Measuring Spin from Relative Photon Ring Sizes. (arXiv:2105.09962v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Broderick_A/0/1/0/all/0/1">Avery E. Broderick</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Tiede_P/0/1/0/all/0/1">Paul Tiede</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pesce_D/0/1/0/all/0/1">Dominic W. Pesce</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gold_R/0/1/0/all/0/1">Roman Gold</a>
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.
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.
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