Overlapping of photon rings in black hole imaging

Abstract

In this paper, we investigate the overlapping of photon rings - higher-order images of a black hole's luminous environment, concentrated near the shadow boundary and expected to be resolved in future observations. We consider a broad class of static spherically symmetric spacetimes and geometrically thin equatorial accretion disk with a prescribed inner radius and infinite outer extent, viewed by a polar observer. Depending on the inner radius of the disk, the thickness of each photon ring varies, and the rings may or may not overlap. By overlapping, we mean that portions of images appear at the same angular position on the observer's sky. To characterize the overlapping, we introduce the radius of merging - the value of the disk's inner radius at which two photon rings of given orders begin to overlap. Since each radius of merging is labeled by two indices corresponding to the image orders, it becomes possible to arrange these radii in the form of an infinite-dimensional matrix where only the upper right-hand corner is filled. This matrix, which we call the "matrix of merging", is a signature of spacetime only, and, once known, it provides a qualitative understanding of the overlapping pattern for any chosen value of the inner radius of the disk. Remarkably, the matrix of merging exhibits several universal properties that hold for all spherically symmetric metrics and can be established even without explicit calculation of light trajectories. Based on these properties, we demonstrate that certain overlapping patterns are universally forbidden across all such spacetimes and for any inner radius of the disk. Examples for the Schwarzschild and Reissner-Nordström black holes are provided. The main application of our study is constraining the spacetime metric and the accretion model using observed photon ring overlaps.

24 pages, 9 figures

References in corpus (59)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Viewing the Shadow of the Black Hole at the Galactic Center
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• Schwarzschild black hole lensing
• Testing the nature of dark compact objects: a status report
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• Gravitational lensing in the strong field limit
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Black Hole Shadows, Photon Rings, and Lensing Rings
• Calculating black hole shadows: Review of analytical studies
• Shadows and strong gravitational lensing: a brief review
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Strong field limit of black hole gravitational lensing
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• Universal Interferometric Signatures of a Black Hole's Photon Ring
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• Reissner-Nordstrom black hole lensing
• Gravitational Lensing by Black Holes
• Constraints on black-hole charges with the 2017 EHT observations of M87*
• The Shape of the Black Hole Photon Ring: A Precise Test of Strong-Field General Relativity
• Lensing by Kerr Black Holes
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Observing the Inner Shadow of a Black Hole: A Direct View of the Event Horizon
• Strong deflection limit analysis and gravitational lensing of an Ellis wormhole
• Strong deflection limit of black hole gravitational lensing with arbitrary source distances
• Photon Ring and Observational Appearance of a Hairy Black Hole
• The Null Geodesics of the Kerr Exterior
• Key Science Goals for the Next-Generation Event Horizon Telescope
• Fermion scattering by a Schwarzschild black hole
• Gravitational lensing in plasma: Relativistic images at homogeneous plasma
• Photon rings of spherically symmetric black holes and robust tests of non-Kerr metrics
• Photon Ring Autocorrelations
• On the Observable Shape of Black Hole Photon Rings
• The Black Hole Explorer: Motivation and Vision
• Toward determining the number of observable supermassive black hole shadows
• Analytical study of higher-order ring images of accretion disk around black hole
• Strong Gravitational Lensing by Schwarzschild Black Holes
• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Shape of higher-order images of equatorial emission rings around a Schwarzschild black hole: Analytical description with polar curves
• Distinguishing gravitational and emission physics in black-hole imaging: spherical symmetry
• Photon rings as tests for alternative spherically symmetric geometries with thin accretion disks
• Unbound motion of massive particles in the Schwarzschild metric: Analytical description in case of strong deflection
• Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects
• Black Hole Photon Rings Beyond General Relativity
• Testing Gravity with Black Hole Shadow Subrings
• Towards VLBI Observations of Black Hole Structure
• Event horizon image within black hole shadow
• Strong deflection limit analysis of black hole lensing in inhomogeneous plasma
• Constraining spherically symmetric metrics by the gap between photon rings
• Relativistic iron lines in accretion disks: the contribution of higher order images in the strong deflection limit
• A Lensing-Band Approach to Spacetime Constraints
• Strong deflection of massive particles in spherically symmetric spacetimes
• Jets and Rings in Images of Spinning Black Holes
• Interferometric signature of higher-order images in a parametrized framework

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