Accretion disks: Revealing the shape of black holes 

If you enjoy movies set in space, such as Interstellar, or if you have kept up with space news since around 2018, you have likely seen an accretion disk: the bright disk around a black hole. But what actually is an accretion disk? How does it form? And why do we even care about them? 

The short answer is that an accretion disk is a doughnut-shaped dust cloud that orbits a black hole. It helps us study the properties of black holes that would otherwise remain invisible. Before we can actually dive in further into what an accretion disk is, we need to take a slight detour to the beginning of the 20th century. At that time, one of the best-known physicists made a remarkable discovery about gravity. 

The bowling ball and the marble 

In the year 1915, during the First World War, the then 36-year-old Albert EinsteinExternal link gave a talk in the Prussian Academy of Sciences. He presented his theory of gravity in which gravity no longer is a force as described by Isaac Newton, but rather a consequence of an object having mass and thus bending spacetimeExternal link around it. 

Very simply, the concept can be demonstrated with a tablecloth and a heavy household object, for example your favourite bowling ball. The tablecloth visualises gravity and the bowling ball represents a large object. Simply span a tablecloth and put the bowling ball in the centre. The bowling ball warps the tablecloth. It pulls the cloth down. Not just exactly where the object is located, but it also extends outside of the area the object touches. Next, take a round, lighter object, for example a marble, and place it on the cloth. It will roll towards the bowling ball. The objects seem to attract each other because of the curvature of the tablecloth. Einstein's theory proposed that this is how gravity works. He was mostly ignored. 

He who trapped light 

There was one problem with Einstein's theory: the first solution is for a universe that is completely empty. Shortly after Einstein published the equations for his theory of general relativity, another German scientist, Karl SchwarzschildExternal link, was fighting on the front lines of the First World War. Yet, he managed to publish a solution to Einstein's equations. 

This solution is fascinating, because it is the first solution to the equations that suggest that the universe is not completely empty. Rather, it has a single point mass. This solution has multiple quirks. For one, in a small region around the point mass, the spacetime is curved to such an extent that not even light can escape. This is a very good working definition of a black hole: 'A region of space time from which not even light can escape'.  

Schwarzschild's black hole is also the solution for a non-rotating point mass. This is surprising, as most massive objects in space rotate. Why would a black hole be the exception? In 1963, almost half a decade after Schwarzschild, Roy KerrExternal link managed to find a solution to Einsteins equations in which the point mass rotates. This shows that black holes need not be the exception.  

The fatal flaw 

All of these solutions, however, suffer from a fatal flaw: at the centre of their black holes there exists a singularity. In other words, there is a region for which the equations spit out infinities and our predictive power breaks. This is a problem because if we want to understand the inner working of our universe, we need to understand what happens at the centres of these objects. 

Alternatives to these simple solutions have therefore been proposed: regular black holes. This means that a solution does not blow up to infinity. The simplest of such solutions was found by Sean Hayward in 2005. Whilst the curvature outside of the event horizon is nearly identical to that of non-regular black holes, inside of the event horizon the curvature smoothly levels out removing that annoying singularity.  

So, physicist have provided a whole range of theoretical descriptions of black holes. If we want to figure out what type of black holes actually exist in our universe, we are in a bit of a predicament. This is because we said that a black hole is a region from which not even light can escape: we cannot actually see black holes. As a matter of fact, the only way for us to directly interact with black holes is either via their gravity or via an electromagnetic interaction. 

Since it is not easy, safe, or feasible for us to travel close enough to a black hole to test its properties ourselves, we need to rely on objects already close to a black hole to spill the tea on the black hole’s secrets. One such object could be a star. However, most stars are quite far removed from black holes. In the event that a star does get close, tidal forces created by the black hole tend to destroy the star. Now it seems like we are back at square one. But what happens to the matter the star is made of after the star is destroyed?  

Assembling the accretion disk 

Some of the matter flies off to infinity and beyond. However, some is attracted to the black hole and will actually start to orbit it. This matter forms the accretion disk. A better formulated description could be 'a disk of not clumpy material (like dust) orbiting a black hole'. The 'not clumpy' part of the definition is just to rule out planets and other such 'clumpy' objects. This dust typically rotates very, very fast, heating it up due to friction. This heat then results in the disk starting to glow. This is a similar process that makes metal glow when in it is heated to high temperatures.

Now, we cannot observe black holes, but we can observe their accretion disks. The shape of the accretion disk is a direct result of the bending of the spacetime. In other words: the shape of the accretion disk is a result of how a black hole works. Differently shaped accretion disks tell us about different types of black holes. A regular black hole, like the Hayward black hole, has slightly less curvature just outside of the event horizon when compared to the Kerr black hole. This means slightly less gravity and a slightly more puffy accretion disk. Thus, a good understanding the different shapes an accretion disk can take, can reveal a lot about black holes. 

This article was written by Robin BotlandExternal link

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