So I hope you have seen that dark matter is darn important for us. Without dark matter, there will be no stars, no galaxies, no us. So now we would like you of course, understand the nature of this dark matter. What actually is it? So, there are actually very limited information that we have with the nature of dark matter. So one thing we know is that it must be moving slowly. We call this property, call it cold. We talk about cold dark matter. Because something is hot, it's moving about very quickly. When something is cold, it moves about very slowly. So we call it cold dark matter. It also must be electrical neutral. If it does have electricity. Then, it should be reflecting a light. Because if you look, if you shine light on it, anything that has electric charge will shine it back to you. But we don't see that, so it must be electrically neutral. It also must be long-lived. As far as we can tell, even our own galaxy has a lot of dark matter in it. Which means that they must survive at least 13.8 billion years, so it must be long lived too. But pretty much these are the only thing we know about the nature of dark matter. But there are a couple of also, quantitative information about it. For example, when we came out this idea that dark matter should make up the pretty much the entire mass of our own galaxy The, the natural speculation was that, well, they may be kind of stars. which are just dim. that we couldn't see them in telescope. So some stellar sized object, which are very dim, and we can see them in telescopes, but may be making up our halo of a galaxy. We call them MACHOs. Which stand for massive compact halo objects. But even though that these MACHOs may not be visible directly in telescopes there are still a way for looking for it, and that's again based on the idea of gravitational lensing. So what we can do is keep monitoring let's say a million stars in a nearby galaxy called Large Magellanic Cloud And, as you keep watching these million stars in here, and we are here on outskirt of the-, our Milky Way Galaxy, sometimes this MACHO may pass through the line of sight towards one of the stars in Large Magellanic Cloud. And when it does, again it warps space, it bends light, so it acts like a lens. And that will collect more light that way. So the, the star you're watching may all of a sudden look, looking like it's flaring up, and then dims down to how bright it was before hand. So this is called the gravitational microlensing event. Even though people looked for it, there was actually very few of those. In that way we can actually, limit the amount of MACHOs that would make up the halo of our own galaxy. So for typical range, or what do you expect from an astronomical objects, this is one solar mass 10 to minus 2 solar masses, 10 to minus 4, 10 to minus 6. Then the MACHOs can be the component of dark matter only about less than 10% of it. So there is just not enough of them. Maybe they aren't any. So, it cannot be these dim stars. So now we have an upper limit on the mass of dark matter to be about ten to minus seven solar masses. So that's how heavy a dark matter can be. On the other hand, if the dark matter is very, very light, then it wouldn't actually fit inside our own galaxy. And if, you may know, that electron is orbiting around the nucleus, so in that case, electron has sort of a shape and certain radius, and that determines the size of an atom. In the same way if the dark matter is rotating in the gravitational field coming out from a given galaxy, they would also give you a blob and shape of dark matter which has a certain characteristic size called Bohr radius. So, you can work this out, using the law of Physics called Quantum Mechanics. And if you're not familiar with this, don't worry about it. So, you can compute given a gravitational force depending on the mass of a let’s say galaxy. And little m is the mass of dark matter. This is the size of the orbit of the dark matter in this gravitation field and that goes. Up as inverse squared of the mass. So the lighter the dark matter is, it becomes fluffy and wider spread. So at some point it wouldn't fit in a galaxy at all. So because dark matter has to fit inside the size of a galaxy the mass cannot be smaller than something. And that number turns out to be actually this one here. 10 to the minus 22 electron volt if you look at the mc squared. So that gives you a range. So we know that it has to be less than ten to minus seven solar masses because of this search for the gravitational lensing. On the other hand it has to be bigger than something, so that the orbit of dark matter can fit inside the galaxy. And this is what we find. So in terms of the unit called Gigaelectron volt, has to be somewhere between ten to the minus 31 and ten to the 50th, so we manage to limit the range of dark matter mass within eight one, 81 orders of magnitude. And that's the progress we made in 70 years since Mister Zwicky pointed out the possibility of dark matter in the 1930s. So, the point here is that we actually know so little about the nature of dark matter, we have pretty much verbal idea on the mass of the dark matter individually. Another piece of information is again a very weak piece of information. We know the dark matter sort of passes through each other in this colliding bullet cluster. So we can also limit how often the dark matter can interact on itself, namely something called scattering cross section. Again, if you're not familiar with this idea of cross section, don't worry about it. This basically tells you sort of the size of dark matter when you scatter them against each other. And that tells you how probable it is, the dark matter. Would get scattered, by each other. And that is based on various data. For example by looking at the shape of cluster of galaxies, and we know that dark matter should not be interacting much more than a certain number. So again what this is telling you, is the dark matter is a weakly interacting object with the rest of us And also with itself. And again, that's how little we know about it. So given this situation, we are trying to switch our idea from MACHOs to WIMPs. So in this case WIMP is an acronym which tells you that they are very, very weak interacting objects, even more weak in interacting than neutrinos we talked about before. And WIMP stands for weakly interacting massive particle. So they’re supposed to be heavy stable particles produced in the early Universe. And heavy, means mass is big, and because of E equal mc squared, that would take more energy to make. So we may not have had enough energy to make them in a laboratory so far But the big bang had such an amount of energy that any heavy particles should have been produced and some of them may be still left over. So this is the idea we will focus on for the rest of the lecture. And the idea is very simple. When everything is very hot and in equilibrium, you, you, you create this dark matter particle as many as any other particles we know. But as the temperature drops, then the dark matter should also come down its quantity because the universe can no longer make them. There is just not enough energy to make them. But once there is, the dark matter’s there the only way to lose it is the dark matter would meet each other and annihilate into some other particle species. So depending on how often they can meet with each other and annihilate we know how much of that is left over, so that this curve shows how much may be left over depending on how often it would meet with each other and annihilate with each other. But once becomes, the universe becomes big enough and the dark matter becomes dilute enough They would stop meeting with each other, so they cannot lose their numbers anymore and then the universe is stuck with certain number of dark matter he has made already. So the dark matter is frozen. That's the word we use. And don't worry about these equations really but when this is a very simple estimate you can make. About how heavy the dark matter particle may be if this idea of the WIMPs turns out to be the right picture and that turns out to be about 300 gigaelectronvolt. And this is, actually, a very interesting number because this is the kind of energy where the LHC experiment is right now, studying. But at the same time, because dark matter is supposed to exist all around us, maybe we can actually capture them. But, because dark matter interacts so little with us, it's very difficult to catch them. They pass through us all the time without us noticing it. So it's like trying to look for- trying to listen to a very, very faint sound in the midst of the metropolis like Manhattan. And of course, that looks totally impossible. So what do you have to do then is to go to somewhere that's very quiet where you can can shut out the noise. So, where should that be? To hear the faint sound of dark matter, we have to go to a quiet space where, but where could such a quiet space be? So, that's the next question to you.
