弱透镜变香蕉：屈曲真正测量的是什么
Weak lensing goes bananas: What flexion really measures
摘要：
在弱引力透镜中，由剪切引起的图像畸变测量偏转质量分布的投影潮汐引力场。对于最低阶，剪切与平均图像椭圆率成正比。如果图像尺寸与剪切变化的尺度相比并不小，则会发生高阶失真，称为屈曲。对于普通的弱透镜，可观测的量不是切变，而是由于质量片简并而产生的约化切变。同样，屈曲本身也是不可观察的。相反，高阶图像失真测量减少的屈曲，即，简化剪切的导数。我们推导出相应的透镜方程的减少弯曲和计算之间的关系的源和图像的亮度矩。假设各向同性分布的源方向，估计减少剪切和弯曲，然后用模拟测试。特别是，屈曲的存在会影响降低的剪切力的确定。这些模拟的结果产生了作为剪切和屈曲的函数的估计量的偏差。我们指出并量化的屈曲形式主义的基本限制，在减少屈曲和源大小的产品。如果该乘积增加到高于导出的阈值，则在局部形成源的多个图像，并且形式主义崩溃。最后，我们展示了如何一般（减少）屈曲场可以分解成它的四个组成部分：其中两个是由于剪切场，携带的E-和B-模式一般。另外两个分量不对应于剪切场;它们也可以被分成相应的E-和B-模式。
英文摘要：
In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image sizes are not small compared to the scale over which the shear varies, higher-order distortions occur, called flexion. For ordinary weak lensing, the observable quantity is not the shear, but the reduced shear, owing to the mass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather, higher-order image distortions measure the reduced flexion, i.e., derivatives of the reduced shear. We derive the corresponding lens equation in terms of the reduced flexion and calculate the resulting relation between brightness moments of source and image. Assuming an isotropic distribution of source orientations, estimates for the reduced shear and flexion are obtained; these are then tested with simulations. In particular, the presence of flexion affects the determination of the reduced shear. The results of these simulations yield the amount of bias of the estimators, as a function of the shear and flexion. We point out and quantify a fundamental limitation of the flexion formalism, in terms of the product of reduced flexion and source size. If this product increases above the derived threshold, multiple images of the source are formed locally, and the formalism breaks down. Finally, we show how a general (reduced) flexion field can be decomposed into its four components: two of them are due to a shear field, carrying an E- and B-mode in general. The other two components do not correspond to a shear field; they can also be split up into corresponding E- and B-modes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
