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

TL;DR

This paper evaluates the robustness of a theoretical prediction that photon ring shapes in black hole images are insensitive to astrophysical details, testing it across various models and identifying key observational challenges.

Contribution

The study extends previous work by testing the photon ring shape prediction across diverse astrophysical profiles, spins, and inclinations, and analyzes the impact of ring width on measurement success.

Findings

At low inclinations, the shape prediction is robust with an appropriate baseline.

At high inclinations, non-uniform ring width complicates shape measurement.

The photon ring shape can potentially constrain black hole spin and inclination.

Abstract

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 whose observation could provide a stringent consistency test of the Kerr hypothesis, with scant dependence on the astrophysical configuration. Gralla, Lupsasca and Marrone (GLM) argued 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 an experimental method for measuring this GR-predicted shape via space-based interferometry. We wish to assess the robustness of their prediction by checking that it holds for a variety of astrophysical profiles, black hole spins and observer inclinations. We repeat their analysis for hundreds of models and identify the width of the photon ring and its angular variation as a main obstacle to their method's success. We qualitatively describe how this width varies with the emission profile, black hole spin and observer inclination. At low inclinations, an 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.