论文标题
在黑洞光子环的可观察形状上
On the Observable Shape of Black Hole Photon Rings
论文作者
论文摘要
在测量黑洞光子环的前景中，在先前的工作中，我们探索了由天空中明亮的狭窄曲线产生的干涉签名。对这种曲线的干涉观察测量其“投影位置函数” $ \ MATHBF {r} \ cdot \ hat {\ Mathbf {n}} $，其中$ \ Mathbf {r} $参数化曲线和$ \ hat {\ hat {\ therbf {\ sathbf {n}} $ DENOTES $ DENOTES $ DENOTES的单位正常vector。在本文中，我们通过显式结构表明，可以从其投影位置完全重建曲线，从而完成了这样一个论点，即空间干涉指定可以原则上确定详细的光子环形状。实际上，近期观察结果可能仅限于单独的可见性幅度，其中包含不完整的形状信息：对于凸曲线，幅度仅编码形状的投影直径（或“宽度”）。我们探索了从其宽度重建凸曲线的自由，从而深入了解了通过技术上合理的未来天文测量所探索的形状信息。最后，我们在此框架中考虑了Kerr的“临界曲线”，并在其形状上提出了一些新的结果。我们在分析上表明，临界曲线是小旋转或倾斜度的椭圆形，而在极端自旋时，它变成了笛卡尔椭圆形的凸面。我们发现了一个简单的椭圆形形状，即“ phoval”，它在整个参数范围内以高保真度再现了临界曲线。
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.
