Tag Archives: Accretion disk

40 Years of Black Hole Imaging (3): from Kerr black holes to EHT

Sequel of the previous post 40 Years of Black Hole Imaging (2) : Colors and Movies 1989-1993

Generalizations to Kerr Black Holes

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).

Doeleman, S.S. : Seeing the unseeable, Nature Astronomy 1, 646 (2017)

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. : Color animation of a black hole with accretion disk, https://www.youtube.com/watch?v=5Oqop50ltrM (1991) (put online in 2011 by J.-P. Luminet).

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 Gravity 13(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].

Nemiroff, R. Trip to a Black Hole https://www.youtube.com/watch?v=ehoOkyHtBXw (2018)

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]

Rogers, A. : The Warped Astrophysics of Interstellar, https://www.wired.com/2014/10/astrophysics-interstellar-black-hole/.

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.: The Science of Interstellar, 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).

 

40 Years of Black Hole Imaging (2): Colors and movies, 1989-1993

Sequel of the previous post 40 Years of Black Hole Imaging (1) : Early Work 1972-1988

First Flight into a Black Hole

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 :

Continue reading

40 Years of Black Hole Imaging (1): Early work 1972-1988

Introduction

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

The Warped Science of Interstellar (3/6) : Accretion Disk and Tidal Stress

Sequel of the preceding post The Warped Science of Interstellar (2/6)

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.

BH_LMC_APOD-BR
Gravitational lensing produced by a black hole in a direction almost centered on the Large Magellanic Cloud. Above it one easily notices the southernmost part of the Milky Way with, from left to right, Alpha and Beta Centauri, the Southern Cross. The brightest star, close to the LMC is Canopus (seen twice). The second brightest star is Achernar, also seen twice. © Alain Riazuelo, CNRS/IAP

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

The Warped Science of Interstellar (2/6)

Sequel of the preceding post The Warped Science of Interstellar (1/6)

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.

CGal_IR_1al
A view of the Galactic Center in X-rays

CGal_*Keck
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.

m31
The Andromeda Galaxy (M31), located at 2.2 million light-years

coeurM31_HST
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

Black Hole Imaging (2) : Heads and Tails

 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 disc, although made of hot gas instead of rocks and ice, has a similar shape, namely circular thin rings.
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