奇异等温球与黑洞的透镜效应
Lensing by a singular isothermal sphere and a black hole
摘要：
大多数星系的中心都有超大质量黑洞。当两个星系合并时，黑洞也会合并。最后一个单一的黑洞可能由于不对称的引力辐射而受到反冲，并且可能不在星系的中心;偏离中心的黑洞也可能由其他方式产生，例如由于不对称的喷流功率而产生的持续加速。我们将主星系模型化为一个奇异的等温球，将黑洞模型化为一个偏心点透镜，用复数符号研究了临界曲线和焦散线。我们确定的关键参数，支配过渡的拓扑结构的关键曲线，焦散线和伪焦散线，并发现图像的数量可以是两个，三个，四个和五个。我们展示了图像配置的例子，包括三个高度缩小的图像被发现接近中心的情况。由于黑洞对图像放大率的扰动，在偏离中心的情况下与其质量成线性关系，而当黑洞位于中心时，则成二次关系。这样的图像难以观察，除非高对比度和高分辨率成像设备（例如，无线电中的平方公里阵列）变得可用。
英文摘要：
Most galaxies host central supermassive black holes. As two galaxies merge, the black holes also merge. The final single black hole may suffer a kick due to asymmetric gravitational radiation and may not be at the centre of the galaxy; off-centre black holes may also be produced by other means such as sustained acceleration due to asymmetric jet power. We model the main galaxy as a singular isothermal sphere and the black hole as an off-centre point lens, and study the critical curves and caustics using complex notation. We identify the critical parameters that govern the transitions in the topology of critical curves, caustics and pseudo-caustics, and find the number of images can be two, three, four and five. We show examples of image configurations, including cases where three highly de-magnified images are found close to the centre. The perturbation on the image magnification due to the black hole scales linearly with its mass in the off-centre case, and quadratically when the black hole is at the centre. Such images are difficult to observe unless high-contrast and high-resolution imaging facilities (e.g., the Square Kilometer Array in the radio) become available.
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