Auto- and cross-correlations for multiple images of corotating hotspots in accretion disks

Abstract: Recent horizon-scale observations of the Sgr A* might open up a new window to study spacetime geometry and accretion matter in the strong-field regime of gravity. Due to the short gravitational timescale for Sgr A*, variable emissions near the galactic center are expected in the observations, including variability in the Sgr A* images and flare motions within ten times gravitational radius. In this paper, we investigate the spatiotemporal auto- and cross-correlations for multiple images of a long-lived corotating hotspot near the black hole. Using the recently developed efficient ray-tracing scheme for point-like sources, we extensively consider multiple images from primary to eighth-order in the correlations. We show that these correlations exhibit a repeated inclined band-like structure in the $\Delta \Phi$-$\Delta t$ plane. And there is a periodic modulation of width of the correlated bands, with the maximum bandwidth increasing with the inclination angles. The point-slope of correlated bands is determined by the lapse in azimuthal angle and time of multiple images, as well as the apparent rotation speed of hotspots. By comparing correlations for lower-order with those for higher-order images, it is found that the fixed points for cross-correlations between lower-order images depend on the orbital configurations of hotspots. It challenges the use of correlations for lower-order images to infer black hole geometries. Additionally, we also examine the influence from hotspot shapes based on semi-analytical formulas. Although the emission shape can significantly influence light curves, it does not change the correlated bands of the correlations.