Image of the thin accretion disk around compact objects in the Einstein-Gauss-Bonnet gravity

We study the optical appearance of a thin accretion disk around compact objects within the Einstein-Gauss-Bonnet gravity. Considering static spherically symmetric black holes and naked singularities we search for characteristic signatures which can arise in the observable images due to the modification of general relativity. While the images of the Gauss-Bonnet black holes closely resemble the Schwarzschild black hole, naked singularities possess a distinctive feature. A series of bright rings are formed in the central part of the images with observable radiation $10^3$ times larger than the rest of the flux making them observationally significant. We elucidate the physical mechanism, which causes the appearance of the central rings, showing that the image is determined by the light ring structure of the spacetime. In a certain region of the parametric space the Gauss-Bonnet naked singularities possess a stable and an unstable light ring. In addition the gravitational field becomes repulsive in a certain neighbourhood of the singularity. This combination of features leads to the formation of the central rings implying that the effect is not specific for the Einstein-Gauss-Bonnet gravity but would also appear for any other compact object with the same characteristics of the photon dynamics.