Imaging supermassive black hole shadows with a global very long baseline interferometry array

Abstract

The imaging of two supermassive black holes by the Event Horizon Telescope Collaboration proved to a new level the correctness of Einstein's general relativity, regarding its prediction of black hole shadows in the highly curved spacetime regime.

Graphical abstract

Keywords

Event Horizon Telescope / very long baseline interferometry / black hole / black hole shadow

null

In the November of 1915, Albert Einstein presented his final version of field equations to describe gravitation as a manifest of a curved spacetime [1]. In the next year, Karl Schwarzschild obtained a spherical static vacuum solution to Einstein’s theory during the wartime [2], and it was coined as “black hole” by John Wheeler about half a century later. Rotating, hence axisymmetric, black hole solutions were discovered by Roy Kerr in 1963 [3]. After more than one hundred years since Einstein and Schwarzschild, black holes are nowadays one of the flagships of curved spacetimes, and serve as a vital concept to many mathematical theorems and a central object to countless astrophysical processes.

Black holes are four-dimensional objects with the existence of event horizon as a defining feature. For a Schwarzschild black hole with mass M, the radius for its event horizon is R_{\mathrm{S}}= 2GM/c^2, within which, nothing, including light, can escape. Geodesic motion of null trajectories shows that, if a photon approaches a Schwarzschild black hole with its impact parameter smaller than the photon capture radius, R_{\mathrm{c}}=3\sqrt{3}{R}_{\mathrm{S}}/2, it will head into the event horizon. Photons with a critical impact parameter R_{\mathrm{c}} travel on an unstable circular orbit and form a gravitationally lensed photon ring [4]. Kerr black holes have qualitatively similar behaviours, but the details have a dependence on their rotation parameter, the spin.

Pioneering theoretical studies showed that, the light from an astrophysical accretion disk around a black hole would form a central brightness depression pattern encircled by a bright emission ring, due to the combined influence of event horizon and gravitational lensing. We refer such an imaging pattern to distant observers as the “black hole shadow” [5], and the imaging feature was realized to be accessible to a global very long baseline interferometry array with current technology [6].

The most important factor of a very long baseline interferometry array is its angular resolution. On the one hand, as is well known in optics, the Airy disk represents the best-resolved spot of light that a perfect lens with a circular aperture can achieve, limited by the wave nature, hence unavoidable diffraction, of light. Therefore, in astronomy, the angular resolution of a telescope with an aperture diameter \mathcal{D} for distant celestial objects is limited by

(1)\begin{array}{l}\delta \theta \sim \sin \delta \theta \sim 1.22{\displaystyle \frac{\lambda }{\mathcal{D}}},\end{array}

with \lambda being the observing wavelength. On the other hand, for a Schwarzschild black hole, its shadow has an angular diameter d about d\sim 10{\theta }_{\mathrm{g}}, where {\theta }_{\mathrm{g}}\equiv GM/(D{c}^2 ) with D being the distance to the black hole. The fact that the angular size of a black hole shadow is proportional to the ratio of mass over distance singles out two supermassive black holes, {\mathrm{M}87}^{\star } and Sgr {\mathrm{A}}^{\star }, respectively at the centers of the giant elliptical galaxy M87 and our own spiral galaxy, the Milky Way, as two most promising sources for imaging [7, 8]. {\mathrm{M}87}^{\star } and Sgr {\mathrm{A}}^{\star } were chosen as the primary targets by the Event Horizon Telescope Collaboration [9], a collaboration that aims to directly contemplate matter and light dynamics in the neighbourhood of black hole event horizons.

In order to resolve a black hole shadow image with an angular diameter d, one needs to have \delta \theta \lesssim d at the least. Therefore, astronomers need to decrease the observing wavelength \lambda and increase the telescope aperture \mathcal{D}. The Event Horizon Telescope observes at a nominal wavelength \lambda = 1.3\mathrm{m}\mathrm{m}, considering the emission spectrum of the accretion disks around supermassive black holes, as well as the propagation characteristics, including interstellar scattering and so on, of light towards the Earth. For a telescope bound to the Earth, the largest “aperture” one can make use of is the diameter of the Earth itself, {\mathcal{D}}_{\oplus }\simeq 1.3 \times {10}^4 km. It is exactly the philosophy behind the initiative of the Event Horizon Telescope [9]. The Event Horizon Telescope coherently uses a large telescope array consisting of a global network of radio telescopes, with an effective aperture diameter roughly the size of the Earth. Because of the unprecedented angular resolution, combined with advanced analysis schemes that are tailored to the Event Horizon Telescope data, the black hole shadows of {\mathrm{M}87}^{\star } and Sgr {\mathrm{A}}^{\star } were resolved for the first time [7, 8]. Representative images of them are shown in Fig.1, and the crescent shadow structures are evident for both black holes [7, 8].

The first image of a black hole shadow was revealed by the Event Horizon Telescope Collaboration in 2019 for {\mathrm{M}87}^{\star }, with data taken by eight telescopes in the April 2017 campaign [7]. These telescopes span geographic locations including Arizona, Chile, Hawai’i, Mexico, the South Pole, and Spain. With various independent tests performed for data processing, calibration, and imaging, combined with extensive comparisons and fits to a library of general relativistic magnetohydrodynamic simulations and synthetic images from ray tracing, the angular crescent diameter of \mathrm{M}{87}^{\star } shadow is finally measured to be [10]

(2)\begin{array}{l}d=42\pm 3\mu \mathrm{a}\mathrm{s}.\end{array}

Supplementing it with the known distance of {\mathrm{M}87}^{\star }, D={16.8}_{-0.7}^{+0.8}\mathrm{M}\mathrm{p}\mathrm{c}, the Event Horizon Telescope Collaboration obtained the mass of the supermassive black hole in M87,

(3)\begin{array}{l}M=(6.5\pm 0.7)\times {10}^9{M}_{\odot },\end{array}

which is consistent with independent measurements from stellar dynamics, and disproves the measurements with gas dynamics [10].

Recently in 2022, the Event Horizon Telescope Collaboration published the second black hole shadow image, now for Sgr {\mathrm{A}}^{\star }, the supermassive black hole residing at our own Milky Way [8]. The image shares the same April 2017 observing campaign as {\mathrm{M}87}^{\star } with the same set of eight telescopes, but its analysis was extended for another three years. The main difficulty in Sgr {\mathrm{A}}^{\star } shadow image construction is ultimately related to its black hole mass, being M\sim 4\times {10}^6 M_{\odot }, about 1500 times lighter than {\mathrm{M}87}^{\star }. In general relativity, the dynamic timescale is more or less proportional to the black hole mass. Correspondingly, the image pattern for {\mathrm{M}87}^{\star } is supposed to vary on a timescale about 5 days (maximal spin) to 1 month (zero spin), while for Sgr {\mathrm{A}}^{\star } it is to vary from 4 minutes (maximal spin) to half an hour (zero spin) [8]. The black hole shadow image for {\mathrm{M}87}^{\star } is therefore basically static during the observation campaign, while the intra-hour variability of the Sgr {\mathrm{A}}^{\star } image severely calls for novel imaging methods. Nevertheless, proper algorithms were developed within the Event Horizon Telescope Collaboration, and a vast number of quality tests verified the data analysis procedure. The angular diameter of the Sgr {\mathrm{A}}^{\star } shadow is measured to be [8, 11]

(4)\begin{array}{l}d=51.8\pm 2.3\mu \mathrm{a}\mathrm{s}.\end{array}

When this number is supplemented with an independent distance measurement from maser parallaxes D=8.15\pm 0.15 kpc, the mass of Sgr {\mathrm{A}}^{\star } can be determined to be {4.0}_{-1.0}^{+1.1}\times {10}^6{M}_{\odot } [12]. Such a mass measurement is in a close agreement with decade-long optical/infrared monitoring of the stellar orbits of S-stars around Sgr {\mathrm{A}}^{\star }, which move at much larger separations to the black hole [13, 14].

For the case of Sgr {\mathrm{A}}^{\star }, as we already have mass-to-distance ratio measurements from stellar orbital dynamics [13, 14], it is useful to turn the reasoning around and use the black hole shadow image to test the nature of Sgr {\mathrm{A}}^{\star } [15]. The measured shadow size is within \sim 10 \mathrm{\%} of what a Kerr black hole predicts. This fact can be folded to put constraints on the parameterized deviations from a Kerr spacetime, as well as ruling out parameter space for black hole mimickers, such as naked singularities [15, 16]. These kinds of novel approaches exploited some untouched parameter space in testing alternative gravity theories. The combination of {\mathrm{M}87}^{\star } and Sgr {\mathrm{A}}^{\star } data even reinforced the power in using black hole shadows to test strong-field gravity [15].

Black holes are fundamental and elegant predictions from Einstein’s general relativity. The concept goes way beyond what Newtonian gravity can perceive. Now the direct measurements of black hole shadows from two supermassive black holes with mass different by a factor of a thousand not only provided us with clues for black holes’ role in the evolution of galaxies [17], but also probed central concepts of curved spacetimes in the highly curved strong-field regime. These studies are strengthened when the polarimetric information is augmented [18]. In the future, extending the global very long baseline interferometry array to the next-generation Event Horizon Telescope and even possibly including telescopes in space [19] will boost the angular resolution further and provide much sharper black hole shadow images. Making black hole shadow “movies” with many more successive high-quality observations is another interesting research direction to engage dynamic processes and investigate time-varying features. Together with gravitational waves [20, 21], as well as orbits of S-stars [13, 14] and radio pulsars [22–24], imaging of black hole shadows is becoming an essential and powerful tool to study black hole physics and the nature of spacetime.

References

[1] A.Einstein, The Field Equations of Gravitation, Sitzungsber. Preuss. Akad. Wiss. Berlin ( Math. Phys. ) 1915, 844 ( 1915)

[2] K.Schwarzschild, On the gravitational field of a mass point according to Einstein’s theory, Sitzungsber. Preuss. Akad. Wiss. Berlin ( Math. Phys .) 1916, 189 ( 1916), arXiv: physics/9905030

[3] R.P. Kerr. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. , 1963, 11 : 237

[4] S.Chandrasekhar, The Mathematical Theory of Black Holes, Oxford University Press, 1983

[5] J.P. Luminet. Image of a spherical black hole with thin accretion disk. Astron. Astrophys. , 1979, 75 : 228

[6] H.Falcke F.Melia E.Agol, Viewing the shadow of the black hole at the Galactic center, Astrophys. J. Lett . 528, L13 ( 2000), arXiv: astro-ph/9912263

[7] K.Akiyama .(Event Horizon Telescope), ., First M87 Event Horizon Telescope results (I): The shadow of the supermassive black hole, Astrophys. J. Lett . 875, L1 ( 2019), arXiv: 1906.11238 [astro-ph.GA]

[8] K.Akiyama, .(Event Horizon Telescope). . First Sagittarius A* Event Horizon Telescope results (I): The shadow of the supermassive black hole in the center of the Milky Way. Astrophys. J. Lett. , 2022, 930 : L12

[9] S.Doeleman E.Agol D.Backer F.Baganoff G.C. Bower A.Broderick A.Fabian V.Fish C.Gammie P.Ho M. Honman T.Krichbaum A.Loeb D.Marrone M.Reid A.Rogers I.Shapiro P.Strittmatter R.Tilanus J.Weintroub A.Whitney M.Wright L.Ziurys, Imaging an event horizon: Submm-VLBI of a super massive black hole, in: Astro2010: The Astronomy and Astrophysics Decadal Survey, Vol. 2010, p. 68, arXiv: 0906.3899 [astro-ph.CO] (2009)

[10] K.Akiyama .(Event Horizon Telescope), ., First M87 Event Horizon Telescope results (VI): The shadow and mass of the central black hole, Astrophys. J. Lett . 875, L6 ( 2019), arXiv: 1906.11243 [astro-ph.GA]

[11] K.Akiyama, .(Event Horizon Telescope). . First Sagittarius A* Event Horizon Telescope results (III): Imaging of the Galactic center supermassive black hole. Astrophys. J. Lett. , 2022, 930 : L14

[12] K.Akiyama, .(Event Horizon Telescope). . First Sagittarius A* Event Horizon Telescope results (IV): variability, morphology, and black hole mass. Astrophys. J. Lett. , 2022, 930 : L15

[13] T.Do, ., Relativistic redshift of the star S0-2 orbiting the Galactic center supermassive black hole, Science 365, 664 ( 2019), arXiv: 1907.10731 [astro-ph.GA]

[14] R.Abuter .(GRAVITY), ., Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole, Astron. Astrophys . 636, L5 ( 2020), arXiv: 2004.07187 [astro-ph.GA]

[15] K.Akiyama, .(Event Horizon Telescope). . First Sagittarius A* Event Horizon Telescope results (VI): Testing the black hole metric. Astrophys. J. Lett. , 2022, 930 : L17

[16] P.Kocherlakota .(Event Horizon Telescope), ., Constraints on black-hole charges with the 2017 EHT observations of M87*, Phys. Rev. D 103, 104047 ( 2021), arXiv: 2105.09343 [gr-qc]

[17] J.Kormendy L.C. Ho, Coevolution (Or not) of supermassive black holes and host galaxies, Ann. Rev. Astron. Astrophys . 51, 511 ( 2013), arXiv: 1304.7762 [astro-ph.CO]

[18] K.Akiyama . (Event Horizon Telescope), ., First M87 Event Horizon Telescope results (VIII): Magnetic field structure near the Event Horizon, Astrophys. J. Lett . 910, L13 ( 2021), arXiv: 2105.01173 [astro-ph.HE]

[19] C.M. Fromm Y.Mizuno Z.Younsi H.Olivares O.Porth M.De Laurentis H.Falcke M.Kramer L.Rezzolla, Using space-VLBI to probe gravity around Sgr A*, Astron. Astrophys . 649, A116 ( 2021), arXiv: 2101.08618 [astro-ph.HE]

[20] R.Abbott .(LIGO Scientific VIRGO KAGRA), ., GWTC-3: Compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run, arXiv: 2111.03606 [gr-qc] ( 2021)

[21] R.Abbott .(LIGO Scientific VIRGO KAGRA), ., Tests of general relativity with GWTC-3, arXiv: 2112.06861 [gr-qc] ( 2021)

[22] D.Psaltis N.Wex M.Kramer, A quantitative test of the No-hair theorem with Sgr A* using stars, pulsars, and the Event Horizon Telescope, Astrophys. J . 818, 121 ( 2016), arXiv: 1510.00394 [astro-ph.HE]

[23] G.C. Bower S.Chatterjee J.Cordes P.Demorest J.S. Deneva J.Dexter M.Kramer J.Lazio S.Ransom L.Shao N.Wex R.Wharton, Galactic center pulsars with the ngVLA, ASP Conf. Ser . 517, 793 ( 2018), arXiv: 1810.06623 [astro-ph.HE]

[24] G.Bower, S.Chatterjee, J.Cordes, P.Demorest, J.S. Deneva, J.Dexter, R.Eatough, M.Kramer, J.Lazio, K.Liu, S.Ransom, L.Shao, N.Wex, R.Wharton. Fundamental physics with Galactic center pulsars. Bull. Am. Astron. Soc. , 2019, 51 : 438

RIGHTS & PERMISSIONS

Higher Education Press