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4.1 Black-hole images

To paraphrase the common proverb, a picture is worth a thousand spectra. Directly imaging the vicinity of a black hole promises to provide direct evidence for the existence of a horizon. However, black holes are notoriously small, and the resolution required for imaging their horizons is, for most cases, beyond current capabilities. For a stellar-mass black hole in the galaxy, the opening angle of the horizon, as viewed by an observer on Earth, is only
( ) ( ) − 4 --M---- 1-kpc- θ = 2 × 10 10M D μarcsec , (18 ) ⊙
where M is the mass of the black hole and D is its distance.

For a supermassive black hole in a distant galaxy, the opening angle is

( ) ( ) --M----- 1-Mpc-- θ = 20 109 M ⊙ D μarcsec . (19 )
This is shown in Figure 4View Image for a number of supermassive black holes with secure mass determinations. The angular size of the horizons of some of the sources are barely resolvable today with interferometric observations in the sub-mm/infrared wavelengths and will be resolvable in the X-ray wavelengths in the near future with the Black Hole Imager [114].
View Image

Figure 4: The opening angles, as viewed by an observer on Earth, of the horizons of a number of supermassive black holes in distant galaxies with a secure dynamical mass measurement (sample of [169]). The opening angle of the black-hole horizon in the center of the Milky Way (Sgr A*) is also shown for comparison.

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 5View Image), a number of observational and theoretical investigations have aimed to probe deeper into the gravitational field of the black hole and constrain its properties.

View Image

Figure 5: The major axis of the accretion flow around the black hole in the center of the Milky Way, as measured at different wavelengths, in units of the Schwarzschild radius (left axis) and in milliarcsec (right axis; adapted from [148]). Even with current technology, the innermost radii of the accretion flow can be readily observed.

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 --- ≃ √ 27GM ∕c2 and roughly independent of the spin of the black hole [75716224110]. 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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