For a supermassive black hole in a distant galaxy, the opening angle is
This is shown in Figure 4
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The black hole that combines the highest brightness with the largest angular size of the horizon is the
one that powers the source Sgr A*, in the center of the Milky Way. Since the first measurements of the size
of the source at 7 mm [89] and at 1.4 mm [79] demonstrated that the emitting region is only a few times
larger than the radius of the horizon (see Figure 5), a number of observational and theoretical
investigations have aimed to probe deeper into the gravitational field of the black hole and constrain its
properties.
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The long-wavelength spectrum of Sgr A* peaks at a frequency of 1012 Hz, suggesting that the
emission changes from optically thick (probably synchrotron emission) to optically thin at a comparable
frequency (see, e.g., [107]). As a result, observations at frequencies comparable to or higher than the
transition frequency can, in principle, probe the accretion flow at regions very close to the horizon of the
black hole.
Even though the exact shape and size of the image of Sgr A* at long wavelengths depends on the
detailed structure of the underlying accretion flow (cf. [116] and [186]), there exist two generic observable
signatures of its strong gravitational field. First, the horizon leaves a ‘shadow’ on the image
of the source, which is equal to and roughly independent of the spin of the
black hole [7, 57, 162, 24, 110]. Second, the brightness of the image of the accretion flow
is highly non-uniform because of the high velocity of the accreting plasma and the effects of
the strong gravitational lensing. Simultaneously fitting the size, shape, polarization map, and
centroid of the image observed at different wavelengths with future telescopes, will offer the
unique possibility of removing the complications introduced by the unknown nature of the
accretion flow, imaging directly the black-hole shadow, and measuring the spin of the black
hole [25].
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