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 :
Technical References for the 3 posts
Abramowicz, M., Jaroszynski, M., Sikora, M. : Relativistic accreting disks, Astron. Astrophys. 63, 221 (1978).
Balick, B., Brown, R.L. : Intense sub-arcsecond structure in the galactic center, Astrophys. J. 194, 265-270 (1974).
Bardeen, J. M. 1973, Timelike and null geodesics in the Kerr metric, in Black Holes (Les Astres Occlus), ed. C. Dewitt & B. S. Dewitt, New York: Gordon and Breach, pp.215–239.
Bromley, B., Chen, K., Miller,W. : Line Emission from an Accretion Disk around a Rotating Black Hole: Toward a Measurement of Frame Dragging, Astrophys.J. 475, 57 (1997).
Bromley, B., Melia, F., Liu, S. : Polarimetric Imaging of the Massive Black Hole at the Galactic Center, Astrophys.J. 555, L83-86 (2001).
Carter B. : Axisymmetric Black Hole Has Only Two Degrees of Freedom, Physical Review Letters 26, 331 (1971).
Carter B. , Luminet, J.-P. : Les Trous Noirs, Maelströms cosmiques, La Recherche 94, 944 (1978).
Carter B. , Luminet, J.-P. : Pancake Detonation of Stars by Black Holes in Galactic Nuclei, Nature 296, 211 (1982).
Chatzopoulos, S., Fritz, T. K., Gerhard, Gillessen, O., S. , Wegg, C. , Genzel, R. , Pfuhl, O. : The old nuclear star cluster in the Milky Way: dynamics, mass, statistical parallax, and black hole mass, MNRAS, 447, 948 (2015)
Cunningham, C. T. : The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, Astrophys. J., 202, 788 (1975)
Cunningham, C.T., Bardeen J.M. : The optical appearance of a star orbiting an extreme Kerr black hole, Astrophys. J.173 L137-142 (1972).
Cunningham, C.T., Bardeen J.M. : The optical appearance of a star orbiting an extreme Kerr black hole, 1973, Astrophys. J., 183, 237
Davelaar, J., Bronzwaer, T., Kok, D., Younsi, Z., Moscibrodzka, M., Falcke, H.: Observing supermassive black holes in virtual reality, Computational Astrophysics and Cosmology 5,1 (2018). https://doi.org/10.1186/s40668-018-0023-7
Delesalle, L. , Lachièze-Rey, M. , Luminet, J.-P. : Infiniment Courbe, TV documentary, 52 mn, France: CNRS/Arte, 1994.
Doeleman, S.S., et al. : Structure of Sagittarius A* at 86 GHz using VLBI closure quantities, Astron. J., 121, 2610-2617 (2001).
Doeleman, S.S., et al. : Event-horizon-scale structure in the supermassive black hole candidate at the Galactic Centre, Nature, 455, 78 (2008).
Doeleman, S.S., et al. : Imaging an Event Horizon : submm-VLBI of Super massive Black Hole, The Astronomy and Astrophysics Decadal Survey, Science White Papers, no. 68 (2009).
Doeleman, S.S., et al. : Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87, Science 338 (6105), 355 (2012).
Falcke, H. : Imaging black holes : past, present and future, Journal of Physics : Conf. Series 942, 012001 (2017)
Falcke, H., Melia, F., Agol, E. : Viewing the Shadow of the Black Hole at the Galactic Center, Astrophys. J. Lett. 528, L13–L16 (2000).
Fanton C., Calvani M., de Felice F., Cadez A. : Detecting Accretion Disks in Active Galactic Nuclei, Publ. Astron. Soc. Japan 49, 159-169 (1997).
Fukue, J., Yokoyama, T. : Color Photographs of an Accretion Disk around a Black Hole, Publications of the Astronomical Society of Japan 40, 15–24 (1988).
Goddi, C., Falcke, H., et al.: BlackHoleCam: fundamental physics of the galactic center. Int. J. Mod. Phys. D 26, 1730001-239 (2017).
Hamilton, A.: Falling into a black hole. http://jila.colorado.edu/~ajsh/insidebh/intro.html (1998-2018). Accessed 2019-02-26.
Hills, J.G. : Possible power source of Seyfert galaxies and QSOs, Nature 254, 295 (1975).
James, O., von Tunzelmann, E., Franklin, P., Thorne, K.S.: Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar. Class. Quantum Gravity 32(6), 065001 (2015).
Johnson, M. D. , Bouman, K. L., Blackburn, L. L. , Chael, A. A., Rosen, J. , Shiokawa, H. , Roelofs, F. , Akiyama, K. , Fish, V. L. , Doeleman S. S. : Dynamical Imaging with Interferometry, Astrophys. J., 850(2), 172 (2017).
Kerr, R.P. : Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics, Physical Review Letters 11, 237 (1963).
Kormendy, J., Ho, L. : Supermassive Black Holes in Inactive Galaxies, Encyclopedia of Astronomy and Astrophysics, ed. P.Murdin, article id. 2635. Bristol : Institute of Physics Publishing (2001).
Luminet J.-P.: Seeing Black Holes : from the Computer to the Telescope, Universe 4(8), 86 (2018) [arXiv :1804.03909].
Luminet, J.-P. : Black Holes, Cambridge University Press, 1992.
Luminet, J.-P. : Interstellar Science, International Review of Science vol.1 n°2 (march 2015) [arXiv : 1503.08305].
Luminet, J.-P.: Image of a Spherical Black Hole with Thin Accretion Disk, Astron.Astrophys. 75, 228 (1979).
Marck J.-A., Luminet, J.-P. : Plongeon dans un trou noir, Pour la Science Hors-Série Les trous noirs (July 1997) 50–56.
Marck, J.-A. : Colored images of a black hole accretion disk for various angles of view, unpublished (1989).
Marck, J.-A. : Flight into a Black Hole, videocassette 11 mn, Meudon : CNRS Images (1994).
Marck, J.-A. : Short-Cut Method of Solution of Geodesic Equations for Schwarzschild Black Hole, Classical and Quantum Gravity13(3) 393–402 (1996).
Marrone, D. P., Moran, J. M., Zhao, J.-H., Rao, R. : An Unambiguous Detection of Faraday Rotation in Sagittarius A*, Astrophys. J. Lett. 654, L57 (2007).
Nemiroff, R. : Visual distortions near a neutron star and black hole, Am. J. Phys. 61, 619 (1993) [astro-ph/9312003].
Nerval, G. de : Le Christ aux Oliviers, in Les Chimères, Paris, 1854. Free translation by J.-P. Luminet.
Ohanian, H. C. : The Black Hole as a Gravitational ‘Lens’, Am. J. Phys. 55, 428-432 (1987).
Page, D.N., Thorne, K.S. : Disk Accretion onto a Black Hole. I. Time-Averaged Structure of Accretion Disk, Astrophys. J. 191, 499-506 (1974).
Palmer L., Pryce M. & Unruh W. : Simulation of starlight lensed by a camera orbiting a Schwarzschild black hole, unpublished (1978).
Pounds, K. A. et al. : An ultra-fast inflow in the luminous Seyfert PG1211+143, Monthly Notices of the Royal Astronomical Society 481(2), 1832-1838 (2018).
Pringle, J. E., Rees, M. J. : Accretion Disc Models dor Compact X-ray Sources, Astron. Astrophys. 21 , 1 (1972).
Riazuelo, A. : Seeing relativity I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars, (2018) [ArXiv :1511.06025]
Sargent, W. L., Young, P. J., Lynds, C. R., et al. : Dynamical evidence for a central mass concentration in the galaxy M87, Astrophys. J. 221, 731–744 (1978).
Schastok, J. , Soffel, M. , Ruder, H., Schneider, M. : Stellar Sky as Seen From the Vicinity of a Black Hole, Am. J. Phys., 55, 336-341 (1987).
Shaikh, R. : Shadows of rotating wormholes, Phys. Rev. D 98, 024044 (2018) [arXiv :1803.11422]
Shakura, N.I., Sunyaev, R. A. : Black holes in binary systems. Observational appearance. Astro. Astrophys. 24, 337-355 (1973)
Stuckey, W. M. : The Schwarzschild Black Hole as a Gravitational Mirror, Am. J. Phys. 61(5), 448-456 (1993).
Thorne K.: TheScienceofInterstellar, Norton & Company (november 2014).
Thorne, K, private communication, 24/10/2014
Viergutz S U. : Image Generation in Kerr Geometry. I. Analytical Investigations on the Stationary Emitter-Observer Problem, Astron. Astrophys. 272, 355–77 (1993) ; Viergutz, S.U. : Radiation from arbitrarily shaped objects in the vicinity of Kerr Black Holes, Astrophys. Space Sci. 205, 155 (1993).
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 :
Black holes are to many the most mysterious objects in space. According to the laws of General Relativity, they are by themselves invisible. Contrarily to non-collapsed celestial bodies, their surface is neither solid nor gaseous ; it is an immaterial border called the event horizon, beyond which gravity is so strong that nothing can escape, not even light.
Seen in projection on a sky background, the event horizon would have the aspect of a perfectly circular black disk if the black hole is static (the so-called Schwarzschild solution) or of a slightly distorted one if it is in rotation (the Kerr solution). Due to strong gravitational lensing, such a « bare » black hole could leave an observable imprint on a starry background. However, in typical astrophysical conditions, whatever its size and mass (ranging from stellar to galactic scales) a black hole is rarely bare but is dressed in gaseous material. Swirling in a spiral motion, the gas forms a hot accretion disk within which it emits a characteristic spectrum of electromagnetic radiation. Giant black holes, such as those currently lurking at the centers of galaxies, can be also surrounded by a stellar cluster, whose orbital dynamics is strongly influenced. As a matter of fact, , if a black hole remains by itself invisible, it “switches on” in its characteristic way the materials it attracts, and distorts the background starry field by gravitational lensing.
Thus, as soon as the basics of black holes astrophysics developed in the 1970’s, the scientists logically wondered what could look like a black hole. Many of you certainly saw didactic or artistic representations of a black hole in popular science magazines, in the form of a black sphere floating in the middle of a circular whirlwind of brilliant gas. So striking they are, these images fail to report the astrophysical reality. This one can be correctly described by means of numerical simulations, taking into account the complex distortions that the strong gravitational field prints in spacetime and light rays trajectories.
Since the first numerical simulations performed 40 years ago, tantalizing progress has been done to detect black holes through electromagnetic radiation from infalling matter or gravitational waves. The first telescopic image by the Event Horizon Telescope of the nearest giant black hole SgrA*, lurking at he center of our Milky Way galaxy, is expected for 2018.
The aim of this series of posts is to retrace the rich history of black hole imaging.
Preliminary steps
Black hole imaging started in 1972 at a Summer school in Les Houches (France). James Bardeen, building on earlier analytical work of Brandon Carter, initiated research on gravitational lensing by spinning black holes. Bardeen gave a thorough analysis of null geodesics (light-ray propagation) around a Kerr black hole. The Kerr solution had been discovered in 1962 by the New Zealand physicist Roy Kerr and since then focused the attention of many searchers in General Relativity, because it represents the most general state of equilibitum of an astrophysical black hole.
The Kerr spacetime’s metric depends on two parameters : the black hole mass M and its normalized angular momentum a. An important difference with usual stars, which are in differential rotation, is that Kerr black holes are rotating with perfect rigidity : all the points on their event horizon move with the same angular velocity. There is however a critical angular momentum, given by a = M (in units where G=c=1) above which the event horizon would « break up » : this limit corresponds to the horizon having a spin velocity equal to the speed of light. For such a black hole, called « extreme », the gravitational field at the event horizon would cancel, because the inward pull of gravity would be compensated by huge repulsive centrifugal forces.
James Bardeen computed how the black hole’s rotation would affect the shape of the shadow that the event horizon casts on light from a background star field. For a black hole spinning close to the maximum angular momentum, the result is a D-shaped shadow.
Apparent shape of an extreme Kerr black hole as seen by a distant observer in the equatorial plane, if the black hole is in front of a source of illumination with an angular size larger than that of the black hole. The shadow bulges out on the side of the hole moving away from the observer (at right) and squeezes inward and flattens on the side moving toward the observer (at left).
The reference is Bardeen, J. M. 1973, Timelike and null geodesics in the Kerr metric, in Black Holes (Les Astres Occlus), ed. C. Dewitt & B. S. Dewitt, (New York: Gordon and Breach) p.215–239
At the time, C.T. Cunningham was preparing a PhD thesis at the University of Washington in Seattle, under the supervision of Bardeen. He began to calculate the optical appearance of a star in circular orbit in the equatorial plane of an extreme Kerr black hole, taking account of the Doppler effect due to relativistic motion of the star, and pointed out the corresponding amplification of the star’s luminosity. He gave formulas but did not produced any image.
The reference is Cunningham, C.T. and Bardeen J.M., The optical appearance of a star orbiting an extreme Kerr black hole, ApJ 173 L137-142 (1972).
One year later Cunningham and Bardeen published a more complete article with the same title. For the first time a picture was shown of the primary and secundary images of a point source moving in a circular orbit in the equatorial plane of an extreme Kerr black hole. They calculated as functions of time the apparent position and the energy flux of the point source as seen by distant observers.
Apparent positions of the two brightest images as functions of time for two orbital radii and an observer art a polar angle 84°.024. The small, dashed circle in each plot gives the scale of the plot in units of M. The direct image moves along the solid line, the secundary image along the dashed line. Ticks mark the positions of the images at 10 equally spaced times.
In the upper diagram showing the distorted image of a circle of radius 20M, we clearly see that, whatever the observer’s inclination angle, the black hole cannot mask any part of the circle behind. We also see that the black hole’s spin hardly affects the symmetry of the primary image (although the asymmetry is stronger for the secundary image).
The exact reference is Cunningham, C.T. and Bardeen J.M., The optical appearance of a star orbiting an extreme Kerr black hole, 1973, ApJ, 183, 237. The article can be uploaded here.
In 1975, Cunningham calculated the effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole. He gave formulas and drawed graphics but no image.
The reference is Cunningham, C. T., The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, ApJ, 202, 788 (1975)
In 1978 Leigh Palmer, Maurice Pryce and William Unruh carried out, for pedagogical purpose, a simulation of starlight lensed by a camera orbiting a Schwarzschild black hole, using an Edwards and Sutherland Vector graphics display at Simon Fraser University. They showed a film clip in a number of lectures in that period, but unfortunately they did not publish their simulation, so that I can’t reproduce here any image.
First calculations for a black hole accretion disk
The same year and quite independently, as a young researcher at Paris-Meudon Observatory specialized in the mathematics of General Relativity, I wondered what could be the aspect of a Schwarzschild black hole surrounded by a luminous accretion disk. Continue reading →
In november 2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and much mediatic excitation arose about it.
This is the fifth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.
TIME TRAVEL INSIDE GARGANTUA
In the last part of the film, the main character, Cooper, plunges into Gargantua. There, beware the tidal forces breaking anything up ! Indeed in the Schwarzschild geometry, the tidal forces become infinite as r -> 0 ; so, even for a supermassive black hole like Gargantua, once past safely the event horizon and approaching the central singularity, everything will be ultimately destroyed. Happily for the continuation of the story, Gargantua has a high spin, and its lethal singularity has the shape of an avoidable ring. Thus the space-time structure allows Cooper to use the Kerr black hole as a wormhole ; he avoids the ring singularity and transports to another region of space-time. In the movie he ends up in a five-dimensional universe, in which he will be able to go backwards in time and communicate with his daughter by means of gravitational signals.
Inner structure of a rotating black hole with a ring singularity
A lot of research has been done on whether the laws of physics permit travel back in time or not. Black hole physics gives interesting results but no firm answers. As seen in the post The Warped Science of Interstellar (1/6), according to Penrose-Carter diagrams a rotating black hole could connect myriads of wormholes to different parts of the space-time geometry. Since two events can differ in time as well as in space, it would be possible to pass from one given position at a given time, along a carefully chosen trajectory, through a wormhole, and arrive at the same position but at a different time, in the past or future. In other words, the black hole could be a sort of time travel machine.
Noneless a journey back through time is an affront to common sense. It is difficult to accept that a man could travel back through time and kill his grandfather before he has had the time to produce children. For the murderer could not have been born, and could not have murdered him, and so on… Such time paradoxes have been pleasantly presented in the celebrated series of movies Back to the future.
In november 2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and much mediatic excitation arose about it.
This is the fourth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.
A HUGE TIME DILATION
The elasticity of time is a major consequence of relativity theory, according to which time runs differently for two observers with a relative acceleration – or, from the Equivalence Principle, moving in gravitational fields of different intensities. This well-known phenomenon, checked experimentally to high accuracy, is called « time dilation ».
The celebrated “smooth watches” by Salvador Dali are a nice metaphor of time elasticity predicted by Einstein’s relativity theory.
Thus, close to the event horizon of a black hole, where the gravitational field is huge, time dilation is also huge, because the clocks will be strongly slowed down compared to farther clocks. This is one of the most stunning elements of the scenario of Interstellar : on the water planet so close to Gargantua, it is claimed that 1 hour in the planet’s reference frame corresponds to 7 years in an observer’s reference frame far from the black hole (for instance on Earth). This corresponds to a time dilation factor of 60,000. Although the time dilation tends to infinity when a clock tends to the event horizon (this is precisely why no signal can leave it to reach any external observer), at first sight a time dilation as large as 60,000 seems impossible for a planet orbiting the black hole on a stable orbit.
As explained by Thorne in his popular book, such a large time dilation was a « non-negotiable » request of the film director, for the needs of the story. Intuitively, even an expert in general relativity would estimate impossible to reconcile an enormous time differential with a planet skimming up the event horizon and safely enduring the correspondingly enormous gravitational forces. However Thorne did a few hours of calculations and came to the conclusion that in fact it was marginally possible (although very unlikely). The key point is the black hole’s spin. A rotating black hole, described by the Kerr metric, behaves rather differently from a static one, described by the Schwarzschild metric. The time dilation equation derived from the Kerr metric takes the form:
In november 2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and much mediatic excitation arose about it.
This is the third of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.
VISUALISATION OF THE ACCRETION DISK
Since a black hole causes extreme deformations of spacetime, it also creates the strongest possible deflections of light rays passing in its vicinity, and gives rise to spectacular optical illusions, called gravitational lensing. Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by an observer nearby.
For this, the team at Double Negative Visual Effects, in collaboration with Kip Thorne, developed a numerical code to solve the equations of light-ray propagation in the curved spacetime of a Kerr black hole. It allows to describe gravitational lensing of distant stars as viewed by a camera near the event horizon, as well as the images of a gazeous acccretion disk orbiting around the black hole. For the gravitational lensing of background stars, the best simulations ever done are due to Alain Riazuelo[i], at the Institut d’Astrophysique in Paris, who calculated the silhouette of black holes that spin very fast, like Gargantua, in front of a celestial background comprising several thousands of stars.
But perhaps the most striking image of the film Interstellar is the one showing a glowing accretion disk which spreads above, below and in front of Gargantua. Accretion disks have been detected in some double-star systems that emit X-ray radiation (with black holes of a few solar masses) and in the centers of numerous galaxies (with black holes whose mass adds up to between one million and several billion solar masses). Due to the lack of spatial resolution (black holes are very far away), no detailed image has yet been taken of an accretion disk ; but the hope of imaging accretion disks around black holes telescopically, using very long baseline interferometry, is nearing reality today via the Event Horizon Telescope[ii]. In the meanwhile, we can use the computer to reconstruct how a black hole surrounded by a disk of gas would look. The images must experience extraordinary optical deformations, due to the deflection of light rays produced by the strong curvature of the space-time in the vicinity of the black hole. General relativity allows the calculation of such an effect. Continue reading →
One year ago, in november 2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and much mediatic excitation arose about it.
This is the second of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.
THE FAST-SPINNING BLACK HOLE « GARGANTUA »
Once on the other side of the wormhole, the spaceship and its crew emerge into a three-planets system orbiting around a supermassive black hole called Gargantua. Supermassive black holes, with masses going from one million to several billion solar masses, are suspected to lie in the centers of most of the galaxies. Our Milky Way probably harbors such an object, Sagittarius A*, whose mass is (indirectly) measured as 4 million solar masses (for a review, see Melia[i]). According to Thorne, Gargantua would be rather similar to the still more massive black hole suspected to be located at the center of the Andromeda galaxy, adding up 100 million solar masses[ii]. Its size being roughly proportional to its mass, the radius of such a giant would encompass the Earth’s orbit around the Sun.
A view of the Galactic Center in X-rays
The analysis of trajectories of stars orbiting around the Galactic Center leads to estimate the mass of the central black hole at about 4 millions solar masses.
The Andromeda Galaxy (M31), located at 2.2 million light-years
Detailed image of the core of Andromeda Galaxy by the Hubble Space Telescope. The central black hole would have 100 million solar masses.
Such enormous black holes are not a science-fiction exaggeration, since we have the observational clues of the existence of « Behemoth » black holes in faraway galaxies. The biggest one yet detected lies in the galaxy NGC 1277, located at 250 million light-years ; its mass could be as large as 17 billion solar masses, and its size would encompass the orbit of Neptune[iii]. Continue reading →
One year ago exactly, in november 2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and much mediatic excitation arose about it.
This is the first of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.
Interstellar tells the adventures of a group of explorers who use a wormhole to cross intergalactic distances and find potentially habitable exoplanets to colonize. Interstellar is a fiction, obeying its own rules of artistic license : the film director Christopher Nolan and the screenwriter, his brother Jonah, did not intended to put on the screens a documentary on astrophysics – they rather wanted to produce a blockbuster, and they succeeded pretty well on this point. However, for the scientific part, they have collaborated with the physicist Kip Thorne, a world-known specialist in general relativity and black hole theory. With such an advisor, the promotion of the movie insisted a lot on the scientific realism of the story, in particular on black hole images calculated by Kip Thorne and the team of visual effects company Double Negative. The movie also refers to many aspects of contemporary science, going from well-studied issues such as warped space, fast-spinning black holes, accretion disks, tidal effects or time dilation, to much more speculative ideas which stem beyond the frontiers of our present knowledge, such as wormholes, time travel to the past, extra-space dimensions or the « ultimate equation » of an expected « Theory of Everything ».
It is the reason why, beyond the subjective appreciations that everyone may have about the fiction story itself, many people – physicists and science journalists – have taken the internet to write articles lauding or criticizing the science shown in the movie. Kip Thorne has written a popular book, The Science of Interstellar[i], to explain how he tried to respect scientific accuracy, despite the sometimes exotic demands of Christopher and Jonah Nolan, ensuring in particular that the depictions of black holes and relativistic effects were as accurate as possible.
The aim of this article is not to write a (inevitably subjective) review of Interstellar as a fiction story, but to decipher some of the scientific notions, which support the framework of the movie.
AN ARTIFICIAL WORMHOLE IN THE SOLAR SYTEM ?
In the first part of the film, we are told that a « gravitational anomaly », called a wormhole, has been discovered out near Saturn several decades ago, that a dozen habitable planets have been detected on the « other side » and a dozen astronauts sent to explore them. In particular, one system has three potentially habitable planets, and it is now the mission of the hero, Cooper, to pilot a spaceship through the wormhole and find which planet is more suitable for providing humanity a new home off the dying Earth. Continue reading →
Until now I published as an author 30 books in my native language (French), including 14 science essays, 7 historical novels and 9 poetry collections (for the interested reader, visit my French blog here.
Although my various books have been translated in 14 languages (including Chinese, Korean, Bengali…), only 4 of my essays have been translated in English.
The first one was :
Black Holes
312 pages – Cambridge University Press, 1992 – ISBN 0 521 40029 5 (hardback) – ISBN 0 521 40906 3 (paperback) – Foreword by Joseph Silk.
Black holes are the most fascinating discovery of modern astronomy. They have already become legendary, and form the basis of many myths and fantasies. Are they really the monsters of science fiction which devour light and stars? Are they purely hypothetical objects from the theory of relativity or are they an observable reality?
In answering these questions, the author takes us on a fabulous voyage through space and time. He explains how stars are born, light up and die. He takes us into the strange world of supernovae, X-ray stars and quasars. We travel on a journey to the very edge of the universe and to the limits on contemporary physics.
“The amount of information conveyed is impressive. The intended audience is readers with some understanding of physics who are seeking a coherent, accurate nonmathematical overview of black-hole physics and all the astronomical situations that the discipline seems to explain. Also, any student embarking on a serious technical study of general relativity or astrophysics will find the book a first-rate overview of an important part of the story. (…) This is an outstanding work of scientific exposition.” — John Barrow, Nature Continue reading →
The thought experiments which have been described in my previous post Back to the basics are more than an intellectual exercise, because if black holes really exist (and we have strong observational arguments to believe that), then there is a good chance that they will be illuminated by a natural light source. For a black hole or a planet the most obvious form of lighting is a star. This star could, for example, be bound to the black hole in a binary system. Although such systems are common throughout our Galaxy, the corresponding black holes would be impossible to detect by this effect, as their image by reflected light would be drowned in the intense light of the direct image of the star itself.
A much more interesting situation from an observational point of view is when the source of light comes from a series of rings of matter in orbit around the black hole. It is believed that a number of black holes are surrounded by such structures, which are called accretion disks. Saturn’s rings are an excellent example of an accretion disk; they consist of amalgamated pieces of rock and ice which reflect the light of the distant Sun, whereas those of a black hole consist of hot gas brighting by itself (another important difference is that the accretion disk of a black hole is continually being supplied with gas, whereas that surrounding Saturn is the remnant of the primordial Solar System).
Planet Saturn and its rings. One can assume that a black hole accretion disk, although made of hot gas instead of rocks and ice, has a similar shape, namely circular thin rings.
The gases fall slowly into the black hole, like water in a whirlpool. As the gas falls towards the black hole it becomes hotter and hotter and begins to emit radiation. This is a good source of light: the accretion rings shine and illuminate the central black hole. One can then ask : what would be the apparent image of the black hole accretion disk ? Continue reading →
The centre of the black hearth,
of setting suns on the shore :
ah ! well of magic Arthur Rimbaud (Illuminations)
As probably all of you already know, the Interstellar movie tells the adventures of a group of explorers who use a wormhole to cross intergalactic distances and find potentially habitable exoplanets to colonize. For the scientific part, the film director, Christopher Nolan, has collaborated with a colleague of mine, the famous physicist Kip Thorne, a specialist in general relativity and black hole theory.
With such a scientific consultant, the promotion of the movie insisted a lot on the realism of the black hole images calculated by Kip Thorne and the team of visual effects company Double Negative. The most striking one shows a glowing accretion disk appearing above, below and in front of the black hole.
The simulation of a black hole with thin accretion disk as shown in the Interstellar movie
As soon as the movie was displayed on the screens, a lot of physics blogs have commented in details the “Science of Interstellar”. Kip Thorne himself has published a such entitled popular book, to explain how he tried to respect scientific accuracy despite the sometimes odd demands of Christopher Nolan, ensuring in particular that the depictions of black holes and relativistic effects were as accurate as possible.
Since, as soon as 1979, I was the first researcher to perfom numerical calculations and publish the simulated image of a black hole surrounded by a thin accretion disk (you can upload the technical article here), to inaugurate this new blog I’ll devote a series of 3 posts to the basics of black hole imaging. A good part is adapted from a chapter of one of my books, published in French in 2006, Le destin de l’univers – unfortunately not yet available in English. Continue reading →
Luminet’s reinstated visualization of a finite Universe, albeit one from which we can exit through one face and simultaneously enter through the opposite one, relies upon a keplerian form of mental sculpture that may be described as plastic rather than algebraic. Luminet’s characteristic lithograph, Big Bang, exploits the spatial vocabulary of perspective to evoke realms beyond the three dimensional. Whereas Escher relied on contradictions and oscillating ambiguity in his graphic art, Luminet suggests plunging, interpenetrating and matter organizes itself into structures on the right; the tumbling dice on the left imply irreversible disorganization arising from chance. The remarkable range of Luminet’s creativity in art and science is integral to his agenda to recreate what he calls a « humanism of knowledge » — not that the arts and sciences are somehow to be conflated, because they work in very different ways, with illogical and logical means. But Luminet argues that they well up from the same instincts and intuitions: « I do not believe that we acquire at the beginning the ‘heart of an artist’ or the ‘heart of a scientist’. There is simply within oneself a single devouring curiosity about the world. This curiosity pushes us to explore it through various languages and modes of expression, » he says.
Martin Kemp, professor of the history of art at the University of Oxford. Excerpt from “Luminet’s Illuminations : Cosmological Modelling and the Art of Intuition”, Nature, 20 november 2003, vol. 426, p. 232
The black hole, Ink (1978)
Big Bang, lithography (1992)
Chronos, lithography (1993)
Voyage à Reims, Ink (1979)
Two Worlds, Ink (1991)
The Observatory (Hommage à Escher), lithography (1993)
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)
