 Okej, veliko slate tudi broj ravaz that after this lecture we'll have a group photo, so please com and come to the picture. So we have a new course, the one on realisation and the speaker is Simsa Ruby. OK, thank you, pleasure being here, thanks for the invitation to give this talk. I realized that I'm one of the last speakers I ti je vršt. To sem vzela, da sem bil ozvodnju, kar dam. Moje plan je, da sem ti vzela delaj, da sem je vzela, da sem je vzela. Zato sem začnila svoj počke značenji, kako je najbolj je podnosnja. oče motovimo, kako smo zdam. V teorii, to je tudi svojo simulacije o češtih. A zato pojelimo z vse obzervationalnega obzervacije v teorenazirašnje. Vsega in vzvednjega, da je za srečno 21 cm probe, ko je zelo vse večo vse probe, a ki je to, da je to, da je to. OK. So, I'm sure you have seen this picture many times. This is the history of the universe. This is one of these renditions. I think this appeared in Science magazine, and I like this one specifically because it has so much details, but it's not different from the other kind of images of this. This is the universe history as we understand it. This is the Big Bang, and their inflation happens. And this is the CMB, the last catering surface. For my purposes, before the CMB, everything was opaque and ionized. So, that's why I showed this. And so, the CMB, you had a separate number of lectures on it. This is, we know, incredibly well. The wealth of information from the CMB is unbelievable. If you started when I started in this field, when I was a student, when I started, CMB fluctuations were not discovered yet. I'm that old. And in 1992, Kobe came up with the fluctuations, and all what we knew about was the amplitude of the fluctuations. There were many, many, many papers, but the only real information in the Kobe papers, which are many, is the scale of the fluctuations. And then other experiments came by and showed us this incredible detail. It's the gift that keeps giving, and will be giving for a while. So, CMB is very exciting. But for the purpose of this talk, the CMB is what the universe became. It's the last catering surface, the coupling and recombination. That's when things became neutron. Hydrogen became neutron. At most. There's still some small fraction of ionized stuff. If we were to live then, the CMB, if humans were there, and they would look at the CMB, the CMB is about, you remember, what's the CMB temperature now? It's about 2.73 Kelvin. This is reached roughly 1,100, 1,200. So, we are talking about something of about 3,000 degrees temperature. It's kind of reddish. So, if we were alive then, if we see the universe, it has a color. It will have a color of red. It's like just something that helped me at least understand the CMB. If you want to think about the CMB, it's like the inverted sun. The sun we see only the last, the chromosphere, the last stuff that releases photons. Everything inside is like the early universe. All what we see is this crust of the hot initial phase of the universe. And it's very similar in terms of physics. This is Thompson's scattering, so it's not very complicated. Anyways, after this phase, the universe keeps expanding, and of course, this color of 3,000 degrees redshifts a little bit more and a little bit more, until it goes out of the optical. It becomes infrared, and then we stop seeing it if we were alive then. That's why this phase was the dark ages. If we were alive, we'd see it dark. There's nothing. Of course, at this stage, there are no stars, no galaxies immediately after the last scattering surface, and the universe becomes a very boring thing. There's nothing except the gas that is adiabatically evolving and cooling. This is not completely true, because the fluctuations that were seeded by inflation have time to grow through gravitational instabilities. At some stage, these things become so nonlinear that they start forming galaxies and stars, first stars and galaxies. And those will emit UV radiation, either in their first generation or second generation of stars, and they start ionizing their surrounding. And the universe will become ionized again. And this phase starts here. So if you remember, this is when the universe was 400,000 years old, roughly, 378,000 years old. This starts when the universe is half a billion years old. So there's about a time fraction of a thousand, roughly, in terms of this evolution. And this basically plunges the universe in this one of the last phase transition in it, where the gas goes from neutral to ionized. This is the epoch of ionization. It's a global phase transition. It's interesting for cosmologists because it's a global phase transition. It talks about the universe as a big thing. It is interesting for astrophysicists because this is where astrophysical objects started. This is when galaxies started and stars started. So it's a significant event in many ways. In other words, this is when barions became very important in the evolution and producing things. It's a very exciting epoch. And the universe before it and after it goes from the unfamiliar to the familiar. The universe before it doesn't have so many galaxies. It's just something that is very weird. After it, it becomes having galaxies and stars, it becomes familiar to us. It's like the universe now. Of course, not exactly, but in rough terms. So this is in terms of why this is interesting. Is that we observe low-rechiefed stuff very well. We have telescopes that go up to rechiefed 6 relatively routinely. But after this rechiefed this is roughly rechiefed 6 and we will come to that in detail. After this rechiefed, it's hard for our telescopes to go there. There is some data now which has been a very exciting development in the last number of years but it's kind of a slow progress. The next piece of information after rechiefed 6, we have rechiefed 1100. So there is this huge lack of information about a big chunk of the evolution of the universe which we would like to understand to put everything in kind of to tie the picture in a very coherent and systematic way. So this is my story. If you don't take anything from my talk take this one and that will be enough to give you the flavor or the big idea. Of course, there's lots of details and I will lie to you if I'll say that we understand everything. We almost don't understand anything in this but we have lots of speculations because of the lack of data but this is changing a lot and I'll try to convince you that we are starting to understand what's happening and in the future we'll understand much more I'm very formal in my way of talking so if you have a question if you have anything that I say that is not clear or please stop me and ask. Ok, so we start with the sources of reionization and if I would ask you what you would think the sources of reionization are the simplest things is the first stars, the galaxies. That's the thing that we see around us. This epoch of rechiefed 6, 7 that you will see why I keep mentioning the stretch of 6, 7 is where galaxies start popping up and we start seeing them then they are the most kind of normal candidate their energy output is huge they can do this reionization quite easily or relatively easily etc. However, they are not the only candidate they are the most favored candidate and probably they are what ionize the universe or most of it there are some details which I will touch upon a little bit talk about population 2 3 versus population 2 stars different types of stars, I will come to that these population 3 are the primordial stars they are stars that are made from the primordial mix of gas which is hydrogen and helium they don't have metals metals for us is anything kind of heavier than helium and population 2 what we now call population 2 there are old stars around us that these times they were young stars and this is the competition and who ionize the universe is this one or this one most people think it's this one it's what makes more normal galaxies but those have played a very important role they came first and then made way to the population 2 that will be part of my lecture today there are also other things like QSOs or faint agents what we call mini quasers these are sources that are fed by by accretion, direct accretion of mass so there are accretion dominated sources and they are not thermal stars are thermal normally they follow Planck's law normally agents and quasers emit things in terms of like power laws mostly they are very hot they are hard photons like X-rays we don't know much about them at high reaches but recently there have been a number a number of quasers discovered at high reaches and there is a speculation that maybe the faint quasers are they are much more there than we expected so they might have played a role although there are limits there so I think the consensus is that QSOs and faint agents did not ionize the universe but they played some role maybe some 10-20% they played a role in heating I'll come to that hopefully in the second or third part of my lectures there's also X-ray binaries which are also kind of something that people consider but there are more exotic things like dark matter annihilation and more exotic scenarios like primordial black holes and stuff like this these are I will not touch upon these things too much but again the consensus is that they don't contribute much if they are there we can use ionization if we understand it very well and see the history very well we can use it to constrain these processes but not the other way around so I'll focus on the conventional pictures but this is to mention that there are other things now so let's start with the first stars this is a big topic and it's mostly done with high high resolution simulations and I will not plunge into it too much but I'll give you the basic physics of it just to give you the flavor of why is it different than so the first generation of stars is formed with the primordial mix of gas and the primordial mix of gas had only hydrogen and helium a bit of lithium but that's almost negligible but it's hydrogen and helium can anybody tell me if you are in the field don't answer this question why is it unusual I mean why this is different from a normal star a star that has hydrogen and helium alone will be different than the sun does anybody know? for producing the heat in the side of the sun well that's true but the dominant thing is the hydrogen burning it's not in the they are being incised as a consequence of the physical reason so that's the right answer I'll explain it in detail so when you the way things of stars form or any kind of these gravitational systems form at the end to form something that is baryonic at the center you start with gravitational instability things collapse at some stage if you have baryons things heat up because you push everything to the center once things heat up pressure prevents things from kind of things collapsing more that's what happens in galaxy clusters actually gas is distributed almost as much as the dark matter actually dark matter is a little bit more concentrated than gas in these systems so in order to form things more to have things condensed more the gas has to lose its energy and the way gas loses its energy is by in astronomy in most processes is there are a number of processes but the dominant one normally is radiative cooling which means if you have a quantum system at an atom it gets excited from the heating to higher energy levels and then it gets de-excited when it's de-excited so that can run away from the system this is the cooling so you lose energy by this radiative cooling process in primordial mix when you have only hydrogen and helium and here hydrogen is the more important one the first level of excitation is limon alpha limon alpha is 10.2 electron volts 10.4, 10.2 I think so if you translate that to a mass if you ask what hello when things collapse they heat up so what mass of a hello that would collapse will get to that temperature 10 to the 4 it will be huge it will be 10 to the 11 10 to the 10 solar masses or 10 to the 9 solar mass that's a very big mass to have before starting forming stars I'll go into that in detail in the universe there were not so many of those very big hellos there was not enough time to accumulate so much mass to heat up these things so quickly so that's why forming these things is very hard it's not easy whereas if you have a little bit of metals tiny bit they have different energy levels much much lower and through these channels so radiative cooling is way much more efficient you only need one in a thousand to become a normal star so these stars if they form the expectation at least the initial expectation was they will be huge because their cooling process is very hard so that's the reason first stars are different than normal stars ok so this is the cooling issue there is another issue let's assume that you manage to get a mass that is collapsing and cooling efficiently how from that you would form a star this is gas that is kind of contracting how from that you would form a star then there is lots of gas and the competition then is as follows it is between the collapse time of the hello if the collapse time is very fast it leaves very little room for nothing to do stuff but if the collapse time is very long then compared long and short always in comparative terms always in comparative terms relative to the local cooling so if you have gas that is contracting and here you have a parcel of gas that is cooling very quickly so what will happen in this one in this very small parcel it will cool down and it will condensate faster than the rest of the gas that is collapsing this is how you fragment stuff right and if you go through it I mean that's the theory in rough terms you should get star masses that we observe in our surrounding so it's a competition between the collapse of the big hello and the cooling time that fragments stuff locally if the cooling time is shorter you will fragment to smaller pieces if the cooling time is large you will not fragment to smaller pieces the problem of these systems if you have hydrogen alone atomic hydrogen the cooling time is not very efficient why unless you get to these very very big masses so if you produce stars there will be huge and people started talking in the beginning at thousand solar mass star or hundreds of solar mass stars now it's different I'll come to it pure atomic hydrogen I didn't mention helium so much but hydrogen dominates everything here pure atomic hydrogen has a problem it's very hard to understand how things would form and I'll go through details a little bit to clarify this picture I'll talk a little bit about what at the end what does to the rest of the IGM population 2 stars so this is the cartoon you start from an over density and at the beginning and then dense thing becomes denser this is gravitational instability and then once thing becomes very very peaky they go on linear and form galaxies so that's the the initial picture and even in nature the rich gets richer and the poor gets poorer that's kind of seems like everything is unfair in the world that's not working so this is the cartoon that I was talking about this is the it's this kind of cloud that is collapsing and as it collapses it heats up and then you need to radiate this heat up to get more condensation and then fragment to form stars so these are the three or four things that we have to worry about and these things in detail that's difficult because you have to go over many many scales so to simulate something like this you have to start from cosmological scales to down to large scale structure things down to galaxies down to the stellar scales and down to even more so that's a huge range of scales so to simulate this thing was not easy the first set of simulations was a big achievement so this is the picture now I was counting on the fact that you will learn something about pressektor but you haven't in this course so far they have oh excellent excellent so you have heard about pressektor so this is taken from this review from Barkanaj and Loeb so here what you see is the mass in terms of solar masses versus the mass fraction in helos and you can see that so that's the mass fraction per megapastic cubed and you can see that big masses like so this is redshift zero here and this is redshift 30 I think that's the and you can see that at higher shifts these are the higher shifts ones you don't have large masses of helos so most helos at the beginning at higher shifts are small too small to make to cool hydrogen that's the argument of the cooling before actually this looks like most initially so you would see that most of the mass is in this small helos because you have so many of them but that's misleading actually most of the mass is at the break that's the pressektor so there is m star which you have defined I hope the typical mass at a certain redshift most of the dominant mass at any redshift is that m star although smaller masses will be much more abundant but big ones are the ones that matter in terms of mass so this is the point I was trying to make that at higher shifts you don't have enough mass to cool to perform helos that have temperature of 10 to the 4 Kelvin so this is another this is another kind of it's the same kind of work done differently so this is the again that's mass as a function of redshift this is for a standard model this is the one sigma two sigma three sigma fluctuations let's focus on the one sigma this says that at redshift 10 you will have masses of order the dominant one will be 10 to the 10 to the 2 and anyways you will have these very big masses 10 to the 10 to the 12 only at very small redshift right at 2 and 3 sigma fluctuations you will get more here there are two lines ignore this for the time being I will come back to it later this is the atomic cooling line so this is below this there is no atomic cooling that is efficient and you can see that you form very little mass that is cooled enough to form this stars with each one this is the temperature again here you have two lines I don't know if you can see them here I can but I don't know from the back it's from the paper itself sorry about the color I couldn't change it in time and so you can translate mass to virial temperature just energy considerations and this is that 10 to the 4 solar mass 10 to the 4 Kelvin that's when each one cools and you can get this Lamin alpha cooling let you ask in a second so this is it again below this there is no efficient cooling and you can see that if you consider the one sigma thing the organization should happen or sources or galaxies should all be formed at very low reaches so this cannot be the story so there must be something else this is this is no this is from theoretical kind I mean it's the presector formalism so you assume that the universe is Gaussian and you assume that things above a certain threshold inflectuations can go on linear come again no no I'll show you where it comes from it's from simulating the cooling it's from calculating the cooling times function I will come to the cooling function it's a very long calculation but say calculation not the simulation or something I cannot hear this one this is mass fraction in mega positive so it's 1 over mega positive or the number density if you want with different with certain mass, hello masses ok now I come to the cooling rates so the cooling rates this is the famous kind of function so the cooling rate of h1 a star that has or a cloud that has only a hydrogen is this red thing and you can see it has a wall here at around 10 to the 4 this is the time in alpha cooling this is things going to the first excited state and going down and you can see that it doesn't cool below 10 to the 4 back this is where 10 to the 4 is and 10 to the 4 basically corresponds to very massive stuff so you have to wait until very massive stuff comes so that you can cool but then something else comes to the rescue and this is kind of has been the breakthrough in the last 10-12 years is that it's true that we only have hydrogen and helium but hydrogen in certain conditions can go from atomic to molecular hydrogen prefers the molecular kind of phase in normal circumstances in very early universe that's not the case but in high densities that would happen some fraction of it will become molecular and molecular hydrogen is different than atomic hydrogen, why molecules have vibrational and rotational modes they have much lower energy transitions therefore I can cool much easier than this jump this huge jump this is I think assumes that one in a thousand of the hydrogen gas is in a molecular phase and you can see that the temperature drops from 10,000 to a few hundred couple of hundred so I can cool things with hellos that are couple of hundred and that if I go back these are these lines so before with the H1 I could also see I could only kind of form galaxies with these very very you know kind of hot things or here very massive things but with H2 I can go now to hellos of order 10 to the 6 10 to the 8 solar masses which are kind of much more abundant at these high densities okay that's the physical picture that's why this is very important now to calculate yes come again that's the H1 cooling rate if you only have H1 is hydrogen atomic hydrogen that's what I mean right the blue dash line is when you have H2 molecular not where the astronomy is confusing when now you have molecular hydrogen okay that real 2 not roman 2 yeah okay so that's what saves you so that drops your cooling from this 10 to the 4 to 10 to the which means that much smaller hellos can now cool and fragment and collapse okay more questions yes yeah I mean this is the the cooling curve is kind of there's a range of energies that it's efficient here but it has a sufficient at lower energies okay yeah why is it because it has these vibrational and rotational so you don't need to push an electron to the limon alpha the fact that the two do this can absorb some of the energy and then emit it as in photons that are related to that transition which is much smaller energy so you can do it much easier actually this is what we see in local star formation stars locally form in molecular clouds what we call you need molecules to do that and that's the reason it's easier to do things with molecules so this is one of the not the earliest paper but this is one of the pioneers a paper by one of the pioneers I mean the first people to calculate this is brome and his collaborator and Tom Abel and his collaborator and they often produce these things and this gives you the the scale of the issue why this is so complicated to simulate so you start from 300 par6 actually you should start from tens of mega par6 but then you zoom on to 5 par6 25 solar radio and then 10 AU atomic units this is a huge resolution and to do this this is an achievement and the way they did it mostly is with AMR adaptive mystery time refinement kind of techniques but I think those guys use mostly gadget so there are a few few ways to do this and you can see that you start from a cloud when you kind of go down and down and down you can actually see the accretion phase that builds up the mass at the central point here we don't have more resolution as you can see but here clearly there is a center and there is an accretion phase and even kind of what do you call tidal spiral arms kind of and where the star forms that's also another issue so the old picture was the initial stars form in the center there is a study that will show in a second that shows maybe the stars not form in the center but in these waves of gravitational kind of arms where you have higher density and then you have more probability to do stuff and the difference is that if you form things here then the mass will be large if you form things here the mass of the stars will be smaller so that's the difference so this is a study in the same year here you see one star forming in the center here you see this fragmentation in these spiral arms why people do this? because we want an idea how massive are the first objects so I gave you this hand waving physical argument but there's lots of more details there's things that have to do with turbulence with angular momentum with magnetic fields which nobody touches of course that's too difficult to do so there's lots of details on top of the cosmological kind of simulations that you need to do the hydrodynamical simulation to reach these resolutions so there's groups don't necessarily kind of agree but they do these things so we need to figure out what is the mass of the initial stars we thought at the beginning of this field that there will be 100 solar masses 50 solar masses if these fragmentations are correct we can get down to 10 solar masses it becomes much easier to make them so there's no consensus yet as far as I know about what is the right answer because again this is complicated stuff in this field and it's incredibly exciting to do this and lots of physics, lots of other things can these things form for instance black holes early on so that's another kind of thing that I'm not touching on but the frustrating thing about these things as much as you would like simulate them and see them in simulations we probably will never be able to see them directly because they are really at the center of these we don't have the resolution to see something like this at 10, 11, 15 or 20 this is kind of that we'll never have in the future so we'll have their collective effect but not individual effect so some of the issues we'll have to see to sort out indirectly ok so to summarize this and put the steps that of the further evolution so the population free stars are expected to have masses now we think it's 10 to 100 how much at the high end how much at the low end there's lots of debate but this is the range just to give you a number a star with 20 solar masses would live for anybody knows how much what's the lifetime of a star with masses and I guess hmm one million one million year so it's very short we are talking about billions of years so they live and die very quickly so that's one thing the other thing is that if that's the range of masses 10 to 20, 10 to 100 we will never see them now because they will be dead long long long long ago right now the universe is full of metals it's contaminated all of that stuff right why they are important so do they ionize the universe by themselves they are they are massive in their life they produce a lot of UV there's I mean massive stars produce UV normally ultraviolet radiation ultraviolet radiation then they explode they contaminate the IGM etc but because of their short time life nobody expects them to ionize the universe by their own their importance actually we think there's some kind of discussion is the fact that they contaminate and there's feedback effects from them that contaminates the rest of the universe the feedback contamination gives rise to population 2 stars because when they explode these things after a million years in their centers they have produced new atoms now nuclear and these have they are not helium and hydrogen anymore they will have more things like carbon and other things and those are very easy to cool and they form much much smaller stars the ones that we are used to ok and those population 2 stars which don't have too much metals but they have metals they produce lots of UV their numbers are large the masses of the galaxies that they kind of the number of galaxies that they can form on is now much larger because they don't have to form in the highest peaks they can form in the lower peak and those can ionize the universe now they do something else they produce lineman-vernar photons for those of you who don't know what lineman-vernar photons are photons in the band between 10.2 electron volt and 13.6 electron volt so this is between the lineman alpha and hydrogen and the continuum and those if you have them they will destroy molecular hydrogen so once they produce them the smaller hellos that didn't produce anything before and they were going to produce population 3 stars cannot do it anymore because this radiation prevents the formation of molecular hydrogen so this is a very kind of complicated process and it depends where you are in the density field but this is it and finally after all of this process which is very schematic over simplified I kind of emphasize this lots of details, lots of work here this finally creates stable galaxies where their virial temperature is 10 to the 4 and something like that high density basically there is a process if you ionize so they can form through a channel of ionization so you ionize so I didn't want to go to these details there is a kind of schemes so you ionize one hydrogen and this ionized hydrogen kind of sticks to another neutral hydrogen and that's how you form it but it needs high densities and it needs normal temperatures so there is lots of conditions I'm trying not to go in too much into details I hope that's the right decision I'm not sure OK, so I'll show you a movie now but I would like to ask people to turn off the light Paolo so this is finally after all of this we have normal galaxies and the question is how these normal galaxies ionize the universe this is a simulation that was done by Marcelo Alvarez and I think Tom Abel was involved this is God's view here in the sense that if you stand outside the universe and look at it from outside how will you see the process of realization happening so you see here there is a cube here you can make it out basically you can see it and these are the first sources of ionization and you will see how they evolve now it's a bit delicate did it work? Yes so you start seeing that these regions around these first galaxies gets carved out with ionization radiation and this ionization radiation increases the number of sites where you have ionizations happening increases and it's a slow process relatively but bit by bit it fills the whole universe there's a perculation process here you can describe it as a perculation process those of you who likes that mathematics can describe this as a perculation until everything ionizes the blue stuff is ionized stuff basically and you will see the galaxies at the end appearing as points but this is the process now we don't know a lot of details so these are the galaxies that did the whole thing now you can see them that's how it started and that's the universe that we are left with we don't know let me just run it again so that you can appreciate it we don't know exactly what are how fast this process is what's the how efficient these things are because you produce UV photons at the stars level but for these UV photons to go out to the intergalactic medium itself and ionize things it needs to escape there's something called escape fraction which is a whole can of worms that people don't really understand how much of these photons go out what's their fraction so this will set up how much of this we will see what's the efficiency of star formation at these modes of forming stars also we don't know so this is kind of an educated guess but there's by no means something certain the time there's normally they put a redshift somewhere and they tell you this will take two redshift bends or something like that but don't believe any of that stuff we really don't know questions so far am I hitting the right level of things are people following or I'm too simple fine people satisfied raise your hand if you are happy okay good oh that's huge well they now let me remember I can't remember exactly what the red is I think it's the range of temperatures that you have in that gas after it's ionized so initially it heats up but towards the end it kind of gets cooled and you can see that it's cooled that's my recollection this is old old thing so I apologize if I didn't answer it correctly okay so now I move to more yes please no no I mean I said we don't think it is the main source of ionization absolutely it produces a lot of UV and it can ionize its surrounding but if you go through the numbers mass and that will become it doesn't add up right but it there might be the you know we might have surprises and actually there are indications that we might we have surprises but they are not completely clear this is I'm telling you what's the conventional wisdom but whether this is true or not it's not clear yet this is an open field so many of these things are not certain okay observational things and to talk about more questions before I move to this okay so there's lots of observational probes and I'll start with observations that we already know that we already kind of learned something from and you will see it's not much but it's improving a lot and in the future we'll have much much more handle on this whole process it's a long laundry you know it's a long list I'll start with the CMB actually you heard about it I'll go a little bit into detail why the CMBs can tell us anything about reionization so that's the first thing in terms of physics of the CMB today I'll tell you a little bit about the limon alpha absorption systems how they teach us about reionization limon alpha emitters and probably I'll start talking about the first galaxies sorry the high-rich galaxies that are also that's something that has been very active in the last decade, less actually but there's lots of other things that one can talk so I'll focus first about the CMB and these things and later I will talk a lot about the 21 centimeter emission okay this shouldn't be here, this should be somewhere else I'll move it later somewhere else right so let me start with the CMB why the CMB tells us anything about reionization right so that's the few slides that will come this is an old topic as you can see from the papers some of them go back to 1994 but most of this is where most of I think this paper where most of the physics is laid out quite nicely there's another nice review and the results are so this is the theory and the results have been coming in recent years especially with WMAP and recently Planck and here how, I mean this is a schematic picture now this is kind of the opposite picture that you see the big bang happens at this at this circumference of this circle this is the last scattering surface right this is where we start seeing the CMB and photons from here come to us and then when come to us they come to us most of the universe as we said is neutral until you we start ionizing the universe at low reaches, when you ionize the universe you are free electrons quite effectively with photons Thomson scattering basically it's a very simple process so from realization to us there is additional scattering of these photons this additional scattering leaves imprint on the CMB kind of measurements it's a secondary process it's not primordial it doesn't happen here it happens on the way of these photons to us that's why we call it secondary but it happens and that's why we can from the CMB say something about realization because it tells us something about where this happens of course this is the wrong picture this depicts things happening suddenly here at the realization realization doesn't happen suddenly it happens gradually et cetera but this is the picture and it turns out that it influence it influences things right so this is you have seen something like this in the lectures of the CMB so I don't need to go to too much details but the dominant contribution happens basically due to Doppler shift of the scatterers so you have a electron that is moving and you have the CMB photon coming and the fact that they interact it basically scatters the photon and changes its temperature a little bit so you see some fluctuations in the temperature and this is the equation that's the Doppler effect of the temperature this function is called the visibility I don't know if you have seen it which is basically the optical depth for Thomson scattering multiplied by the velocity right so this is the process I think the mathematics is nice but it's the intuitive understanding is the important one is the fact that you have scattering of photons it destroys their coherence because they scatter that's the main effect so let me show you so this is the visibility function that I mentioned that go into this calculation but again it's interesting if you want to know the details but the physical picture is very simple the physical picture is as follows and these are the two things that I will describe so the physical picture is as follows so we have the CMB the CMB we see through this power spectrum which has these kind of power at different scales these are coherent because you have power at different scales it means that you have coherence of fluctuations at certain scales otherwise the coherence destroys there's no correlation at these scales now if you have photons that scatter a lot before they arrive to you that coherence is destroyed because they don't come to you all of them some of them scattered there and if the process is very efficient most of them scatter that will destroy the whole coherence so you should not see the CMB as we see it so this figure is an old figure from Sugiyama 1995 who was one of the pioneers of this and he shows the power spectrum that we now all know and love as a function how much optical depth for Thomson scattering there is on the way in other words how many free electrons on the way of the CMB to us these photons see and it starts from zero which means no reionization whatsoever the universe is neutral until now and this is what you should see which is roughly what we see now if you go to half you will see that the coherence is getting destroyed it means the amplitude is going down it doesn't happen at the largest scales because this is beyond the the the causality scale the L of L of 200 that's where the light horizon at recombination so that's not affected at all these are happen at causal kind of things but you can see that the coherence gets destroyed in other words the amplitude goes down and the smaller scales affected more than the large scales if you have larger and larger and larger and look at two if you have things that are completely unionized this will suppress completely these fluctuations the CMB would look like this so the fact that you see don't see this means the universe has very little new ionized have very little free electrons on the way from the last cethering surface to us it tells us one thing that's the first thing you learn from the CMB that's almost nobody mentions normally which taken for granted the first thing you learn from the CMB that the universe became neutral at some stage that's the first lesson from the CMB right it also teaches about unionization but the first thing because you see this it means these effects are very little so the universe became neutral at some stage so that's very important bit the second thing so we are not at these levels absolutely not now what happens if the level of ionization is smaller so you go from this range of 0.03 this is from I forgot to give the credit for this figure this goes from very low tau to very large tau low tau means low number density of free electrons on the way and large tau is larger still not very big I mean it's nothing compared to these numbers and you can see that there is a shift so this is the influence of these ionizing photons on the amplitude of the CMB fluctuations the temperature fluctuations I haven't talked about polarization yet so you should expect an effect on the amplitude of the fluctuations so that's the first thing now these things do more why do they do more now let's kind of make this model a little bit more simplistic let's assume that you had last scattering surface from here that the photons come and then suddenly see a cloud at range of 10 of ionized stuff then you can write this visibility function that I talked about before as this combination it's the probability of transmission so the photons that come from here will kind of continue the probability that they continue plus the scattered stuff that's the photons that come from here scattered into our directions so that's a picture that we can live with and we can calculate all kinds of simple things here but you can see that this term that comes from here is very negligible these are the photons scattered from the CMB they were coming in that direction and then they hit this ionizing ionized stuff and they came to us so this is very small so that means that this ionization stuff is not that large so that's another kind of way of saying the same thing now let's look at polarization so ionization should reflect itself in the temperature fluctuations now we'll talk about that polarization itself which is much more sensitive that's why people, as you can imagine because people mention the tau in the same breath when they talk about polarization so normally the CMB is polarized why is it polarized? because it's Thompson scattering if you have a little bit polarization before it will remain polarization it kind of maintains polarization any scattering process produces polarization so normally when you talk about polarization there are and now I'm throwing you back to your electromagnetic course there are four stocks parameters if you remember we normally talk about stocks parameters the first one is the second one is the third one is the third one is the fourth one is the fourth one is the fourth one is let's talk about stocks parameters the first one is the total intensity that's the normal stocks that's stocks i what they is called and then there are another three there are stocks q and u that are linearly polarized and then there is stocks v and that's circular polarization circular polarization we will neglect here it's not important, it happens in certain circumstances but mostly we'll neglect when people talk about polarization in the CMB they don't measure the circular polarization there's nothing that measures it they only measure linear polarization which means q and u and q and u have different symmetries so this one looks like this this one looks like this if you rotate by 90 degrees you get this symmetry in both and if you rotate in 45 degrees you do this symmetry and normally there is the polarization angle defined in this way and the polarized intensity what they call polarized intensity is p which is the amplitude of square root of q squared plus u squared so basically the amplitude in the polarization so this is what we use normally if you go to radio astronomy which I'll mention later these are the parameters they use CMB they decided to use something else let me do it here what they do in the CMB they take a combination of q and u and form things that called e and b polarization they are simple linear transformations of these q and u what they do they reflect symmetries you combine q and u to form e in such a way that if you put a mirror in front of your universe make a parity transformation it looks exactly the same the b mode is the opposite the symmetry changes direction so the sign changes so you can form these types of things why they do it? because of practical reasons not because of fundamental reasons so this is I took this I think from Wayne Hu's webpage so if you have two waves coming to a scatterer this is the electron in the electron frame of reference the electron moves up and down when you scatter if it moves like this it will keep this in this mode it will go up and down like this now if you come from this side now I think I don't know why it doesn't have it imagine you have another wave coming from this side that does this and this one would also kind of have scatter over the same photon it will produce something a little bit different so this direction the combined thing that comes out from the scattering will be different so if this is different than this you will get something that's polarized so that's the simple Thompson's scattering ok now e and b modes I talked about them this is how they produce them I will not go into this too much in the b mode there is a parity flip in the e mode there is no flip now if you look at at recombination let's assume that this is the horizon scale recombination we know what's the horizon scale at recombination it's almost one degree all of these processes that I'm talking about scattering Thomson scattering produces polarization that would happen within the causal causal distance time scale so at recombination I shouldn't see any polarization I will see decay of polarization at scales larger than one degree otherwise at l's that are smaller than 200 because they are not causally connected so there is no connection between the polarization there and the polarization there right so if there is no if there is no there is nothing else other than the last scattering surface at reach of 1100 the scale at which I should see fluctuations in the polarization is l of 200 and below in other words larger l's smaller scales but not above because the above scales are not causally connected I took that one out right so I'll make a mishmash a little bit to show you the point I'm trying to make this is a famous picture from W map these are a number of different power spectra I'm sure you have seen something like this power spectra of EE and TE did they follow or not yet did they see power spectra like this yes, okay so if you look at the EE mode that's the E mode polarization power spectrum that's the green one you should see that so this is the primordial expectation from the last scattering surface you see here fluctuations but here you should see something that drops to this direction instead we see this point which is at l of a few which means that we are seeing polarization happening at much larger scales but either there is something in the fundamental physics of these things that we don't understand or the one degree on the sky one degree is here that's the one degree that's the peak that's the l200 after l200 it should decay because you don't have causal connectivity they are far away from each other they don't know about each other polarization but suddenly you had this this measurement here what does that mean so now I'll go back it means that the scale at which we measure is not this it's much larger but it cannot be larger than the horizon scale therefore it has to be at a different time cannot be at the last scattering surface it must be much much closer where the horizon has increased a lot to produce fluctuations on these scales this is why we get this very small effect at very small ills because the horizon later recombination at reach of 10 or 20 is much larger to number 30 40 degrees rather than one degree so what we measure is not the horizon scale at recombination but the horizon scale at or the fluctuation scale if you want at reanalyzation that's why this measurement is important so these are simulations that show you the very low multiples so if you go back to this normally this is the L of 200 it's here now we are going to below 10 from 50 to 10 it's this that we should get so let me go back so this is the cmb itself the primordial cmb but if you have tau that is between 0.04 and 0.08 these are the colors 0.08 this is 0.04 this is the effect of ionization on the cmb so it's only in this very very low L mode that you see this effect that's why for instance such small experiments in cmb cannot see this you need very large scales for whole sky that's why only plan W map can produce this stuff there are two effects there one is the amplitude the more tau you have the more free electrons you have you have a larger effect versus the 0.04 but there is another effect which is a little bit more subtle which is where the peak is the peak moves from right to left you see it it also has to do with the scale when ionization happens so we learn something about it from when it peaks if we can model this kind of upturn very well we can learn a lot this is a simulation this is the effect on the polarization this is the effect on the cross power spectrum of Te so this is the EE the E mode polarization another thing this is from Planck paper this is from last Planck paper which gives this surprising result but this is all simulations so far and the gray area here there is the is basically the uncertainty the cosmic variance basically I don't know if you can see the gray area but there is a gray area this is a word of warning which we all knew for a long time but the Planck people did in demonstrating it this is a number of different reorganization scenarios you can see this there is one that happens almost suddenly this red one raises and then a little bit more later this bit is the helium thing we are talking about hydrogen alone but there is helium helium ionizes later because it needs much more energy for the second electron to ionize the first electron ionizes almost immediately this is another kind of scenario where things ionize recombine and then ionize again all kinds of scenarios all of them you see them when you calculate their power spectrum they kind of almost lie on top of each other the C and B cannot tell us the details it's an integral constraint it tells us basically how much of this scatters when it comes to us how it scatters here or here we don't know ok so when they tell you the redshift of ionization from C and B is 7 there is an assumption there and the assumption is about the history of reorganization they tell you it's a sudden reorganization or kind of gradual there is a big assumption there you actually can produce this by having a very low level of ionization from redshift 100 to 0 you get the same result you can think about models like this ok W map so I think I'll finish with W map and Planck I was planning to go more but I spent too much time on these things so W map the first W map result that came it was 2004 and in 2004-3 something like this they claimed that tau that they measured was 0.17 0.17 was huge was unbelievable and of course like in every other field theoreticians can explain everything and there were lots of papers explaining this 0.17 except that people kind of started this is not right not right with this turns out that they had some problems immediately almost a year or two after that this number to 0.09 first 0.0 so there is a trend they started for 0.11 and then 0.09 and then 0.085 0.088 something like this the reason is this is a very difficult measurement when you do CMB and I'm sure you have heard this there is foregrounds that you have to clean in total intensity in the temperature we understood then in polarization the sky looks crazy the galaxy doesn't appear at the center alone there is these huge arms of things when something called the north polar sphere that goes from B of 0 the galaxy would center up it's a very different game also they had some systematic issues in the data so this is the this was the best estimate until recently but Planck then started getting results and Planck they have very funny names lolybop that means low L likelihood something probability and I think these PO were added to have lolybop in the acronym something but it's their pipeline basically of producing stuff for us this VHL that's the high L that comes from a different so also from Planck there's all kinds of things but they produced this tau which is way too small that's really small so we started when 0.107 and now we are at 0.05 it's almost didn't ionize and to reach of 6 we are getting really a problem a couple of months ago I was in a workshop on realization in Munich there's lots of discussion and the running joke was if we were 10 years we'll have negative tau because of the trend which kind of looks anyways, this is what tau is this is the level of tau it's very small but notice the rubars they're not that small so 2 sigma effect can take you I think they are 1 sigma 2 sigma effect can take you back 0.075 so there's lots of uncertainty in this game and again this doesn't say much about the details it tells us only about the integral and if you take certain realization scenarios something that so this is modeled like like a function like this where ionization happens so if you look at the neutral fraction goes like this where the center is the reionization redshift and this is delta z they have some sort of model there and they kind of constrain both I'll tell you what the difference between the green and blue in a second so let's look at the blue the blue tells us that the reionization redshift is about between 6 and 10 but the delta z can be from 2 to 8 it means you cannot constrain how yeah it can be very wide for both scenarios the difference between the two is that the blue one has the data from the scene be alone this one the green has another prior in statistics means that you assume something information that you know and the prior here was that ionization ends at redshift 6 in construction you see this flip here that says we ask it to finish at redshift 6 and it gives you this so it's kind of tighter constraints but again it's okay I'll stop here tomorrow I'll continue it took me more than I expected but I hope I care more about you understanding what I say than covering stuff so I hope that's the right strategy and I hope you'll enjoy it more questions? anything before I finish? okay thank you