Gravitational Lensing

Astrostatistician Alan Heavens on general relativity, how lensing can be used to observe dark matter and whether Einstein’s theory of gravity might be wrong

videos | June 23, 2020

Gravitational lensing is the bending of light by the gravitational field of matter. It’s predicted by Einstein’s general theory of relativity, and, in relativity, space and time are combined into an entity called space-time, which can be curved. Part of Einstein’s theory tells us how space-time is curved, and it tells us that matter curves space-time. To get an idea, if you imagine a rubber sheet and you place a large, heavy ball on it, then the rubber sheet will distort. The other half of general relativity is that space-time tells matter how to move, so if you imagine firing a small ball bearing onto this rubber sheet, then its orbit gets changed; it doesn’t go in a straight line.

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This phenomenon also happens with light as well, so light gets bent by the gravitational field of matter. This has a number of effects which are useful in astronomy: one is that the position of objects in the sky will change because the light has been deflected. This was tested very famously one hundred years ago in an experiment by Sir Arthur Eddington where they looked at the light from stars which were almost behind the Sun. The light passing close to the limb of the Sun gets bent by gravity, and it changes the position of the stars relative to each other. So, by making a comparison of the positions when the Sun is almost in the line of sight and when the Sun is somewhere else, you can detect what the bending of light was. It’s difficult because the Sun is very bright, so what they did was to wait until there was an eclipse when the Moon passed in front of the Sun. By complete coincidence, the Moon is about 400 times smaller in radius than the Sun, but it’s 400 times closer, so it blocks out the light very nicely. The results were a subject of some debate, but they favoured Einstein’s theory in comparison with Newton’s theory, which predicts that the stars should move by exactly one-half of what Einstein’s theory predicts. Subsequent experiments have come down very firmly in favour of Einstein’s explanation.

The second effect is that sources which are gravitationally lensed will get brighter typically. We see that when stars go behind other stars, then the background star gets brighter and then fades back to its normal brightness. We can use that to do various things. One is that if the star in the foreground has a planet, then there’s an additional piece of lensing by the planet, and you can detect planets this way. The other thing that we can do with that is to try and work out what the dark matter in the Milky Way is. We conclude that it’s not predominantly in the form of dark objects such as black holes or brown dwarfs because there isn’t enough of this so-called microlensing that takes place in the galaxy.

The third effect that lensing has is to change the shape of the images. We see that in quite extreme circumstances when, for example, if you have a very rich cluster of galaxies that may have a thousand galaxies in an agglomeration, the mass is so grave that the light gets distorted enormously. It can get distorted into very long, thin arcs. Sometimes, you can even see the same galaxy twice; that light can get bent through two or more directions and still arrive at the telescope. That can tell us a lot about the intervening lensing object.

One of the uses that’s been put to is to determine something about the nature of dark matter.

There’s a cluster called the Bullet Cluster, which consists of two clusters which collided with each other about 150 million years ago. The stars in the galaxies just passed through each other. The chances of an interaction are very, very small, so we see these two clusters, the separated galaxies, having gone through each other. But clusters of galaxies also contain a lot of gas and when the gas interacts, it collides, gets shock-heated and stays in the middle. So we see hot gas in the middle, and we see the galaxies on either side, and we can use gravitational lensing to work out where the dominant mass contribution is. It turns out to be associated with the galaxies. So, the dark matter has passed through in a collisionless way and has ended up where the galaxies are; it hasn’t stayed in the centre. There’s a lot of it: most of the mass is in that dark form. That’s a challenge for other theories of gravity, which try to do away with dark matter because if there was no dark matter, we would expect the lensing effect to be associated with the gas because it has much more mass in it than the galaxies. But we don’t see the mass there; we see it associated with the galaxies. So those are very strong lensing effects.

What we also see is very weak lensing effects that occur all over the sky. In fact, if you look at a distant galaxy, then the light that you see has been distorted a little bit, and the shapes have been changed by one or two per cent typically, and that’s happening all over the sky. It’s a bit of a nuisance, but on the other hand, it’s a source of signal because the distortion pattern tells us a lot about the Universe. It’s quite challenging because we don’t know what shapes the galaxies should be before being lensed, but we can look for a statistical signal that is all the way across the sky. The light from these distant objects has been travelling for many billions of years, during which time the Universe has evolved, so the Universe has got more clumpy as gravity has pulled objects in, so it tells us about how quickly the growth of structure has taken place. That depends on the theory of gravity and other things, such as the amount of dark energy in the Universe, which is the dominant contributor to the Universe’s energy budget. So it’s a very good way of telling us about the constituents of the Universe and also about the gravity law.

This is a relatively young subject. The first time this was discovered was in about the year 2000, but it’s now a standard tool for probing cosmology. We can also test the gravity law because light and slow-speed particles respond to gravity in different ways, and in Einstein’s theory, there’s a very simple relationship between those two. So, if we compare the distribution of mass from lensing and look at the distribution of matter from slow-speed objects like galaxies, we can test this theory.

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So, where are we up to now? What have we learned from this so far? Everything so far points to Einstein’s gravity being perfectly fine and that the dark energy is in the form of Einstein’s cosmological constant. There are some indications that perhaps the Universe is not quite as clumpy as we expect from lensing. It’s not yet significant enough to be a concern, but if that’s established, and that requires better data which will come from the European Space Agency Euclid satellite, which will be launched in a few years,  ̶  if that discrepancy still holds up, then it’s an indication that maybe our picture is not quite right and that Einstein’s gravity maybe needs changing on large scales or the dark energy is not quite Einstein’s cosmological constant, that is a more complicated and even more mysterious object.

So, I look at the statistical analysis of lensing, and we devise ways of trying to do this in a principled statistical way. It’s a complicated statistical problem because the signal is very small; we need large volumes and large numbers of objects to do the scientific inference. But from the physics point of view, it’s a very beautiful signal which depends essentially only on gravity. In detail, it’s much more complicated, but the basic physics is really really nice and simple. So I think we tend to fall into two camps: half of us would like to find something new and something wrong with Einstein’s gravity, and the other half would like to say, well, it’s really fun to be working at a time when you really establish that the theory is right and our understanding of the Universe is right. I think I probably lean slightly towards the latter.

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Professor of Astrostatistics, Imperial College London
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