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首页> 外文期刊>The Astrophysical Journal. Letters >Analytical solutions of singular isothermal quadrupole lens
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Analytical solutions of singular isothermal quadrupole lens

机译：奇异等温四极透镜的解析解

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Using an analytical method, we study the singular isothermal quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the singular isothermal sphere lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this Letter, including the deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic, and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. We find that naked cusps will appear when the relative intensity k of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity, as found by Dalal. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations where a point source infinitely approaches a cusp or a fold. The sum of the magnifications of the cusp image triplet is usually not equal to 0, and it is usually positive for major cusps while negative for minor cusps. Similarly, the sum of magnifications of the fold image pair is usually not equal to 0 either. Nevertheless, the cusp and fold relations are still equal to 0 in that the sum values are divided by infinite absolute magnifications by definition.
机译：使用一种分析方法，我们研究了奇异的等温四极（SIQ）透镜系统，它是可以产生四个图像的最简单的透镜模型。在这种情况下，径向质量分布与奇异等温球面透镜的轮廓一致，并且切向分布是通过在单极组件上增加一个四极来给出的。本信中已研究了SIQ透镜的基本特性，包括偏转电势，偏转角，放大倍率，临界曲线，苛性，伪苛性和过渡轨迹。得出了光源在轴上的图像位置和放大倍数的解析解。我们发现，当四极对单极的相对强度k大于0.6时，会出现裸露的尖头。根据SIQ镜头的放大率不变理论，Dalal发现，四个图像的带符号放大率总和应等于1。但是，如果光源位于裸露的尖瓣上，则左三个图像的总放大倍率小于不变式1。使用这种简单的镜头系统，我们研究了点光源无限接近尖瓣或褶皱的情况。尖瓣图像三元组的放大倍数总和通常不等于0，对于大尖瓣通常为正，而对于小尖瓣通常为负。类似地，折叠图像对的放大倍数之和通常也不等于0。但是，尖峰和折叠关系仍然等于0，因为根据定义，总和值除以无限的绝对放大率。

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