Event Horizon Telescope

Last updated

Event Horizon Telescope
The Event Horizon Telescope and Global mm-VLBI Array on the Earth.jpg
Event Horizon Telescope.svg
Alternative namesEHT  Blue pencil.svg
Website eventhorizontelescope.org Blue pencil.svg
Telescopes Atacama Large Millimeter Array
Atacama Pathfinder Experiment
Heinrich Hertz Submillimeter Telescope
IRAM 30m telescope
James Clerk Maxwell Telescope
Large Millimeter Telescope
South Pole Telescope
Submillimeter Array   Blue pencil.svg
Commons-logo.svg Related media on Wikimedia Commons

The Event Horizon Telescope (EHT) is a large telescope array consisting of a global network of radio telescopes. The EHT project combines data from several very-long-baseline interferometry (VLBI) stations around Earth with angular resolution sufficient to observe objects the size of a supermassive black hole's event horizon. The project's observational targets include the two black holes with the largest angular diameter as observed from Earth: the black hole at the center of the supergiant elliptical galaxy Messier 87, and Sagittarius A*, at the center of the Milky Way. [1] [2]

Astronomical interferometer array of separate telescopes, mirror segments, or radio telescope antennas that work together as a single telescope

An astronomical interferometer is an array of separate telescopes, mirror segments, or radio telescope antennas that work together as a single telescope to provide higher resolution images of astronomical objects such as stars, nebulas and galaxies by means of interferometry. The advantage of this technique is that it can theoretically produce images with the angular resolution of a huge telescope with an aperture equal to the separation between the component telescopes. The main drawback is that it does not collect as much light as the complete instrument's mirror. Thus it is mainly useful for fine resolution of more luminous astronomical objects, such as close binary stars. Another drawback is that the maximum angular size of a detectable emission source is limited by the minimum gap between detectors in the collector array.

Radio telescope form of directional radio antenna used in radio astronomy

A radio telescope is a specialized antenna and radio receiver used to receive radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency portion of the electromagnetic spectrum emitted by astronomical objects, just as optical telescopes are the main observing instrument used in traditional optical astronomy which studies the light wave portion of the spectrum coming from astronomical objects. Radio telescopes are typically large parabolic ("dish") antennas similar to those employed in tracking and communicating with satellites and space probes. They may be used singly or linked together electronically in an array. Unlike optical telescopes, radio telescopes can be used in the daytime as well as at night. Since astronomical radio sources such as planets, stars, nebulas and galaxies are very far away, the radio waves coming from them are extremely weak, so radio telescopes require very large antennas to collect enough radio energy to study them, and extremely sensitive receiving equipment. Radio observatories are preferentially located far from major centers of population to avoid electromagnetic interference (EMI) from radio, television, radar, motor vehicles, and other man-made electronic devices.

Very-long-baseline interferometry type of astronomical interferometry used in radio astronomy


Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth. The distance between the radio telescopes is then calculated using the time difference between the arrivals of the radio signal at different telescopes. This allows observations of an object that are made simultaneously by many radio telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.

Contents

The idea was first envisioned by German radioastronomer Heino Falcke in 1993. [3] He later co-led, along with Michael Kramer and Luciano Rezzolla, the EU-funded Black Hole Cam project in which theoretical aspects of black hole imaging with VLBI were further developed. [4] [5] The current director of the Event Horizon Telescope collaboration is American astrophysicist Sheperd Doeleman (Harvard-Smithsonian CfA), whereas Falcke (Radboud University Nijmegen) chairs its science council. [6]

Heino Falcke German astronomer

Heino Falcke is a German professor of radio astronomy and astroparticle physics at the Radboud University Nijmegen. He was a winner of the 2011 Spinoza Prize. His main field of study is black holes. In 2013, a team under his lead earned a 14 million euro research grant from the European Research Council to further studies of black holes.

Michael Kramer is a German radioastronomer and astrophysicist.

Luciano Rezzolla researcher

Luciano Rezzolla is an Italian professor of relativistic astrophysics and numerical relativity at the Goethe University Frankfurt. His main field of study is the physics and astrophysics of compact objects such as black holes and neutron stars.

The first image of a black hole, at the center of galaxy Messier 87, was published by the EHT Collaboration on April 10, 2019. [7] The array made this observation at a wavelength of 1.3 mm and with a theoretical diffraction-limited resolution of 25 microarcseconds . Future plans involve improving the array's resolution by adding new telescopes and by taking shorter-wavelength observations. [1] [8]

Telescope array

Soft X-ray image of Sagittarius A* (center) and two light echoes from a recent explosion (circled) Sagittarius A*.jpg
Soft X-ray image of Sagittarius A* (center) and two light echoes from a recent explosion (circled)

The EHT is composed of many radio observatories or radio telescope facilities around the world to produce a high-sensitivity, high-angular-resolution telescope. Through the technique of very-long-baseline interferometry (VLBI), many independent radio antennas separated by hundreds or thousands of kilometres can be used in concert to create a virtual telescope with an effective diameter of the entire planet. [9] The effort includes development and deployment of submillimeter dual polarization receivers, highly stable frequency standards to enable very-long-baseline interferometry at 230–450 GHz, higher-bandwidth VLBI backends and recorders, as well as commissioning of new submillimeter VLBI sites. [10]

Submillimetre astronomy astronomy with terahertz (< 1 mm)-range light

Submillimetre astronomy or submillimeter astronomy is the branch of observational astronomy that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a few hundred micrometres and a millimetre. It is still common in submillimetre astronomy to quote wavelengths in 'microns', the old name for micrometre.

Polarization (waves) property of waves that can oscillate with more than one orientation

Polarization is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string (see image); for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids. In some types of transverse waves, the wave displacement is limited to a single direction, so these also do not exhibit polarization; for example, in surface waves in liquids, the wave displacement of the particles is always in a vertical plane.

Each year since its first data capture in 2006, the EHT array has moved to add more observatories to its global network of radio telescopes. The first image of the Milky Way's supermassive black hole, Sagittarius A*, was expected to be produced in April 2017, [11] [12] but because the South Pole Telescope is closed during winter (April to October), the data shipment delayed the processing to December 2017 when the shipment arrived. [13]

South Pole Telescope telescope at the South Pole

The South Pole Telescope (SPT) is a 10-meter (394 in) diameter telescope located at the Amundsen–Scott South Pole Station, Antarctica. The telescope is designed for observations in the microwave, millimeter-wave, and submillimeter-wave regions of the electromagnetic spectrum, with the particular design goal of measuring the faint, diffuse emission from the cosmic microwave background (CMB). The first major survey with the SPT–designed to find distant, massive, clusters of galaxies through their interaction with the CMB, with the goal of constraining the dark energy equation of state–was completed in October 2011. In early 2012, a new camera (SPTpol) was installed on the SPT with even greater sensitivity and the capability to measure the polarization of incoming light. This camera operated from 2012–2016 and was used to make unprecedentedly deep high-resolution maps of hundreds of square degrees of the Southern sky. In 2017, the third-generation camera SPT-3G was installed on the telescope, providing nearly an order-of-magnitude increase in mapping speed over SPTpol.

Data collected on hard drives are transported by commercial freight airplanes [14] (a so-called sneakernet) from the various telescopes to the MIT Haystack Observatory and the Max Planck Institute for Radio Astronomy, where the data are cross-correlated and analyzed on a grid computer made from about 800 CPUs all connected through a 40 Gbit/s network. [15]

Sneakernet An informal term for the transfer of electronic information by physically moving media.

Sneakernet is an informal term for the transfer of electronic information by physically moving media such as magnetic tape, floppy disks, compact discs, USB flash drives or external hard drives from one computer to another; rather than transmitting the information over a computer network.

Haystack Observatory American observatory affiliated with MIT

Haystack Observatory is an astronomical observatory owned by Massachusetts Institute of Technology (MIT). It is located in Westford, Massachusetts (US), approximately 45 kilometers (28 mi) northwest of Boston. Haystack was initially built by MIT's Lincoln Laboratory for the United States Air Force and was known as Haystack Microwave Research Facility. Construction began in 1960, and the antenna began operating in 1964. In 1970 the facility was transferred to MIT, which then formed the Northeast Radio Observatory Corporation (NEROC) with a number of other universities to operate the site as the Haystack Observatory. As of January 2012, a total of nine institutions participated in NEROC.

The Max Planck Institute for Radio Astronomy (MPIfRA) is located in Bonn, Germany. It is one of 80 institutes in the Max Planck Society. 50°43′47.6″N7°4′9.2″E

Messier 87*

First image of the event horizon of a black hole (M87*) captured by the Event Horizon Telescope Black hole - Messier 87 crop max res.jpg
First image of the event horizon of a black hole (M87*) captured by the Event Horizon Telescope

The Event Horizon Telescope Collaboration announced its first results in six simultaneous press conferences worldwide on April 10, 2019. [18] The announcement featured the first direct image of a black hole, which showed the supermassive black hole at the center of Messier 87, designated M87*. [1] [19] [20] The scientific results were presented in a series of six papers published in The Astrophysical Journal Letters . [21]

The image provided a test for Albert Einstein's general theory of relativity under extreme conditions. [9] [12] Studies have previously tested general relativity by looking at the motions of stars and gas clouds near the edge of a black hole. However, an image of a black hole brings observations even closer to the event horizon. [22] Relativity predicts a dark shadow-like region, caused by gravitational bending and capture of light, which matches the observed image. The published paper states: "Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity." [23] Paul T.P. Ho, EHT Board member, said: "Once we were sure we had imaged the shadow, we could compare our observations to extensive computer models that include the physics of warped space, superheated matter, and strong magnetic fields. Many of the features of the observed image match our theoretical understanding surprisingly well." [21]

The image also provided new measurements for the mass and diameter of M87*. EHT measured the black hole's mass to be 6.5±0.7 billion solar masses and measured the diameter of its event horizon to be approximately 40 billion kilometres (270 AU; 0.0013 pc; 0.0042 ly), roughly 2.5 times smaller than the shadow that it casts, seen at the center of the image. [21] [22] From the asymmetry in the ring, EHT inferred that the matter on the brighter south side of the disk is moving towards Earth, the observer. This is based on the theory that approaching matter appears brighter because of relativistic beaming. Previous observations of the black hole's jet showed that the black hole's spin axis is inclined at an angle of 17° relative to the observer's line of sight. [1] From these two observations, EHT concluded the black hole spins clockwise, as seen from Earth. [1] [8]

Producing an image from data from an array of radio telescopes required much new mathematical work. Four independent teams created images to assess the reliability of the results. [24] These methods included both an established algorithm in radio astronomy for image reconstruction known as CLEAN, invented by Jan Högbom, [25] as well as self-calibrating image processing methods [26] for astronomy such as the CHIRP algorithm created by Katherine Bouman and others. [24] [27] The algorithms that were ultimately used were a regularized maximum likelihood (RML) [28] algorithm and the CLEAN algorithm. [24]

Collaboration

The EHT Collaboration consists of 13 stakeholder institutes: [6]

A schematic diagram of the VLBI mechanism of EHT. Each antenna, spread out over vast distances, has an extremely precise atomic clock. Analogue signals collected by the antenna are converted to digital signals and stored on hard drives together with the time signals provided by the atomic clock. The hard drives are then shipped to a central location to be synchronized. An astronomical observation image is obtained by processing the data gathered from multiple locations. EHT-infography.jpg
A schematic diagram of the VLBI mechanism of EHT. Each antenna, spread out over vast distances, has an extremely precise atomic clock. Analogue signals collected by the antenna are converted to digital signals and stored on hard drives together with the time signals provided by the atomic clock. The hard drives are then shipped to a central location to be synchronized. An astronomical observation image is obtained by processing the data gathered from multiple locations.

Institutions affiliated with the EHT include: [29]

Related Research Articles

Black hole Astrophysical object from which nothing can escape

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Messier 87 Galaxy in the Virgo Galactic Cluster

Messier 87 is a supergiant elliptical galaxy in the constellation Virgo. One of the most massive galaxies in the local Universe, it has a large population of globular clusters—about 12,000 compared with the 150–200 orbiting the Milky Way—and a jet of energetic plasma that originates at the core and extends at least 1,500 parsecs, traveling at relativistic speed. It is one of the brightest radio sources in the sky and a popular target for both amateur and professional astronomers.

Supermassive black hole Largest type of black hole; usually found at the centers of galaxies

A supermassive black hole is the largest type of black hole, containing a mass of the order of hundreds of thousands, to billions of times, the mass of the Sun (M). Black holes are a class of astronomical object that have undergone gravitational collapse, leaving behind spheroidal regions of space from which nothing can escape, not even light. Observational evidence indicates that nearly all large galaxies contain a supermassive black hole, located at the galaxy's center. In the case of the Milky Way, the supermassive black hole corresponds to the location of Sagittarius A* at the Galactic Core. Accretion of interstellar gas onto supermassive black holes is the process responsible for powering quasars and other types of active galactic nuclei.

Chandra X-ray Observatory space observatory

The Chandra X-ray Observatory (CXO), previously known as the Advanced X-ray Astrophysics Facility (AXAF), is a Flagship-class space telescope launched on STS-93 by NASA on July 23, 1999. Chandra is sensitive to X-ray sources 100 times fainter than any previous X-ray telescope, enabled by the high angular resolution of its mirrors. Since the Earth's atmosphere absorbs the vast majority of X-rays, they are not detectable from Earth-based telescopes; therefore space-based telescopes are required to make these observations. Chandra is an Earth satellite in a 64-hour orbit, and its mission is ongoing as of 2019.

Sagittarius A* Supermassive black hole at the center of the Milky Way

Sagittarius A* is a bright and very compact astronomical radio source at the center of the Milky Way, near the border of the constellations Sagittarius and Scorpius. It is likely the location of a supermassive black hole, similar to those generally accepted to be at the centers of most if not all spiral and elliptical galaxies.

Onsala Space Observatory astronomical observatory in Onsala, Sweden

Onsala Space Observatory (OSO), the Swedish National Facility for Radio Astronomy, provides scientists with equipment to study the Earth and the rest of the Universe. The observatory operates two radio telescopes in Onsala, 45 km south of Gothenburg, and takes part in several international projects. Examples of activities:

The Joint Institute for VLBI ERIC (JIVE) was formed in 1993 by the European Consortium for VLBI, and since then, it is the central facility of the European VLBI Network (EVN). In 2015, JIVE became a European Research Infrastructure Consortium.. Very Long Baseline Interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes. Normally the participating radio telescopes function individually, working on their own specific projects. In the case of VLBI, they all observe the same source at the same time, allowing much higher spatial resolution. There are many complex and challenging hurdles that need to be overcome to enable this effort. One challenge is the data processing requirement. JIVE operates the "EVN Data Processor" - a special-purpose supercomputer for astronomical VLBI data correlation. In a recent demonstration of JIVE 14 telescopes from in Australia, Chile, China, Finland, Germany, Italy, the Netherlands, Poland, Puerto Rico, Spain, Sweden and the UK participated in joint observations of the active galaxy 3C120. The participating telescopes included:

Submillimeter Array Array of radio telescopes in Hawaii

The Submillimeter Array (SMA) consists of eight 6-meter (20 ft) diameter radio telescopes arranged as an interferometer for submillimeter wavelength observations. It is the first purpose-built submillimeter interferometer, constructed after successful interferometry experiments using the pre-existing 15-meter (49 ft) James Clerk Maxwell Telescope and 10.4-meter (34.1 ft) Caltech Submillimeter Observatory as an interferometer. All three of these observatories are located at Mauna Kea Observatory on Mauna Kea, Hawaii, and can be operated together as a ten element interferometer in the 230 and 345 GHz bands. The baseline lengths presently in use range from 16 to 508 meters, and up to 783 meters (2,569 ft) for eSMA operations. The radio frequencies accessible to this telescope range from 180–418 gigahertz (1.666–0.717 mm) which includes rotational transitions of dozens of molecular species as well as continuum emission from interstellar dust grains. Although the array is capable of operating both day and night, most of the observations take place at nighttime when the atmospheric phase stability is best.

Fulvio Melia American physicist

Fulvio Melia is an Italian-American astrophysicist, cosmologist and author. He is professor of physics, astronomy and the applied math program at the University of Arizona and was a scientific editor of The Astrophysical Journal and an associate editor of The Astrophysical Journal Letters. A former Presidential Young Investigator and Sloan Research Fellow, he is the author of six English books and 230 refereed articles on theoretical astrophysics and cosmology.

Feryal Özel is a Turkish-American astrophysicist born in Istanbul, Turkey, specializing in the physics of compact objects and high energy astrophysical phenomena. As of 2019, Özel is a professor at the University of Arizona in Tucson, in the Astronomy Department and Steward Observatory.

The CLEAN algorithm is a computational algorithm to perform a deconvolution on images created in radio astronomy. It was published by Jan Högbom in 1974 and several variations have been proposed since then.

Laura Ferrarese Italian astrophysicist

Laura Ferrarese is a researcher in space science at the National Research Council of Canada. Her primary work has been performed using data from the Hubble Space Telescope and the Canada-France-Hawaii Telescope.

Daniel Batcheldor is an Anglo-American astrophysicist, a professor at Florida Institute of Technology, Head of the Department of Aerospace, Physics and Space Sciences, and Director of the Jacobus Kapteyn Telescope.

Greenland Telescope

The Greenland Telescope is a radio telescope that is currently installed and operating at the Thule Air Base in north-western Greenland. It will later be deployed at the Summit Station research camp, located at the highest point of the Greenland ice sheet at an altitude of 3,210 meters.

CHIRP (algorithm) image reconstruction algorithm, notably used for the first imaging of a black hole

The CHIRP algorithm is a Bayesian algorithm to perform a deconvolution on images created in radio astronomy. The acronym was coined by lead author Katherine Bouman in 2016. The development of CHIRP involved a team of researchers from MIT’s Computer Science and Artificial Intelligence Laboratory, the Harvard-Smithsonian Center for Astrophysics and the MIT Haystack Observatory, involving Bill Freeman, Sheperd Doeleman, to name a few. It was first presented publicly by Bouman at the IEEE Computer Vision and Pattern Recognition conference in June 2016.

Jan Arvid Högbom is a Swedish radio astronomer and astrophysicist.

Andrew Chael is an American astrophysicist and a member of the Event Horizon Telescope imaging working group and team that created the first simulated image of a black hole.

Sheperd "Shep" S. Doeleman is an American astrophysicist. His research focuses on super massive black holes with sufficient resolution to directly observe the event horizon. He is a senior research fellow at the Harvard–Smithsonian Center for Astrophysics and the director of the Event Horizon Telescope project. He led the international team of researchers that produced the first simulated image of a black hole.

References

  1. 1 2 3 4 5 6 The Event Horizon Telescope Collaboration (April 10, 2019). "First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole". The Astrophysical Journal Letters . 87 (1): L1. doi:10.3847/2041-8213/ab0ec7.
  2. Pallab, Ghosh (April 10, 2019). "First ever black hole image released". BBC News. Retrieved April 12, 2019.
  3. "Black Hole Cam". blackholecam.org. Retrieved April 12, 2019.
  4. "EU-funded scientists unveil first ever image of a black hole". erc.europa.eu. Retrieved April 12, 2019.
  5. 1 2 "Even Horizon Telescope Organization". eventhorizontelescope.org. Retrieved April 13, 2019.
  6. 1 2 Susanna Kohler (April 10, 2019). "First Images of a Black Hole from the Event Horizon Telescope". AAS Nova. Retrieved April 10, 2019.
  7. 1 2 O'Neill, Ian (July 2, 2015). "Event Horizon Telescope Will Probe Spacetime's Mysteries". Discovery News. Retrieved August 21, 2015.
  8. "MIT Haystack Observatory: Astronomy Wideband VLBI Millimeter Wavelength". www.haystack.mit.edu.
  9. Webb, Jonathan (January 8, 2016). "Event horizon snapshot due in 2017". BBC News. Retrieved March 24, 2016.
  10. 1 2 Davide Castelvecchi (March 23, 2017). "How to hunt for a black hole with a telescope the size of Earth". Nature. 543 (7646): 478–480. Bibcode:2017Natur.543..478C. doi:10.1038/543478a. PMID   28332538.
  11. "EHT Status Update, December 15 2017". eventhorizontelescope.org. Retrieved February 9, 2018.
  12. "The Hidden Shipping and Handling Behind That Black-Hole Picture". The Atlantic. Retrieved April 14, 2019.
  13. Mearian, Lucas (August 18, 2015). "Massive telescope array aims for black hole, gets gusher of data". Computerworld. Retrieved August 21, 2015.
  14. Overbye, Dennis (April 10, 2019). "Black Hole Picture Revealed for the First Time – Astronomers at last have captured an image of the darkest entities in the cosmos". The New York Times . Retrieved April 10, 2019.
  15. Landau, Elizabeth (April 10, 2019). "Black Hole Image Makes History". NASA . Retrieved April 10, 2019.
  16. "Media Advisory: First Results from the Event Horizon Telescope to be Presented on April 10th". Event Horizon Telescope. April 1, 2019. Retrieved April 10, 2019.
  17. Lu, Donna (April 12, 2019). "How do you name a black hole? It is actually pretty complicated". New Scientist. London. Retrieved April 12, 2019. “For the case of M87*, which is the designation of this black hole, a (very nice) name has been proposed, but it has not received an official IAU approval,” says Christensen.
  18. Gardiner, Aidan (April 12, 2018). "When a Black Hole Finally Reveals Itself, It Helps to Have Our Very Own Cosmic Reporter - Astronomers announced Wednesday that they had captured the first image of a black hole. The Times's Dennis Overbye answers readers' questions". The New York Times. Retrieved April 15, 2019.
  19. 1 2 3 "Astronomers Capture First Image of a Black Hole". European Southern Observatory. April 10, 2019. Retrieved April 10, 2019.
  20. 1 2 Lisa Grossman, Emily Conover (April 10, 2019). "The first picture of a black hole opens a new era of astrophysics". Science News. Retrieved April 10, 2019.
  21. Jake Parks (April 10, 2019). "The nature of M87: EHT's look at a supermassive black hole". Astronomy. Retrieved April 10, 2019.
  22. 1 2 3 The Event Horizon Telescope Collaboration (2019). "First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole". ApJL. 87 (1): L4. doi:10.3847/2041-8213/ab0e85.
  23. Högbom, Jan A. (1974). "Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines". Astronomy and Astrophysics Supplement. 15: 417–426.
  24. SAO/NASA Astrophysics Data System (ADS): Seitz, Schneider, and Bartelmann (1998) Entropy-regularized maximum-likelihood cluster mass reconstruction cites Narayan and Nityananda 1986.
  25. "The creation of the algorithm that made the first black hole image possible was led by MIT grad student Katie Bouman". TechCrunch. Retrieved April 15, 2019.
  26. Narayan, Ramesh and Nityananda, Rajaram (1986) "Maximum entropy image restoration in astronomy" Annual Review of Astronomy and Astrophysics Volume 24 (A87-26730 10-90). Palo Alto, CA, Annual Reviews, Inc. p. 127–170.
  27. "Affiliated Institutes". eventhorizontelescope.org. Retrieved April 10, 2019.