Photon Ring Interferometric Signatures Beyond The Universal Regime

TL;DR

This paper develops a perturbative method to analyze interferometric signatures of black hole photon rings beyond the universal regime by accounting for finite ring width effects, improving modeling accuracy for M87* observations.

Contribution

It introduces a novel perturbative approach to include finite width effects in photon ring visibility calculations, extending previous universal regime models.

Findings

Higher-order corrections are essential for accurate visibility modeling.

The method applies to GRMHD simulation images of M87*.

Corrections depend on ring width and baseline length.

Abstract

We calculate the interferometric signatures of black hole photon rings beyond the universal regime by perturbatively including the effects of finite ring width. Our approach first slices a thick ring into a series of thin rings, each of which falls within the universal regime. We thus calculate the visibility of the thick ring by aggregating the contributions from each thin ring, and then perturbatively expand the result into polynomials of the baseline length $u$. We show that the visibility amplitude of a thick ring depends on its "center-of-light" diameter; it also includes additional higher-order corrections due to the width of the ring, with the leading correction terms proportional to $u^2$ for the envelope and $u^3$ for the phase. We apply our method to images ray traced from general-relativistic magnetohydrodynamic (GRMHD) simulations and demonstrate that incorporating the higher-order corrections is crucial for accurately modeling the visibility of the first photon ring around M87*.