 You have it here. All right, welcome back. So we have the third lecture about reorganization. OK. Hello, everyone. Welcome to the last lecture of reorganization. It's a short course. I hope I was targeting as wide audience as I can from your background. I hope the experts of you or some people who know a little bit about the field didn't get bored during my talks. I'll continue with this thread of giving the flavor rather than the too much details, although today will be some details. So I told you last time I finished with this that about the global evolution of the Delta TB and different parts are driven by different things. I told you that this bit, which is a negative dip, will be wonderful if we can get to, because that will cover redshift of, where is the redshift? It's up there between 30 to 100, 150. That's great if we can do it. But that's kind of futuristic. We have to go outside the earth. This one is caused by cosmology. Average evolution of the universe doesn't need any structure formation, nothing to see this. This is, as I told you, this has to do with the coupling and the Compton heating and all of that Compton coupling, et cetera. So this is average. This doesn't need astronomy to see this. This one is a bit more, it's related to the first objects you just need to start seeing astrophysical objects. And this we have hope to see at redshift 30, between redshift 10 and 30, with SKA, probably, or HERA. Although it's not easy. I'll come to that why it's not easy. It's very difficult, actually. The current experiments are here. And as you remember from my last equation, this is driven by mostly either density fluctuations, 1 plus delta. But this is the smaller contribution. The main contribution for this is this. It's this term that has to do with the fact that you ionize some of the intergalactic medium. And then you have a lot of contrast between 0 and 1, things that are completely ionized and things that are completely neutral. So this is where we are now. So this is the easier of these three eras. This is the easier to track, although it has the smallest amplitude, because it's actually the highest frequency or the smallest redshift, range. In this business, and that's what I will focus on today. I'll talk about some experiments, and specifically low-far I'll focus on. But in this business, the lower the frequency you go to, the harder it becomes, much harder. And we are talking about frequencies here of tens of megahertz, here 50, 200, and here between 100 and 200. This is where this thing is expected to be. Just to remind you, if you have any course on plasma physics, you remember the plasma frequency thing? So if you calculate the plasma frequency for the ionosphere, for our ionosphere, you can see that it's of the order of 10, 20 megahertz. So in other words, at these frequencies, our atmosphere becomes reflective. So these things come and bounce back to space. So that's why we have to go to the moon. So that's at least one of the reasons, or two other places. Anyways, let me kind of now talk about two things. So we are talking about ionization. Ionization happens when you have photons that are, if you have a sources, that emit UV photons, things that have energy larger than 13.6 electron volt. And normally you would ask, if I have one source, one source of ionization, and the rest of the universe is neutral, how the profile would look like around this source? And here what I have in mind is stellar sources versus quasars, X-ray sources, right? So things with power law. Just to understand what the tradeoffs in this game. The first thing you have to worry about, if I have a photon that is ionizing photon, have an energy, potentially ionizing photon, that has an energy larger than 13.6. So you would ask first, what's the mean free path? The mean free path is given by this formula. It's one over the number density of hydrogen. In this case, it's neutral hydrogen, because if it's ionized, it doesn't get absorbed. It's already ionized. Ionizing photon will continue. So I should have put H1 here, not H. And sigma is the cross-section for absorption, for Lyman-Alpha absorption. Now the Lyman-Alpha absorption cross-section is the energy dependent. And it roughly goes like energy to the minus 3. In other words, sigma of H as a function of energy goes is proportional to E over E0, where E0 is roughly to the minus 3, where E0 is 13.6 electron volts. So it's clear from this. The number is not exactly minus 3. It's roughly minus 3. So what we get from this is that things that are more energetic have less likelihood to be absorbed, to ionize things. So x-rays, which have much more higher energy, have much harder time ionizing the intergalactic medium rather than photons with 13.6 electron volts, 14 electron volts, et cetera. Yes, please. I'll come to this. I'm still here. I'm going down this equation. So this is the mean free path. And this is the bound free cross-section for this process. Now let's put numbers. We know that what the baryon density is. This is an old number. It's not updated with the current plank thing, but it's roughly correct. This is the baryon density, a number density at reach of 0. So this is as a function of redshift. Sigma 0 at 13.6 is this. This is a famous number. And this is E0. These are the things. So you calculate what's the mean free path. Now let's assume that you have a photon that has exactly 13.6 electron volts. What's the mean free path of this? It's 2 kiloparsecs. So if you emit a photon after 2 kiloparsecs, it gets absorbed by the mean intergalactic medium. I haven't considered fluctuations over densities or anything. It's just the mean intergalactic medium. However, if you take 1K AV photon, that's an X-ray photon. That's not even hard X-ray. That's just a normal X-ray photon. The mean free path becomes 1 megaparsecs. So in other words, it travels 1 megaparsec before it gets on average, before it gets absorbed. So if you want to ionize, you better produce things that are closer to this energy, because this is much more efficient in ionization. X-ray do something else. And that's where it comes here. This was supposed to be, it is an animation, but I did it in open office at the time. And when I translated to PowerPoint, it stopped being an animation. So I'll describe the animation by words. So if you have a photon, this is a photon of 13.6 electron volt, or close to that, a little bit higher. This photon sees a huge, the cross-section for this versus an electron, versus an atom, sorry, this is a hydrogen atom. So this photon sees the hydrogen atom as a huge thing. That's the cross-section, right? It's big. And it ionizes it. So what you should have seen, that this electron goes away with some energy. But because the energy of the photon that is coming is low, relatively, then the excess energy after the atom took 13.6 to ionize, the excess energy for kinetic motion is tiny, is little. And that's what this arrow is describing. Whereas if you have X-ray photon, the X-ray photon sees the atom as a tiny thing, because the cross-section is small. And if this ionization happens, the excess energy that the electron that flies has is huge. Because out of this 1 keV, 13.6 electron volts went to the ionization, the rest should go somewhere else. And it normally goes to kinetic energy, normally. Actually, it goes to a few things. I'll go to that. Now, if you have an electron that has so much energy, where it will energy will go? It will go to collisions and to heating. So X-rays are very good at heating, whereas UV, or UV above 13.6, are very good at ionization. So that's why if you want to heat stuff, it's better to have X-rays in this game. There is another thing I want to mention, which goes back here. That also comes a theme that comes a lot in these types of things. Again, it has to do with this optical mean of the mean free path. Higher energy photons have much larger penetration power inside things, just because of this fact, because of the cross-section becomes small. So you might have a galaxy. There is a concept called self-shielding. If you have a galaxy that shields itself from outside photos, what it means, self-shielding, I will not go into details of it. What it means, if you have a high density area and you ionize, then the density is high enough that recombination becomes very efficient. Recombination goes like the density squared. So if the density is high, the recombination is higher. And then once you ionize something, if the density is high enough, it immediately recombines. So for low energy photons, they cannot penetrate, because they ionize the skin, and the skin immediately recombines. So there is no penetration power. But if you have harder photons, they can penetrate. No problem. And they can prevent things. We can heat things or ionize things inside, et cetera, et cetera. So this is something that you have to keep in mind. Again, I'm not going to details. This is just a generic description. In a famous paper by Shul and Fansteinberg in 1986, this is one of their figures, they asked themselves, if I have an X-ray photon, and this X-ray photon scatters or gets absorbed, in other words, ionizes some photon, what does that leftover energy do? If you have one KAV photon that has ionized a hydrogen atom, take 13.6 out for ionization, the rest is a lot. You're still almost with one KAV. Where does this energy go? And he worked out that roughly it goes to three parts equally. It depends on details a little bit. It depends basically on the neutral fraction or the ionized fraction. But in principle, it's this 30%, third, third, third, roughly. And where it goes? It goes third of it roughly, although this is not accurate. It depends on the situation. This is these other curves for different incident energy from 28 electron volt to very high energy. Third of the energy, the leftover, this is called secondary effects, because the electrons that get out, it's not a direct cause by the photon, but it's a cause by what the electrons that come out of the ionization do. So we call them secondary effects, secondary heating, secondary ionization. So three things. One, these electrons can ionize their surrounding, because they are so fast, some of the energy collisionally can ionize their surrounding. So that's ionization. Another effect is because they collide the heat. So they heat the surrounding. Roughly third of the energy goes for the heating. And the third goes for excitations. So they can collide, or instead of ionizing the other hydrogen atoms, they can excite them from the ground state to higher states. So these three effects are divided roughly equally. It's not completely accurate. You have to take this term into account, which is the ionized fraction of the medium. But roughly this is correct. And here what I show is the fraction that goes to ionization. That ionizes its surrounding. So this is kind of basic physics of this whole process. Back then, we wanted with my former student, Rajat Thomas, we wanted to look if you have an isolated quasar or an isolated star. The difference between a star and a quasar is that star produces thermal radiation. It's Planckian, and it has some UV photons, but doesn't have 100 electron volt or 1 keV photons. That doesn't come. Whereas quasars, for instance, they are tor-low sources. They are non-thermal processes. So they can have very high energy photos. We wanted just to see this, what you get. And it's a bit... It's an old plot, so I don't think it's very clear. But anyways, so if you take a certain mass, and this is, I think, these are the stars, and these are the... No, it's the other way around. This is the quasar, and this is the quasar, and this is the star. And you can see that stars can ionize things very efficiently. Their ionization fronts are very abrupt here, very strong, whereas this is the quasar. It's a bit harder. You have to plug in lots of photons here to get the same effect. But the main thing is with the heating. So this is the heating. This is the kinetic temperature in both cases. And you can see that the front, so this is where things are ionized. If you look at the blue thing, this is where things are ionized, and this is where this transition between ionized and neutral, and you can see that the border is very sharp. Whereas with quasars, because they have this penetration power, it's very, very wrong. So I mean, it's kind of extended thing. And that has an effect on the spin temperature and the brightness temperature. And the two would look a bit different, very different. For the stars, it would look that you have here some certain in this region, some spin temperature, but inside it will be zero. But the interesting bit is for the quasar. For the quasar, inside where things are completely ionized, the spin temperature is zero because hydrogen is completely ionized. You remember the spin temperature depended on the hydrogen content, the neutral hydrogen fraction. Immediately after it, the heating is very efficient, so the intergalactic medium gets heated above the CMB. And therefore you get this positive dip. But far away, where baryons are still cooling, they are colder than the CMB. This is very high-rechips before the intergalactic medium got heated to 10.4. They are still very cold. But these collisions, these secondary electrons make it very efficient for the spin temperature to be coupled to the baryons, to the gas, which is very cold. And then you see the effect on the brightness temperature in this very negative dip. And of course, far away, these photons will be completely absorbed and they will not reach there and you will not see it. So this is, if you go to the chief 30, you look at the profile like this, you say, oh, there are x-rays there, right? That's the dream. It's just a simple calculation that we made at different red shifts with different black holes. And this is, I think, the lifetime of the quasar at the time that we assume. So, I mean, this is poor man's kind of arguments. These are just to see the physics, but if you do want to do the full monte, the full shebang, you have to go through to radiative transfer type of simulations. So there are not only cosmological simulations with gas and dark matter and what have you, but also you have to take into account the radiative feedback, right? That the radiation processes from this and this is a very difficult story. I'll let you ask in a second. So people do all kinds of approximations and there is all kinds of things to do here in simulations. Some of these simulations try to get the full physics completely as much as they can. Of course, that's never possible, but they do as much as they can and some of these simulations, if you have 100 megaparcy volume that you want to simulate, that they can take a year on a supercomputer to finish. So it's a very hard business to do to get the details and details. But there are people like myself, but like others like Andre Missinger who have and Mario Santos who have other kind of ways to do this in a very approximate way, very kind of poor man's simulations, just to get instead of simulating one case and know it in gory details, you can simulate many, many cases, but the details you have to be careful with, okay? So these are the two approaches in this simulation. I will not show you too many of these, but that's just a list of things that people do that you have to take into account. Yeah, this one? What's the question? Are these? Oh, so what we did here, this is a simulation, but it's a simple simulation. We put the intergalactic medium as a uniform and then we calculate for one single source the radiative transfer bit. So here you don't have dynamics, you don't have, it's just the radiative transfer bit. And it's ferrically symmetric, so it's simple. You put all the physics, you can do any physical effect you want because it's one dimensional, so it's easier. This is just to give you the flavor. It's not, I mean, the details have to be done differently. So we use this, this is again, one of these semi-approximate methods. I showed you before in the first lecture, this movie, which was done with much better simulations. These are our simulations. Again, these are poor man's simulations. And the difference between the two cases, for instance, this here we considered as a quasar type of thing. I would admit my life that quasars ionize the universe. That's clear now. But it's just to see what's the difference between things with X-ray sources and things with thermal sources. Just to see different examples, this is the stars and you can see that with the X-ray sources it's very rapid, whereas with stars it's very extended. So this is higher shift, this is lower shift when the universe ionized, right? So which one is the, I mean, these are very two different pictures that you can see. Okay, so this is kind of the theory. Now let's go to the experiments. And that's where the excitement is. We are looking at specific windows in radio. So let me go back to this figure that I showed you before just to remind you this one. So here we are considering looking at this type of radiation. This is, I mean, the location of these three is not completely certain, especially these two. This is kind of certain, but these two are not. So this can be moving left or right. Probably in the recent years, this thing has been moving to the right, lower and lower red shifts. So this is where we want to look first with the current instruments, and that's of the order of 150 megahertz, megahertz. Remember, CMB is done with gigahertz, right? 100 gigahertz is the sweet spot there. That's where things start 100 to 100. That's where things, of course, they start from 30 gigahertz, but I think the most sensitive CMB channel in plank is about 100 megahertz, a gigahertz. So there's three orders of magnitude difference in frequency. That's a lot, which adds a lot of problems for us. That's part of our problems. You will see why. So let me go through this. So this is the same figure that we always show about the history of the universe, but this is done in the way that we will see it in radio, in radio astronomy. So again, this is the CMB. Before it, the universe is opaque and ionized. After it, it becomes neutral, and bit by bit, it gets ionized. This is the epoch of realization. It's these bubbles that are forming, and this is how we want to see it. This is a picture of low-far center. Low-far is a big thing. I think I'll have a slide that explains it, but this is generic for all these instruments that look at this, especially interferometers. Now, this radiation starts from here at 21 centimeter. So we want to track the neutral part, and when the neutral part disappears, it means the universe is ionized. So you see 21 centimeter before, and then bit by bit start disappearing, and at the end, it disappears completely. It means the universe got ionized. Okay, so that's the principle. 21 centimeter, so the radiation starts at 21 centimeter. This is roughly the rate of 10, seven, eight, whatever, and as it comes to us, it gets stretch shifted. It gets stretch shifted from 21 centimeter by a factor of 10, it's about two meters. So this is two meters astronomy, right? That's the relevant wavelength. Whereas CMB, it's millimeter, right? 1,000 times difference. Well, a little bit less than millimeter, anyways. But then you go down, no, it's micrometer. Am I translating this correctly? Anyways, it doesn't matter. So from 20 centimeters reaches us to two meters. Two meters, that's radio. That's 150, 140 megahertz. So that sits where we should look. Now, in its way, like in the CMB experiments, we get lots of foregrounds. Actually, we get a huge amount of foregrounds. We envy the CMB people because our foregrounds are atrocious, you'll see how. Part of the foregrounds is these extra galactic sources. These are galaxies, radio galaxies basically, which are kind of active galactic nucleus. There are two famous types, et cetera. And so they are small point sources in the way that you can see. So those are, there's a lot of those. And you have to take them out. There are so many of those that they are confused you. So you have to know how to deal with them. Then there's another part which is due to our galaxy. That's the synchrotron. It's the same synchrotron that you heard about in the CMB. But it's much, much, much larger for us. Way much larger. If you remember the plot, I don't know if you have shown that plot about the CMB. CMB normally, you have the synchrotron going this way as a function of frequency. This frequency going this way. And dust going this way. And the CMB, primary CMB sits here. This is at 100 gigahertz roughly. This is what worries us. It keeps going and going and going and going. And we are here, thousand times smaller frequencies. So synchrotron for us is huge. We have no band whatsoever of frequency where our signal is larger than the synchrotron or the dust like the CMB has for the temperature. For the B-modes, that's a different story. They have the life like us, but for the temperature it's easier. Okay, so this is this. And this is not the nastiest bit. The nastiest bit is the ionosphere, actually. It's our ionosphere. What happens is that these waves come to us and they enter the ionosphere. The ionosphere is ionized. That's why you call it the ionosphere. And then there are all kinds of refractive and things change. The ionosphere distorts the wave and it does very horrible things to it. So you have to get rid of this effect of the ionosphere. That and some other bit about the instrument is called in a radioastronomic calibration. And that's the hardest part of all of this. So this is hard stuff. And then this signal comes. It adds all of these kind of things. It gets distorted, adds foregrounds. And then at the end, there are all of these, you see these windmills that we put there? We are worried about those. Those are not astronomical, but they are man-made. What they do currently in many places, they try to build these windmills to be 100 meters high. In the Netherlands, they are doing this. Why is this dangerous for these types of things? And you will see these things. You see them on the ground. So our detectors are very simple. You will see a picture. They are stuff that is on the ground. If you put something on the ground, it's horizon is very limited because the earth goes like this, right? So if you have man-made sources, you don't see them far away. They are kind of limited. So if you put it in the Netherlands where there's lots of people living and there's lots of man-made stuff, on the ground, that's safe. You go a few kilometers and you stop seeing stuff. But if you build something that is 100 meter and that thing reflects whatever comes to it to us, then your horizon stops making a few kilometers. It becomes hundreds and thousands of kilometers. And that's bad, right? So we are worried about these things. These things called RFIs. I mean, not only this also, airplanes can produce anything that is man-made called RFI, radio frequency interference. Satellites, we see satellites. Easy, right? You see Hubble space, there's lots of fun things going on there. And then all of this signal goes into these kind of stations. These are interferometry units. And the signal from those goes to this supercomputer. This is the old supercomputer that we used it. That we were using Blue Gene. This cost us a number of million euros at the time. Now we use GPUs, 200,000 euros. Actually less, right? That's more slow. More slow saves you a lot. We started with millions of euros for computing. Now it's hundreds. Well actually 100, 120,000 euros is quite cheap. Stunning. If you can use GPUs, use GPUs. It's not good for every problem, but... Everyone knows what GPUs are? Have you played games in computers? Yeah? That's what games do. They use these GPUs. They don't use CPUs. They are called graphic something units. Processing units. In a nutshell, they do very little operations. They are very little. They sum or add. But there are plenty of them, right? It turns out that people who want really numerical stuff that is heavy in certain problems, this is much more better than something that CPU that is very heavy, very sophisticated. Because if you want, for instance, I'll give you an example. For these types of things, interferometers, you know what you do. You take two units and multiply them. So all what we do to do the signal here, we multiply things, two things, and they are completely independent. This, the multiplying these two is different than multiplying these two. So you can do all of them simultaneously. It's embarrassingly parallel. So for parallel processes and many of them, these things are wonderful and they can speed up things by huge factors, right? So that's why you can buy them cheap. Anyways, so they are good for certain types of simulations, even numerical simulations of dynamics, people are trying to do things with them. We use them for calibration, but for correlations, but we all use them for calibration, which is also an interesting problem. Anyways, currently there are a number of experiments that are trying to detect the signal and I think this list is not complete almost. This is low-far, this is the unit of low-far. The technology here in principle, it's not simple, but in principle it's simple. It's the same idea, many of you are too young to remember maybe antennas of TV, antennas on rooftops. This is how we used to watch TV, not with cables, but with radio. This is roughly the same idea, right? So, but of course the detector here are very sophisticated. So we, in low-far, we have tens of thousands of those. There's a lot. Another experiment, so this is low-far. It's European, it's based, it started with the Netherlands, but it kind of spread out and now there are many European countries, Germany, Sweden, England, the UK in general, and France, and Poland, and what have you. I mean, there's so many countries involved in it. That's low-far. This is MWA, that's an experiment that started, that is Australian MIT kind of collaboration. It's based in Australia and they also have some results. Paper is something that started in Berkeley with the late Don Bakker and it took off. They have published some results. It's quite a nice experiment. GMRT, that's the Indian, Great Meter Wave Radio Telescope. Some results from there I probably will show. And then I show also the future. SKA will be stunning. I'll show you a movie, an old movie. I don't think they have produced a new movie towards the end. Probably this will be the last thing in my lectures. It's the movie. This is HERA, which is kind of an upgrade of paper. This is an American project and both, I mean, there's preparation going on for both. I mean, these are will be incredibly nice. These are kind of backfinders that we are trying to understand the problems, what we should look at, what are the difficulties, and we hope to take something with it, but we'll see. Now, this is a complicated plot. I will not explain the equation, don't worry. I will not go there. This is what you will take as a first thing when you look at radio data. There's something called visibility and stuff like that, which is different than the CMB visibility. Right, so let me explain to you a bit radio interferometry. This is the purpose of the slide. It's very simple. Normally, when you have a normal telescope, a dish, and you want to look at a certain place in the sky, you just point. You just turn the dish to that side, and then you look at it, and then all these parallel rays of radiation that come to you get focused naturally in the focal plane, and then you see what you see. In this game, we do differently. You saw our element. It's just a dipole, just two elements like this. So dipoles see all the sky. You cannot say, I just want to look there. So how do you decide I want to look there or there or there? You do it with a neat trick, like what interferometry do, it's interferometry. So if I have two elements of these dipoles, I mean this picture is misleading. These are not dishes, they are just dipoles. And you want to look at this source. What do you do? You say, OK, radiation from this source will hit this element earlier than this element by how much? By this separation, C delta T, where this delta T is dependent on the baseline, on the distance between the two, and the angle to the source. So you pick up radiation that comes at certain time, T here. And then you say the same wave arrived here at T plus delta T. And then you take those two signals and correlate them. These are the two things that you correlate. So timing, the clocks are very important in this. They have to be incredibly accurate. And you pick up the right times and correlate the signal at the right times. That means that you look at the same source. So that's the simple kind of intuitive way of looking at this. You have learned long ago in physics that when you do interferometry, you look at Fourier space. This is what we measure. We don't measure in real space. We measure Fourier transform of the sky. So we don't measure the whole sky. We measure one point. So each pair of antennas at a certain time, when they look at the sky, they have one point. So this is your UV plane. This is called UV plane, which is kx, ky. Why they call it UV? That's the tradition in radio astronomy. But it really means kx and ky, Fourier x, Fourier y. And at every incident, you have a dot here. So you sample one point in your Fourier plane. And as the sky rotates, actually the Earth rotates, but the way we see it is that the sky rotates, these points start moving. And after 24 hours, this point will complete a closed ellipse if you are looking there. If you are looking there, it will be a bit more complicated. It will be half an ellipse here and attached, half ellipse there with different properties. But we don't observe 24 hours. We normally observe at night for various reasons. Eight hours. So it means that you have to sample this to have a point here with the one baseline that starts here, another baseline will start here, another baseline will start here. And when the Earth rotates, the three will complete this ellipse. So that's called synthesis. That's the synthesis of your track. Now, once you have done that, that's nice. You have recovered one track in your k Fourier space. Now, if you have many, many, many of these baselines, some of them will be here. Some of them will be closer. Some of them will be farther away. And then you will get a filled area in this UV plane. And if you remember, Fourier space and real space are equivalent. They are one-to-one transformation. So if you get information real Fourier space, you get information in real space. You can image everything. You just Fourier transform your signal. The problem is that you don't cover your Fourier space completely because you need the infinite amount of antennas to do this and infinite amount of distance, you know, distribution of distances. So you get areas that are filled. And here, this will be for low-far, for instance, this will be very filled. But at the center, there will be missing stuff. And there will be an out-on boundary with a sharp drop. So you will have a disk that is filled with data. But outside of it, there is nothing. Inside of it, there is almost nothing. And once you have boundaries in Fourier space, you go to real space, you get sync functions. That's called side lobes. Very simple. This is what we do when our radio astronomers tell you side lobes, that's it is. It's this kind of these boundaries that when you transform, they produce these ripples. That's why radio images look crappy. They're not nice because of all of these things. But there are other things, of course, much more complicated. OK, but this is basically what we are measuring. Yes, please. A different direction. Because then you have to store every data point. And then you could do the correlation in hindsight. And that becomes huge. I'll tell you about the number of data, the data load that we have. And then you will understand. Otherwise, you will have to store every data point at each antenna, at each time stamp for good. That's not petabytes. I mean, that's way much more. We just can't do it physically. We can't do it. OK, I explained this. This is another figure that came out from Viborielic's PhD, where this is not a cartoon. These are real simulations of different effects. I talked about them. And I talked about the atmosphere. I didn't talk about the other complication, which is the instrument response. So this is the signal. These are the foregrounds. This is what we measure at a certain frequency. You add to that the ionospheric effect and the instrument response. And then you have, so this is what we measure. And in principle, we want to reverse this and isolate the signal itself. So that's the big challenge. As you can see, it's very challenging. Look at the numbers. The signal, if you remember, I told you 28 millikelvin yesterday in the equation. It's actually not 28. 28, if your resolution is fine, infinite. If you go to the resolution of galaxies. With the resolutions we have, three arc minutes or so, the signal is much smaller. It's of the order of 5 to 10 millikelvin. So that's the extragalactic stuff is of the order. This is the RMS, basically. The extragalactic stuff is of the order of 1 Kelvin, 0.8 Kelvin. And the foregrounds from the synchrotron is of the order of, here we write 5, 3, 1, 10. It depends on the area you look at. So you can see that your signal is 3 orders of magnitude smaller than your foregrounds. You have to dig this out from the data. That's one challenge. How you dig it out? It's there's lots of work that's done on this. So I'll talk about this for a few minutes. So first of all, the foregrounds, what they are. And I mentioned what they are, actually the highest component is the synchrotron. It's the galactic, it's the synchrotron galactic. It's about 70%. And 30% of it is extragalactic, which is these point sources. This is the first time this has been measured. This is from our group that this is a work that is done by Bernardi, basically, Gianni Bernardi, basically, mainly. But it had a lot of effort. This is not low far. This is before low far. We had this Worcesterburg telescope, and still is in existence. But it had this thing called low frequency front end, which is able to measure in 150 megahertz. And we measured the foregrounds. And for the same first time, people see foregrounds in these frequencies. And you can see the power spectrum. This is not LL plus 1 over 2 pi. It's just the CL squared, the CL itself. And you can see that in this is the power spectrum of the foreground as a function of L. This is the power spectrum of the synchrotron, basically. And then you hit a floor, which is the noise floor. The second thing here is the foregrounds in polarization. The difference that you have very few polarized sources in astrophysics. So you don't have this noise floor from the sources. So you can go down and down and down and down. Although the signal is smaller, polarization shows you things clearer. OK, so this is actually VBOR's PhD. So let's think, how can we dig a signal that is three times, three orders of magnitude smaller than the foregrounds? Can it be done? I'll give you an example, which then immediately kind of it's an analogy. It's not a direct example. If you look at a mountain, mountains are of the order of 1,000 meters, a few hundred meters. And at the mountain, there is a tree there. You can distinguish the tree from the mountain. There's no problem. The tree is a few meters. This is the analogy. You can do it. The reason you can do it is that the appearance of the tree is different than the appearance of the mountain. Right? In this game, the difference between the foregrounds and the signal that we are after is as follows. The foregrounds are mostly synchrotron, even the extragalactic one, they come from this. Synchrotron is smooth along the frequency. That's a smooth function. Whereas cosmology, you have bubbles and fluctuations, so it will be structured along the frequency. This is how you separate the both the two. You have to do it in a smart way and careful way. There's lots of debate about what's the best way to do it. But it can be done. And here we showed that it can be done. How, et cetera, I will not go into details. Right. So I'll show you the lo-far case. I don't have so much time. Some of these figures will be just plots and pictures. But so lo-far, this is kind of an artist impression. This is Northern Europe or Western Europe. If you don't recognize, this is England. This is old. I should have changed this. I have a different one. Oh, God. Sorry. This is completely old. There's a new one. For instance, the UK has only one. You mentioned the UK and things go hayward. Sorry for the English people. OK. So the UK has only one. So this is old. Sorry. I didn't replace it in other places. It has been replaced. Most of the antennas, this is the Netherlands. Most of them are in the Netherlands. Germany has even more than now. Poland has three. Italy has none. France has a huge thing, which is called super, super, it's really a large part. And Sweden has one. OK? And now they are talking also with the Baltic countries in Riga, actually, to Latvia, to have a station there. So we will see. So it's a truly European thing. It started as a Dutch experiment. The Dutch government decided to give it money, not from science, actually, from the Ministry of Trade or something like this. But in our story, but it's relevant to this. Anyways, and it has two types of antennas. There is low frequencies, LBA, which are from 30 to 90 megahertz. Those are irrelevant to, well, they are not very interesting for our purposes. They are not as sensitive as they should be. Although the frequencies range is interesting, but the antennas themselves are not very interesting. The other bit is this HBA, this high band antennas, or array, that are from 115 to 240 megahertz. Those are interesting for the epiprofranization, as you remember. And you start from this element. You put it in a tile, four by four. And these tiles, you put in something big, we call stations. And, well, this is very old. I don't know why I took this one. I have much, much newer ones. OK. Anyways, so let's look at this. So we started flattening the field. So this station, this is roughly 100 meters. It's like a football field. So it's a big thing. And for a big thing, it has to be very flat. You don't your antennas one doing this and one doing that. So that complicates life. So you want to flatten it. It's like optical astronomers polishing their mirrors. That's exactly what we are doing here. But this is our polisher. So it's a tractor because it's big stuff. This piece of equipment, which looks very crude, is actually incredibly sensitive. It has lots of GPUs and lots of things. And the requirement for the telescope is to flatten the field down to, I think, 3 centimeters RMS. That's quite on a football field. Yeah, that's like 2 centimeters. It's very small. And when they started in 2008, they started in November. And it was incredibly rainy. The Netherlands, it rains a lot, especially in the winter. So it's very muddy. There's lots of areas that are swamps originally. It's low. The water level in the Netherlands because it's so flat and low, you dig a little bit. Water starts coming up. So they started doing it. And these are the wheels of the tractor impression. This is much more than 2 centimeters, 3 centimeters. These are two engineers who are making the measurement. This is really not flattened. They told the directors, it doesn't work at this weather. The directors wanted to have something very quickly. They told them to keep working until this happened. And yeah, so you find the driver tell us. So then they stopped. But after that, they worked again in the spring. And you get this wonderful stuff now they manage. You can see two types of antennas. These things that are covered, these are the high-band antennas. These are the interesting one for us. And these things are the low-band antennas, low-band array, which is less interesting for us. This is an area in the center. So the low-band is designed as follows. It has a core, which is about 2 kilometers. And then it has larger kind of baselines that go 1,000 kilometers, well, in hundreds of kilometers within the Netherlands. But then they go to all of Europe with 1,000 kilometers. And this is the center of the core. It's called in Dutch superter. It became now a scientific word. It means the super mound, terp in Dutch is mound. And it's clearly man-made. Paper doesn't, nature doesn't draw circles like this often. Sometimes it does, but not often. And if you look at this, for instance, look here, the typical way it's a Mickey Mouse type of thing. You have two ears of these high-band antennas. And this is the face. That's the low-band antenna. That's kind of the design. If you stare at this kind of enough, you will see these Mickey Mouse face everywhere. So this is wonderful in the winter when it freezes. It's nice to have ice skating around it. My colleagues like to do it. It's quite nice. OK, let me skip this. We have a certain group of people that works. I'll jump this. Well, there's a joke there, so I'll have to do it. We used to meet, we used to. Not anymore, twice a year as a group. The whole group from Groningen, that's where the center is, but from other parts of the world. And the winter one is always lousy in Europe. So we meet in Groningen. But the spring one, we want to go somewhere sunny. So we make a point for going somewhere sunny. And this is in Barcelona, close to Barcelona. And everybody smiles in this. And the other one, everybody looks like this. I mean, it's not. Anyways, so what are our main scientific targets? Like all the other experiments, we want to see the global evolution, this function, how it goes up and down. But this is one piece of information. The other things we want to know, power spectra, higher order statistics, can we image? We would like to cross-correlate our data with other probes, like Lime and Alpha emitters, like galaxies, like quasars, et cetera. And there is something called 20 centimeter force. Now, this stuff is difficult. And the more we work on it, it becomes clearer how much more difficult than we expected it is. So in order, if you want to do something so difficult and to convince the community that you have discovered, first of all, to convince yourself that you have discovered something worth of publication and convince the community, which is much harder, you have to do a number of things. And this is what we learn from particle physicists, from these huge experiments that particle physicists do. There are two things that you can do. First of all, you have unbelievable amount, as much as you can, internal checks of your data. You cut the data in time, say, half the time and the other half. And if you, this is the signal in one time and you don't see it in the other, you become suspicious. You cut it in frequency, in directions, in what have you. You have to do as much as you can in terms of consistency checks. So that's one. The other one is to produce a pie and end-to-end pipeline of what you would measure, not only the signal, which is this simulation that I showed you before. You have to simulate the signal, the telescope, the sky, the ionosphere, everything you can, even the RFIs if you can, and put them in your pipeline so that you at least have an initial understanding of what they will do to your signal. And if what you claim you're measuring is really what you are measuring. At least you have a promising start. And believe me, everything you put in this will be very simple, peanuts, relative to what the data will give you, because the complication of the data is much more complicated than whatever you can think of. So if you fail here, most likely you will fail with the real data, unless you are incredibly lucky. And there is an effect that you didn't take into account all together. Right, so for us we have a number of windows. We look at certain things. And so different experiments has different strategies. I will not go into that. That becomes too much detail. Some of us have bigger field of view. Some of us have smaller field of views. It depends what you decided to do for various reasons. This is a map. This is a famous Hezlem map at 408 megahertz. This is not the 150 megahertz, but it's close enough to see how the sky looks like. So when they tell you polarization is a problem in the CMB, that's why it's a problem. That's polarization. It gives you, oh, I mean, it's huge. This is the North Polar Spare. And in polarization it even looks worse. This is the total intensity. But that's what you are kind of fighting with. So you have to target areas that are relatively clean. Because as I told you before, your foregrounds are one Kelvin. But if you look, for instance, here, your foregrounds will be hundreds of Kelvin. Right? The RMS and the... Yeah. Okay, so we choose a number of them. Our main two fields are this, the NCP, North Celestial Pole. We chose this one, although it might not be the best one. But we chose it because we can see it every night in the year. Right? It's the North Polar Star. And then you can see it always. Yes, please. So I think this is the eclip... This is the ecliptic, I think. Yeah? This is the plane of the galaxy. Right? So this is in galactic coordinates, what they call the roll call kinds of... You know, this is not my kind of expertise, but this is... So this is the galaxy, and this is in ecliptic coordinates. But you twist the coordinates so that the galaxy is... looks straight. Normally in large-scale structure, if you talk about large-scale structure, you will take different types of coordinates, galactic coordinates, or even supergalactic coordinates if you look at the very large-scale structures. Right? So... But this is not done here. Okay? But, I mean, this is not very important. The importance of this is that you see that this is the North Celestial Pole relative to the ecliptic. It's... You know, everything is on the top. And this is another one, 3C1N6. It has a quazer, very kind of strong quazer, which is also for a number of reasons. Now, what do we want to measure? We want to measure this... If you look at what you want to measure, for instance, one of the things that you can measure is the variance as a function of... of redshift, of these bubbles of ionization versus not ionization. And normally you expect it to peak why it has this structure. It's very simple. So, at the beginning, there's no ionization bubbles. Remember, the equation goes like this. 1 plus delta xH1 and plus other terms. Those are the interesting terms for the low redshift stuff. The spin temperature issue is not interesting anymore. I mean, it doesn't change things so much at low redshift. So, when things are not ionized, this is one. Remember, these are interferometers. I forgot to say something very important about interferometers. The measure differences, variance, right? That's a very important thing. So, you should see contrast. So, if this is one, your contrast is driven by delta. Delta is tiny, right? Delta is small unless you go to very non-linear structures. But in the last case structure, this is small, especially at high redshift. So, this contrast is small. But bit by bit, what will happen is that you'll start having bubbles, right? Then, what control the contrast is not 1 plus delta. It becomes this term that is important, right? So, you will see lots of contrast. When, where is the most contrast you will see when the universe is half ionized roughly, right? Because that's half of it is in bubbles of zero x and in other xH1 and others are in one. So, that's the most contrast you have. So, that's where it peaks. But after a while, you have more and more and more and more ionized regions and the neutral stuff becomes smaller and smaller so the contrast goes down until the neutral stuff disappears altogether, then your contrast is zero. So, this is what you see. This is this leveling off and kind of dying of the signal. Okay? So, this is what we would like to see first. This is a complicated transparency. Don't just forget about the details. I'll just tell you the story. This is a simulation that we put in hand. That's the blue thing. We added everything. We put it through our pipeline. We added everything. Noise, foregrounds, what have you. And then we did the extraction. We did the inverse thing. You know, the signal extraction. At the end, we asked what we can get and we got these points. And we fit them with this type of curve, this function. And we asked how, with what's certainly we can measure our signal, given a certain amount of time of observation and you can see we can detect it with six sigma certainty, which is very good. That's very promising. Unfortunately, the noise has, it became clear that the noise is higher than we expected so it will be a bit harder but it's quite doable. Yes, that one. That's this. Yeah? It's this functional kind of parameterization. It's just the amplitude of this. It basically corresponds to the amplitude of this thing. I think here, delta Z is harder to get as you can see but I think, yeah, it's the full, I mean, we defined it as this delta Z in this function so you can fit it. So it's not really full what have max but it's related to that. It's not a Gaussian. This is not a Gaussian. We also want to measure power spectra. Again, there are two studies that we did in separate times. Again, the blue thing here is the original thing and this is what we could recover. We thought we could recover and we do very well. The power spectrum stores much more information in principle than just the global history. It tells you what's the typical size of bubbles, how fast this thing happened, et cetera, et cetera, which shed light on the sources, their type, et cetera. This is another study that we did later and also it confirms the red is then is the signal and the blue dots are what we expect to recover. So this was kind of very promising. There is another thing that we can look at. I like this. So I'll spend a couple of minutes explaining it through skewness. You remember what skewness is? Yeah, it's the third moment of the distribution and you measure it and it's very neat. So let's go through that. You have had a structure formation thing so let me go through it. Initially, when you have, again, when you are at higher shifts, you are controlled by delta. Delta at very higher shift is a Gaussian field. As you go to lower and lower shifts, delta becomes a little bit skewed, right? It becomes log normal, roughly. You remember that? Yeah, it becomes, in other words, it stops being like this. It becomes a little bit like this, just a bit with a tail. That's because you start forming very non-linear objects, you know, the first objects. Okay, so skewness measures the asymmetry in your PDF. Right? If it's positively skewed, it means the tail is to the right. If relative to the center. If it's negatively skewed, it means that the tail is to your, the outliers is to your left. In this case, it's the right. In cosmology, in general, you cannot be more empty than empty, but you can be very dense. So it's always positively skewed. Okay? So that's the thing. So at the beginning, you expect this skewness of the signal at higher shifts to be positive. So these are simulations. And let's look at that. This is a simulation. It's a bit positive here. You can see it's coming from positive. But something nice happens. Well, nice, something happens. These are the highest density points. They become galaxies. What do the first galaxies do? They produce radiation. They start ionizing stuff. So they disappear from your instrument. Where do they appear? Here. At zero. Because they have no signal whatsoever. So now you have a strange distribution. You have a kind of a log normal that is truncated. But then you have another one, which is at zero. There's a delta function at zero. So what happens to your skewness is as follows. Initially, before this, it was positively skewed. But because many of these points move from here to here, it becomes negatively skewed. Right? Because it's on the other side. So you can see here what's happening. Becoming negatively skewed. Okay? And then with time, what you will have is that this will look like this. Because many of these high density regions will be ionized more and more and more. And this will be larger and larger and larger. Okay? So once this becomes larger than this, then the PDF is not controlled by this. It's controlled by this. Then this is the outlier of this. Not the opposite. Then you go back to positively skewed. Right? And that's what you see here. It goes back to positively skewed and it goes forever. Until everything disappears. Now what you will really see is not this. It's this. Again, here we will start with positively skewed. You go, I mean these are fluctuations. But anyways, you go and then it goes almost to zero. And then it goes negative. And then it goes positive. In principle, it should continue to up there. What happens is that when things ionized, what you will see is noise. Noise is Gaussian. It has zero skewness. Once everything is ionized, all what you are blended up with Gaussian noise. So your skewness should go back to zero. And then it goes back here. It's very neat. If you find this, it's very hard to mimic this with a systematic. Of course, it's harder to measure than the power spectrum or the RMS. But if you can measure it, it's very neat. I always skip this in talks because it takes time. Here, I had time so I can do it. Okay, so we are drawing towards the end. Let me show you what are the current results. This is from MWA. And these are the power spectra as a function of K. You have seen this way of power spectrum. This is that kind of, it's basically you have learned about P of K, right? I missed some of your talks, but probably you explained this. Another way of putting the power spectrum is this. This is like L multiplied by L plus one over two pi in the C and B. Why you put it like this? You can translate this easily to RMS. It gives you immediately intuition about the scale of the RMS. Because the RMS is the integral of P of K, proportionate at least, dK. From certain scale to a certain scale. So when you do it like this, you immediately have an intuition about the RMS of this thing. In this rendition, in this kind of way, in this representation, white noise is not flat. It grows with K. Now, this is that same type of thing, but in our case, other than unlike the delta in cosmology, because we talk about delta T, it has a temperature unit, it has units. But in general, in cosmology, this thing has no units. When you talk about over densities, when you talk about temperature, it has units. This is what you expect. This is a simulation with a signal, and this is where we are now with this experiment. We're very far away, but we are getting there. Right? It looks all those of magnitude, but the things are improving quite rapidly. This is the results of GMRT. Again, these are measurements that, oh, I forgot to put Chika, the name of the person who did it. Sorry about this. But Chika et al. I think this is led by Willie Penn and collaborators just to give credit. This is the area of the sky they look at, and this is the power spectrum calculation. This is their best bin here, and this is the simulation. Again, there is many orders of magnitude here. The best results currently are from, oh, this is also a bit old. There's a newer result that goes down to actually about here, much lower than this. I don't know why I didn't, somehow something went wrong with my transparencies. There's a newer result that gets you lower here, but it's still an order of magnitude larger than the expected signal. So we are getting there. Low far, we have been trying for a while to get put up our limits, but all the time finding systematics, we recently have starting to understand the systematics. So we have no reliable result yet to put out, although we thought we have. But anyways, so that's where this thing stands. We can also do imaging if we are lucky, but I will skip this. I really have no time. I'll just show you one thing. There's all kinds of details about what you have to do and simulations. Right, let me show you data from low far for just to, so this is one of the fields. You remember this 3C196? We are very proud of this picture. This is a picture that looks incredibly boring. That's what low, that's what radio pictures don't really look like. It's just points, but we are incredibly proud of this. This is a picture of a field of a number of degrees that has a dynamic range. You know what the dynamic range is? Yeah, it's the ratio between your highest point in the image and lowest point, which is normally set by the noise, the lowest point. So it's your peak kind of maximum signal and so that's the dynamic range. How many orders of magnitude you cover in this image? The larger, the better. Here we have six orders of magnitude. Unbelievable, you can peel this six times with orders of magnitude and you can still see new things until you go down to one in a million then you see only noise. Right, so that's great. Now, one of the things we do because we have dipoles is that we can do polarization. So you can do stocks I, Q, U and V, basically, or even circular polarization. Polarization, you can do a trick. And now this is a result that we got that had nothing to do with cosmology, with the OR, with anything. I'll just show you a neat result that we got as a side kind of present. When you have polarization, polarization is an important thing for us because I told you things are smooth in frequency. That's true in total intensity, in stocks I, but in the other stocks parameters, it goes up and down. So you have to understand them very well. If they leak back to your stock's eye, that's not good. You cannot distinguish the two. But if you look at the polarization, it's interesting by its own right. There's lots of people who do that for living. Cosmology is not everything in the world. There's many other things that people do. So I will not explain this. I'll just explain it very, very kind of intuitively. So what you do, you look at the polarization, you look at each frequency that you get from the data. This is for this field, 3C1 and 6. And then you roughly Fourier transform it along the frequency. Only along the frequency, actually you make a transformation, you do it with lambda, with the wavelength rather than the frequency, with lambda squared, and then you Fourier transform for various reasons. They are explained here. But what that says is that you have a structure along your frequency or your wavelength. You will see it if it's kind of smeared. You will see it when you Fourier transform along the frequency, you will see it kind of very strong. And if it's not, you don't see it. Forget about this. So this is what you see. So now you move to this new space where you move in Fourier. And it's called phi. This phi is this Fourier conjugate of your lambda squared. So it's your Fourier component now, Fourier variable. And you will see a movie here that I was told that I can do all of, yes, instead of all of stairs. And what you will see here is that this is noise mostly. There's nothing much. But when you go down, you start seeing objects. Let's look at this. I'll show you this again. So again, if you have nothing, you will expect to see noise-like. Sometimes you see sources that are point-like. These are sources that we didn't deal with very well. But then at some stage, there's this huge structure that we didn't expect. Again, again. I'll stop it at some stage. Now it starts, oops, what did I do? It's refusing to stop. Yeah, look at this. We had no idea what this is. You see these straight lines? They are real. This thing, you see this thing? That's real. These things are not. These are instrumental things. But these straight lines are real. We had no idea what's this. We still have no idea what's this. And if you look at it at a different frequency, look at this. What the hell is that? Look at this, these kind of canals of these. You can put a ruler here and it kind of follows it. Right? This is clearly something related to the magnetic field in the galaxy. But what it is exactly, we still are not sure. Yeah, I'll skip this one. So what Vibor, this is again, Yelet-Shital paper. What he did here, I should stop in few minutes. I guess I'll stop. I remember that I should stop. He did this. He took these five slices. These four, this is called ferrari depth slices, which are this conjugate of the frequency. This new coordinate. And he took the maximum of emission at range of those and just add them together. And if you have kids, you know that this is how kids would do stuff. So that's how they would kind of draw. But this is nature. You see these things. I mean, every time I talk about this in colloquia or seminars, people ask me, is this cosmic strings or not? It's not, it's probably magnetic fields. It was very intriguing. But you see it. What the heck is that? We don't know. And we see it only in polarization. We don't see it in total intensity for various reasons, but yeah, actually we could correlate this structure and if I go back to here, you see this structure at a certain density. We could correlate it with plank, dust, magnetic field, dust inferred magnetic field. So this is really magnetic field stuff. We wrote a couple of papers on this. This is the first time and probably the last time I'll write something about the intergalactic medium magnetic field, interstellar medium magnetic field and dust. I've never dreamt I'll do that. Anyways, okay. So this is the other field that we have just to show you the progress that we got. This is when we started, this is this NCP field. It looks very bad. As I told you, I mean, this most noisy, there's so many artifacts. And this is where we are now. I mean, it's the same picture. Look at the huge progress. This is the deepest radio image ever at these frequencies. And what we are interested in are not these points which are, these are jets of, these are AGNs with jets going on and there's number, you will see double doubles. For instance, this thing, it starts here and goes like this and continues here. There are double doubles and so it's these quasars that are active a number of times and you see them. But we are not interested in this. We are not interested in the empty stuff between. That's where our signal is. Right, and hopefully with time, maybe in a year, maybe more, maybe less God knows, we'll be able to detect the UR with these types of experiments. Let me show you, end up with this movie that was done long ago before the split. SKA now is something that will be built in two countries. In the past, there was a competition between them and this was done by a Australian group. So it doesn't say so, but the landscape is kind of Australian at the beginning. You can see, but now we know it will be split. But anyways, this will be SKA, SKA will be the future. It's a multi-billion kind of, I mean, I think the numbers are billion to two billion dollars, the euros that people are assigning to it. And with this, I would like to end. So let's start this, right. It has even sound, I can't make it. Ah, so you'll start with the three types of, SKA is three things, it's not one thing. And these are the big dishes, these are the highest frequencies. And you can see how big it is. Never anything like this has been attempted. These are the dishes. And they will be kind of grouped together in these concentrations. This part of the dishes will be now in South Africa, not in Australia. So these are the dishes, and there is dense arrays and sparse arrays. And the dense arrays are the lower frequencies. Now they are talking about the sparse arrays. This is the, these are the arrays that are the antennas that are interesting for the EOR. And for the cosmic dome. This is what you should get. Of course, the antennas look differently. They look like the picture I showed before. Now we have, and these are the dense arrays. These are frequencies in between, the high frequencies and the low frequencies. This goes from 1.4, 1.2 gigahertz down to, I think 300 megahertz. This is very interesting for BAOs, for burying acoustic peaks. I mean, the science case for SKA is overwhelming. It's actually stunning. It seems to, it seems that it will happen. So they start with a core, you have these three things in a core, and then this tells you what's the baselines that you expect. It extends to many kilometers, and you go farther and farther. So that's why I'm saying it's Australia. If you know Australia, that mountain behind, that's this red rock in the center of Australia, so they were hoping to get it. Anyways, but the expectation is you get thousands of kilometers baselines. This is incredibly exciting stuff. Still in its infancy, it's a field for the future. It will probably take a decade or two to get, to exploit the potential, or startups to exploit the potential. I was not kind of educated as a radio astronomer. I'm just a simple cosmology theorist, but I got thrown to this, and it's really a fantastic field. Thank you very much. Thank you, I hope you're using it.