UP part of global research team to present the first image of Sagittarius A*

Revealing the black hole at the heart of our galaxy

Astronomers have unveiled the first image of the supermassive black hole at the centre of our own Milky Way galaxy. The announcement was made at simultaneous press conferences around the world. Professor Roger Deane, an Extraordinary Professor at the University of Pretoria and Director for the Centre of Astrophysics at the University of Witwatersrand and Wits Postdoctoral Fellow, Dr Iniyan Natarajan, were part of this global collaboration with the Event Horizon Telescope team. They are the only two African-based representatives who are part of the global team of more than 300 astronomers.

This result provides overwhelming evidence that the object is indeed a black hole and yields valuable clues about the workings of such giants, which are thought to reside at the centre of most galaxies. The image was produced by a global research team called the Event Horizon Telescope (EHT) Collaboration, using observations from a worldwide network of radio telescopes.

The image is a long-anticipated look at the massive object that sits at the very centre of our galaxy. Scientists had previously tracked stars orbiting around something invisible, compact, and very massive at the centre of the Milky Way. This strongly suggested that this object — known as Sagittarius A* (Sgr A*, pronounced "sadge-ay-star") — is a black hole, and today’s image provides the first direct visual evidence of it.

Although we cannot see the black hole itself, because it is completely dark, glowing gas around it reveals a telltale signature: a dark central region (called a “shadow”) surrounded by a bright ring-like structure. The new view captures light bent by the powerful gravity of the black hole, which is four million times more massive than our sun.

“We were stunned by how well the size of the ring agreed with predictions from Einstein’s Theory of General Relativity," said EHT Project Scientist Geoffrey Bower from the Institute of Astronomy and Astrophysics, Academia Sinica, Taipei. "These unprecedented observations have greatly improved our understanding of what happens at the very centre of our galaxy, and offer new insights on how these giant black holes interact with their surroundings.” The EHT team's results are being published today in a special issue of The Astrophysical Journal Letters.

Because the black hole is about 27,000 light-years away from Earth, it appears to us to have about the same size in the sky as a donut on the Moon. To image it, the team created the powerful EHT, which linked together eight existing radio observatories across the planet to form a single “Earth-sized” virtual telescope [1]. The EHT observed Sgr A* on multiple nights, collecting data for many hours in a row, similar to using a long exposure time on a camera.

According to Prof Deane, “Southern Africa holds a distinct geographic advantage to host new EHT telescopes, especially to make movies of the Milky Way’s supermassive black hole, which lies directly above us in the southern sky. A campaign to add these game-changing African nodes to the global network is underway with several national and international partners, including Wits and the University of Pretoria. This effort has a strong synergy with the future African expansion of the Square Kilometre Array mid-frequency array centred in the Karoo National Park, with the South African Radio Astronomy Observatory’s MeerKAT telescope serving as a precursor”.

The breakthrough follows the EHT collaboration’s 2019 release of the first image of a black hole, called M87*, at the centre of the more distant Messier 87 galaxy.

The two black holes look remarkably similar, even though our galaxy’s black hole is more than a thousand times smaller and less massive than M87* [2]. "We have two completely different types of galaxies and two very different black hole masses, but close to the edge of these black holes they look amazingly similar,” says Sera Markoff, Co-Chair of the EHT Science Council and a professor of theoretical astrophysics at the University of Amsterdam, the Netherlands. "This tells us that General Relativity governs these objects up close, and any differences we see further away must be due to differences in the material that surrounds the black holes.”

This achievement was considerably more difficult than for M87*, even though Sgr A* is much closer to us. EHT scientist Chi-kwan (‘CK’) Chan, from Steward Observatory and Department of Astronomy and the Data Science Institute of the University of Arizona, US, explains: “The gas in the vicinity of the black holes moves at the same speed — nearly as fast as light — around both Sgr A* and M87*. But where gas takes days to weeks to orbit the larger M87*, in the much smaller Sgr A* it completes an orbit in mere minutes. This means the brightness and pattern of the gas around Sgr A* was changing rapidly as the EHT Collaboration was observing it — a bit like trying to take a clear picture of a puppy quickly chasing its tail.”

The researchers had to develop sophisticated new tools that accounted for the gas movement around Sgr A*. While M87* was an easier, steadier target, with nearly all images looking the same, that was not the case for Sgr A*. The image of the Sgr A* black hole is an average of the different images the team extracted, finally revealing the giant lurking at the centre of our galaxy for the first time.

The effort was made possible through the ingenuity of more than 300 researchers from 80 institutes around the world that together make up the EHT Collaboration. In addition to developing complex tools to overcome the challenges of imaging Sgr A*, the team worked rigorously for five years, using supercomputers to combine and analyse their data, all while compiling an unprecedented library of simulated black holes to compare with the observations. The South African team’s contributions included precision measurements of the black hole ring size using a suite of algorithms, as well as developing the sophisticated software suite used to simulate realistic EHT datasets. These were critical in order to compare theoretical predictions with the observations, and in turn to test theories of gravity.

Scientists are particularly excited to finally have images of two black holes of very different sizes, which offers the opportunity to understand how they compare and contrast. They have also begun to use the new data to test theories and models of how gas behaves around supermassive black holes. This process is not yet fully understood but is thought to play a key role in shaping the formation and evolution of galaxies.

“Now we can study the differences between these two supermassive black holes to gain valuable new clues about how this important process works,” said EHT scientist Keiichi Asada from the Institute of Astronomy and Astrophysics, Academia Sinica, Taipei. “We have images for two black holes — one at the large end and one at the small end of supermassive black holes in the Universe — so we can go a lot further in testing how gravity behaves in these extreme environments than ever before.”

Progress on the EHT continues: a major observation campaign in March 2022 included more telescopes than ever before. The ongoing expansion of the EHT network and significant technological upgrades will allow scientists to share even more impressive images as well as movies of black holes in the near future.

Notes

[1] The individual telescopes involved in the EHT in April 2017, when the observations were conducted, were: the Atacama Large Millimeter/submillimeter Array (ALMA), the Atacama Pathfinder Experiment (APEX), the IRAM 30-meter Telescope, the James Clerk Maxwell Telescope (JCMT), the Large Millimeter Telescope Alfonso Serrano (LMT), the Submillimeter Array (SMA), the UArizona Submillimeter Telescope (SMT), the South Pole Telescope (SPT). Since then, the EHT has added the Greenland Telescope (GLT), the NOrthern Extended Millimeter Array (NOEMA) and the UArizona 12-meter Telescope on Kitt Peak to its network. 

ALMA is a partnership of the European Southern Observatory (ESO; Europe, representing its member states), the U.S. National Science Foundation (NSF), and the National Institutes of Natural Sciences (NINS) of Japan, together with the National Research Council (Canada), the Ministry of Science and Technology (MOST; Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA; Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, the Associated Universities, Inc./National Radio Astronomy Observatory (AUI/NRAO) and the National Astronomical Observatory of Japan (NAOJ). APEX, a collaboration between the Max Planck Institute for Radio Astronomy (Germany), the Onsala Space Observatory (Sweden) and ESO, is operated by ESO. The 30-meter Telescope is operated by IRAM (the IRAM Partner Organizations are MPG (Germany), CNRS (France) and IGN (Spain)). The JCMT is operated by the East Asian Observatory on behalf of the Center for Astronomical Mega-Science of the Chinese Academy of Sciences, NAOJ, ASIAA, KASI, the National Astronomical Research Institute of Thailand, and organizations in the United Kingdom and Canada. The LMT is operated by INAOE and UMass, the SMA is operated by Center for Astrophysics | Harvard & Smithsonian and ASIAA and the UArizona SMT is operated by the University of Arizona. The SPT is operated by the University of Chicago with specialized EHT instrumentation provided by the University of Arizona. 

The Greenland Telescope (GLT) is operated by ASIAA and the Smithsonian Astrophysical Observatory (SAO). The GLT is part of the ALMA-Taiwan project, and is supported in part by the Academia Sinica (AS) and MOST. NOEMA is operated by IRAM and the UArizona 12-meter telescope at Kitt Peak is operated by the University of Arizona.

[2] Black holes are the only objects we know of where mass scales with size. A black hole a thousand times smaller than another is also a thousand times less massive. 

Click on page 2 for a timeline of how long it took to get the first image of Sgr A or click on the infographic. Click on the infographics in the sidebar to learn more about what it took to produce this image. Click on the video in the sidebar to fly through the Milky Way into Sgr A. 

Video Banner caption and credit: Why do we observe at 1.3mm wavelength? Because the plasma around Sgr A* is transparent. Credit: CK Chan/UArizona

The timeline to Sgr A*

Supermassive black holes are the most monstrous objects predicted by Einstein’s 1915 general theory of relativity. These cosmic bodies energize the luminous centers of most galaxies, where they convert the gravitational potential energy of in-falling matter to radiant power and jets of charged particles that stretch for tens of thousands of light years. Despite their commanding presence, black holes remain "unseeable," as they consume the very light that could illuminate them and remain hidden behind a superheated haze of stellar matter. 

The Event Horizon Telescope (EHT) is making these mysterious objects observable. During the EHT’s initial 2017 campaign, data were collected from a synchronized array of eight ground-based radio telescopes trained at the centers of two galaxies. An unprecedented international effort, this project involved more than a dozen institutions and a global collaboration exceeding two hundred researchers. The result: the first visual evidence of a black hole at the scale of the event horizon, the point of no return. This radiolight image opens a new window into intensive investigations of spacetime within such an extreme environment. 

The EHT project is the culmination of a two-decades long effort to image a black hole. But, the legacy of testing Einstein’s general relativity stretches back a century to the expedition of astronomer Arthur Eddington. Armed with instrumentation to study a total solar eclipse on the island of Principe, Eddington confirmed what Einstein predicted: that light emanating from stars in apparent position near the Sun would bend in response to gravity. 

The eclipse of May 29, 1919, would become the first proving ground of relativity. Major contributions by Schwarzschild, Kerr, Penrose, Wheeler, Hawking, and others through the 20th century focused specific attention on black holes physics and the nature of the event horizon itself. Since 1919, black holes have transformed from theoretical interstellar vacuums to become the pulsing hearts of nearly every galactic system. Within this same period, breakthroughs in computer storage and processor technology allowed the capture and analysis of astronomical data sets in enormous quantities. Bolstered by Moore’s Law, data processing equipment became faster and more capable of complex computation. Radio telescope instrumentation also advanced, with increased sensitivity and greater precision.

Shaped by this rich legacy, the EHT project emerged from the natural convergence of high angular resolution techniques and a growing corpus of simulations of the event horizon environment. 

TIMELINE

EVENT

1859

Perihelion advance of Mercury discovered.

1887

Michelson-Morley experiment.

1909

Ehrenfest paradox motivates Einstein to develop General Relativity.  

1915

Einstein proposed theory of General Relativity describing geometrically how matter and energy bend spacetime, giving rise to gravity. 

1915

General Relativity explains perihelion advance of Mercury. 

1916

Schwarzschild solves Einstein's field equations for a point mass, effectively discovering the event horizon. 

1919

Deflection of starlight by the Sun, Eddington confirms General Relativity. 

1952

Development of aperture synthesis principle in Cavendish Lab, Cambridge, UK making interferometric imaging possible (Nobel Prize 1974 - Martin Ryle and Tony Hewish)

1954

Gravitational redshift observed in 40 Eridani B by Popper, ApJ 120, 316 (1954). 

1964

Shapiro delay measured in radar to Venus. 

1967

First radio astronomical observations using very-long-baseline interferometry (VLBI), Broten et al. Science 156, 1592 (1967)

1973

Bardeen on black hole mechanics, Comm. Math. Phys. 31, 2 (1973).

1974

Discovery of binary pulsar (Hulse-Taylor) which leads to proof of gravitational waves (Nobel Prize 1993). 

1976

Gravity Probe A: gravitational time dilation. 

1979

Luminet on imaging a spherical black hole with thin accretion disk, A&A 75,  1-2 (1979).

1982

First 3-mm-VLBI observations (Owens Valley to Hat Creek in California, USA), Readhead et al. Nature 303, 504 (1983).

1985

First 7 mm-VLBI transatlantic and global observations, Marcaide et al. ESOC 22, 157 (1985)Bartel et al. Nature 334, 131 (1988).

1988

Strong gravitational lensing probed by VLA observations of the radio source MG 1131+0456, Hewitt et al. Nature 333, 6173 (1988). 

1989

First VLBI fringes at 1.3 mm: Padin et al.: 223 GHz VLBI observations of 3C 273, ApJ 360, L11 (1990). 

1994

First VLBI fringes at 1.3 mm between IRAM telescopes (IRAM 30-meter Telescope and IRAM NOEMA Observatory), Greve et al. A&A 299, L33 (1995).

1995

Detection of six AGN at 1.3 mm: Krichbaum et al.: 215 GHz VLBI observations of bright Active Galactic Nuclei, A&A 323, L17 (1997). 

1995

First determination of the size of Sgr A* at 1.3 mm using the IRAM 30-meter Telescope and the IRAM NOEMA Observatory: Krichbaum et al. - A&A 335, L106 (1998).

1998

1.3 mm VLBI program at MIT/Haystack started with S. Doeleman.

1999

Computing the shadow of the black hole in Sgr A*: Falcke, Melia & Agol: Viewing the Shadow of the Black Hole at the Galactic Center, ApJ 528, L1 (2000). 

2002

First transatlantic VLBI at 2 mm (four antennas),  Krichbaum et al. EVN Conf 125 (2002).

2003

First transatlantic VLBI at 1.3 mm betwen the IRAM 30-meter Telescope and the Heinrich Hertz Telescope  Krichbaum et al. ECF 189 (2005) after unsuccessful attempt in 1999 (Doeleman & Krichbaum SMVS 173, 1999).

2007

Gravity Probe B: frame dragging. 

2007

Event-horizon-scale observations of Sgr A* at 1.3 mm: Doeleman et al.: Event-horizon- scale structure in the supermassive black hole candidate at the Galactic Centre, Nature 455, 78 (2008). 

2009

Launch of Event Horizon Telescope program at a meeting of the American Astronomical Society. 

2011

Start of the ALMA Phasing Project to develop capability to observe with ALMA in VLBI mode. 

2012

First EHT collaboration meeting in Tucson, Arizona, and letter of intent to cooperate on EHT signed. 

2012

Discovery of event horizon scale structure within M87 (Doeleman et al 2012).

2013

Discovery of extreme polarized emission at the Galactic Center at 1.3 mm: Johnson et al.: Resolved magnetic-field structure and variability near the event horizon of Sagittarius A*, Science 350, 1242 (2015). 

2013

Asymmetry in the structure of Sgr A* at 1.3 mm: Fish et al.: Persistent Asymmetric Structure of Sagittarius A* on Event Horizon Scales, ApJ 890, 90 (2016). 

2013

Extension to the EHT array to Chile confirming Sgr A* asymmetry at 1.3 mm: Lu et al., Detection of intrinsic source structure at ~3 Schwarzschild radii with Millimeter-VLBI observations of Sgr A*, ApJ 859, 1 (2018). 

2014

European BlackHoleCam project started (funded by the European Research Council) and joins EHT. 

2015

LIGO detection of gravitational waves (Nobel Prize 2017). 

2015

First 1.3 mm VLBI detections to the South Pole Telescope, and first 1.3 mm VLBI detections to the Large Millimeter Telescope in Mexico. 

2015

Beamformed ALMA joins VLBI - fringes to APEX - ALMA Technical Notes 16 

2017

First full EHT observations including phased ALMA, SPT, LMT, SMT, SMA, JCMT, IRAM 30m, APEX. 

2017

EHT collaboration established through Collaboration Agreement. 

2018

VLTI/GRAVITY measures of orbit at ISCO radius of Sgr A*. 

2019

First image of a black hole presented by the EHT, corresponding to results based on 2017 observations from Messier 87.

2020

Nobel Prize in Physics to Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity" and jointly to Reinhard Genzel and Andrea Ghez "for the discovery of a supermassive compact object at the centre of our galaxy."

2021

First image in polarised light of the observations of Messier 97.

2022

EHT results of the 2017 observations of Sgr A*.

Credit and Attribution: Table and text compiled from preparatory work carried out in April/May 2019 by Suana Crowley, and others)

A brief history of Sgr A infographic

Click on the infographic called A brief History of Sgr A in the side bar to enlarge.

The EHT consortium consists of 13 stakeholder institutes; the Academia Sinica Institute of Astronomy and Astrophysics, the University of Arizona, the Center for Astrophysics | Harvard & Smithsonian, the University of Chicago, the East Asian Observatory, Goethe-Universitaet Frankfurt, Institut de Radioastronomie Millimétrique, Large Millimeter Telescope, Max Planck Institute for Radio Astronomy, MIT Haystack Observatory, National Astronomical Observatory of Japan, Perimeter Institute for Theoretical Physics, and Radboud University.

May 12, 2022

  • Estimated Reading Time: 12 minutes

Table of contents

Researchers
  • Professor Roger Deane
    University of Pretoria (UP) astrophysicist Professor Roger Deane was part of the international group of scientists who have captured the first image of a black hole. His group worked to develop simulations of the complex, Earth-sized telescope used to make this historic discovery. These simulations attempt to mimic and better understand the data coming from the real instrument, which is made up of antennas across the globe.

    About four years ago, Prof Deane started working with the team on the Event Horizon Telescope (EHT), which captured the image that was globally released today (Please see up.ac.za for the official media release). Prof Deane, who grew up in Welkom in the Free State, developed a passion for astronomy from an early age, when he was dazzled by the excellent view of the Milky Way.

    Downplaying his contribution to the capturing of the first image of a black hole, the 36-year-old Associate Professor of Physics said, “I’m still blown away by the image. It hasn’t really worn off yet. I’m just proud and honoured to play my small part in this amazing international team.”
    UP Vice-Chancellor and Principal Prof Tawana Kupe congratulated Prof Deane on his contribution to the EHT. "This young scientist is an inspiration to scientists on the African continent. Our staff and students are innovative and creative thinkers who excel in cutting-edge research, and this discovery is a great example of what can be achieved if we work together across borders and disciplines. UP is already at the forefront of world-class research and, as one of the largest knowledge producers in South Africa, we make an impact on issues of critical relevance to Africa and the world. We produce high-quality research that matters,” he said.

    According to Prof Deane, as with any major physics experiment, one needs to understand the effects that the instrument itself may have on the data. “In the case of the EHT, we built a simulation package that physically modelled a number of non-desirable effects that prevent one from seeing any sort of black hole shadow feature.”

    The EHT observes what radio astronomers consider to be a very short wavelength, about 1 mm, which means the distance between two consecutive peaks of light is 1 mm. “This is about 200 times smaller than the wavelength of light that MeerKAT observes, and presents many challenges to the telescope design, data processing and analysis.”

    Prof Deane said, “Just a small amount of water vapour in the atmosphere could completely erase the signature of the black hole shadow. This is why the EHT stations are at very high altitudes in some of the driest places on Earth.” There are a multitude of other aspects to accurately model in an instrument as sensitive and complex as this telescope. “We incorporate as much of this information as we can physically model in software. This accurate simulation of the telescope enables astronomers to better understand the real observations, discriminate between theoretical black hole shadow models, and insights into the characteristics and performance of the telescope itself.” He explained that this also allows scientists to accurately predict the impact of adding new antennas in the global network, as is planned for the African Millimetre Telescope (AMT) project in Namibia.

    The first image of a black hole is a significant milestone for the EHT, but much lies ahead as the team works towards testing Einstein’s general theory of relativity. To do so, they will need to continue to improve the images through array expansion in Africa and elsewhere with improved algorithms. Prof Deane says his group is now focused on three things: “Expanding our simulations to model the case where light from the black hole may have preferred orientation – think about how polarised lenses reduce the sun’s glare from the sea – performing detailed simulations on new prospective sites, and exploring a range of probabilistic modelling techniques to extract the properties of the black hole shadow.”

    What did it feel like being part of a team of 200 highly talented scientists who have worked on this project?

    “It has been a privilege – I have learned a great deal in all spheres. One of the aspects of my job that I love the most is working with astronomers from around the world from a diverse set of backgrounds and perspectives. The dramatic result unveiled today has required a combination of the world’s best engineers, theorists, and observers. I’m thrilled to be a part of that team. It has also been challenging, apart from practical aspects like the geographic and time zone differences.”

    At UP, this Y1 National Research Foundation-rated scientist is leading the new Astronomy Research Group which is focused on MeerKAT, the Square Kilometre Array, and the technique of creating virtual Earth-sized telescopes like the EHT and the African Very Long Baseline Interferometry Network.

    When he moved to UP in January 2018, there were no other astronomers at the institution. “By July, we should have scaled up to approximately 14. We are hoping to finalise a joint South African Radio Astronomy Observatory-UP South African Research Chair Initiative Chair in radio astronomy by then as well. Over 100 UP students registered for the first year astronomy course in 2019, a dramatic increase, so there is clearly a need to grow the number of faculty positions in astronomy to deal with the teaching and postgraduate student supervision demand.”

    The UP Astronomy group’s science-driven approach is in keeping with the realisation that this new era of complex, big-data telescopes requires technical expertise and new algorithmic approaches. A significant part of his UP research group’s work is focused on machine learning with the UP Computational Intelligence Research Group in the Department of Computer Science, and instrumental work in collaboration with UP’s Electrical, Electronic and Computer Engineering Department.

    Looking ahead, Prof Deane is very excited about growth in astronomy, saying that, “South Africa has an increasing number of astronomy-related success stories to help spur our youth into science and technology careers. I think our government, through the Department of Science and Technology, has been very strategic in that regard, with payoffs that will be far-reaching and long-lasting.”

    Professor Roger Deane on the University of Pretoria’s astronomy programme

    When did UP’s astronomy programme start?

    UP’s Department of Physics has had astronomy undergraduate courses for many years. The current radio astronomy research group started at the beginning of 2018 with my arrival. UP has among the largest astronomy enrollments in undergraduate courses in South Africa, showing great potential to grow into a large research group.

    Approximately how many students do you have?

    In July this year, we should have scaled up to approximately 13 (1 faculty, 2 post-docs, 1 PhD, 3 MSc, 6 Hons). We are hoping to finalise a joint South African Radio Astronomy Observatory-UP SARChI Chair in radio astronomy by then as well, which should increase the cohort to at least 20.

    Why is big data important, and what is the computational capacity of the MeerKAT and the Event Horizon Telescope (EHT)?

    The EHT raw data was 4 petabytes in size. Unlike EHT, which observes one astrophysical object a time, MeerKAT will detect many millions and have archive sizes even larger than an annual EHT campaign. To analyse this data and ensure we enable all the exciting discoveries to come, we have to get in step with the fourth industrial revolution (4IR) and employ artificial intelligence and machine learning approaches. Astronomy is a key contributor to the 4IR, as highlighted by President Cyril Ramaphosa in this year's State of the Nation address. At UP, the Astronomy and Computational Intelligence Research Groups are working closely together to ensure our university plays a leading role in this en route to the Square Kilometre Array. The UP Astronomy group’s science-driven approach is coupled with the realisation that this new era of complex, big-data telescopes requires technical expertise and new algorithmic approaches. A significant part of the UP research group’s work is focused on machine learning with the UP Computational Intelligence Research Group in the Department of Computer Science, and instrumental work in collaboration with UP’s Electrical, Electronic and Computer Engineering Department.

    How is UP leading in investing and promoting astronomy as an academic and research discipline?

    UP has taken a forward-thinking, strategic approach by investing in the Inter-University Institute for Data Intensive Astronomy (IDIA). It is one of three university partners who are ensuring they will be able to deal with the data processing and analysis demands of MeerKAT and SKA. UP has also taken a strategic decision to invest in the technique of Very Long Baseline Interferometry – the very same approach the EHT uses. This is with a view to taking a leadership role in the African VLBI Network and the second phase of the Square Kilometre Array, ensuring South Africa and Africa are at the forefront of the spectacular science these VLBI arrays will perform.

    How does UP’s astronomy programme – and South African astronomy in general – measure up in the global astronomy community?

    In the UP Department of Physics, we are building a new astronomy group that is both science-driven and technically savvy. We have demonstrated that in the EHT project, and we are heavily focused on making leading contributions towards MeerKAT, which will eventually extend across the African continent as the SKA. It's important that South Africa benefit scientifically from the astronomy investments that the South African government has made through the Department of Science and Technology. To do so, universities need to play their part in investing in research expertise. UP is in the process of stepping up to that responsibility, with this EHT announcement being a first example of the fruits of that investment.
    More from this Researcher

Related Video

Related Infographics

Related Gallery

Other Related Research

Copyright © University of Pretoria 2024. All rights reserved.

Share