标题： 折叠和尖点附近参数化透镜模型族的退化现象 显示英文标题

标题： Degeneracies of parametric lens model families near folds and cusps

摘要： 我们提出了一种方法，利用 Wagner 和 Bartelmann（2015）推导出的透镜势导数的模型无关比值，选择能够描述围绕折叠和尖点附近的双象和三象引力透镜图像的透镜模型族。 通过比较这些模型无关的势导数比值与特定参数范围内整个透镜模型族沿临界曲线的数值确定的势导数比值，来选择模型。这种比较会返回透镜模型族能够在其中再现观测结果的参数范围，以及观察到的图像集合可能出现在临界曲线的哪些部分。 如果从观测中推断出的模型无关的势导数比值超出了为透镜模型族计算出的比值范围，则可以排除该模型族作为给定参数空间体积内的可行模型。 我们将这种方法应用于具有外部剪切的奇异等温球族，并以星系和两个星系团（JVAS B1422+231、SDSS J2222+2745 和 MACS J1149.5+2223）的透镜效应为例，结果显示我们的通用方法得出的结果与先前模型拟合的结果非常一致。 显示英文摘要

摘要： We develop an approach to select families of lens models that can describe doubly and triply gravitationally lensed images near folds and cusps using the model-independent ratios of lensing-potential derivatives derived in Wagner & Bartelmann (2015). Models are selected by comparing these model-independent ratios of potential derivatives to (numerically determined) ratios of potential derivatives along critical curves for entire lens model families in a given range of parameter values. This comparison returns parameter ranges which lens model families can reproduce observation within, as well as sections of the critical curve where image sets of the observed type can appear. If the model-independent potential-derivative ratios inferred from the observation fall outside the range of these ratios derived for the lens model family, the entire family can be excluded as a feasible model in the given volume in parameter space. We employ this approach for the family of singular isothermal spheres with external shear to examples of lensing by a galaxy and two galaxy clusters (JVAS B1422+231, SDSS J2222+2745, and MACS J1149.5+2223) and show that the results obtained by our general method are in good agreement with results of previous model fits.