Photon ring test of the Kerr hypothesis: Variation in the ring shape

Abstract

Context. The Event Horizon Telescope (EHT) collaboration recently released horizon-scale images of the supermassive black hole M87∗. These images are consistently described by an optically thin, lensed accretion flow in the Kerr spacetime. General relativity (GR) predicts that higher-resolution images of such a flow would present thin, ring-shaped features produced by photons on extremely bent orbits. Recent theoretical work suggests that these photon rings produce clear interferometric signatures that depend very little on the astrophysical configuration and whose observation could therefore provide a stringent consistency test of the Kerr hypothesis. Aims. We wish to understand how the photon rings of a Kerr black hole vary with its surrounding emission. Gralla, Lupsasca, and Marrone (GLM) found that the shape of high-order photon rings follows a specific functional form that is insensitive to the details of the astrophysical source, and proposed a method for measuring this GR-predicted shape via space-based interferometry. We wish to assess the robustness of this prediction by checking it for a variety of astrophysical profiles, black hole spins, and observer inclinations. Methods. We use the ray tracing code Gyoto to simulate images of thin equatorial disks accreting onto a Kerr black hole. We extract the shape of the resulting photon rings from their interferometric signatures using a refinement of the method developed by GLM. We repeat this analysis for hundreds of models with different emission profiles, black hole spins, and observer inclinations. Results. We identify the width of the photon ring and its angular variation as a main obstacle to the method's success. We qualitatively describe how this width varies with the emission profile, black hole spin, and observer inclination. At low inclinations, our improved method is robust enough to confirm the shape prediction for a variety of emission profiles; however, the choice of baseline is critical to the method's success. At high inclinations, we encounter qualitatively new effects that are caused by the ring's non-uniform width and require further refinements to the method. We also explore how the photon ring shape could constrain black hole spin and inclination.