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、分布和聚集的信息是通过将引力透镜模型拟合到给定的观测结果中，从对强引力透镜制度下星系扭曲图像的观测中得出的。然而，模型拟合是一项繁琐的（手动）微调工作，它并不是唯一的，因为许多不同的镜头模型可以产生相同的多幅图像。为了避免这些问题，我们开发了一种独立于模型的方法来表征透镜，该方法仅基于对多重成像源的观测和引力透镜形式的一般特性。我们的方法产生了一组简单的方程，用于计算临界曲线上透镜势的导数（比率），该曲线根据观察到的形状、方向和近距离多幅图像的相对距离确定其在天空中的位置和方向角。另外，给定多个图像之间的时间延迟，确定局部表面质量密度和剪切以及由于透镜效应而产生的图像放大倍数。原理证明结果表明，我们的方程组具有足够高的准确度和精度，可用于星系团中心部分的重建。由于我们的方法不需要手动添加质量，也不需要耗时的参数优化算法，因此它是一个很有前途的工具，可以全自动分析大量的多图像来描述星系团中的局部暗物质分布。本提案的目标是将我们的原型转化为一个工作系统，并测试其在集成到无网格自由形式全局聚类-潜在重建算法时所实现的精度和准确性的改进。

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.