关于多重Einstein环
On Multiple Einstein Rings
摘要：
最近对引力透镜的一些调查发现了双爱因斯坦环的例子。在这里，我们调查分析多个爱因斯坦环的发生。我们证明，在非常一般的假设下，最多一个爱因斯坦环可以产生于一个单一的平面透镜一个单一的背景源的质量分布。因此，两个或更多的爱因斯坦环只能出现在多平面透镜中。令人惊讶的是，我们表明，它是可能的一个单一的来源，以产生一个以上的爱因斯坦环。如果两个点质量（或两个等温球）在不同的平面上与观察者和光源在光轴上对齐，我们表明，有多达三个爱因斯坦环。我们还讨论了这两种模型的图像形态，如果轴对称被打破，并给出了第一个实例的放大率不变量的情况下，两个透镜平面。
英文摘要：
A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.
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