Gravity versus astrophysics in black hole images and photon rings: Equatorial emissions and spherically symmetric space-times

¹ LIRA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, 5 Place Jules Janssen, 92190 Meudon, France
² Laboratoire de Physique de l’École normale supérieure, ENS, F-75005 Paris, France
³ Instituto de Astrofísica de Andalucía-CSIC, Glorieta de la Astronomía s/n, E-18008 Granada, Spain

^⋆ Corresponding author: irene.urso@obspm.fr

Received: 31 March 2025
Accepted: 28 June 2025

Abstract

Context. The Event Horizon Telescope (EHT) collaboration released in 2019 the first horizon-scale images of a black hole accretion flow, opening a novel route for plasma physics comprehension and gravitational tests. Although the present unresolved images deeply depend on the astrophysical properties of the accreted matter, general relativity predicts that they contain highly lensed observables, the so-called photon rings, embodying the effects of strong-field gravity.

Aims. Focusing on the particular case of the supermassive black hole M87* and adopting a geometrically thin equatorial disc as a phenomenological configuration for the accreting matter, our goal is to study the degeneracy of space-time curvature and of physically motivated emission processes on plane-of-sky EHT-like images observed at 230 and 345 GHz.

Methods. In a parametric framework, we simulated adaptively ray-traced images using the code GYOTO in various spherically symmetric space-time geometries for a comprehensive class of disc velocities and a library of realistic synchrotron emission profiles. We then extracted the width and the peak position of 1D intensity cross sections on the direct image and the first photon ring.

Results. We show that among the investigated quantities, the most appropriate observables to probe the geometry are the peak positions of the first photon ring. Small geometric deviations can be unequivocally detected regardless of the motion of the disc, ranging from Keplerian rotation to radial infall, if the black hole mass-to-distance estimate is accurate up to around 2%, with the current uncertainty of 11% being just sufficient to access extreme deviations.

Conlcusions. The equatorial set-up of this paper, which is favoured by present EHT observations of M87*, is adapted to modelling future measurements at higher observing frequencies, where absorption effects are negligible, and with higher resolution, indispensable to resolving the photon rings. Additional work is needed to investigate if our conclusions hold for more realistic disc configurations.