标题： 天体测量方法中薄吸积盘低阶像的像差效应 显示英文标题

标题： Aberration effect on lower-order images of thin accretion disk in the astrometric approach

摘要： 随着事件视界望远镜对超大质量黑洞的观测技术的进步，人们一直在持续探索这些图像能揭示哪些关于基础物理的信息，包括时空几何和天体物理辐射源。 受彭罗斯关于刚性球体的像差公式的启发，该公式阐明了速度增加并不会使球体的外观变平，我们扩展了研究，以探讨吸积辐射图像的行为。 本文研究了有限距离观测者在克尔-德西特黑洞周围薄吸积盘图像上的像差效应的影响，特别关注主图像、次图像和$n=2$图像。 我们采用解析光线追踪场景，并扩展天体测量方法以研究存在像差情况下的图像。 这项研究具有非平凡性，因为我们不假设特定形式的像差公式，而是所有像差效应都来自于一种称为天体测量方法的坐标无关且四维标架无关的框架。 我们的研究发现，对于运动的有限观测者，低阶图像的形状会高度失真，而主图像的形状和大小比$n=2$图像更易受到像差的影响。 这一发现表明，理论上可以根据其独特的变化将主图像与阴影区分开来。 显示英文摘要

摘要： With recent advancements in observing supermassive black holes with the Event Horizon Telescope, there has been persistent exploration into what the images can reveal about fundamental physics, including space-time geometries and astrophysical emission sources. Inspired by Penrose's aberration formula for a rigid sphere, which clarified that increased speed does not flatten the appearance of the sphere, we extend the studies to the behavior of the images of accretion emissions. This paper examines the impact of aberration effects on the images of a thin accretion disk around Kerr-de Sitter black holes for finite distant observers, specifically focusing on the primary, secondary, and $n=2$ images. We employ the analytical ray-tracing scenario and extend the astrometric approach to investigate the images in the presence of aberration. This study is non-trivial because we do not assume a specific form of the aberration formula, instead, all aberration effects emerge from a coordinate-independent and tetrad-independent framework referred to as the astrometric approach. Our study finds that the shapes of the lower-order images get highly distorted for finite observers in motion, and the shapes and sizes of primary images are more sensitive to aberration than those of the $n=2$ images. This finding suggests that the primary images could theoretically be distinguished from the shadow based on their distinctive variations.