After five years of calculations and analysis, the international collaboration of the Event Horizon Telescope (EHT) delivered on May 12, 2022 the image of Sagittarius A* (Sgr A*), the giant black hole lurking at the center of our galaxy (the Milky Way), 27 000 light-years from Earth. Until now, its presence was only indirectly perceived, from a few radio emissions and the observation of the trajectories of stars orbiting at high speed around a gigantic but invisible mass. After the one obtained by the EHT in 2019 of the gigantic black hole M87* at the heart of the distant elliptical galaxy M87, this is the second direct image of this type of object that we have to date.
Remember. The very first telescopic image of a black hole surrounded by a disk of hot gas had been unveiled in April 2019 by the same EHT teams: it was the black hole M87* located at the center of the giant elliptical galaxy M87, 50 million light-years away. The observations of Sgr A* had been made in April 2017, during the same campaign as those of M87*. If it took five years of analysis for Sgr A* against two for M87*, it is because during the exposure time of the observations – of the order of an hour –, the light emission of the gas disk around Sgr A* is very variable, whereas that around M87* is almost fixed. The reason is that Sgr A* has a mass 1500 times smaller than M87* (4 million solar masses for SgrA* against 6 billion for M87*), so that the characteristic time scale of the luminous variability, given by the simple formula GM/c^3, is much faster: 20 seconds, against several hours for M87*.
Figure 2. The montage illustrates the huge size difference between M87* and SgrA*, relative to the size of our solar system.Figure 3: Due to its giant size, the light structure around M87* varied very little during the 4 days of observations in April 2017.
Attempting to capture a sharp image of SgrA* in an exposure time of one hour was therefore like taking a picture of a dog running after its tail. It took considerable integration work to reconstruct a sufficiently sharp “average” image of SgrA*, as Figure 4 clearly shows.
Figures 4a-b. On the left, several tens of shots of SgrA* show its large temporal variability, to the point that the reconstruction of an averaged image cannot accurately reproduce the state of the accretion stream (uncertain position of the overbrightness). On the right on the other hand, for M87*, due to its giant size, the light structure around it has varied very little during the 4 days of observations performed in April 2017, so that the averaged image reflects the actual state of the accretion stream quite accurately.
To achieve the angular resolution needed to image SgrA* and M87*, equivalent to the tiny angle at which we would see an apple on the Moon from Earth, the EHT used a network of radiotelescopes stretching from Antarctica to North America via Chile, the Hawaiian Islands, and Europe so as to have the equivalent of a single planet-sized instrument operating in interferometric mode.
Figure 5. The eight radio telescopes of the EHT array in use in April 2017.
What is striking at first sight is that the two photographs of M87* and SgrA* look very similar: in the center, a black shadow, image of the event horizon (name given, I recall, to the intangible surface of a black hole) enlarged by a factor of 2.6 (as I had shown in my 1979 paper, cf. fig. 6), surrounded by a yellow-orange luminous corona (in false colors), blurred and with spots of highlighting.
Figure 6. Diagrams from my 1979 paper and my popularization book “Le destin de l”univers” (2006), illustrating how the “shadow” of a black hole is the magnified image of its event horizon by a factor of 2.6, due to a gravitational lensing effect. A very thin ring of light, called the photon ring, encircles it.Figure 7. The two similar telescopic images of M87* and SgrA*.
The most important difference is the appearance of three distinct spotlights in the bright ring of SgrA*, whereas the ring of M87 is continuous with two contiguous highlights. Similarly, the central shadow appears less round for SgrA*, probably due to the large number of images that had to be integrated during the hours of observation.
A catalog of several thousands of numerical simulations has been established for comparison with the EHT images and to fix probable ranges of values for the physical characteristics (viewing angle, spin, etc., see below) of SgrA*. Hot ionized gas is rapidly rotating around the black hole, forming spiral arms that become brighter at their tangency with the photon ring, where the light is amplified by strong gravitational lensing. It is these bright points that are integrated in the course of time, and that give the general structure of the luminous rings.
Figure 8. Thousands of numerical simulations by the EHT teams were required to reconstruct a clear image of SgrA*.
Accretion disk or photon ring?
What exactly do these two historical pictures reveal?
Figure 9. First numerical simulation of a black hole surrounded by an accretion disk, published in January 1979, with captions added. The shadow of the black hole is in the center. The “top image” is the direct (so-called) primary image of the accretion disk, distorted however by the gravity field. The ISCO (Inner Stable Circular Orbit) is the last stable orbit marking the inner edge of the accretion disk. The luminous ring surrounding the shadow is the superposition of the secondary, tertiary, etc. images of the accretion disk forming the the photon ring. The Doppler effect due to the motion of the gas at relativistic speed explains the strong asymmetry of the apparent luminous flux seen at great distance. The calculated luminous flux is however “bolometric”, i.e. integrated on all the wavelengths of the electromagnetic radiation.Figure 10. Numerical simulations made with Jean-Alain Marck in 1989, using my 1979 calculations but adding false colors and variable viewing angles (starting from 0° for an equatorial view to 90° for a polar one), thanks to the progress of computers at the time.
to point out the striking similarities:
Figure 11. Striking similarities at first glance between the telescopic images (top) and the numerical simulations (bottom)
and to draw quick conclusions about the structure of the accretion disk and the angle from which it is seen from the Earth:
Figure 12. A tempting interpretation at first sight…
I confess that I myself got carried away by this interpretation, which on the one hand flattered my pioneering calculations, on the other hand was in no way denied by the EHT researchers, who on the contrary rolled out a red carpet for me at the first conference held on the subject at Harvard University in June 2019.
Figure 13. My dinner talk at the Black Hole Initiative Conference held at Harvard University on May 20-22, 2019 after the release of the first telescopic image of M87*.
So much so that, as much for the image of M87* as for the more recent one of SgrA*, this interpretation has been taken up in most of the popular science media. Especially since the specialized articles published by the EHT researchers, full of technical details, remain strangely vague on the question…
However, the physical reality is always more complex than our first reading grids. A finer analysis, made since 2019 on M87* and reinforced in 2022 by that of SgrA*, suggests that the luminous “donut” shaped corona is not the direct image of the gaseous accretion disks orbiting their respective black holes, and that the spotlights do not completely reflect the real state of the gas around the black hole, nor do they translate the Doppler effect due to the relativistic rotation of the gas! Continue reading →
Unfortunately Marck’s simulations of black hole accretion disks remained mostly ignored from the professional community, due to the fact that they were not published in peer-reviewed journals and, after their author prematurely died in May 2000, nobody could find the trace of his computer program…
Then, unaware of Marck’s results, several researchers of the 1990’s were involved in the program of calculating black hole gravitational lensing effects in various situations. Stuckey (1993) studied photon trajectories which circle a static black hole one or two times and terminate at their emission points (« boomerang photons »), producing a sequence of ring-shaped mirror images. Nemiroff (1993) described the visual distortion effects to an observer traveling around and descending to the surface of a neutron star and a black hole, discussing multiple imaging, red- and blue-shifting, the photon sphere and multiple Einstein rings. He displayed computer-generated illustrations highlighting the distortion effects on a background stellar field but no accretion disk, and made a short movie now available on the internet (Nemiroff 2018), two snapshots of which are shown in figure 1.
Figure 1. Trip to a black hole by Robert Nemiroff, 1993.
The first simulations of the shape of accretion disks around Kerr black holes were performed by Viergutz (1993). He treated slightly thick disks and produced colored contours, including the disk’s secondary image which wraps under the black hole (figure 2). The result is a colored generalization of the picture by Cunningham and Bardeen (1973) shown in 40 Years of Black Hole Imaging (1).
Figure 2. Primary and secondary images of a simple accretion disk model around a Kerr black hole, seen by a faraway observer. Colors indicate combined gravitational and Doppler shifts (from Viergutz 1993).
More elaborate views of a geometrically thin and optically thick accretion disk around a Kerr black hole were obtained by Fanton et al. (1997). They developed a new program of ray tracing in Kerr metric, and added false colors to encode the degree of spectral shift and temperature maps (figure 3). Zhang et al. (2002) used the same code to produce black-and-white images of standard thin accretion disks around black holes with different spins, viewing angles and energy bands (figure 4).
Figure 3. False color contour maps showing how the monochromatic radiation emitted by a Keplerian accretion disk would be seen at infinity for various values of the inclination angle to the plane of the disk (top to bottom : 5°, 45°, 85°). The left column refers to a non-rotating black hole, the right one to a rapidly rotating black hole with a=0.998 M. The white zones stand for the regions with zero redshift. Left-hand side of the disk is approaching the observer and blueshifted (from Fanton et al. 1997).
Figure 4. Disk images of accretion disks extending up to 20 Schwarzschild radii for different spins of Kerr black holes, viewed in different energy ranges and inclination angles (from Zhang et al. 2002).
Ben Bromley et al. (1997) calculated integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, in order to get an observational signature of the frame-dragging effect (Figure 5).
Figure 5. Image of a geometrically thin disk around an extreme Kerr (maximally rotating) black hole seen at an inclination of 75°. The inner and outer radii of the Keplerian (circularly rotating) disk are at 1.24 M and 6 M. The colors encode the apparent light frequency, the white strip divides redshifted and blueshifted regions. The asymmetric appearance of the inner disk edge results from the frame-dragging effect of black hole rotation (from Bromley et al. 1997).
In 1998 Andrew Hamilton started to develop for a student project at the University of Colorado a “Black Hole Flight Simulator”, with film clips that have been shown at planetariums, also available on the Internet. The first depictions were very schematic, but the website was constantly implemented. It now offers journeys into a Schwarzschild or a Reissner-Nordström (i.e. electrically charged) black hole with effects of gravitational lensing on a stellar background field, as well as animated visualizations of magneto-hydrodynamic simulations of a disk and jet around a non-rotating black hole (Hamilton 2018).
Journey into and through an electrically charged (non realistic) Reissner-Nordström black hole, from Andrew Hamilton, 2010
From Idea to Reality
A turning point in the history of black hole imaging came when the possibility of viewing in practice the shadow of SgrA* with VLBI radio astronomy techniques was first discussed (Falcke et al. 2000, Doeleman et al. 2001). Heino Falcke, Fulvio Melia and Eric Agol (who curiously did not quote my 1979 article) developed a general relativistic ray-tracing code that allowed them to simulate observed images of Sgr A* for various combinations of black hole spin, inclination angle, and morphology of the emission region directly surrounding the black hole (figure 6).
Figure 6. Images of an optically thin emission region surrounding the galactic black hole SgrA*. The black hole is maximally rotating (a = 0.998) in the top row and non-rotating in the bottom row. The emitting gas is assumed to be in free fall (top) or on Keplerian shells (bottom) with a viewing angle 45°. The left column shows the ray-tracing calculations in general relativity, the other columns are the images seen by an idealized VLBI array at 0.6 mm and 1.3 mm wavelengths, taking account of the interstellar scattering (from Falcke et al. 2000).
In 2001, Ben Bromley, Fulvio Melia and Siming Liu provided maps of the polarized emission of a Keplerian disk to illustrate how the images of polarized intensity from the vicinity of SgrA* would appear in future VLBI observations (Figure 7).
Figure 7. Polarization maps at three wavelengths (1.5 mm, 1 mm, 0.67 mm from top row to bottom row) calculated for the galactic black hole candidate SgrA*. The left most column shows how the radio maps might look seen from a close observer, the other columns show how the map might look from Earth with our vision blurred by gas in interstellar space (from Bromley et al. 2001)
Indeed, in parallel with but rather independently from the theoretical simulations reviewed here, the work to image SgrA* by VLBI experiments had begun also back in the 1970’s, after the discovery of the compact radio source Sgr A* at the center of the Milky Way and its identification as the likely emission of gas falling onto a supermassive black hole (Balick and Brown 1974). And as soon as it was realized that the shadow of SgrA* could really be photographed in the forthcoming years, the program of imaging black holes with or without accretion disks and/or stellar background field developed at a much accelerated rate. Several dozens of papers with more or less elaborate visualizations bloomed out, so many that I’ll stop my illustrated history of black hole imaging at this turning point.
As already suspected a long time ago, the gravitational dynamics of stars orbiting the Galactic Center SgrA, as observed for more than 20 years, give a good estimate for the centeal black hole mass : 4.4 millions solar masses. Credit : Keck Observatory.
On the observational side, successive radio imaging observations progressively reduced the size of emission region if SgrA*. A breakthrough was to extend VLBI to 1mm wavelength, where the scattering effects are greatly reduced and angular resolution is matched to the shadow of the galactic black hole. Then the collective effort was named the “Event Horizon Telescope” as the natural convergence of many historical and parallel works done by several independent teams in the world (Doeleman et al. 2009). The later measurement of the size of the 6 billion solar mass black hole in M87 gave a second source suitable for shadow imaging (Doeleman et al. 2012).
Optical image of the giant elliptical galaxy M87 taken by the Hubble Space Telescope. Its core emits an enormous jet of relativistic plasma. At its very center, M87 harbours the second-largest black hole as seen from Earth, M87*, with a mass of 6.6 billion Suns but over 2000 times farther away than Sagittarius A*.
Now the Event Horizon Telescope Consortium involves 20 universities, observatories, research institutions, government agencies and more than a hundred scientists who hope to make black hole imaging a reality as soon as 2019. The first telescopic image of M87* was delivered on April 10th, 2019.
Sheperd Doeleman, director of the Event Hoziron Telescope, at the press conference of April 10th 2019 in which the first telescopic image of black hole M87* was shown.
The path from idea to reality can take very a long time. Imaging black holes, first with computers, now with telescopes, is a fantastic adventure. Forty years ago I couldn’t hope that a real image would be reachable in my lifetime and that, thanks to contributions by so many dedicated colleagues, my dream would become true.
In May 2019 I was invited to give the keynote talk at the 3rd Black Hole Initiative Conference at Harvard University and I could warmly congratulate the EHT team. The young commputer scientist Katie Bouman led the development of one of the various algorithms for imaging black holes. We were glad to meet each other, the young and the old !
With Katie Bouman on 21 May 2019 at the Black Hole Initiative Conference, Harvard University
Here is the video of my talk :
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In 1989-1990, while I spent one year as a research visitor at the University of California, Berkeley, my former collaborator at Paris-Meudon Observatory, Jean-Alain Marck, both an expert in general relativity and computer programming, started to extend my simulation of 1979. The fast improvement of computers and visualization software (he used a DEC-VAX 8600 machine) allowed him to add colors and motions. To reduce the computing time, Marck developed a new method for calculating the geodesics in Schwarzschild space-time, published only several years later (Marck 1996). In a first step Marck started from my model of 1979 and calculated static images of an accretion disk around a Schwarzschild black hole according to various angles of view, see Figure 1 below.
Figure 1. False-Coloured images of a black hole accretion disk for various angles of view by J.-A. Marck & J.-P. Luminet , 1989 (unpublished).
In 1991, when I went back to Paris Observatory, I started the project for the French-German TV channel Arte of a full-length, pedagogical movie about general relativity (Delesalle et al. 1994). As the final sequence dealt with black holes, I asked Marck to introduce motion of the observer with the camera moving around close to the disk, as well as to include higher-order lensed images and background stellar skies in order to make the pictures as realistic as possible. The calculation was done along an elliptic trajectory around a Schwarzschild black hole crossing several times the plane of a thin accretion disk and suffering a strong relativistic precession effect (i.e. rotation of its great axis), see figure 2 below.
Compared to my static, black-and-white simulation of 1979, the snapshot reproduced in Figure 3 below shows spectacular improvements:
Figure 3. Colored image of a black hole accretion disk as seen by a moving observer at 7° above the disk’s plane. The observer uses a camera equipped with filters to convert into optical radiation the emitted electromagnetic radiation. The arbitrary coloring encodes the apparent luminosity of the disk, the brightest and warmest parts being colored yellow, the colder parts red. The transparency of the disk was enhanced in order to show the secondary image through the primary, as well as some background stars. Compared with figure 8 there are additional distortions and asymmetries due to the Doppler effect induced by the motion of the observer himself. As a result the region of maximum luminosity has no more the shape of a crescent (from Marck 1991)
The full movie is available on my youtube channel :
I felt dizzy and wept, for my eyes had seen that secret and conjectured object whose name is common to all men but which no man has looked upon — the unimaginable universe. Jorge luis Borges, The Aleph (1949)
