 the wrong announcement, so the dinner and music tonight is on the Adriatico Terrace, and it starts at 7.30 vrata, everybody is welcome 10 euros also. And it will go in the possibility of weather if it rains it will be inside but most likely it will be on the terrace. Ok, so where the second lecture is on the ionization. That's fine. Now it disappeared. Should I start? We'll come back to the second lecture. Yesterday I stopped, I'm still talking about probes of reorganization, and this will be the theme most of this talk and tomorrow. So last time I talked about the CMB as the probe, and it gives us this integral constraint. Today I'll continue with that line. There's lots of new data. I will not go through the details of everything, because there's really lots of new data. But I'll give you a flavor of the other things. So the CMB was one of the big constraints, which unfortunately became weaker and weaker with time, as I mentioned yesterday. Today I'll talk about something that has become stronger and stronger in time, which is the Lyman Alpha Forest. And this is... I'm not sure I have any of you know what is the Lyman Alpha Forest, because you have very different backgrounds. So when you look at quasers at very high ratchets, quasers are unlike stars. Stars emit in kind of thermal radiation. Quasers are more power-low type of radiation, because the source of energy is different. It comes from the Christian disc, and it has a normally kind of a power-low dependence on energy. So it emits in continuum, and it has this typical shape, and normally it looks like... You will see it anyway, but this is a quaser, and the way we look at it, you will see it in data in a minute, if you have very high resolution spectrum, and this is one of these kind of... In the last 20 years it became very, very... This is the advent of 8 and 10 meter telescopes that made this stuff possible. It's a huge... It's a very kind of exciting field, it has been for a while. Where you look at a quaser and you look at the spectrum, and the spectrum has all kinds of features, some of it has to do with the emission from the quaser itself, but the other things have to do with how the energy that is emitted by the quaser is absorbed in the intervening intergalactic medium. And this has a long history. It started 65, I think, with the first predictions by Ganand Peterson, and it was seen, and then there was people, proposing all kinds of mechanisms why we see this absorption, from small hellos to other things. Nowadays we understand this absorption. It's basically the diffuse intergalactic medium, basically the elementary structure and large scale structure in the universe, where you have a little bit over densities of baryons, and that kind of absorbs some of the emitted energy. And the optical depth for absorption is basically this. It's basically the number density of hydrogen, neutral hydrogen, because that's when the absorption, it's done on Lyman alpha, so it depends on the neutral hydrogen. Sigma is your cross-section, which is a standard number, and dx is the line of sight. You will see it in different version in a minute, but divided by 1 plus z, because there is a redshift as it comes. So when an energy comes out of the quasar, as it goes to us, it redshifts, and then the resonant energy of Lyman alpha, in other words, the Lyman alpha emission or absorption in that redshift, kind of redshifts a little bit, so you see that there is absorption at different parts of the quasar. And from this we learn a lot apparently. So this is a typical quasar. This is not very high redshift quasar. You will see why in a minute. Immediately you see that there is lots of noise here, and when you see something like this, you immediately think either this is very high redshift, that is very hard to see, or it's very low redshift. And the reason it's very low redshift, because we cannot see this from the ground if it's very low redshift, this is HST. And HST doesn't have a big mirror, doesn't spend too much time on it, but anyways it shows the features. You will see other spectra in a minute. And normally this is a typical kind of spectrum. You see this very prominent feature, that's the Lyman alpha emission at the quasar redshift. This is the thing that comes out of the quasar itself. Red words of it, this is angstroms, longer wavelength, red word of it. You will see not so much structure. It's kind of basically a bit of emission lines, mostly from metals in that system. And blue words of it, at smaller redshifts, you will see that the spectrum here gets absorbed at many places. So most of these absorption are not noise. This is noise, but those big ones are not noise. And there's lots of things that you can learn from this, I'll show you another spectrum in a second. With a movie they have different names, these absorption features depending on what their strength and all of that stuff. So most of these features are called the forest line. This is the Lyman alpha forest. When you have something so deep, it calls the Lyman alpha system. And there's here, these are DLA's, well, the Lyman alpha system, there's a break, and there's the limit. And there's three classifications for this absorption, because this absorption tells us something about the intensity, the column density, how much along the line of sight, how much the integral of density integrates along the line of sight of that system you see. So things that have high column densities like this, they are called DLA systems. These are intermediate, they are called Lyman limit systems. And the very weakest ones, the thinnest ones, they are called forest lines, basically Lyman alpha forest. And the nature of these things is a bit different. If you look at the DLA system, I'll show it to you here. So this is a movie that was, you will see the credit at the end of the movie. So what you will see in this movie is a quasar. The quasar is here. And this is the radiation that comes out of the quasar. And you will follow the radiation as it comes to us. So as this radiation comes to us, all of these features will experience redshift. They will redshift a little bit. So the spectrum you will see it shifting. And then when it hits this radiation, for instance, hits this cloud, it will be absorbed at the local resonant line, which is the Lyman alpha at that redshift. So it will absorb different part of the feature. And you will see when you hit something like a galaxy, you will see much deeper absorption, because the density is much higher, the column density is much higher, et cetera. Clearly, because when these things absorb, they are in the intergalactic medium, you learn about the intergalactic medium. So let's run the movie. It's kind of very educational movie. It's made by one of the students of Martin Henhilt. I have to give the credit to Martin. Ah, this is challenging. The thing is that it's very tiny on my screen. Oh, god. Right, it works. So I'll stop it. Go back. We'll see. It will work eventually. So you see that this radiation. First of all, you see that this is shifting to the left. To the left, no, to the right. And as it shifts, so it passed this cloud, and this cloud has this very strong absorption. This stuff doesn't get absorbed by Laman Alfa, because it is never in resonance with Laman Alfa. It's always higher energy than Laman Alfa. So that's something that, sorry, lower energy than Laman Alfa, so it's never in resonance. So we'll continue, and you'll see that this is how the forest is built up. Now, you see another thing here. You see there? This is the Laman Alfa. This will be the Laman Beta, because Laman Beta is also having, but it's weaker. And this is the Laman Gamma, et cetera. And until you get to this thing, which is the Laman Limit, that's where things break, right? I mean, it's basically ionized. And so we continue. Now you will see a big thing coming, like a galaxy in a second. There it is, and you will see the feature that will come there. Right. And you see this feature. This is the Laman Alfa system. That's because we are passing through galaxies. So these systems are less abundant. They are less kind of there, but they teach us about high density features, like galaxies. And you can notice if you... Do you remember the Vojt profile? Have any of you know what the Vojt profile is? No. Okay. So I'll... Well, if you know, you know, but many people, I guess, don't know. So the shape of the line is determined by a number of things. In quantum physics, normally, the shape of the line is determined by a number of things. One of them, there are a couple of things like velocity dispersion. If you have gas that has lots of velocities, it produces Gaussian type of absorption. So the line should be Gaussian. But another effect, for instance, define its lifetime of the transition will create a Lorentzian. That's also turbulence created by Lorentzian. Whereas velocities and temperature create Gaussians. So normally the shape of the line is a convolution between these Gaussians and these Lorentzians. And in the very strong lines the Lorentzian part dominates. In the very weak parts, the Gaussian part dominates. So these are very well described by Gaussian features, whereas the strong one is Lorentzian. It has nothing to do with column density, the shape of the Lorentzian. It's basically the quantum effect. It's the shape of the line. It's just the fact that you have lots of these types of things. Anyways, so we continue. And then you can see all kinds of things. Here there are absorption, that you've seen. So these are metal lines in emission, but these are absorptions due to metal lines. So if you have metals in the intergalactic medium, which have different absorption features than the Lyman alpha, you see them mostly here. Of course they will appear also here, but their number will be very small. So this is dominated by Lyman alpha. And you can see that this division between Lyman alpha and Lyman beta will be blurred in a second, because these things, which are in Lyman beta, will go into the region where Lyman alpha is. So there will be a mixture of things. And this is what you normally see. So if you have a very good telescope, like cake or the VLT, and you have spectra for three nights, this takes a long time. You look at a spectrum of a quasar at reach of three. It takes a long time to get very high resolution spectra. You see something like this. Now the thing that is at the top, this red line, which kind of covers everything, that's called the continuum. This is the really intrinsic property of the quasar, whereas the rest of the absorption feature have to do with the intergalactic medium. This is how we learn about the intergalactic medium. OK? That's fine? Good. So now we go ahead. This is a real spectrum, but this is not an HST spectrum. This is a cake spectrum. This is one of the... Sorry. There are two spectra here. I'm sorry. There are two spectra. One is an HST spectrum. You see the redshift. The redshift is very small. In these windows we cannot see from... The atmosphere is a problem. We cannot see from the atmosphere. We have to go up. And this is at reach of three. This is one of the best quasars that were studied. This is not noise. You can resolve these things. I mean, nowadays we see them in details of details. They just look so crammed because there are so many of them. And you can see that the main features of the continuum, this stuff like this and here there's another, they are kind of very similar. You can see two things that... First of all, that they are very similar in continuum, as I mentioned. Of course, there are different redshifts, but they are shifted to the rest frame of both. So they look exactly the same. But one thing that you can see that the number of absorption features here is much, much smaller than here. Do you know why? This is the expansion of the universe. This is the expansion of the universe. Anybody that doubts the expansion of the universe, here it is. The universe is much less denser at reach of point one five than it is at reach of three. It's actually less denser by 30 times almost. So that's... Anyone, you know, can doubts the universe expands? This is one of the nice ways to see it. And as you can see, red words of this Lyman-alpha, the intrinsic Lyman-alpha emission, there are not so many things, but they are very useful stuff, because you can learn about, for instance, if this is... You identify this as a certain line, as a certain metal, you can from it use things to say, what's the temperature around, what's the pressure, what's its redshift, et cetera, et cetera. And then you study these features. Now let me go through this formula. I showed a similar formula before a similar formula to this, a number of formulae here. First of all, the cross section has to do with a number of things. So the resonance line, the frequency is the original frequency, shifted by one plus z, depending on the redshift at which this is absorbed, and there's also a peculiar velocity effect, because that's where things happen. Now, if you substitute this here, this is what you will get. It's the same formula that you got before, this one, but now I put it in a really the proper way, where this is the line element, represented in terms of... This is CDT, basically, but you take Barbara's book and look at how z, dz, dt, looks like from Hubble law, from Friedman equation and plug it in the formula. This is what you get. So all of this is basically CDT, and this is, again, the same thing. And you can see that this tau, this optical depth is very sensitive to the number density of neutral hydrogen. The fact that we see this stuff tells us that the neutral hydrogen fraction is of the order of 10 to the minus 4. This fact that we see this means that the universe is ionized, because if there were more neutral hydrogen than this ratio, well, this is another one, this is one of the most, this is kind of the same one in more detail. So if there were more neutral hydrogen in the intergalit medium, this is what you will see, nothing, because there is lots of hydrogen in the universe and it will absorb everything if it was neutral, but it's not. So this is our main evidence, now with hundreds of those systems, if not thousands of those systems, that the universe is ionized at lower edges. So in the previous talk, I told you the CMB teaches us that the universe became neutral on some stage, this shows us that the universe became, you know, ionized at some stage, so there must have been an epoch of reionization. So this is the evidence. Now, what I showed you before was Richard III, this is a very kind of famous figure, famous plot. This is one of the highlights of Sloan. To my mind, this is probably the most important result of Sloan, but yeah, that's debatable, but it's one of the most important, not the most important. This is from a series of papers from Fanit Aal, that's 2003-2006, this is the 2006 compilation. What you see here is a compilation of all the higher shift quasers that Sloan have seen, I think they are 19 or something like this in number. And you see in all of them the same kind of thing, this is the Laman-Alpha emission and then you see these are absorptions. Now, why you see this like this, this is the same spectrum I mentioned as here. So there's an effect that I forgot to mention, which is very important. Let me go here. At lower shifts, these absorption features are very far apart. If you go to higher shift, like we see here, they become very close. Let's imagine now we go a little bit higher. What will happen, these lines will be crowded. So if you had at lower shift lines that looked like this, these are Gaussians in my hand. So I cannot do better than this for Gaussians. This is lower shift. At higher shift, they will get closer and closer. So this there will be something at Richard III, there will be something like this. But at higher shift, what will happen is that the first line which looked like this will basically enter to the second line which looked like this. So what you will see is that there are two lines in one. Yeah, that's called crowding. Now this is with two lines. Imagine you have many of those. So what you will see in practice is a lot of wobble here, which has to do with the tips of the lines. And it will look like emission lines, they are not emission lines, they are absorption features that are mixed together. And this is exactly what you are seeing here. Right? This is the same Lyman-Alfa emission, but this is where these features are. Now this figure, in this figure the equations are ordered in such a way that the lowest one is the lowest redshift, but this is very high redshift. This is redshift 5.74, right? And you can see that we go to higher and higher redshifts. How we know that? From the position of the Lyman-Alfa emission, the Lyman-Alfa feature, it goes in that direction, in these it's higher redshift. Now, if you look at those ones at low redshift, you see this one, it has lots of wobbles here. So it means that you have lots of this stuff, right? But if you go up and up and up, you see for instance this one, there is nothing. It's completely wiped. And that was a surprise. Cos you would expect that this will evolve slowly, these things, these features will become weaker and weaker and weaker, but you don't expect them to be suddenly like this. So something has changed at higher redshifts. At around redshift 6, 6 point something, something changes. And this is expressed in another famous plot from the same series of papers where this is again from Fan et al 2006, where you can calculate from the shape of the line, the width, that optical depth for these lines, the effective optical depth, because you have to stack a lot of things. And this is how it looks like, so it's very highly... So this is the... GP stands for Gun Peterson. This is the name of the effect. And this is how this tau evolves as a function of redshift from low redshift quasars to a higher redshift quasars, from redshift 3, a bit by bit it rises and rises. And if nothing happens in the universe, it just have the same kind of features, it will follow this dashed line. But at redshift 6, you see that this optical depth for absorption becomes much higher. And this is a sign that you have more neutral fraction in the universe at these redshifts. So this is the tail of the reionization period. Now, is this significant to tell us when reionization happens? No, the reason is very simple. At these regions, the ionized fraction or neutral fraction, the neutral fraction is of the order 10 to the minus 4, 1 in 10,000 even less of particles are neutral. It's enough to do one order of magnitude more. Instead of having 1 in 10,000 neutral, you can have 1 in 1,000 neutral and you will recover this effect. It's still very highly ionized universe, but it's less ionized by a little bit. When it did most of the ionization, we don't know from this figure. This is the tail. So all what we can learn from this is that the tail of ionization happens somewhere and we are seeing just the end of it around 6. Okay? So that's that. Now, in the last, this is 2006, now it's a decade, 10 years exactly, and there's lots of other observations and people have been adding higher redshift and higher redshift quasars. This guy has the record. This is 7.085. We have another couple of them a bit lower than 7. There's another one from U-Kids. This is from... I think this is from U-Kids, actually. This is from U-Kids. There's another one from Vista, I think. That's a bit lower. This is a paper by Mortlake et al. from 2011 and it sees this quasar. Again, they put it in a very unusual way relative to what we have seen, but this is the limit of their observation. You see the Lyman-Alfa feature. This is the stuff redwards of the Lyman-Alfa and this is the stuff bluewards of the Lyman-Alfa. So this will be the Lyman-Alfa forest in principle and this will be the things that do not get attenuated too much. And this is silicon, carbon, all of these lines and we use them actually to get all kinds of information about temperature and things like that. And this is where the Lyman-Alfa and the Lyman-Beta starts. Lots of things were done here and there's lots of studies. And you can see people go into this kind of... to this region. So this region is the region where you move from... where the ionization or the neutral IgM or the IgM in general, how much it is, we don't know, is clear. So this is blowing up this. There are a number of lines here. Look at the black line. This is the black line. The black line is this very high-rechiefed quasar. The other two lines are two different quasars that are also very high-rechiefed. This is 6.4 and 6.5, I think. They are very high-rechiefed quasars. And you can see that the transition from the Lyman-Alfa to the forest where the forest should be is much, much sharper in this high-rechiefed one. Right? So this is an evidence for more neutral stuff. Turns out, no. So the more sharp you are, the more absorption you have because suddenly it gets absorbed. Turns out that this stuff is ionizing itself. So you are not seeing the ionization of the whole universe. You are seeing the quasar cleaning up its surrounding, basically. And so this is... We don't learn much from this quasar, unfortunately, although it's such a high-rechiefed about realization. We learn about the quasar itself. And it turns out that this quasar specifically is very new. Its lifetime is probably of the order of, I don't know, a few million years, 0.1 or 2 million years. So probably the duty cycle of a quasar is about 10 million years. Quasars shine, get very active 10 million years, and they are shut down for 90... Well, these are the average number, of course. Every quasar is different, and they shut down for 100 years. That's called the duty cycle. And so this has been newly turned on. The quasar in our galaxy is dormant, right? But it will be active at some stage, I guess. And that's hopefully not in our lifetime, but it will be active at some stage. OK. So from these things you can learn a lot, but not as much as you have hoped. But still, people are really, really going after these things, and their interpretation is very interesting and exciting, and tell us about the quasars themselves and about the intergalactic medium. OK. Next. There's more questions about this before I stop. Yes, please. In redshift? Yeah, it depends. Yeah, it depends when ionization happens. So the question is how far you can... Deep you can go in terms of redshift in quasars. I mean, the question implies the following. If you have neutral intergalactic medium and you have a quasar, all of its radiation, blue words of the Lime and Alpha line will get absorbed completely, so you will not see it. It will be much harder to see it. So that depends when ionization happens. In 7, you still have something, but it's not clear whether this implies that ionization happened already, or you have neutral stuff, it's not clear. Yeah, you can, of course, you can. There's no problem. Actually, we hope that we have some of those for the 21 centimeter, but then they have to be radio loud. That's a completely different story. But you can, right? So initially people hoped from this sudden drop that oh, the neutral intergalactic medium is cleaning everything up, but it turns out that this quasar is new, so it might be its own influence. This figure, which I don't want to explain, forget about this figure, it basically says when a quasar, after how much time the quasar lifetime or activity will stop being relevant. So for certain neutral fraction around it, for instance, this line after 0.1 million years of being active, its activity doesn't matter anymore, and this is for neutral fraction of one, it actually takes much more time to discern the quasar activity from the intergalactic medium kind of state. Okay, so now I'll go to another, one of these also surprises in the last couple of, yeah, one and a half decades I think now. They are called Laman Alpha emitters. These are galaxies. You don't see them around us, but at higher altitudes you suddenly start seeing them. So these are higher altitudes galaxies, but they have very high fraction of their emission in Laman Alpha, right? That's why they are called Laman Alpha emitters. So they are relatively dust-free. They are selected through narrowband filters, so in you do imaging, you have filters to do colors, and if you have lots of narrowband filters, you can pick them up at higher altitudes. The best telescope for this is Subaru, so it turns out to be, but there are many other telescopes that have been doing at least, in terms of the initial discoveries, Subaru was fantastic, and it's still a fantastic instrument. They have a new camera on it, called Hypersupreme, or Hypersuprime, depends which side of the ocean you are. And it's kind of producing a lot of these data. So, again, the argument here, why they are useful for us, for probing realisation, if you have emission in Laman Alpha, and this Laman Alpha is at high redshift, as it progresses at redshifts towards smaller kind of frequencies a little bit, and if you happen to have neutral hydrogen around it, the neutral hydrogen, well, absorb it, and you will not see it. So, you can follow these objects at higher redshifts, and you see when they kind of disappear, and I'll come to that in a second. And so, these are objects that are interesting in their own right, and we think they are low mass hellos of 10 to the 11, 10 solar masses, and this has been a huge kind of field in the last few years, and I'll quote a very kind of classic paper by McQueen, I think it's part of his PhD, where he kind of asked, what can we learn from these Laman Alpha emitters about realisation? And he had three scenarios. The above ones are simulations of the universe, of the ionisation level of each one in the universe, basically. So, here you have ionized stuff, and the black is the neutral stuff. So, it's the opposite, basically. White is ionized, and black is neutral, and these are three simulations at certain redshift, where here you have the ionized fraction is 30%. So, out of every 100 hydrogen atoms, 30 are ionized, right? So, that's what it means. Here it's 50%, and here 70%, right? So, this is highly ionized, this is a little bit ionized. And then he simulated these galaxies at high redshift. These are Laman Alpha emitters in his simulation. And he asked, if I put these behind this, in this environment, what will I see from Earth? And you can see that because you have lots of neutral hydrogen here in the surrounding intergalactic medium, it will absorb most of these things, and it will obscure them. So, in highly neutral intergalactic medium, you will see few. In highly ionized IgM, fewer neutral hydrogen, you will see a lot of them. So, that's normal. So, it turns out there are a number of ways to use these things to constrain the ionization. One of them is the Lamanofsi function. If you see less versus more, that tells you about the intergalactic medium. There is another thing that is apparent from these three things, is the clustering. This is more clustered than this, right? Because you see the stronger one. So, the clustering turned out to be a very useful probe, and you will see numbers coming out of the clustering of these things. You can also look at the spectra and the line profiles. That's a bit more detailed thing. I'll skip here. Ok. And this is how they look like, these things. They are not very impressive, but actually these are very high-rich. This is incredibly impressive. I'm not an observer myself, although I'm talking about observations, but if you look at these things. So, what you see here is basically, this is a spectrum as a function of, this is a wavelength as a function of space, right? So, that's on the sky, this direction, and this direction is the wave number. And you can see this blob here is the galaxy, right? So, if you collapse this, you will get this. And you can see the emission. This is the Laman alpha, right? It's very noisy. But I think by I even you can immediately say that there is something there. So, these are these guys. And we learned a lot from them. So, they started from 5.7, and then we went higher and higher. One of the surprising things if you look at the Lamanosti function, that it's kind of, it doesn't evolve much between 3 and 5. There is another line here, which is this cyan. Between Rechev 3 and almost 6, it doesn't evolve so much. But suddenly at Rechev 6.6, it evolves, it becomes fainter. So, again, this indicates something happens between 6 and 6.6, right? The universe becomes a bit more neutral. And here is, oops. And here it, how it looks like in terms of kind of likelihood and where it happens. These are the parameters of the Shekstar function that they fit. This is old figure. This is not in prep anymore. This is 2012, I think. Yeah, this is 2012, I think. This is very old slide. In this paper, which is very highly cited paper, you can turn these Laman alpha emitters to and ask what's the fraction that we see relative to the other galaxies. So, at lower Rechev, you see a small fraction, but as you go to higher and higher Rechev, more and more of these Laman alpha emitting galaxies are seen. But suddenly at Rechev 6, it drops. Again, this indicates the same thing. So, this is where we are nowadays. And this has given us more constraints on realisation. And I will give you a figure at the end that sums up all of this stuff. I think I'll skip this. I don't have so much time. I'm already half through my talk. You can use something else. I'll show you something else that you can use. These are spectra, again, of Laman alpha. And you can... This is really how they look like when you kind of expand these figures. We really see this stuff. It's not lines like this. They are really resolved. From the average width of these lines, you can learn something about the temperature. I told you that the Gaussian shape is determined part of it by the temperature. So, you can measure actually the temperature. You can use them as a thermometer for the intergalactic medium temperature. This is very cool. There's no way... Measuring the temperature of a gas in the intergalactic medium is very hard, but they give us this kind of possibility. This is a simulation, of course. This is for a cold intergalactic medium versus hot intergalactic medium. In average, you have narrower lines in the cold case versus the hot case. And you can use that to measure the temperature. And we did that in 2000 in this paper. It was very involved for a number of years in these studies. And also this paper did the same thing. And recently, Bolton et al. You can measure the temperature. So, this is the temperature of the intergalactic medium as a function of redshift. Initially, we used to see this rise in temperature and then sudden jump. The sudden drop. Now, people don't see this drop. They see a mild drop, not a very sudden drop. But anyways, this indicates the transition from helium 1 to helium 2. This is when quasar dominate, start forming and then they ionize helium completely. Remember, helium has two electrons. One electron is... when you ionize is roughly like hydrogen. But the other one is much deeper potential. Well, so you have to overcome the Coulomb attraction. And for that, you need the 54 electron volts. That's not UV already. That's x-ray. So, quasars give you that. So you can ionize those. And we see this signature of helium getting ionized at lower regions. This is really the last phase transition. The big phase transition. But then what we did, we used the temperature a little bit above this at redshift 4 to extrapolate back in time and say, ask when the universe was really ionized. And from this, it's an old study. I don't want to make too much of it. From these extrapolations, you get to redshift 9 roughly. This is also by Bolton et al. It's a newer study and they don't start from redshift 4. They start from redshift 7. Again, you see something similar that the universe ionizes by redshift 9. Which is consistent with the kind of picture that's coming from Planck nowadays. I'll skip this. So, I'll mention a few words about this. This is, again, these are galaxies now. We have also, there has been this very big breakthrough in high redshift galaxies. Not through Lyman alpha, but through this technique of dropouts. I think the record now is about, there was a claim of redshift 10 recently. But that is kind of questionable. But at least redshift 9, we see galaxies at redshift 9. It's amazing that we go so deep. And the idea is basically very simple. A galaxy will emit in Lyman alpha and it has this certain SED, spectral energy distribution. So, if you have the filters, a number of filters in terms of, so it's like a postman spectroscopy. If you have a filter that is centered where the galaxy emits the most and have other filters at different frequencies, then you should see that where it centers, that's the redshift and where it's not. You'll see it disappearing. So, actually the appearance in the filter tells you where the redshift roughly. That's called redshift photometric redshift type of thing. Anyways, so these are a number of galaxies that you see these are filters in astronomy. They have the various names. It doesn't matter, but you see a galaxy here that appears in certain places in other places. And from this we can deduce its redshift. This has been possible because of HST. HST made this possible, especially the correction of the mirrors. You are too young, but the initial mirrors of HST were a disaster. And so they had to go and fix them. And since they fixed them, it became a completely new game. We got new imaging filters, et cetera. It's called WIFPIC3, this camera. And within a few months everything changed. And we started seeing these very high redshift things. And now we see a lot of them. I will not go into these details. Again, I don't have so much time. This is from a recent work by Roberto Netaal, where people asked the following. If I take these galaxies and assume that the following assumptions, now we have lots of these galaxies and we can construct some luminosity function of these galaxies, et cetera, et cetera. If I assume, first of all, that their ionization is consistent with a very steep slope. In other words, what I see, I can translate, what I see, I can translate to ionizing radiation. So this translation from the UV, from the limel alpha to the UV that ionizes is given by the luminosity function, or the spectral density function. And that I assume I know. And it has this slope of minus 2, which is the limit that is allowed physically. So that's one thing. So you assume something about their spectra. The other thing, you assume that out of these photons that they produce UV photons, ionizing photons, 20% escape the galaxy. This is also very uncertain. In the local universe, very low rate of the universe, you can get 1% of these photons escaping. In other places, you get 20. So this number, which is called escape fraction, is all over the place. And there's also a debate about what it really means. But anyways, you assume some number and you assume that this luminosity function that you assumed, you see normally the strongest galaxies. So you assume that you know how the luminosity function behaves at the faint side, where you don't see stuff. And not only assume that, you assume it to be correct down to this magnitude of minus 13. This is incredibly faint. So there is lots of assumptions. If you assume all of that stuff, what this figure says, here it is, that if you calculate the Thomson optical depth, this is the Planck result, these galaxies are consistent with Planck. This is all what it says. So in other words, if all of these assumptions are correct, the galaxies we see in with HST are enough to ionize the universe. These are pop-2 galaxies. These are normal galaxies. Again, there's lots of assumptions and probably all of them are wrong. But, yeah, people do as much as they can. Of course, we need more evidence, but it might be bright. If you see here also the W map result, which was higher, you see that in the W map case, these things would not work. In other words, if the optical depth for ionization was higher from the CMB, we would have needed something else, not normal galaxies. Maybe population 3, maybe quasars, but I think this is astonishing that we are here. So if this is correct, so I'll give you a puzzle now. If this is correct, that implies that ionization is very rapid. It happened at reach of 6, between 7 and 6, it's done. That's it. Aha, now let's go to another kind of piece of evidence. This is a very messy figure, but I'll try to explain to you what we see. So, what people do, they take Laman Alpha forest again, and from it you can deduce the opacity of the intergalactic medium, because all of it comes into account, which depends on how many ionized hydrogen you have. So you do the balance, and you can get the following. At these low rate shifts where you measure stuff, you can get the number of ionizing photons per barion. How many photons per barion, ionizing photons per barion, you will have. If you have half a photon per barion, it means that at most you can ionize half the universe. Half of the... If you have 100 ionizing photons per barion, it means that you have so many ionizing photons that you will certainly ionize the universe. OK? These guys with the study, it's this number here. And at rate shift 6 is barely one from these Laman Alpha systems. Maybe if you push it a little bit, it becomes two. So you have two ionizing photons per barion. Two for ionizing photons per barion, it means the ionization process is to be so efficient that you use all the ionizing photons to ionize the universe. None of them escapes and do another. Now, if you remember structure formation and projector, the number of hellos increases like mad with rate shift. Right? So if this is correct, it means actually that the ionization process is very, very drawn out, right? Because we don't see... I mean, if it ionizing at rate shift 6 completely, then this should jump here to about 10 or 100 ionizing photons per barion. We don't see that. So it must be a very gradual process from this data. So this suggests it's a slow ionization. This suggests it's a rapid ionization. Yeah, God knows what's the answer. But it's kind of interesting period. I mean, you want these uncertainties, otherwise it's not interesting. OK, so this is again the same story. Now, I'll summarize the data with this. I actually spent too much time on these things. This is a very recent paper, it's still in last rupees, where these guys, Greig and Mezinger, Mezinger as this machinery that does maximum likelihood, MCMC, Monte Carlo Markov chain, type of maximum likelihood. And he put everything together with his student, Greig. And so they deduce this history of ionization. So this is a likelihood feature. It includes all kinds of data. So this one is what is called dark pixels. I didn't talk about it. This is the pixels in the Lyman alpha forest that are completely dark. They have no emission whatsoever. They are just basically like that. So you saw them in the spectra. This is from the Lyman alpha fraction, which is Lyman alpha that I talked about before. This is Lyman alpha clustering, emitter's clustering. This is the damping wing. Kind of fast, you go from the Lyman alpha emission down to zero. And these two kind of hashed line, one is W map, the big one, and the small one is blank. And you can see that we are getting to arrange where you have this type of history. The uncertainties are very big still, but things are tying up, right? It's not as uncertain as it was something like five years ago or ten years ago. Of course, any of these things can turn out to be wrongly interpreted, and this will be wrong. So have to be careful with these things. But this is the status. Questions, yes please. Come again. Why this is too big? The dark pixels is this one. This one is this, this is this damping wing. This is this higher shift quasar that you saw, how fast it is. Yeah, yeah, it's very little and it's very specific quasar, and it has its properties, it's not clear. I mean, there's lots of argument. And some people, like Andre Messinger, kind of, he argues for that this is really the intergalactic medium. Some people think, no, no, no, these are the intrinsic properties of the Lyman alpha emitters themselves. So there's this uncertainty, but yeah. Okay, this is where we are and now I'll spend the rest of this talk and tomorrow on the future, which is this new probe that people have been thinking about for a long time, but now it's becoming, you know, almost available. It's not available completely, but people are working very hard on it. It's very exciting stuff and I'll talk about it. We are now involved in LOFAR, which is one of the instruments that are looking at this radiation from higher shifts, but there is the future, which is SKA. The Americans are building something. SKA is the square kilometer array, which is a huge thing that will also look at these things and the Americans are building HERA, which is again another telescope that looks at these things in radio in 21 centimeter. So how many of you learned 21 centimeter emission before coming here? Ah, okay. So you know more than I expected. Okay, very good. But I bet you didn't know the history. So I like history, so I think it's quite nice. So I'll tell you a bit of the history of this. So this is one of these wonderful stories. So this line is a forbidden line. You will see in a minute. And in astronomy the story goes like this. In the Netherlands there was this guy called Jan Oort. If you haven't heard of Jan Oort, you should have. He's famous not only from the Oort cloud, he's famous for many, many things. He was a professor at Leiden during World War II. These are the years. And then it was German occupation and scientists were not allowed to go to universities, so they would kind of gather in small places, in houses, in cellars, and stuff like this. And there was this student there to look bright. But his advisor was in Utrecht and he was in jail, I think, or something like this. He was kind of more restricted. So he couldn't supervise him. So Jan Oort suggested to this guy, it's called Henk van de Hulst, to look at these forbidden lines in astronomy. So Jan van de Hulst went there and calculated, this is under a war, a horrible war that was going on, but these people could focus and do stuff. And he showed that it is very, very interesting for astronomy. This was written in 1945 and it was published in a local magazine in the Netherlands. Nobody has seen it, that the Dutch have kind of predicted this. And then they became kind of a competition. Who would see it first from our galaxy? And there were two groups working on it, one in Harvard and Brussels and the other one is Oort himself. And the Dutch were ahead of the rest. So what Oort did at the time, he took two German radar batteries after the war. They have done their damage. Now they can be used in a good way and made a telescope out of them. And tried to look at it. Unfortunately for him, there was a fire in the instruments and that set them back a couple of years which made the Harvard group beat them to the detection. But it was these days, in these days people were much more gentlemen now and the Harvard group waited with the publication until the Dutch found the line themselves. I think also to confirm what they have seen but also in terms of courtesy to Oort and his group. And if you look at when this was published, it's nature 1951, 168356 and this is 1951, 168357. So there were two pages, one after the other, published one after the other. So this was nice. But at the time we were known about this thing. So there was an initial calculation, it was very approximate. And then you would ask what are the excitation mechanism? How you excite these things to radiate? I'll show you that in a second. And then again Oort talked to a physicist who was I think in Amsterdam, Wouter. This is a Dutch name. You should pronounce it Wouterhausen. I didn't know this before going to the Netherlands. But this is that. He proposed a mechanism for excitation. And I'll show you his paper. Oh, I can do this, right? This is the paper of Wouterhausen. This is the paper, all of it. It's marked by red. Five paragraphs. And he has an effect after him. All what he says is that there is a mechanism of excitation by Lime and Alpha. That's all what he says in this. No calculation, nothing, just blah blah. But yeah, you have to be first and lucky and do something important. Actually the real kind of paper in this field is by field himself. And these are a number of papers in 1958. They are wonderful papers. So they are full of physics. He uses Einstein population. Kind of Einstein A, B and therefore stimulated emission and absorption and all of that stuff to calculate all of these effects. And so this is really what sets up the field. But nothing was much done by this in terms of high redshift and cosmology. This became a very active field for galaxies. That's where radio galaxies started. People started looking at radio galaxies. At some stage it became important when Zeldovich has proposed his structure formation. Because you know now we work with CDM. CDM is a bottom up type of so you form things small and then go big. The hierarchical thing, right? Whereas Zeldovich had a top-down model which starts with the pancakes, Zeldovich pancakes. These are the first things that collapse and then smaller and smaller things do collapse. Nowadays we know that was wrong. That is not the way it goes. It goes the other way around. But Zeldovich has proposed this model. If his model was correct you can use each one hydrogen to probe these Zeldovich pancakes. So people looked at this and that didn't yield much. Especially after CDM was kind of confirmed as the paradigm this is back in the 80s. The only person that was pushing this as a probe of hieratift stuff is Martin Ries. He would have a paper every decade almost with one of his students or one of his collaborators starting with a paper before this with Hogan, Greg Hogan and Ries. So there is a Hogan and Ries 82, 83, something like that. And then Scott and Ries pointed out that this is possible. Everybody ignored them until this paper came. So this paper is really the beginning of this field in terms of the theory. It's by Pierre Omedau. He was in Cambridge at the time and every Mike's in were in Cambridge at the time and Martin somehow convinced them that oh it's interesting to look at this and they came up with a really kind of interesting paper that said we can do this. And immediately after this, after a couple of years, there was a paper by observers confirming that we can do it from the observational side. So this is the history of this line and these two set up in motion many of these kinds of projects that are now happening on radio telescopes. So radio telescopes are going through a golden era now. They haven't done that for a long time. Kind of stagnated for a while but now they are really exciting. Let me go back. Let's talk about physics a little bit and the basic physics and tomorrow I'll continue with this. At what time I finish? At 5? So what is the 21 centimeter? It's a spin-spin interaction between the electron and the proton. It's a hyperfine transition and you have two states in this. Either the two spins of the electron and the proton in the hydrogen, in neutral hydrogen are anti-parallel. In this case the total spin is zero, because one up and one down. Therefore s is zero. It's a singlet state. That's important. The other option is that the two spins are parallel. Then the sum is one and then you will have a triplet. Again this is very important. You will see in a second moment. Then you go from here to here. This is the ground state, this is the parallel spin is the excited state and this emission gives you a radiation at 21 centimeter. If this fluid is in equilibrium with its surrounding in thermal bath or something like this you can describe the density of states at the excited case versus in the ground case by this Boltzmann factor. The three comes from the statistical weight of triplet versus singlet 3 to 1. This T star is KT basically the energy of the transition. We know that. It's 21 centimeter. This number we know very well. It's measured to this. This is a shorthand for the ambient temperature. That's called the spin temperature. In this field the spin temperature means the ratio between the excited and the ground states. That's the shorthand. Not always you get equilibrium but still you translate from you still use the term of spin temperature. This temperature of the line itself that corresponds to 21 centimeter is very tiny. It's 5 microelectron volt. It's not much. That's about 6 actually. The lifetime, it's a forbidden state situation, so the lifetime of this transition is about 10 million years. It's very, very, very long. But we have lots of hydrogen in the universe. Therefore it happens much more often. The question is how you pump the line. If you have something goes from here to here how you excite it again to go here. There's a bit of physics now involved that I have to explain. There are many mechanisms that can do this. Excite. One of them is the C and B itself. The C and B if you remember is a Planckian. Planckians have this very, very, very long tail at low energies. There's the Vien kind of tail which is exponential, it cuts off but at low energies the tailor something, I forgot the name side then you get a very, very long tail. If you have photons that have the energy of this transition they will excite the state. That's one mechanism. It's very important. This stuff will come back in how we calculate these things. The second mechanism is this Vauthausen field effect. For good reason field is there as well. I'll show it to you here. This is the effect. If you have Lyman alpha photons what Lyman alpha photons do they excite your hydrogen atom from the ground state to the alpha state. But this is a very short lift state that kind of decays back immediately to the ground state. But when it decays back immediately to the ground state it has to decide am I in this state or in this state which one wins? This. Because it has a statistical weight three times higher than the other one just more states. So they will preferentially go to here. Right? And this way you have excited. So if you have a system that was here have a Lyman alpha photon getting things up there and it would go down, it's more likely three times more likely to come back to this one rather than this one. That's why the triplet is important. And the third mechanism is collisions. If you have things collide they can excite as well. And our field in his famous paper in 1958 asked what is the relationship between the spin temperature and the C and B temperature the kinetic temperature and Lyman alpha temperature. Turns out that one approximation he made and it's valid almost always you can show that is that the Lyman alpha photons have the same kind of they induce the same temperature as the kinetic temperature the gas temperature around. So basically you have a competition between the kinetic temperature the gas temperature and the C and B temperature. And you have these coupling kind of constants. If these coupling constants dominate then your spin temperature will be like the gas temperature. If your coupling constants do not dominate the C and B will win and your spin temperature will be like the C and B. This is again important for the following reason. If your photons from this emitted 21 centimeter photons have the same temperature as the C and B you will not see them. It's like looking at a red dot and cannot distinguish them from the C and B because they have the same temperature. Therefore in order to see this effect we have it has to decouple from the C and B these temperatures have to be different than the C and B and luckily the gas temperature in the universe is different than the gas temperature than the C and B temperature. The C and B temperature for instance now is 2.73 Kelvin the gas temperature is about into the four. You remember this cooling curve the cooling curves decide this. It's about 10 to the 4. Almost any kind of system except if it's inside the sun or something but the diffuse thing intergalactic medium and then it's 10 to the 4. Again all of this because of the laminar. So it's a competition between these two temperatures. So I explained this is the collegional coupling which I kind of mentioned but so from all of this you can make this calculation it's a linear calculation still you have to go through some details and what we measure in radio telescopes it's called the brightness temperature it's a short hat from the intensity it's basically the number of photons that you measure and if you have a black body the brightness temperature is the temperature but if it's not a black body it's different. Now the temperature which means the intensity the number of photons that get to your telescope so this is the CMB and it travels through some cloud and this cloud has certain spin temperature certain temperature that is associated with this transition some of this of this CMB will be absorbed this is the absorption probability and some of it will be transmitted this is the transmission probability this is what you saw in the previous lecture as the probability for not scattering transmission probability but we don't measure really this as I said you don't measure the temperature itself you do measure the temperature difference between these photons and the CMB because that's you differentiate if they are the same you don't see the difference so you have to do this difference to see stuff and this is the way if you rewrite this in this way this is what you get and then you can expand this you know what it is it's this optical depth for this transition this is E10 this comes from Einstein but look at fields paper it's quite nice it's one of the nicest paper I've seen in astronomy it has lots of physical insides and then you go through this calculation it's a long calculation it's the end of the day so I will not go through it but at the end you will get that the optical depth is proportional to the density 1 plus delta this is a term that has to do with rechev distortions and this term has to do with neutral fraction and this is the spin temperature and this is the non-rechev dependence if you put all of this together you get to this equation which is the basic equation we work with it looks messy but it's really very rich so let me explain this and stop here I hope maybe another one after this just to give you so if you calculate this this is done first by field but later by Madao and other people later you get to this formula first of all delta TB delta TB it's equal 28 millikelvin this is the scale we are looking at things in terms of temperature of orders of tens, few tens of millikelvin if not ten millikelvin it's very cold at these very low frequencies that's hard to measure then it's proportional to 1 plus delta that makes sense the more density you have the more emission you will have that also makes sense this naive looking thing XH1 that's the neutral fraction this is how much, what's the fraction of hydrogen that is in that neutral state if this is zero it means all hydrogen is ionized you shouldn't see this effect at all because there is nothing to emit if it's one which means everything is neutral you should see the maximum of it so this also makes sense this is a more complicated one and I'll spend some time on this this has to do with the difference between the CMB and the spin temperature again if the spin temperature is equal to the CMB you see nothing ok so that's this effect and all of these are kind of there's another term here which I ignored but it should be there, it's this one it's exactly this one, I forgot to copy this is to copy it here so and these are just constant ok so this is the and if you measure at higher shifts for instance you will have that the universe is neutral so this will be one and you will have that in certain shifts that the spin temperature is much higher than the CMB if the spin temperature is much higher than the CMB this term is one you can neglect the CMB and it becomes TS over TS then all what you measure is one plus delta cosmology that's actually much better than the CMB if you get it right because this CMB is one slice in redshift this can be many many slices in redshift right if we can measure it so from this and this and this thing that I forgot which is the redshift distortions you learn about cosmology from this and this you learn about the mesophysics of ionization bubble sources etc so this is a very rich phenomena that you have learned mostly about this at higher shifts you learn mostly about this at higher shifts you learn mostly about this term alone and that's I will explain to you I do this and I finish here I think I started a few minutes late I don't want to get stuck on this next time so what does this show this figure it has lots of insights and the first to point out this is Loeb and Zaldariaga and then Pritchard and Loeb and then we have done some stuff on it now let's look at two things that decide the spin temperature I told you the spin temperature is a competition between the CMB temperature and the gas temperature now if you look at the CMB after the coupling we know what is the CMB temperature and it drops like 1 plus z so this is this blue thing so this is the temperature as a function of redshift we know it and it doesn't change but what happens to the gas if you think about it the initial impression is that the gas after the coupling should cool adiabatically no that doesn't happen immediately because you still have even after decoupling a little bit of ionized stuff and the universe is dense enough so that Compton scattering is still efficient so Compton scattering keeps the gas at the same temperature as the CMB CMB photons Compton scatter on the gas electrons and they keep it at the same temperature it doesn't drop immediately after the decoupling at redshift 1100 this actually waits until about redshift 200 then the universe becomes cold enough and dilute enough because of the expansion that this process is not very efficient anymore then the gas is free if the gas is free it cools down for you can make this calculation and this is a homework if you want ask yourself how an adiabatic gas a gas a novel gas would cool adiabatically in an expanding universe you can show that it goes like one plus it squared it cools very efficiently much more efficiently than the photons than the CMB so if the gas drops this is the green stuff it drops very fast but then at low redshift when the first objects start forming up the gas again and then the gas goes up until 10 to the 4 that we see now but gas can get cold very very quickly ok so these are the two things now what does the spin temperature do the poor spin temperature is torn apart the gas wants it and the CMB wants it and the question which one wins at high redshift they are both the same so the spin temperature has easy life it's the same temperature as the rest but when we go to lower redshifts from a little bit lower than 200 what happens is that you still have because the universe is still dense relatively you have a lot of collisions collisions couple the spin temperature to the gas although the gas become colder than the CMB the spin temperature sticks to the gas because of these collisions so here here the spin temperature sticks to the gas and becomes colder than the CMB but after a while the universe keeps expanding and this collision thing stops being so efficient then the CMB veers toward the gas sorry the spin temperature veers toward the CMB again so it goes from the gas to the CMB now what happens later there are two options but most people think the option is this dashed line you start forming new new galaxies the first galaxies the first objects then they start emitting line in alpha and they x-rays what those do they really again couple the spin temperature back to the gas they pull it from the CMB back to them so this goes like this and then here the ionization happens which means the gas gets heated to 10 to the 4 and then everything goes up right so now if you go back to this equation and forget about the rest at very high rates delta is very small therefore this is almost one nothing is ionized and these are just cosmological numbers nothing much and this is one first you remember the spin temperature gets coupled to the gas and it goes down it goes negative right so the spin temperature is smaller than the CMB so this term becomes negative over the spin temperature ok then after a while the spin temperature goes to the CMB then this becomes zero because the spin temperature equals to the CMB at some stage now later oops again this goes down which means you again have another negative period and then at the end this becomes so hot hotter than the CMB that the CMB is ignored and this becomes like one now there is asymmetry between positive and negative here if the spin oops sorry if the spin temperature is much larger than the CMB this term can be maximum one ts over ts however if the spin temperature is much smaller than the CMB this term can be minus thousand no one stops it from being minus thousand so you can see it in absorption much much stronger than you see it in emission that's the difference between positive and negative ok and people have kind of worked out this paper by Richard and Lope that showed this change in the brightness at very high redshift this is you see this absorption that's called the dark edges absorption then you go back to zero and then you have another absorption that's in the cosmic dawn when the first object starts forming and then again it goes back to zero but then it jumps over because of realization happening and you can see this can't instruments focus on this this tiny thing this is where we are and this refers to redshift about 10 this is what we are trying to observe future instruments like SKA hope to see this which would be very nice this is hopeless from the ground absolutely hopeless because of the atmosphere you better go to the moon to do this and some people are thinking about the moon actually the best place in the solar system is Mars go to Mars and the best place ever go out of the galaxy then you can see that anyways so this is for dreamers people dream to do this maybe I will not see it in my lifetime at least in my career but you maybe see it that it's done from the moon but this is really exciting for the future we are now focusing on this and I'll stop here thank you for your patience