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

Abstract: 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.