论文标题
在用简单的极曲线的黑洞阴影的近似值上
On the approximation of the black hole shadow with a simple polar curve
论文作者
论文摘要
一个嵌入明亮，光学上薄的发射区域中的黑洞在其图像上刻有几乎圆形的“阴影”，与观察者的视线相对应。阴影边界取决于黑洞的质量和自旋，通过高分辨率图像提供了两种属性的可观察签名。但是，阴影边界的标准表达式最自然地通过Boyer-Lindquist Radii而不是图像坐标来参数。我们使用椭圆和称为Limacon的曲线家族来探索阴影边界的简单，近似参数化。我们证明，这些曲线为所有黑洞的旋转和倾斜提供了出色，有效的近似值。特别是，我们表明Limacon的两个参数自然解释了由质量和自旋产生的三个主要阴影变形：大小，位移和不对称性。这些曲线对于直接拟合到干涉数据的参数模型方便，它们揭示了从具有实际测量限制的图像估算黑洞特性时预期的变性，并且它们为使用黑洞图像的KERR指标的参数测试提供了自然框架。
A black hole embedded within a bright, optically thin emitting region imprints a nearly circular "shadow" on its image, corresponding to the observer's line-of-sight into the black hole. The shadow boundary depends on the black hole's mass and spin, providing an observable signature of both properties via high resolution images. However, standard expressions for the shadow boundary are most naturally parametrized by Boyer-Lindquist radii rather than by image coordinates. We explore simple, approximate parameterizations for the shadow boundary using ellipses and a family of curves known as limacons. We demonstrate that these curves provide excellent and efficient approximations for all black hole spins and inclinations. In particular, we show that the two parameters of the limacon naturally account for the three primary shadow deformations resulting from mass and spin: size, displacement, and asymmetry. These curves are convenient for parametric model fitting directly to interferometric data, they reveal the degeneracies expected when estimating black hole properties from images with practical measurement limitations, and they provide a natural framework for parametric tests of the Kerr metric using black hole images.
