Measuring Spin from Relative Photon Ring Sizes

TL;DR

This paper proposes methods to measure black hole spin by observing multiple photon rings around M87* with the Event Horizon Telescope, breaking degeneracies in previous measurements and enabling tests of general relativity.

Contribution

It introduces two novel observational schemes to determine black hole spin using photon ring measurements, independent of ring shape and emission location.

Findings

Multiple photon ring observations can break degeneracies in black hole parameter estimation.

Proposed methods could produce the first horizon-scale spin estimates from strong lensing.

Future observations can enable high-precision tests of general relativity.

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.