sábado, 26 de novembro de 2011

6. Gravitational Lensing - Sean Carroll - Dark Matter, Dark Energy: The Dark Side of the Universe

This lecture was less quantitative and more visual, which makes for a nice change of pace. But no less conceptual as the previous lectures, it demonstrates how observations of gravitational lensing confirm the Zwicky and Rubin conclusions of the need for a factor of five times the ordinary matter to account for dynamics of galaxies and their clusters. The more agreement the better of course, but lensing will play a role later in the course when trying to account for the composition of dark matter.

The best part of the lecture, and one of the best so far in the whole course, is the tale of the so-called Bullet cluster. This is actually two galaxy clusters nearby each other. The majority of the "ordinary matter" is in the form of x-ray gas, as expected. It's usually located between the galaxies of a given cluster, yet in this case it's located between the two clusters themselves, thereby implying a recent interaction. As when galaxies interact without affecting stars but only their interstellar gas, clusters interact without affecting galaxies but only their intergalactic gas. Gravitational lensing enables a rough map of the gravitational field, implying that most of the matter is centered around each galaxy cluster at the center of their own field.

These observations have two important implications. One is that most of the matter is not in the ordinary matter of x-ray gas, but is in some unseen form centered around each of the galaxy clusters. This is our good old friend, dark matter. Two, our current theory of gravity is correct, since some had suspected dark matter observations to just be a sign of a faulty theory. This also implies something about the charge of dark matter, since it did not interact like the charged particles of ordinary matter in x-ray gas did. Thus the world of particle physics is next on our plate in order to characterize dark matter and eventually, dark energy.

I want to make a comment about the appearance of so much knowledge about the universe. Ten years ago a similar type of course would probably have presented how much we had just discovered about the Hubble constant, solving the long and great debate between low or high values. A course ten years before that could talk about implications of dark matter, ten years before that the implications of inflation theory, etc.

Yet all along we had no clue about all of these recently discovered fundamental aspects, and I think we still don't. Dark Energy only shows us how much we don't know. But this has not been pointed out by Sean, so until he does, I will be a little disappointed about his bias. Robert Hazen's "Origins of Life" course does admit the ignorance of their field. In fact, Hazen's course is centered around this point of admitting ignorance. Though cosmology is the more experienced of the two, I believe both fields to be in the same state of just beginning to realize how much is unknown. I actually think this makes it all the more exciting! Please see my reviews on this "Origins of Life" course:


By now we're convinced beyond any plausible doubt that there is something called dark matter in the universe. What we've done is looked at the dynamics of bound systems, moving under their mutual gravitational fields. We've looked at galaxy rotation curves, the stuff moving outside galaxies, and we've looked at clusters of galaxies, large samples of hundreds of galaxies, and thought about both what the galaxies are doing, and what the hot x-ray gas in between the galaxies is doing. We find either way that you can't explain the motions we see, unless there's more matter in the universe than the stuff we can directly observe. So this should be evidence that closes our mind about whether there is dark matter in the universe.

Except that, of course, as scientists we don't like to close our minds until we really are as sure as we can possibly be. So in this lecture, we'll try to make another convincing case, from another completely independent set of information that points to exactly the same conclusion, that in galaxies and clusters, there's much more matter there, than the matter that we actually see.

What we did, when we looked at the motions of galaxies and clusters, was really mapping out the gravitational field of those objects. So again, when Einstein told us that whenever we have stuff in the universe, it creates a gravitational field. So we have a sure-fire way of finding everything there is. Just map out the gravitational field and use that to work backwards, to figure out how much stuff there is in the universe.

So we did that, but we'd like to do the same thing in a different way. We took advantage of the fact that particles, whether really individual particles or entire galaxies, move in a very determined way in the presence of a gravitational field. Yet they're not the only things affected by gravity. Even light itself is affected by gravity. That's part of the conclusion that Einstein was able to draw from the fact that gravity is the curvature of spacetime itself. Nothing escapes gravity's influence, so even a beam of light passing through a gravitational field, will be deflected.

This process of deflecting light due to gravity, is called gravitational lensing. We can use it as a completely independent way to figure out how much stuff there is in the universe. So the basic idea is simple. You take an object which gives rise to a gravitational field, and pass a beam of light past that object. The attractive force of gravity will bend the light ray as it passes by. In an extreme example, it can bend it quite a bit.

So we see an artist's impression of a gravitational lens that might be formed by a galaxy, with the thing being lensed as a quasar. That is a very bright nucleus of a galaxy, the center part of a very young galaxy, very far away and giving off a lot of light, so that they look just like points to us, like stars do. So quasar means quasi-stellar object, since originally they looked like stars. Now we know they're actually galaxy sized things in the very early universe.

So you look at a quasar far away, and you look at many of them until you get lucky enough to find an example of where there's a quasar far away, yet in between you and the quasar is a galaxy or cluster of galaxies, or something like that. If the gravitational field of the thing in between you and the quasar, is sufficiently strong, you can actually deflect that light from that quasar on both sides of the lensing object, and get multiple images, two images, of the quasar.

So this is something people have been looking for, for a long time. In the 70s and 80s they began to actually find them. So you can find pictures of this that look exactly the same astrophysical object, very far away. It's because there's something in between that is breaking up the image into multiple copies. You might ask how do we know that these two images that look the same, are really of the same object in the background? The answer is of course that we can take their redshift and find out how far away they are.

If you find two objects that look the same, and they're right next to each other, maybe with a little fuzzy thing in between, and you measure their redshifts and see they are equally far away, it's very likely that what you're doing is looking at exactly the same object. In fact you can do more than that. You can be more precise looking at the spectrum of light from that object and really verify that they are two different copies of the same thing.

So the reason it's called lensing is because it's the exact same kind of thing you would get when light passes through a piece of glass that is not absolutely uniform. If you have a piece of glass that is warped, that has different shapes, then the image of something you see behind it, will be distorted when you see it. You can do that correctly to make a lens that focuses on you or defocus, yet when you see any arbitrarily warped piece of glass, it will always give you distorted looking images. It's the same kind of thing, except instead of a piece of glass, we're now looking through a distorted spacetime, distorted by the stuff in between us and the stuff we're looking at.

This idea of gravitational lensing, of light being deflected as it passes through a gravitational field, goes back to Einstein himself. While he was working on his field equations, trying to derive the General Theory of Relativity, he was already thinking ahead. He was mostly coming up with the theory in his mind, through experiments, but was already thinking ahead to how we will know whether this theory is right? How will we test it against the data?

Of course we already had a theory of gravity from Newton which was really good. Everyone thought it was the best theory ever invented. Yet now Einstein is coming along with a different theory. There was already one piece of information that people knew about even before General Relativity, which is that the motion of the planet Mercury around the sun was not quit right. It was not quite moving in the orbit you would have predicted according to Newton's law of gravity.

So what do you do when something moves in an orbit which is not quite predicted by Newton's law of gravity, you invent dark matter! That's in fact exactly what was done. A French astronomer named Le Verrier invented an invisible planet that was supposed to be existing between the orbit of Mercury and the sun, which he called Vulcan. Unsurprisingly it was discovered several times, yet each time by mistake since it's not actually there. The idea was this new planet was a mass that was distorting the motion of Mercury, yet turns out not to be right.

It turns out that it was in fact gravity behaving differently. When Einstein invented General Relativity, one of the first things he did was to test what the orbit of Mercury should be like in his theory, and he found that it agreed. This was in Einstein's own words, the happiest moment of his life, when he realized that his new theory, fit this already existing data.

Yet he was also a good enough scientist to realize that it wasn't good enough to fit already existing data. You needed to make predictions for data that hadn't been taken yet. So as soon as Einstein invented General Relativity, he realized that the fact that everything is affected by gravity, means that even light will be so affected. This is something that Newton's theory didn't say anything about. So he was making a precise prediction that would be different in General Relativity versus Newtonian gravity.

However, the problem with his prediction was that it was very tiny. No one even knew about galaxies at the time, so Einstein was just thinking about stars, or perhaps the sun, which is the closest thing to us that is a large, massive object. Yet still the gravitational field of the sun in absolute terms, is just not that much. The amount of deflection that you get of light by the sun, is a very tiny angle.

There's an even more profound problem, when trying to use the sun as a gravitational lens, which is that the sun is tremendously bright. So if the sun is sitting there, and you're looking close by, hoping that it will lens some object through its gravitational field, the problem is you can't see any other objects, you just see the bright blue sky beside it.

There is one loophole to this problem of course, which is the possibility of a total solar eclipse. If you're lucky enough to be in the right place at the right time, when the moon goes in front of the sun, then the sun is still there, gravitationally lensing things behind it, still deflecting the light of stars that are nearby, yet suddenly you are not blinded by the sun itself. So if you take a picture of some stars in the sky and then wait until some future moment when the sun is in front of them, and there is a total eclipse, taking a picture of those stars yet again allows you to compare the image of those stars and positions on the sky, with the sun there and without.

If General Relativity is correct, the gravitational lensing effect of the sun, will distort the positions of those stars in your image, on the sky. So fortunately for Einstein, he invented General Relativity in 1915, and there was the perfect eclipse that was going to happen in 1919. Now of course by 1915, most people in the world, when you ask what was gong on in 1915 if they're physicists, will say that Einstein was inventing General Relativity. Most others will say that World War I was going on. So WWI ended a few years after Einstein finished his Theory of General Relativity.

So the eclipse came up in 1919, and an expedition was launched to make observations of it by Sir Arthur Eddington, a British astrophysicist and a very respected scientist in his own right. So he launched the expedition, went and took images of the stars in the sky, both before and after the sun was there, and he compared them. When he got back to England, they developed the film and realized that in fact, yes there was gravitational lensing of these stars. There was deflection of light by the sun, exactly as Einstein had predicted.

So what you had was a theoretical construction by a famous German scientist, being verified by an observation done by a famous British scientist, and it was actually taken at the time to be a very nice example of international cooperation among scientists, even though these countries were on different sides during WWI, they still agree that spacetime is curved, which is a good thing to agree on!

It also was the thing that launched Einstein's celebrity. Back in 1905, when he was inventing Special Relativity, Einstein wrote many papers that made him famous in the scientific community. Everyone by 1915 appreciated the genius of General Relativity, yet in 1919 when Eddington showed that the sun was deflecting light, just as Einstein had predicted, it made the front page of the New York Times. The general public suddenly realized that Isaac Newton had been superseded as the leading person to understand how the universe works, and Einstein took on that mantle. That was when he really became a public figure and often used his public persona to good purposes.

These days we go beyond just looking at the gravitational lensing of the sun, and use it as a tool to weight things. So the foremost thing we'll use it to weigh, are of course, clusters of galaxies, which we believe to be fair samples of what is in the universe.

There is another use that we'll just mention parenthetically, and get to in more detail in later lectures. That is to look for individual dark stars. If you have a dark star, some form of thing that is about the size of the sun, meaning anywhere from 100 to one millionth the mass of the sun, you can find those by using their gravitational lensing effect, because they move through the sky. So they're dark, but are moving through the sky and every once in awhile they will pass in front of a visible star. You can see the effect of the gravitational lensing on that visible star. It's very tiny, and is called microlensing. That's a way to find dark stars within our galaxy, which is something we'll talk about later when we discuss what the dark matter might possibly be.

Yet right now we're trying to establish that dark matter really does exist, so we'll use gravitational lensing to weigh clusters of galaxies. In other words, to map out the gravitational field of a cluster of galaxies in some detail. You can see, if you think about it, that there is an obstacle to doing this, that is not there for the sun or thee dark stars we might find via microlensing. The obstacle is that the cluster of galaxies is not moving in the sky. Both the cluster and whatever is behind it are sitting there on cosmological timescales, so even if you see something being lensed behind it, what you want to do is find out how much lensing there is, but you don't know ahead of time, where the object was. If the lens was not there, where would you see it in the sky? You can't compare before and after images, because nothing is moving, and the universe is more or less static over these very large distances.

So what you try to do, is figure out how much deflection of light you really have, even though you can't first put the lens there and then move it. You just have to deal with the fact that it's there. Well there's actually two different techniques that people have worked out to use, to figure out how much deflection of light there is. The first one was implicit in the first example we showed, the fact that you have strong gravitational lensing, is a lensing that is so strong that you see more than one image of the background object. Then you can figure out the angle by which it is lensed.

If you have one object in the background which passes through a cluster of galaxies, and you see two images of it, then there's an angle on the sky that is telling you the angle by which the light is being deflected. That is called strong gravitational lensing, and leads to some very pretty pictures that can show how strong the lensing is of some strong background galaxies.

The other possibility is weak gravitational lensing. This is actually much more common than strong lensing, where you're very lucky to find such a good example. Weak lensing is the idea that if you have a cluster of galaxies, and have a bunch of galaxies in the background, they will all be distorted by just a little bit. If you only had one galaxy in the background that passed through the gravitational lens, you wouldn't know what it was supposed to look like and where it was supposed to be, so it wouldn't help you in figuring out how much lensing is going on.

Yet if you have many galaxies in the background, their images will be distorted in a systematic way by the gravitational field of the cluster. So the fact that they begin to line up, not due to any intrinsic alignments, but because of how the light has passed through the clusters of galaxies, is going to be able to tell you how much lensing there was. So both of these techniques are in fact going to be used.

We see another image of a cluster of galaxies. We can see a couple of visible galaxies in the middle, and then also up and to the right, there is a bright red object which is an ancient star-forming region. It's an intrinsically interesting object all by itself, forgetting about dark matter and just thinking about astrophysics. This is some proto-galaxy that is coming to life, bursting with new stars and giving off a lot of radiation. It is in the background of this cluster of galaxies. We can measure its redshift and see it's very far away, and we see that it's distorted a little bit. It's aligned in a certain way that is sort of circularly wrapping around the cluster of galaxies.

So next we see an animation of how NASA scientists have been able to reconstruct the image of that star-forming region is distorted by the fact that it passes by the cluster of galaxies. So what you see is an initial image, giving off radiation. The light from that image passes by a cluster of galaxies, and as it does so, it is warped, going from a fairly square image at the beginning, to one in which it is distorted into this little ellipse.

We see yet another image, which is a reconstruction once again, of what would happen if we were to violate all the laws of physics, go faster than the speed of light, and travel from us here on earth, back to that star-forming region, going by the cluster of galaxies. What you see at first is the cluster of galaxies with the star-forming region in the background that's distorted into a little ellipse, and as you zoom past the cluster, what you see revealed is the original shape of the star forming region, which is actually closer to a rectangular shape than to this ellipse.

So you see that the effect of the cluster of galaxies, acting as a gravitational lens, is to change the shape of the background star-forming region. If you have enough examples of this, you can reconstruct how much gravity there was in the cluster.

So here is a more typical example of what you actually see with data. We see a cluster of galaxies once again, one we've already seen. Yet now we look more closely at it, in particular at the tiny galaxies on the outskirts of this cluster. Many of these galaxies are not in the cluster itself. They are behind the cluster and their light is passing next to it, on its way to us.

So what we see if we look at the galaxies in the background, is a systematic alignment of circles and regions of galaxies that are all little arcs. These arcs all wrap around the original cluster, due to the distorting effect of the gravitational lensing caused by the heavy gravitational field of all the mass in the cluster. You can see the number of arcs and the amount by which they're distorted.

If there were only one of them there, it might just be that this galaxy looked like an arc, all by itself! Yet if there are so many of them, there shouldn't be any reason why galaxies are lining up in such little arcs, especially if they are at different redshifts themselves. The reason why we see these little arcs, is due to the lensing effect of the cluster.

We know enough to take that data, the number of arcs and their distortions on the sky, to reconstruct from it, the total gravitational field of the cluster of galaxies. So we'll not be surprised to hear the answer, Sean hopes, which is that the total amount of mass needed to explain the amount of gravitational lensing, is five times as much as the amount of ordinary matter in this cluster of galaxies. In other words, the total mass that we've reconstructed by dynamical mechanisms, looking at moving galaxies and moving gas, matches, or is in correspondence with, the total amount of mass that is implied by gravitational lensing observations.

So this is nice and is telling us we are on the right track. If we didn't get that answer, it would have been very interesting. What if you have weighed this cluster of galaxies using two very different methods, but you're trying to measure the same quantity, and you've gotten a different answer. That would mean that you didn't understand something, either about clusters of galaxies, gravity, General Relativity, or something like that.

The fact that the two methods agree, giving us the same answer for the masses of these clusters of galaxies, seems to imply that we are on the right track. You can never be 100% sure that you are on the right track, since it's always possible you are being tricked one way or another. What happens is that as you collect more data, and get more examples of what is going on, the chances that you are being tricked, get smaller and smaller. At some point, it becomes a waste of your time to contemplate that you're being tricked, and you should just say, "Well now I have found something."

There are enough independent things pointing to the existence of dark matter in clusters of galaxies, that we've reached the point where either we should say that the dark matter really does exist, or that something even more profound is going on, something with gravity itself.

So lets look at one pretty picture, and then one profound example, both being hot off the press as new results in cosmology. The pretty picture is a three-dimensional map of the dark matter distribution in one direction of the sky. This is from the COSMOS Survey undertaken by NASA, and basically what they did is they said, "Lets take every telescope we have in all the different wavelengths of the electromagnetic spectrum, and point them at the same region of the sky."

So they took images with the Hubble Space Telescope, images in x-rays, infrared, radiotelescopes, ultraviolet images, and tried to reconstruct not just the picture of the sky in one direction, but the entire three-dimensional distribution of stuff. They have both the redshifts to different objects, and the images at each redshift. So what they can do from that, is reconstruct where the dark matter is. It's a little bit of a rough reconstruction. It's not highly precise, but you see the answer in this picture.

There's a distribution of dark matter throughout space. That distribution more or less matches where we see the ordinary matter. It matches it more than well enough, that we can say we are on the right track, so that where we think the dark matter is, is really where it should be.

On the other hand, it doesn't match it perfectly. So right now, one of the hot topics is research on things just like this, asking if the things that we see, which indicate that there is dark matter in a place where there is not a bunch of ordinary matter, is an indication of some novel mechanism in the evolution of galaxies and clusters that removes ordinary matter from dark matter, or if it's just that the data are not very good yet?

This is a kind of thing where we really don't know the answer yet. We're at the point where we do have a belief, a strong belief that there is something called dark matter, but the detailed dynamics of the dark matter and how it evolves along with the ordinary matter, is something we don't yet fully understand, and there's a lot more work to be done in that direction.

Now lets show Sean's favorite example, which is something called the Bullet Cluster of galaxies. It's a sequence of images of the same object, using different techniques. The first image is just a picture from the Hubble of this cluster. If you stare at it long enough, and you're a professional observational cosmologist, you will go "Aha, that is actually two clusters of galaxies."

There is a large concentration of galaxies on the left hand side of the picture, and the right hand side has a slightly smaller concentration. So you can actually take the redshifts and show they really are associated with each other, and are gravitationally bound. So this isn't just a chance superposition of galaxies at different distances.

So this is in interesting example of a double cluster of galaxies. There are two more or less independent objects, yet at the same redshift, so are right next to each other, cosmologically speaking. So remember we said that when we just think about ordinary matter in clusters of galaxies, forgetting for a moment about dark matter, in a cluster of galaxies, even the ordinary matter is mostly in between the galaxies, mostly in the form of hot, x-ray gas that is not concentrated in the galaxies themselves. Something like 2/3 or 3/4 of the ordinary matter is in this hot gas.

So when you see a cluster like this, especially one with an interesting shape, it's fun to take a picture of that cluster in x-rays and see where most of the ordinary matter is. So the next image shows us in pink, an x-ray image of this Bullet Cluster, a picture of where the ordinary matter is. It's glowing in x-rays and what you see is actually quite remarkable. The place where the ordinary matter is, shining in x-rays, is displaced from where the galaxies are. The ordinary matter is also coming in two clumps, just like the galaxies are, yet they are in between the clusters of visible galaxies.

Somehow the location of where the ordinary matter is, where most of the hydrogen and hot gas of this cluster is, is not in the same location as where the galaxies are. So this is interesting, yet it's not a complete mystery. There is a very simple explanation for how this could come to be. The explanation is that in the recent cosmological past, these two clusters of galaxies collided and went right through each other. You have to sort of think separately about the dynamics of the individual galaxies and of the dynamics of the hot gas in between.

The galaxies are fairly sparsely spread through the cluster. If you take the total area you see in a galaxy, it's only a tiny fraction of the size of the cluster as a whole. So when these two clusters went right through each other, came out the other side, the individual galaxies didn't even notice. They just went from one side and came out the other one. So you started with two groups and ended with two groups, perfectly the same and separate.

However, the hot x-ray gas inside these clusters of galaxies, does notice the hot x-ray gas inside the other one. So when these two groups come together and collide, there is a shock front set up, in the hot x-ray gas. The gas is slowed down from moving, but the fact is that it's interacting with the gas in the other cluster. So what we see is that basically the gas gets stuck in between, and you get a separation between where the galaxies are and where the gas is, in between.

That is of course, intrinsically interesting to astronomers, who would like to understand how clusters evolve in cosmological history. You don't get many examples of two clusters of galaxies passing through each other, so it's a lot of fun just to think about that.

Yet also from our point of view, we're interested in dark matter and dark energy, so it provides a unique opportunity to ask what the dark matter behaves like. If we believe that there really is dark matter in these clusters of galaxies, one of the features of dark matter is that it doesn't interact very much. This fact is most obviously displayed by the fact that the dark matter is dark. Most of the interactions over cosmological length scales of things in the universe, are either through gravity, which affects everything, or through electricity and magnetism, which affects charged particles.

So even atoms which are neutral, are made of charged particles, which is why we can see them. Dark matter is not charged, otherwise it would be easy to see, and they would not be dark. So the dark matter, to a very good approximation, is "collisionless." The dark matter particles go right through each other and do not bump into each other.

That's the reason why in an individual galaxy the dark matter halo is some big puffy thing, the bright visible stars have condensed and settled into the middle of this halo, because ordinary matter can bump into other ordinary matter, cool off, and settle down to the middle. Dark matter falls into a galaxy and just passes right through, so ends up in a big, puffy cloud while the ordinary matter settles into the middle.

So we want to know where the dark matter is in the Bullet Cluster? We started with two separate clusters, both with ordinary matter and dark matter. They passed through each other, the hot gas got stuck in the middle, so what did the dark matter do?

The next image is a reconstruction based on data of where the dark matter is in the Bullet Cluster. In particular, it's a reconstruction of where the gravitational field is in this cluster, based on gravitational lensing observations in the background. What we see is quite remarkable. The dark matter, or at least the gravitational field in this cluster, is centered on where the galaxies are. Yet remember that the galaxies are not centered on where most of the mass is located, which is in the hot gas in between the galaxies, and it was displaced. Yet the gravitational field stuck along with the galaxies.

The next picture superimposes where the gravity is located, and where the matter is located. The gravity is in blue on the outsides and the matter is in pink on the inside, giving off these hot x-rays. We see a very clear example of where the gravitational field in this cosmological object, is pointing in a different direction than where most of the "ordinary matter" is located. This can't be explained if you don't believe in dark matter! If you only believe in ordinary matter, the stuff that is causing the gravity, is the ordinary matter. So the stuff where the gravitational field is, should be where the ordinary matter is.

In fact, this is not only good evidence that there is dark matter in the sense that there's a lot more stuff than what we see, but it's also good evidence that we're on the right track when it comes to gravity. Up until now, we could always have believed that the reason why the gravitational field in an individual galaxy or in a cluster of galaxies is stronger than it should be, is because we didn't quite understand how gravity was working on large scales. Einstein and Newton were somehow going wrong on the scales associated with clusters and individual galaxies.

This Bullet Cluster result is telling us that that's not right. There is no way to understand how the gravity could be pointing in a different direction than the ordinary matter, if there was just a modified theory of gravity, but there's no actual dark matter. We'll discuss this result a lot more in future lectures, seeing whether you can get rid of dark matter and dark energy by modifying gravity. Yet right now we're confident enough to move on with the conclusion that there really is a lot of dark matter in our universe.

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