Observational signatures from higher-order images of moving hotspots in accretion disks

The efforts to probe the horizon-scale structure of black holes, such as Event Horizon Telescope and GRAVITY interferometer, might provide valuable insights into the strong-field regime of Einstein's theory of gravity. In the near field region of a black hole, the observational signatures of moving hotspots might potentially reveal the mechanism causing the flares, or reflect the spacetime geometries. This paper develops a ray tracing scenario to study higher-order images of moving hotspots in a thin disk around a spherical black hole. Our ray-tracing scenario establishes a one-to-one mapping between emission locations and observer's sky. It enables us to perform infinite-precision simulations for the images, because the emission sources are projected directly onto the image plane. Furthermore, we show that a source located anywhere outside the black hole can be repeatedly mapped onto the observer's sky, from primary to higher-order images. We investigate the observational signatures of hotspots, focusing on temporal fluxes and flux centroids from the primary to sixth-order images. The hotspots are considered to be moving in circular, escape, and plunging orbits. Our results find that the higher-order images can be categorized into two types. Within each type, the temporal fluxes exhibit a self-similar profile. Furthermore, as the hotspots approach the event horizon of a black hole, the fluxes from higher-order images alternately dominate the observed flux, which subsequently result in the flux decaying with time in an oscillatory manner.