论文标题
时间延迟镜头的过度约束模型redux：角尾如何摇动径向狗
Over-constrained Models of Time Delay Lenses Redux: How the Angular Tail Wags the Radial Dog
论文作者
论文摘要
由爱因斯坦环（Einstein Rens）良好约束的重力镜头的径向质量分布的两种特性是Einstein Radius R_E，XI2 = R_E Alpha''（r_e）/（R_E）/（1-kappa_e），其中Alpha'（r_e）'（r_e）和Kappa_e是第二驱动的perivativativative和defultion的第二驱动。但是，如果径向质量谱和角结构之间存在密切的数学关系，那么椭圆形的环境也可以很强地区分具有相同XI2的径向质量分布。 Millon等人的椭圆形模型很好地说明了这个问题。 （2019）。当使用爱因斯坦环约束径向质量分布时，模型的角结构必须包含自然界中预期的所有自由度（例如，外部剪切，恒星的不同椭圆形和深色物质，对椭圆形结构的适度偏差，与轴的适度扭曲，轴的适度，椭圆度梯度等适用于辐射的层状，等级的结构是远程和敏感的。 Einstein环的模型具有太少的角度自由度，将导致径向质量分布之间的偏见可能性很大，并且基于重力镜头时间延迟，H0非常精确但不准确的H0估计值。
The two properties of the radial mass distribution of a gravitational lens that are well-constrained by Einstein rings are the Einstein radius R_E and xi2 = R_E alpha''(R_E)/(1-kappa_E), where alpha''(R_E) and kappa_E are the second derivative of the deflection profile and the convergence at R_E. However, if there is a tight mathematical relationship between the radial mass profile and the angular structure, as is true of ellipsoids, an Einstein ring can appear to strongly distinguish radial mass distributions with the same xi2. This problem is beautifully illustrated by the ellipsoidal models in Millon et al. (2019). When using Einstein rings to constrain the radial mass distribution, the angular structure of the models must contain all the degrees of freedom expected in nature (e.g., external shear, different ellipticities for the stars and the dark matter, modest deviations from elliptical structure, modest twists of the axes, modest ellipticity gradients, etc.) that work to decouple the radial and angular structure of the gravity. Models of Einstein rings with too few angular degrees of freedom will lead to strongly biased likelihood distinctions between radial mass distributions and very precise but inaccurate estimates of H0 based on gravitational lens time delays.
