Assessing the impact of instrument noise and astrophysical fluctuations on measurements of the first black hole photon ring

Currently envisioned extensions of the Event Horizon Telescope to space will soon target the black hole photon ring: a narrow ring-shaped imprint of a black hole's strong gravity produced in its images by highly bent photon trajectories. In principle, the shape of the photon ring encodes information about the geometry of the underlying black hole spacetime. In practice, however, whether or not this information can be extracted from the ring shape depends on several factors, ranging from the astrophysical details of the emitting source (such as the magnitude of its plasma fluctuations) to the specific configuration of the interferometric array (such as the separation between its telescopes, or the level of noise in its instruments). Here, we employ a phenomenological model to assess the impact of astrophysical fluctuations and instrument noise on the inferred shape of the photon ring. Our systematic study of several astrophysical profiles suggests that this shape can be measured even in the presence of instrument noise across a wide range of baselines. The measurement accuracy and precision appear relatively insensitive to the noise level, up to a sharp threshold beyond which any measurement becomes incredibly challenging (at least without recourse to more sophisticated data analysis methods). Encouragingly, we find that only a few snapshot images are generally needed to overcome the impact of astrophysical fluctuations and correctly infer the ring diameter. Inference becomes more challenging when analyzing the visibility amplitude in a baseline window that is not entirely dominated by a single photon ring. Nevertheless, in most cases, it is still possible to fit a ring shape with the correct fractional asymmetry. These results provide excellent prospects for future precision measurements of black hole spin and fundamental astrophysics via black hole imaging.