关于黑洞光子环的可观测形状
On the Observable Shape of Black Hole Photon Rings
摘要：
受测量黑洞光子环的前景的启发，在以前的工作中，我们探索了天空中明亮的窄曲线产生的干涉签名。这样的曲线的干涉测量观测测量其“投影位置函数”$\mathbf{r}\cdot\hat{\mathbf{n}}$，其中$\mathbf{r}$参数化曲线，并且$\hat{\mathbf{n}}$表示其单位法向量。在本文中，我们表明，通过明确的建设，曲线可以完全重建从其投影位置，完成的论点，空间干涉法可以在原则上确定详细的光子环形状。在实践中，近期观测可能仅限于可见度振幅，其包含不完整的形状信息：对于凸曲线，振幅仅编码形状的投影直径（或“宽度”）的集合。我们探讨的自由度，在重建凸曲线的宽度，让洞察形状信息探测技术上可行的未来天文测量。最后，我们考虑克尔“临界曲线”在这个框架中，并提出了一些新的结果，其形状。我们分析表明，临界曲线是一个椭圆在小自旋或倾斜，而在极端的自旋成为一个笛卡尔椭圆的凸包。我们发现一个简单的椭圆形，“phoval”，它重现了在整个参数范围内的高保真度的临界曲线。
英文摘要：
Motivated by the prospect of measuring a black hole photon ring, in previous work we explored the interferometric signature produced by a bright, narrow curve in the sky. Interferometric observations of such a curve measure its "projected position function" $\mathbf{r}\cdot\hat{\mathbf{n}}$, where $\mathbf{r}$ parameterizes the curve and $\hat{\mathbf{n}}$ denotes its unit normal vector. In this paper, we show by explicit construction that a curve can be fully reconstructed from its projected position, completing the argument that space interferometry can in principle determine the detailed photon ring shape. In practice, near-term observations may be limited to the visibility amplitude alone, which contains incomplete shape information: for convex curves, the amplitude only encodes the set of projected diameters (or "widths") of the shape. We explore the freedom in reconstructing a convex curve from its widths, giving insight into the shape information probed by technically plausible future astronomical measurements. Finally, we consider the Kerr "critical curve" in this framework and present some new results on its shape. We analytically show that the critical curve is an ellipse at small spin or inclination, while at extremal spin it becomes the convex hull of a Cartesian oval. We find a simple oval shape, the "phoval", which reproduces the critical curve with high fidelity over the whole parameter range.
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