravitational lensing regime by fitting gravitational lens models to a given observation. Yet, model fitting is a tedious (manual) fine-tuning work and it is not unique because the same set of multiple images can be produced by many different lens models. To forgo these problems, we develop a model-independent approach to characterise the lens which is based on observations of multiply-imaged sources and general properties of the gravitational lensing formalism only. Our approach yields a simple set of equations to calculate (ratios of) derivatives of the lensing potential at the critical curve, which determines its position and orientation angle in the sky from the observed shape, orientation, and relative distances of close-by multiple images. Additionally given time-delays between the multiple images determine the local surface mass density and shear and the magnifications of the images due to the lensing effect. Proof-of-principle results show that our set of equations has an accuracy and precision high enough to be useful for the reconstruction of the central parts of galaxy clusters. As our approach does not require manual ad-hoc addition of masses, or time-consuming parameter optimisation algorithms, it is a promising tool to fully automatically analyse a large amount of multiple images to describe local dark matter distributions in galaxy clusters. The goal of this proposal is to turn our protoype into a working system and to test the improvements in precision and accuracy that it achieves when being integrated into a mesh-free free-form global cluster-potential-reconstruction algorithm.