Measuring Spin from Relative Photon Ring Sizes

Abstract

The direct detection of a bright, ring-like structure in horizon-resolving images of M87* by the Event Horizon Telescope is a striking validation of general relativity. The angular size and shape of the ring is a degenerate measure of the location of the emission region, mass, and spin of the black hole. However, we show that the observation of multiple rings, corresponding to the low-order photon rings, can break this degeneracy and produce mass and spin measurements independent of the shape of the rings. We describe two potential experiments that would measure the spin. In the first, observations of the direct emission and $n=1$ photon ring are made at multiple epochs with different emission locations. This method is conceptually similar to spacetime constraints that arise from variable structures (or hot spots) in that it breaks the near-perfect degeneracy between emission location, mass, and spin for polar observers using temporal variability. In the second, observations of the direct emission, $n=1$ and $n=2$ photon rings are made during a single epoch. For both schemes, additional observations comprise a test of general relativity. Thus, comparisons of Event Horizon Telescope observations in 2017 and 2018 may be capable of producing the first horizon-scale spin estimates of M87* inferred from strong lensing alone. Additional observation campaigns from future high-frequency, Earth-sized and space-based radio interferometers can produce high-precision tests of general relativity.

arXiv commentSubmitted to ApJ, 16 pages, 14 figures

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• Calculating black hole shadows: Review of analytical studies
• Photon rings of spherically symmetric black holes and robust tests of non-Kerr metrics
• Analytical study of higher-order ring images of accretion disk around black hole
• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Observational predictions of LQG motivated polymerized black holes and constraints from Sgr A* and M87*
• Separating Astrophysics and Geometry in Black Hole Images
• Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects
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• Horizonless spacetimes as seen by present and next-generation Event Horizon Telescope arrays
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