标题： 广义的模型无关强引力透镜特征刻画 I：理论基础 显示英文标题

标题： Generalised model-independent characterisation of strong gravitational lenses I: Theoretical foundations

摘要： 我们将Wagner和Bartelmann（2016）提出的与引力透镜无关的方法推广到最一般的形式，并以一阶近似为基础。除了相对距离、椭圆率和时间延迟外，我们还利用了一组多像的取向角度相对于它们的连接线来实现这一目标。 对于跨越临界曲线的两个对称图像，取向角度还可以确定临界曲线的斜率以及连接图像之间临界点上的第二个（归一化）挠度系数。 它还允许放弃最大图像延伸轴垂直于临界曲线的对称性假设。 对于几乎形成巨大弧的三个图像，所假设的图像对称性程度也减少到最一般的情况，从而可以描述源不需要放置在两个在尖点处会合的折叠对称轴上的图像配置。 对于给定的一组多像，我们设定了我们的方法适用性的限制，展示了在图像合并的情况下可以获得哪些信息，并分析了由于透镜势的泰勒展开在星团尺度NFW模型的折叠情况、星团尺度SIE模型的折叠和尖点情况下的可达到的精度，并将广义方法与Wagner和Bartelmann（2016）的方法进行了比较。 对于靠近临界点不到30%（有效）爱因斯坦半径的多像，临界点的位置重建偏差小于5"；对于图像到临界点的距离小于15%（有效）爱因斯坦半径的折叠情况，临界曲线的斜率及其在尖点附近的形状偏差小于20%。 显示英文摘要

摘要： We extend the model-independent approach to characterise strong gravitational lenses of Wagner & Bartelmann (2016) to its most general form to leading order by using the orientation angles of a set of multiple images with respect to their connection line(s) in addition to the relative distances between the images, their ellipticities and time-delays. For two symmetric images that straddle the critical curve, the orientation angle additionally allows to determine the slope of the critical curve and a second (reduced) flexion coefficient at the critical point on the connection line between the images. It also allows to drop the symmetry assumption that the axis of largest image extension is orthogonal to the critical curve. For three images almost forming a giant arc, the degree of assumed image symmetry is also reduced to the most general case, allowing to describe image configurations for which the source need not be placed on the symmetry axis of the two folds that unite at the cusp. For a given set of multiple images, we set limits on the applicability of our approach, show which information can be obtained in cases of merging images, and analyse the accuracy achievable due to the Taylor expansion of the lensing potential for the fold case on a galaxy cluster scale NFW-profile, a fold and cusp case on a galaxy cluster scale SIE-profile, and compare the generalised approach with the one of Wagner & Bartelmann (2016). The position of the critical points is reconstructed with less than 5" deviation for multiple images closer to the critical points than 30\% of the (effective) Einstein radius and the slope of the critical curve at a fold and its shape in the vicinity of a cusp deviate less than 20\% from the true values for distances of the images to the critical points less than 15\% of the (effective) Einstein radius.