# BLOG: Heidelberg Laureate Forum

Laureates of mathematics and computer science meet the next generation

A key tenet of the Heidelberg Laureate Forum is the importance of collaboration: collaboration between those at the top of their field and those just starting out; between researchers from all over the world; and between those working in a broad variety of fields. This is exemplified by the strong bond between the Lindau Nobel Laureate Meetings and the Heidelberg Laureate Forum.

9th Heidelberg Laureate Forum Foto: Christian Flemming

The Lindau Nobel Laureate Meeting is a gathering of Nobel Prize winning scientists and young researchers. The themes cycle through Physics, Chemistry, and Physiology/Medicine. Each year an exchange takes place, where a laureate is selected to give a guest lecture at the respective meeting, at at Lindau, and during the Heidelberg Laureate Forum. This year, the Lindau Lecture was given by German astrophysicist and co-director of the Max Planck Institute for Extraterrestrial Physics Reinhard Genzel, who was awarded the Nobel Prize in Physics in 2020.

Reinhard Genzel’s Nobel Prize was awarded in recognition of his work discovering a supermassive compact object at the centre of our galaxy, which we can say with a large degree of certainty is a black hole. But all that is to come later. The story of this discovery starts over a century ago, with a certain Physicist known as Albert Einstein.

### A lecture 100 years in the making

In 1915, Albert Einstein published his theory of general relativity. I could write an entire book on general relativity (indeed, people have) but the key thing to note is that the theory gave a set of equations, describing how matter and radiation influence the geometry of space and time (together known as space-time). One of the results of these equations was the prediction of black holes.

Within a year of Einstein publishing his equations of general relativity, Karl Schwarzschild had solved the equation in the specific case of a single spherical non-rotating mass. This solution leads to the calculation of the size of the event horizon of a non-rotating black hole, and suggests that all the mass of a black hole can be found beyond the event horizon.

The event horizon is talked about a lot when describing black holes. It’s the (non-physical) boundary from which it’s impossible for anything outside to make observations about anything inside. Essentially this means it’s a boundary from which light can’t escape, due to the gravitational pull of the black hole.

At this point, though it was known that Einstein’s equations were solvable under specific conditions (i.e. for configurations with high symmetry), it was unclear if they could be solved in general. Enter Roger Penrose, or should I say Sir Roger Penrose. Penrose’s seminal paper, titled “Gravitational Collapse and Space-Time Singularities,” looked at the topology of space and was able to prove that the formation of a black hole is an inevitable event when the curvature of the gravitational potential exceeds a given amount. That is to say, there is a point at which, upon the implosion of an object such as a dying star, the formation of a singularity with apparently infinite gravity is unavoidable.

This is a hugely significant conclusion: Penrose had proven that black holes could exist, and that in certain conditions, they must exist.

### Look to the skies and see

The next step was to actually find a black hole, and that’s certainly easier said than done. Part of the difficulty with black holes is that, by definition, no light escapes – meaning other methods must be employed to measure and observe them.

In 1963, Schmidt, Lyden-Bell, and Rees made a series of breakthroughs. Physicists had detected quasi-stellar radio sources, or quasars. The light emitted from these quasars was faint, but scientists were still able to analyse the spectra of light, which indicated that the composition of the quasars included hydrogen, helium, and other abundant elements. There was one main difference though – the light from these gases was shifted towards the red end of the visible spectrum. Schmidt proposed that this red-shift was due to the expansion of the universe. This would imply that the quasars are very far away – but for the quasars to be visible at all, their radiation would have to be immense.

Soon a theory emerged: perhaps the quasars have a black hole at their centre? This is rather difficult to prove though, so physicists set about devising ways to collect evidence for the black hole – for example, by observing its gravitational effect.

Around this time, in 1971, a new approach for finding black holes was proffered. Lynden-Bell and Rees published a paper conceding that quasars are rare, but they hypothesised that perhaps the majority of galaxies have a black hole at their centre. Perhaps we don’t need to look so far away to find a black hole. Perhaps there is a black hole at the centre of the Milky Way.

### The centre of the galaxy

Throughout the 1970s, galactic centres (that is, the centres of galaxies) became the primary object of study. The centre of the Milky Way is, after all, a lot easier to study than far-off quasars. As Genzel said: “It’s our laboratory”.

The Milky Way is a disc galaxy, of which we sit on the outskirts. Looking into the centre is not simple though. Interstellar dust in the way diminishes optical light by a factor of about $\frac{10}^{12}$, so we cannot optically see the centre of the Milky Way.

There is a dense cluster of stars at the centre of the Milky Way, and at the centre of that is a compact radio source called Sagittarius A*, often abbreviated to SgrA* (pronounced “sadge-ay-star”). With a diameter of roughly 50 microarcseconds, and a mass of a few million solar masses, this is a strong candidate for being a black hole.

How do we measure it then? Charles Towns used spectroscopy to measure the motion of gas clouds in the centre. His work wasn’t received very well though, as there were concerned that the gases could have been moved by magnetic fields or winds from stars instead of by SgrA*. Even supposing they were moved by SgrA*, it still wasn’t possible to rule out a cluster of neutron stars.

Thankfully, as has been a repeated pattern in this story, breakthroughs were round the corner.

### Adaptive Optics

When looking at the stars, those romantics among us may be delighted by their gentle twinkling – but it’s an astronomer’s nightmare. The Earth’s atmosphere results in a blurring effect on light from distant sources.

A new technology was developed to use mirrors to “undo” the effect of the Earth’s atmosphere. This technique is known as adaptive optics, and is now standard. This technique was pioneered by Reinhard Genzel himself, and is part of the work which earned him his Nobel Prize.

Adaptive optics works by measuring the blurring caused by the Earth’s atmosphere using a very bright reference star close to the object of study. Very bright stars are hard to come by, but it is possible to artificially simulate one by shining a powerful laser intro the Earth’s atmosphere.

These measurements are continuously taken, allowing computer-controlled mirrors to deform and correct for the blurring effect of the atmosphere in real time.

### I think we’re going to need a bigger telescope…

Alongside other astronomers from the Max Planck Institute for Extraterrestrial Physics, Genzel was able to precisely measure the velocities of a group of stars situated within 0.1 arcseconds of SgrA*. This measurement of roughly 200 km-1, gave the mass of SgrA* as about 4.31 million solar masses, with a high degree of accuracy.

To improve on this result, Genzel and his group opted to focus on one particular star. S2 is only a distance of 17 light hours from the centre of the Milky Way.

The orbit of S2 is approximately 16 years, giving only a limited number of opportunities to measure it. May 2018 marked the pericentre passage of S2 (its closest approach to SgrA*). Leading up to this, astronomers were against the clock, trying to ensure they had a big enough telescope to accurately take the measurements they wanted.

Prior to this point, the European Organisation for Astronomical Research had four 8m telescopes in Cerro Paranal, comprising the Very Large Telescope (who says scientists aren’t good at naming things?). Using a network of tunnels, they were able to combine these four into one “virtual” telescope, 130m in diameter. This experiment was known as the GRAVITY experiment, and was overseen by Reinhard Genzel.

On May 19th 2018, S2 passed SgrA* at it’s closest orbit of about 14 billion kilometers per hour and GRAVITY was ready. Genzel’s team compared their position and velocity measurements with earlier observations of S2, and with predictions made using Newtonian gravitational physics. The Newtonian predictions didn’t match the measured results. But the predictions made by general relativity did.

General relatively predicted that if SgrA* is a black hole, the telescopes would record a gravitational redshift in the spectral lines of S2 as a result of the black hole’s gravity. This was indeed observed, and in fact this marked the first time anybody had observed such a difference from the Newtonian predictions caused by the motion of a star orbiting a supermassive black hole.

### Edging closer

These discoveries were revolutionary, but S2 is still far from the event horizon. In 2018, Richard Genzel was also able to observe a light source even closer to SgrA*. Every few days, the black hole itself emits a flare. Researchers at the Max Planck Institute measured the motion of the centroid of these emissions around the centre of the black hole, determining that, as predicted, the gases were moving at a speed of 30% the speed of light. The scientists were also able to measure the polarisation of the light, and learned that the event horizon is highly magnetised.

As a result of the discoveries of Genzel and his team, radio astronomers can now look towards a black hole, and see the shadow of photon propagation in the vicinity of the event horizon. If that’s not poetry, then I don’t know what is.

You may have actually seen the result of this yourself. Images created of this were released in May of this year and, honestly, my heart is fluttering just thinking about it.

### 40 Years in the Making

Despite Genzel’s progress, there’s still a lot more work to be done, and the European Space Agency is planning to launch a very ambitious experiment called LISA with the aim of answering many of the questions that remain.

Throughout the lecture, Reinhard Genzel was rather modest, and never mentioned that the discovery of a supermassive compact object at the centre of our galaxy was his own work. In fact, it was what he won his Nobel Prize for.

There was one thing in particular that Genzel said during the lecture that really stuck with me. I think it sums up very neatly the theme of collaboration running through the heart of the Heidelberg Laureate Forum, and seems like a fitting quote to end with.

“This is teamwork. This is teamwork and really trying to push and push again.”

### Posted by Sophie Maclean

Sophie Maclean is a mathematician and maths communicator based in London. She has previously worked as a Quantitative Trader and a Software Engineer, and now gives mathematics talks all over the UK (and Europe!) on a variety of topics. She is also a member of the team behind Chalkdust Magazine and always has a project on the go! You can follow her on Twitter at @sophiethemathmo.

### 2 comments

1. Sophie Maclean wrote (22. Sep 2022):
> […] There is a dense cluster of stars at the centre of the Milky Way, and at the centre of that is a compact radio source called Sagittarius A*, often abbreviated to SgrA*
> […] one particular star. S2 is only a distance of 17 light hours from the centre of the Milky Way. […] The orbit of S2 is approximately 16 years, […]
> General relatively predicted that if SgrA* is a black hole, the telescopes would record a gravitational redshift in the spectral lines of S2 as a result of the black hole’s gravity.

Gravitational redshift is not capable of being recorded by telescopes (as receivers).
Instead, redshift in general, and gravitational redshift in particular, is a relation (a real number ratio) between the frequency of a sender, and the corresponding reception frequency of a receiver.

Moreover, general relativity does not involve any predictions about whether, or not, any spectral lines occur in emissions of any astronomical objects or senders. (Such predictions may rather be the subject of (standard) models of atomic and astro physics).
Instead, general relativity is concerned with how to compare frequencies between separate senders and receivers at all, and with how to determine geometric and kinematic relations between senders and receivers to begin with.

p.s.
Sophie Maclean wrote (22. Sep 2022)
… in the HTML-file of this SciLogs webpage:
> […] <span style=”background-color:#fcb900″ class=”tadv-background-color”> </span>

Hereby submitted through a SciLog comment, for documentation and for the benefit of SciLog commenters in general,
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