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.

Shadows and photon rings of regular black holes and geonic horizonless compact objects

“…Let us stress however, that the Lyapunov exponent is not a direct observable, while the relative fluxes between successive photon rings will be hard to achieve. Other potential observables of interest are the ring's shape (such as its width) [92] and, more promising still, the so-called auto-correlation functions, namely, the correlations of observed brightness fluctuations across different times and locations since they exhibit a universal structure [95], whose analysis goes far beyond the scope of the present work.…”

“…This shape of the profile was originally developed to match the results of GRMHD for rotating (Kerr) black holes in order to explore the structure of their photon rings, see e.g. [92], so we will simplify the problem a little bit given the spherical symmetry of our setting.…”

Disentangling photon rings beyond General Relativity with future radio-telescope arrays

“…Many alternatives to Kerr black holes are characterized by a photon-ring structure that is distinct from the predictions of GR. In particular, photon rings may be more separated, calling for a broadening of dedicated studies in GR [59,67,85,[88][89][90][91] to settings beyond GR [92][93][94][95]. We discuss three examples to make this point: regular black holes, horizonless spacetimes and parametrized black-hole spacetimes beyond GR.…”

Shadows and photon rings of regular black holes and geonic horizonless compact objects

“…This profile was originally thought to match the results of GRMHD for rotating (Kerr) black holes in order to explore the structure of their photon rings, see e.g. [76], so we will simplify the problem a little bit given the spherical symmetry of our setting. In particular, the constant µ is related in such models either to the innermost circular time-like orbit (ISCO) radius or to the inner horizon of a Kerr black hole, and we shall take here their restrictions and match it to the non-rotating and uncharged (Schwarzschild) case.…”