 everything works before we start the recording? All right. Are you ready, Celine? I'm not sure. This thing that usually disappears, but do you see? Yeah, I see the whole slide, so it's fine with me. All right. May I ask before I start? Just if I can have a feeling because I see a number of students reducing. Is it really hard to follow? Do you want me to go slower or give more details? Or if I maybe just put it in the chat, maybe we can have a look. Again, I'm blind, so... Okay, so please participate. Let us know if you should go with more detail, more slow, or the pace is fine. Maybe I can have a look at the stop. So, Max say it's all good. Dari as well. Okay, all our positive comments, so I think you can just keep on the same line. Okay, great. There's a question about more references. Okay. If you don't have them today, you could prepare them for tomorrow. I cannot do that. And also, I promise on nuclear synthesis that I'll do tomorrow because I'm a bit rushed now. So, I'll try to get as much as I can today, so that tomorrow can be just wrapping up and showing you the whole story. And then I'll also have a nuclear synthesis. So, I can start now. Is that okay? Yes, please. So, we are very happy to have Celine who will deliver the fourth lecture. So, please go ahead. Thank you. All right. So, this is the fourth lecture, but I'm going just to finish the third lecture, which was on particle candidates. This is just to remind you, so we were talking about the really density yesterday and the candidates. One thing, at some stage, I think there was some confusion because this graph is showing the number of particles, not the number density. And just in the middle part, what I was showing you really in this graph has to be the number. So, I should be the exponential times the AQ, which I didn't write yesterday, which might be why some of you were confused. So, hopefully you understood that you have a number of processes through the evolution of the universe, the dark matter particles annihilate, and eventually you have a number today. So, we use that to get the cross-section. And I assure you that in the 70s, people were actually deducing that dark matter had to be heavy. And then, 25 years later, the whole picture changed. And we started to propose light dark matter, but then we also started to move from a more modal approach instead of theory. So, at some stage, a lot of people introduced new mediators, which we call the dark sector. And in this case, obviously, it changes everything, because in this case, basically, you pass from initial assumptions, which were the dark matter annihilates, annihilates into some of the particles. It annihilates because of the same number density of dark matter, the same, I mean, the dark matter has the same number density as anti-dark matter particles. And then we moved to a state where we started to think, well, actually, we could think about an asymmetry between the number density. We could think about new mediators. We could think about a different type of annihilation and so on. But it was still conventional. And in the last decade, really, people have questioned absolutely everything. And so, now there is no need to have to impose that the dark matter and anti-dark matter be the same, number density be the same. We could also imagine that the dark matter totally disappeared and a process made it reappear. So that's called regeneration. We could also imagine that there are many dark matter candidates, but if there are many dark matter candidates, the density has to be split in between the different species. And so the question is, how do you do this? I mean, this has to be arbitrary, because you don't measure it. So because of this, because it has to be arbitrary, you lose the prediction. And we also know now that the dark matter doesn't have to be thermal. So this is an important point that I will speak about today. And we also now start to say, well, maybe it doesn't annihilate it, or if it annihilates, maybe it annihilates into a sector which is invisible to us. So really, the last decade or 20 years, basically, have been a complete revision of our knowledge. And that on this land, because we don't see the dark matter. So the moment we will see an evidence for dark matter, this would change, you know, this would tell us which one we need to take. For now, everything is open, and everyone is exploring every single way possible, as it should be. So far, I was talking about thermal dark matter, and I will continue tiny bit, but I want to show you exceptions to the idea of computing the value density using the freeze out. So I mentioned a few seconds ago, the regeneration mechanism, but here's also something else called the freezing mechanism. And in the freezing mechanism, which is also an old idea, in fact, but in the freedom mechanism, the idea is dark matter has very weak interactions, so weak that in fact, they never really terminate. So in the early universe, they're not thermal. But eventually, or they have, but they have, I mean, they would be thermal potentially, but they don't have any interaction, which are important enough to actually stay and follow the normal thermal density. But then eventually, because the universe goes down and the density density is basically decreased, there is a moment where somehow it comes in equilibrium. And that's a moment where essentially, it can start annihilate and the number density can decrease. So this freezing mechanism is really a late entry to the freezing because it's coming in, if you want, it's coming in the thermal regime. And then eventually, you can compute the annihilation cross-section, and you can compute essentially the number density that you left with at the end of this mechanism. This is a mechanism which is used for any particles, which has very weak interactions. I see that Julian has a question. Yes, please, Julian. Go ahead. Yes, hello. So I was wondering, what are actually the limits of dark matter not really interacting at all? So neither have a freeze out nor a freeze in. So it has this abundance and it stays there for the whole universe. Yeah, that can happen too. But then you cannot do anything about that. I mean, this is a worse scenario because if nature has whatever reason I choose on this, then we can't really tell anything because it would have been produced in the right number, I mean, the right value. And then we can't really prove it, basically. So that's why people don't really discuss it. But that's a possibility, though I really hope that's not realistic nature. The other thing people have proposed was what they call cannibal dark matter, which is basically, instead of having two dark matter give something else, three dark matter can give two dark matter. And by doing this, and then eventually but by doing this, they read the dark matter candidate. So that allows you to basically get a bit of, I mean, to change the results, the usual results from thermal dark matter. So it can be a thermal dark matter candidate and yet doesn't behave like a thermal dark matter candidate from the point of view of a really density calculation. So I don't want to spend too much time. I just wanted to raise my attention to the fact that people are becoming more and more innovative and creative, but there are plenty of exceptional messages. Now the non thermal candidates. So what if the dark matter was not was not produced firmly in the early universe? And one of those case would be, for example, what we call sterile natrinos. So a natural which is not exactly the active natural and that mixed with the active natural. In this case, it's a valid candidate, but you have to be obviously you have to compute the density again. And those candidates, they don't necessarily need like that and to decay. So you have to compute the decay rate. The expression is written here is not that interesting in terms of showing, see, showing you the expression. But typically the mass range, what I wanted to do your attention is the mass range is around a few key. And that is interesting. And I will explain probably tomorrow the details, but that is interesting because I mentioned the free streaming before. Most particles will experience the free streaming, but it's not like for active natrinos. It's enough to form structure. So it's just a limit where you can actually form all the structure which has been observed. So most candidates are actually quite attractive in the sense that they may in fact solve some problems that we see in cosmology. And obviously they're related to the natrinos. So it's quite appealing in that sense that it's a new sector, but it's a new sector which you cannot expect because you know that natrinos have mass and you need to explain why they do. Now a few years ago, there was a lot of interest for these particles. And that is because at some stage people realized that there was a line, 3.5 keV, which could be produced by 7 keV-stera natrinos. And so the first paper was by Kehra Bazajian. But then there was a lot of controversy and in fact there was some people, notably Stefano Profumo and Tesla Giaclama, who realized that while 3.5 keV is potassium basically, so you can have just a pollution and some objects that can just be the line of rotation. And that can be basically a systematic effect in the observation, in your measurement. Now that was quite funny because that's why they said the discovery of the 3.5 keV line in the galactic center at the critical look at the original line across the stream of targets. They had another paper after where they say it's basically going bananas in reference to refinement. Potassium is in bananas. But essentially there was a lot of paper looking at that and saying it's probably not due to dark matter. So to be honest, I don't know where we are with this, but I don't think people believe it's a strong evidence for sterile that we know. I think a lot of people think that the signal probably is more related to astrophysics now. But it's to show you that in principle dark matter can also be in that range and we can have some interesting signature. Sorry, I see the Chivam as a question. Yes, please Chivam, go ahead. Yeah, so I had this question in the previous slide. In the previous slide, yes, there are processes like three to two and two to three. So these processes will be mass suppressed. So what kind of coupling, the order of coupling that would be required for these kind of processes to actually contribute in the grail density, abundance calculation? Yeah, so I'm afraid you would have to go back to the paper. So I put the reference. I mean, this was the new version with at the bottom of the screen, you can see. But if you have two strong couplings, I mean, two large couplings, you can see you have efficient annihilation. So you're going to read the dark matter a lot. So in principle, you can do that, but you shouldn't do it at a moment where you have critical observations. So it depends on the dark matter mass. So if a dark matter is fairly heavy, in principle, we can do it fairly early. I mean, we can have large couplings and that should be fine. If your dark matter is light, then you have to be very careful because you read the dark matter and you have consequence. Notably, you modify before streaming length and so on. So you need to be very careful. Okay, yeah, thank you. And then we have another question by Max. Oh, okay, hi. Can you hear me? So yeah, so since we already came back here, I wanted to ask you a question about the pre-prison mechanism. So can you maybe give some tuition about how? So what are the properties of these particles that for high temperature, they have a low interaction rate. But for low temperature, it gets high because I cannot think of a scenario why this should make sense, such a thing. Sorry, maybe I mis-explained this. You start with particles which have a number density, which is what it is, but it's too low for being interesting. However, so maybe, sorry, I'm going to explain it differently. It's a number density, okay? So it's a number per volume. At a given time, you have a certain volume. The volume is small in the early universe. So if the number density is very, very tiny, you have a conversation between N and B and the volume. If the number density is very large, then the number density is obviously large, okay? So as the volume decreases, then the number density in principle decreases. But what's going on is that all the other particles, they couple. So you have a reading flow. I mean, if you want to change the number of all the particles, they couple. By that, I mean, they annihilate, they produce photons. So you have little bumps in the temperature of the universe because the particle eventually finishing photons, some of the particles which decay. Just you follow me? Yes, I think I understand what you're saying, but I don't understand why, how this answers my question. So if I understood your question, is why do they freeze in the night? Why do they come back to the thermal spectrum? Is it what you're saying? Yes, and in particular, because you wrote it, so such a thing would happen if the particle, so if the rate of the particle, the interaction rate is and the proportion to the temperature. So if this is the case, then I can understand why this freeze in could take place, but I cannot even imagine why this rate should make sense. So why, how could the particle have this rate, which is inter-proportional to the temperature? Yeah, so I propose, I found a way to explain that tomorrow because I'd like to move on. I can put more details tomorrow and I can show you tomorrow in detail, because I think I need to show you the equations and I don't have them with me right now. Is that okay? I thought maybe there was some easy intuition, but okay, yes of course. The interaction rate is just the way you have to write the interaction rate, and even that you have, so the interaction rate is usually sigma vn, but here you don't, the sigma v is not necessarily the annihilation, so you have also the scattering, and what you have to account is also, so you have two number density in principle when I write the Vosman equation, which is a number density for dark matter and the above species. That's what maintain them in contact. Now you have, when you use the Vosman equation, that's why I wanted to write a slide for that, because when you write the Vosman equation, you see that you get rid of a dark matter density and you're left with the other one. So they're still, they're still maintained in contact. It's just because the other one is decreasing and sometimes disappearing. I think it's easier if I show you a slide. All right. Yeah, so another example of non-terminal dark matter is the following, is the action. And the action, so again I think I have to rush today, so I can't really give you many details, but I think you have lectures anyway on this topic. But actions basically are the typical, I mean, related to QCD, so you have a QCD like Ranjan. Can I just ask, there was lecture on action already, right? Or something like that? No, there wasn't yet. Maybe Stefan Nagori will cover it, or not sure. Okay, so I have two slides, so then I'll take time for the, thanks. So you have a QCD, like Ranjan, which is written here, in which you have a part to describe the gluons, another part to describe the quarks. And then you have this interaction, the last term. So the last term in principle can give rise to a CP value in term. And this is controlled by a phase, which is called theta. So the question is, I mean, theta can be here, can be in this term, but in practice we don't feel it. So it must be small. And the question is, why is it small? And in fact, why is it potentially zero? Since it could be here. So the way to explain this is that if you have, and I took this from the postdoc in my group, Kieran, who is an expert, but typically, if you have your potential and you have, if you have a particle, an action here, let's say which particle is rolling down the potential, this will basically generate a tilt in the potential, which can help you mitigate the operation of this violating term. And so you have a tilt, which is there to compensate the violating term to cancel it, basically. So in order to kill the last term in the Lagrangian, you have a certain value for the tilt, which is noted here as the initial tilt, theta. So the analogy I can give you, which is an analogy, Piazzetti gave a long time ago, but I think it's very good. If you have an inclination for a floor and you have a table on top of that, the table will be such that it remains flat. And so the question is, why does it remain flat? It could have been, it could have felt this term. We could have felt the inclination. So there is something Americanism, which is actually making sure that you don't feel this term. And so in this case, this is called the axiom. And the axiom, the axiom basically is written as an axiom field is giving, is related to the term theta by the axiom field divided by a scale at which you have this breaking of symmetry, the Pesci-Queen symmetry. And so you have the scale at which it happens, fA. And you can see that now you have, you can write a field like basically the exponential, it's a complex field, the exponential of Iax, the field, the axiom field divided by this scale. So you have basically a phase, exponential i theta. And that's what gives you basically the mechanism corrections. So it's a weird concept because it's basically saying, well, there is a symmetry, you don't feel it. And you may not feel it because there is a mechanism to, in a sense, compensate for its existence. But if that's true, then this means that you should observe that it should be a field, an action field in this case, feeling the universe because obviously, PCD is everywhere. So there are several scenarios to break the Pesci-Queen symmetry. You can break it before inflation or after inflation. So I'm just showing one case where it's basically before. And so you start with massless action, and then eventually you have inflation. So you stretch every wavelength, and then eventually you have PCD phase formation. You have the tilt in your potential, and then the action gets its mass. And from there, basically, you have to live with an action field. Now, the good thing about having an action in this case is that eventually, so the particle mass would be extremely small. I will come back in a second on this. And you may say, oh, this is not a good dark matter candidate then. But what counts is not the fact that there is a particle mass associated with this field. What counts is that actually this field has interactions. And so it's really the notion of field relevant particles. So you can understand the notion of, you can speak about particles, but for that matter, the effect on the universe comes from the coherent effect. So it has to be about a field relevant particle. So this is really different from everything I showed you before. And that field basically has that oscillation. And so it's not like the normal scenario. I will explain again tomorrow why there are differences, but you have to keep in mind that not only is different because it's a field relevant particle, but on top of that the cosmology is a little bit different. That said, you can compute a relative density, and like everything else, it needs to be the same order as what is observed. And so the relative density is more or less on the right ballpark, 0.1. But then it depends on the on the scale effect. And it's normalized here to 10 to the 12 GV. So you can see that if you change this value, then you don't get the right value density. And then it's multiplied by the initial tilt dimension. So in principle, to get 0.1, you immediately get that you can see what you need. Now, why did I tell you it's a good dark matter candidate, but actually the cosmology is different. It's for the following. So first of all, we can solve this equation to see how it behaves in the universe. So it's just an oscillation equation, but it's actually done. And the only thing I want to show you here, because I will need it tomorrow, is that initially you have your axon field revolving with time. But initially you see that the axon field is starting to oscillate. And when it starts to oscillate, it doesn't disappear. But it's actually it's actually introducing some patterns, which eventually you should be able to see. So this is the way you produce axon. But this is a mechanism which in principle, you can trans because it changed forms in the universe. And I show I don't have enough. I mean, I need to present other things tomorrow in order to explain why I think it's important. If you want more details, Karen really has plenty of slides and they're extremely good. So here are the reference. And I think you can you can learn a lot from me. Now, the other thing I wanted to mention is self interacting dark matter. So I mentioned, well, we mentioned a little bit before that self interacting dark matter can explain the bullet cluster. So I can just show you if you have if you remember there was this cluster, which is a merger. And we can see that the ordinary matter essentially stays in the center while the dark matter has gone through. But you can set a limit on the dark matter interaction. And you can see that the dark matter interaction is around tend to I mean, it's basically around the Thompson cross section. But it basically tells you that it doesn't interact the same way as it interacts with values. That said, it may interact with itself and you can compute the cross section. So the first evidence was not evidence, but the first people to propose that there was an evidence for self interacting dark matter was actually a sugar and standard. And what they were saying at the time is that there is a number of anomalies, which so this paper was actually in 2000. Those anomalies 20 years later are still present. One is a number of a small number of satellites. And the other problem which is called the problem is the density inside objects. And they were saying that maybe if you have some some dark matter which is interacting, then you can self interact and then you can actually solve a problem instead of having a large density in the galactic center, for example, whatever object you look instead of having very large dark matter density, you may actually reduce it by invoking those self interactions. Now, a lot of people have looked at it and it comes and goes. It's fashionable. And sometimes people just forget it and then comes back. So the bottom line is that when I show you that in the 2000, we were also thinking about light dark matter and light mediator, then people realize, well, actually, if you have a light mediator, for example, then it could act like a photo. And so, but it's, it's a photo prime, it's not a normal photo. So it could be actually a particle, which is a mediator of the dark forces or the dark matter forces. And so in this case, you can think about the dark column if you want. And so you're back to thinking the dark matter is more or less behaving like the summer model, except that it's not necessarily the same strength of interaction, not necessarily the same mass as we used to and so on. And so this was one of the paper, which I think was really instrumental in looking at self-interacting dark matter from the point of view of particle physics. You can see that you can have a potential and so on. So that's why I'm saying the idea is more like a dark column in this case. You have two types of mediator. Yesterday I mentioned the dark photon or dark z prime. You can also have a dark scalar because especially after discovering the heaps, you can think maybe you have a heaps one. Yeah. So I had this question regarding the self-interacting dark matter that since this this kind of dark matter can actually answer the problem of small-scale structure formation. And so what can be the off-putting things about this kind of a scenario? What can we disregard this kind of thing? I don't think you can. You can just put limits on it. So one thing I should say, and again it will become much clearer tomorrow, one thing I should say is that you can call self-interacting dark matter anything which is self-interacting. But you start to speak about strongly self-interacting then you have you define a scenario and you have a certain cross-section. If you don't observe that then you can say okay we are already doubted. But nothing prevents you to consider a weaker self-interactions. So that's why I'm saying I don't think you can really exclude it. You can just put a limit on the interaction cross-section. What kind of masking would this kind of a scenario give? Is there a limit to that? No, I don't think so. Well the limit is always as I said at some stage you enter a range of actions and so on so more field. But I think Kiwi is perfectly valid. I'm not saying I didn't follow the literature with great detail so I'm not sure how low people go but you know in a sense you can do whatever because it's just a dark matter interaction with itself. So there's no constraint. You don't need to annihilate into something which has a mask which you know which would set a limit. So as long as you have you have a cross-section which is not as long as your cross-section doesn't exceed a term sum cross-section which you don't see the term sum cross-section here but you see something almost like this 210 to minus 24 centimeter square is the same ballpark. As long as you have a cross-section which doesn't exceed that and you have a mediator which is not excluded by experiments then that's fine. So it's a question of playing with the couplings and playing with the mask and that's it bonus. Yeah, thank you. All right, next question is by Tong. Yep. Hello Professor. So I have a question about the oscillation, the damping oscillation of the SEM that you showed. So can you go back to the slide or the curves? My computer is always a bit precious. So when I see at first SEM, the SEM field is brought down to the minimum value. So it can be because at first it's the H, the Hubble constant is so much larger that in the equation we can neglect the final term and then we have the better. Yeah, exactly. You can take the different limits and when you solve it you see that indeed it's a two different regime. So as soon as, so it's basically the equivalent of, in a sense it's equivalent of a decoupling. So you have to be in the horizon. I didn't explain what was the horizon but you need basically, you have wavelength. So it's hard to explain again without any support but you have some wavelength and those wavelengths if they have a physical implication they need to be in the horizon. If they exceed the horizon they don't have any physical implication. So you have to be inside the horizon and this is that moment basically. So you have this transition from basically being the same order of the horizon to the other right if you want to being inside the horizon, being exceeding the horizon. Okay and my second question that from the key term in the strong CB sector. So it can come, it's a solution that we have the axiom field or scalar axiom field but if for example like my advisor, he has the idea that comes from the vector dark matter. So there may be many possibilities to show this the strong CB problem besides axiom. Sorry, I'm a bit lost. Where were you? So the theta term, so Pesi queen assume that it may come from a scalar field axiom but like so my superbike might have a new idea like they can come from a vector dark matter. Yeah, sorry because the connection was a little bit bad. Yes I mean you could couple them. So axioms eventually, I'm not going to speak about this but indeed the way to fund them is basically that they interact with the magnetic field and they would produce a photon and I guess you can revert the problem. You can say well they would be created by photons. Now in practice you can't really do that because you don't have enough energy but if the photon is basically mixed with a vector, sorry with another photon like a photon prime then you have the photon prime would have a mass and then you can create the axiom. I think that's what you're referring to. Okay, thank you. All right, next question if I please go. Yeah, so about the self-interactive matter, you said it helps with reducing the density in the core of the galaxy. Is this the core curve's problem? All right, thanks so much. Yeah, hello. So I have a question regarding the petroquin symmetry breaking scale. So like if there is a lower bound on the leximetry breaking scale, I mean... Yeah, so I should have put another plot there but you have to, if you want the axiom to be the dark matter which you don't necessarily have, I mean it doesn't have to be, but if you say that it's a dark matter planetate, then the formula that I wrote there, it's basically telling you you have to play with a different, I mean you have to die. So the tilt and FA, but they basically tell you what is the order of magnitude for this breaking. But you can see that FA is really high, so you're not going to probe it. I mean it's not easy to probe. Okay, so like if the axiom is not a dark matter, so like then the symmetry breaking scale can be much lower? Seven, you can do whatever you want. I mean... Okay, thank you. But not whatever you want because there are experiments looking for them. But in principle, you can, I mean, if you don't want the axiom to be the dark matter then, in principle, it can live anywhere. It's just that then you have to look for it with experimental device and then the limits come from the experiments, not from the theory reasons. Okay, okay, thank you. I showed a plot here. I think I showed a plot where it was, but I should probably, I will try to add another one to show you where the axiom lies with the different constraints. There are plenty of constraints. And again, Karen is one who is actually maintaining the plot with the constraints on action. So it would be good if I want to know. All right. So I want to, so this is now a lecture for really. And I wanted to speak about the signature of dark matter, the astro and cosmic signature. And I think I'm a bit light. So I think probably we'll have to finish tomorrow the lecture for, but it's okay because I can shorten the section five. And then I will show all the things that I promised to show today and make clear synthesis. So the first thing is how do you detect dark matter? So if it's an axiom, as we say, well, that's a little bit more difficult, but there is a way which is the production of photo. If it's a particle, then, and if it decay or annihilate, then it will produce something else. And in principle, you can see this something else. And that's the way you can trace back to dark matter. So this technique of saying the product who, I mean, seeing the product that the dark matter produce is called the indirect detection technique. Now it's mostly, we use it basically, mostly for looking into space. So let me do the argument and then I can answer the question maybe. So I show you a spiral galaxy and I show you rotation curves for a spiral galaxy yesterday. There was a question, actually, I will answer also on elliptical galaxies. So you have rotation curves. And as we said yesterday, most of them are fairly flat and clearly have showed that the visible galaxy is embedded into a much bigger structure, which is a dark matter. And now what is very important here is that because it's a dark matter yellow in principle, if it's made of particles which either decay or annihilate, then you should see those products. So say that the dark matter annihilates into electrons, then you should see electrons in the dark matter yellow in principle. So how do you do that? Well, as I say in principle, you have, so if you assume that the dark matter annihilates and it annihilates into standard model particles, then you should have dark matter, sorry, you should have standard model particles a bit everywhere in the galactic yellow. So the way you want to do is basically look at different directions and see if you can see traces of, for example, the electron or the standard model particles in further away from the galactic disk. Now, you have to be careful because obviously there will be more particles produced where the density of dark matter is the highest. So you need to make sure that you know the dark matter density and then that tells you basically where the annihilation product would be or where the decay product will be. In previous lecture, I told you the dark matter had to be stable. That doesn't mean that it never decays, it just tells you that the lifetime is very, very long. So you will not, if it decays, it will be a very slow decay. So you cannot expect many particles to be produced, but still there will be some. So then the questions which instrument you're going to use, depending on which kind of product you want to see, then you're going to use different techniques. So I'm going to first show you the primary edge, the history of it, and then I will show you what kind of products people have looked and then show you how we can determine. So the first people, I'm sorry, this is here is more important. The first people who started to think about detecting dark matter this way, so indirectly, there's a number of people, the sticker was one, there is Joe Silk and a number of other people, but you can see the immediate reaction was to say, well, you could trans dark matter in principle with gamma rays. Now, I told you that matter has to be neutral, so then you may say, but how can it actually produce gamma rays if it's neutral? And that's because it will annihilate into something else, or it will be coupled to charged particles and eventually those particles will produce some photos. So you see here an important paper, this was in 1978, and this was really the first paper, I believe, which was starting to say we can detect dark matter by the annihilation product, and the annihilation product can produce a continuum of gamma ray, and a continuum is important because it tells you that you would have gamma rays that less energy, but the other thing is it also can produce a mono-energy decline because the dark matter can produce via a loop diagram, for example, two photons, and these photons will trace the dark matter mass. So anyway, so here it's about dark matter annihilation, and this annihilation eventually producing the substantial amount of photons. So here are the diagrams which I was mentioning just before. You can have the direct production of photons via some charged loops, for example, and then the photons have one energy, so you start with two dark matter particles, and that produce there would be non-rativistic in the dark matter halo. So they produce two photons with an energy which is basically equal to the dark matter mass. So this is a bit of an holy grail because if you observe this photon with, I mean, at, if you see the lines and you don't think those lines are related to some astrophysical sources, then you have a measurement of a dark matter mass straight away. So it's extremely important because if you can identify that those lines are actually emitted by the dark matter, then you have a measurement of a dark matter mass, so it's the best you can achieve. But as I said, you can also have a continuum of photons, and one way to produce it would be actually that you have annihilation into fermions or anti-fermions, for example, into charged particles, and then they would emit some photons, and those photons, well, eventually you can detect them, but you know that their energy would be always smaller than the dark matter mass. So if you see photons which you don't think are emitted by an astrophysical source, that's great, because you can say, well, it's probably dark matter origin, but it doesn't really help you pinpoint the dark matter mass. So it's extremely valid, but not as powerful as seeing a line emission. Otherwise, you can have Bremstra-Lune emission, if you produce, for example, these fermions, you can have synchrotron emission. Synchrotron radiation is very important because it gives you an emission basically in radio. So you started with particles of very high energy, perhaps, but the signature would be actually a very low energy would be in radio. So in terms of photons, the dark matter can produce basically anything except photons which are in the visible range, because if it does that, we would have seen it already, and we wouldn't be looking for it for the last 50 years. So in a sense, you're free. If you propose a dark matter model from the particle physics point of view, anything is okay, as long as obviously you do not exceed the experimental bounds, but also as long as you're not right in the visible region. So gamma rays and X-rays is a logical signature, because usually the dark matter is heavy, as I told you, but for Lieuwenberg arguments, people thought dark matter has to be heavier than a photon. In reality, it can be lighter than that. So it could emit something like X-rays. But also, if it produces electrons and positrons, we know it's going to produce eventually, or there will be associated signature in microwave and radio. All right, so people have looked for those photons. As I showed you in the paper, the first paper was 78. But in 1984, there was another important paper which was published by Simke and Srenki, which was saying, well, actually, it's a way to produce anti-matter. And in this case, they were focusing on anti protons. But in reality, you can think about positrons and so on. So this was a very instrumental tool, because if you found, for whatever reason, if you detect some antimatter in our galaxy, and if you think that the amount of antimatter you detected is far greater than what you expect, then potentially you have trace back. You have found the dark matter. Now, what is really interesting is that if you remember in the first lecture, I was mentioning there is an asymmetry between the number density of particles and anti-particles. There's almost no anti-particles left. Well, in the galaxy, it's not that true, because you have astrophysical sources which recreate this antimatter. But it doesn't recreate it in equal number. And so you have less. You still have less matter when you have all of antimatter. And you can make the prediction more or less. So if you found much more antimatter than you expected, you probably have a good indication that there is some dark matter. Do you think it's a good moment to take a five minute break? Okay, so that's a resume in five minutes. All right, if you wish, we can continue. Okay. I've seen some questions in the chat. You missed that one. I guess I can collect them at the end of the lecture. There were no more than this one, I think. Yeah, I think there's a few, but it's okay. I will write them. Okay, sure, sure. Thanks. In the Q&A, no? Yeah, or I can watch more. There's a raise hand by Alessandro. So please go ahead, Alessandro. Hi. Well, I have a question about one thing we have said before. Well, we have said that the probe of the existence of dark matter is the fact that we can detect a gamma ray or radio background. But how we can distinguish this event from other cosmological events like gamma reverse or other type? Yeah, that's a good question. It's very hard and this is why actually often people say we discover dark matter and it happens that it's not the case because precisely it's super hard to distinguish where it's not the right physical source. I will mention it after I will show you the examples where it's not here. The only thing one can do is model as much as possible what you expect from an astrophysical source and then see there is a deviation to that. But again, in some cases it could well be that it's an astrophysical source and there is one issue where I think it's always too late. Okay, thank you. Okay, I'm with the team. Okay. All right. Yeah, so now we, sorry, actually wrong slide. Sorry, I'm too late. So I was going to show you the theoretical prediction and then I will show you the experiments and then I will show you the results and where indeed Alessandro is right, it's very hard to detect whether it's dark matter or an astrophysical source. So as I said, we need to look in some directions and we know that the annihilation will be everywhere in yellow but it depends on the dark matter density. And so now you've seen the Bosman equation and the Bosman equation is the one we're going to use except that now we're not in an expanding universe because we're looking at the galaxy. So for the expanding universe, we had minus 3 hn which represents the expansion of the universe. Now we can let this term away. We don't need to take it into account. And then we had sigma vn square if it's an annihilation, if it's a particle which annihilate and we had minus n0 but minus n0 was only relevant when we were doing a thermal dark matter candidate in the early universe and now we're not doing that anymore so we can also give this term away. So we left with a very simple equation which is the number density of dark matter particles evolve with time as a depletion, it's minus the annihilation cross-section times the number density of dark matter square. Now every time the dark matter annihilates eventually will produce some photons. It may produce one, it may produce many so in reality here I'm making a shortcut and I wrote that the number of photons is basically equal to the number of dark matter particles, the number density as it evolves. That's not exactly true but for now we're going to assume that every time a dark matter annihilates and produce a pair of electron positrons the minimum is there would be at least one photon. So in this case you have a simple relationship you say okay the number density of photons, the evolution of that number density is simply given by the annihilation cross-section times the number density square. So this is your prediction for the evolution of number of photons in yellow that's it. But now you have a dn dt and so you probably don't know what to do with it and you just have to remember that a dt is proportional to a length and that is basically the line of sight. So you look into direct into specific direction and that gives you basically the number of photons in that direction. So all you need to do is an integral over the direction. So you do the line of sight, the integral over the line of sight of your dn gamma dt and that is basically in principle the flux of gamma that you expect in that direction. Now you just use the equation that you obtained with sigma v and dn square and that gives you basically the number of the flux of photons in that direction. That is extremely simple. The issue is that actually you don't know the number density of dark matter straight away but you do actually have access to the quantity which is the energy density. So you don't know the number density because actually you don't know the dark matter mass. If you knew the dark matter mass you would access it but you don't. So the only thing you can say is you can determine the density of dark matter in one direction and therefore you can integrate this over the line of sight and that gives you the flux of photon in that direction. So that is a formula at the bottom of the slide. Now the term which is in the blue box which is the integral of the line of sight of a density square is called the J factor and in fact, Piero Liu, Cissar was one of the first to compute those factors. If you have the same integral but you actually had for the integral of a line of sight of only the dark matter density, hour one, not two, so you have a decay for example, then in this case it's called the defector like decay. But like this as I wrote it is a J factor and you can see that this has nothing to do with dark matter particles per side just a density of dark matter in a specific direction. So you can do this for any kind of model and then you multiply by the properties of dark matter which is the annihilation cross-section divided by the dark matter mass square. So this flux obviously will depend now on the particle that you assume for the dark matter. If it annihilates a lot then you will have a huge flux. If it's very light, you will have a very large flux. If it's really heavy, the flux would be minimal if the cross-section is for example relatively weak. So it all depends on the candidate you're going to choose but the flux can be easily computed once you specify a model and the J factor can be computed whatever model you're thinking of if you assume a particle and not a field. Okay, so yesterday I showed you the spiral galaxy, the rotation curves for spiral galaxy and I told you they're more or less all the same, more or less all flat. So you have a velocity, you have velocities related to a mass per volume and that is basically related to an energy density. So you can just access or you can see now it's not very hard. You take the derivative of this and that gives you basically a density profile. So the energy density for the dark matter so the density profile. So here is the result basically of its exercise which is taking the derivative of the mass and using the velocity and you obtain the plot which is on the right which is the density profile of dark matter in a spiral in this case, supposedly in a milky way but that works more or less any spiral galaxy which is fairly big. Now the point which is interesting is that you can see that so you're on the plot on the right, you see many many profiles possible. So you have many lines blue, green, etc. So if you can't distinguish your color let me just say what is important is you have many possibilities which are displayed on this plot but they're all the same above 10 kPa. They all converge, they all agree. Below 10 kPa they actually disagree. So some models predict that the dark matter density is actually very caspy because it's basically diverging and other models predict that it's actually forming a curve if you want it's fairly flat. And for a long time people didn't know even for our milky way where we are and there is always a question whether this is true. Which kind of profile do we have depending on the size of the object? So dwarf galaxies, smaller galaxies seem to have a density profile which is more flat than for our galaxy. Cluster of galaxies not necessarily clear, it's maybe more compatible with a cusp. So this is really the question of which kind of density we have. Now you may say why is it so uncertain? So just so to put things in context, this is the dark matter density in our galaxy for example. Now it's related, it's really the translation of a velocity of rotation velocity which is on the left. We know that the dark matter halo, the dark matter mass becomes more prominent at very large distance from the galactic center to compensate the fact that there is dissipation, there is this halo which is slowing down basically everything, or not slowing down but maintaining cohesion if you want, at very large distance. But very close to the center, this is really the domain of the barium. The dark matter, I mean you can see that the mass per volume for the dark matter is not actually very, is not prominent and you mostly, the velocity is mostly dominated by the bariumic matter. And so you can see that because the velocity for the halo is going to zero, you have a lot of certainty how exactly it's going to zero. And that's why you see, and obviously if it's our galaxy it's even harder to measure because it's dominated by the barium which are very bright. So you have a lot of uncertainty on that specific curve for the rotation velocity and as a result you can't really determine with a lot of precision the density of the dark matter in the core of our galaxy but it's true actually for other galaxies there's always, I mean it's always a very difficult exercise. For many galaxies now we know that nonetheless and for cluster two we know that it seems like the profile tends to diverge and it tends to be like one over r at small distance. So the closer of a center you are, it seems like most of galaxies and bigger galaxies and clusters of galaxies seem to behave like the density is proportional to one over r. But for small galaxies like dwarf galaxies it's not really clear yet and they actually seem to be more constant so they seem to be more quarry. All right so now that you have this in mind I just wanted to go back to this question yesterday or a few days ago on the elliptical galaxy because I thought it was very interesting in fact the question I show you a rotation velocity and that's really easy to define to look at stars for example in an object which is which is rotating but when it's an elliptical then you don't really have a perfect trajectory so it would be more elliptical trajectory but you can still define the velocity and those objects are much harder to I mean basically it's much harder to determine their velocity so for a long time a lot of people were saying well actually you don't need so much dark matter in those objects and often when there is you know there are claims that there is no dark matter in the galaxies often related to elliptical galaxies but nonetheless and that is that is one paper I'm not sure how much consensus it has but it's one paper which is very interesting because it looks at one elliptical galaxy which is fairly big and you can see the rotation curve for that elliptical galaxy which is on the left and you can see the total which is fairly flat and then you can see the stars which is decreasing because there is dissipation and you can see the dark matter going up like for for a spiral galaxy and then there is a contribution from a black hole so it's more or less in this case like a spiral galaxy they're not all like that and but usually it seems like most of important dark matter it's more as I said last time it's an exception when it doesn't and that is related I mean the way people prove it usually is more using x-rays and other techniques but more or less all of them even if they're not perfectly perfectly flat they also have a velocity which you can eventually determine which gives you access eventually to the profile I should I wanted to show you but I think I might not spend too much time but the thing I wanted to show you is that there are uncertainties on those plots and the fact that there are uncertainty on this plot means that when you try to determine the density of dark matter in these objects it is uncertain so you can say well the profile you know is I'm sorry I should have said it's a Navarro French work like it's written at the bottom but you can't really say how well it is and then there are parameters gamma and fa beta which you can determine but it doesn't mean that you have perfect determination on those parameters and usually you have gamma equal one as I say for our galaxy it doesn't mean for the others it's exactly the same so it doesn't mean that the dark material profile is universal Carlos Frank usually with one of the other usually says they have to be but I guess we don't know yet I think it's the first statement I'm not an expert obviously but I think there is no consensus yet on the form in all those objects all right just it's a parenthesis I'm not going to mention it but if you want so I show you the flux of photons I just added a formula which is the same but I just added the fact that the dark matter can annihilate into cosmic rays with slight modification of the formula I show you but the main thing is you can do this line of sight integration analytically I would encourage you if you like doing maths it's a very nice calculation and there's something quite magical which which happened which is that you see that you have a divergence in in the core of that profile so at very small distance the profile diverge so when you do the integral in principle it diverges so in principle it's not physical it should stop at some stage and it may stop if dark matter annihilates it may stop because dark matter is disappearing but in principle if dark matter does annihilate it could go up forever and that is not physical now the point is when you do this integral you also have to integrate over your angular resolution and you never have an experiment which is perfect so you never see quite the center so you will never see the divergence and so in reality even though you have a divergence or it looks like you have a divergence your flux would be finite it would be larger toward the center but it would be finite because it would be cut by the fact that your instrument you know telescope or whatever have a certain angular resolution and would not be able to see perfectly the what happened in at r equals 0 basically all right so I show you how I show you that we expected annihilation or decay potentially into standard model particles and in this case that gives us a signature I mentioned photons and I would like to just say well whatever what happened if we forget about the photons and we're just focusing on the standard model fermions which have been produced and that's essentially the cosmic ray so if a dark matter annihilates or decay into standard model fermions then they will they will be in the yellow they will propagate and eventually some electrons for example will meet some positrons and then eventually annihilate and you can produce all sorts of things for example it can be all the QCD processes and so eventually you will form what you form in an accelerator you can form counts mesons and all sorts of things so it's very important if you really want to determine to prove that you have detected dark matter for example if you have a flux of gamma ray which you think is related to dark matter then you should also see somehow the cosmic ray so you need to make and we call it multi messenger you need to make predictions which take into account all the possible particles which you produce and which could be observed so now the point is the cosmic ray when you produce them they don't stay like this in the yellow they actually propagate they diffuse in fact so you have an equation of diffusion which is very complicated because in for example for the Milky Way you have a magnetic field you have wind you have also you have convection you have all sorts of things and so in principle you have to describe when the cosmic ray have been basically produced by the dark matter you have to explain how they move through the galaxy and eventually can be detected on earth so you have this is just an example for for a diffusion equation but this equation has to be solved and eventually you get a spectrum out of it which I just wanted to show you here what it doesn't I mean I'm showing you an example of different values for dark matter mass 10 gv 100 gv 1000 gv so tv 10 tv the only reason why I'm showing you this is that you will notice that usually for it's not true for all but for many of the channel you see that the prediction dark matter is producing photons in the shape of of a bell basically you you just see this parabolic I mean parabolic flux why is it important because well anything else produces the same any astrophysical source produce exactly the same signature and in particular a millisecond pulsars a millisecond pulsars can emit for example the electron they produce gamma rays and they produce gamma rays more or less like what you see here in this in this figure so the previous question from alessandro I think was how do we distinguish um we can't I mean the best thing you can do is just try to correlate many signatures try to identify whether an astrophysical signature gives you you know the right signature in whatever electron neurons and so on and if there is some anomaly then you can say that it's likely there is something else but you need to know your background so it's like exactly if you're working at LHC you know you need to know the background here's the same problem you need to know your background extremely well the only difference with LHC is you can't redo the experiment you don't control any of the parameters and so it's in a sense it's much more complicated same thing you can see it's always the same parabolic shape I've already I mentioned radio before so I just wanted to show you some some limits but if a dark matter is too light and I told you before yesterday I told you I like light dark matter personally but if it's too light like for example a GEV you have to be careful because it can actually produce more radio emission than the central black hole so you have to be careful when I say well you can assume certain cross-section and certain mass you can but obviously you have constraints and in some cases the constraint tells you well it's already excluded you can also in principle you could also have a microwave signature so the dark matter can annihilate and produce electron and positrons and you will see that in the Planck experiment literally or WMAP so you can see it for example Planck is looking at the temperature of the universe and for that a different channel they have several frequencies they have 33 gigahertz which was the smallest frequency they were looking at but they also have the highest which is called 8 which is 857 gigahertz it's called HFI and the dark matter can produce basically signature in plug and we can look for it and we have looked for them and we found that basically Planck didn't detect dark matter so you can put elements on it so just a little parenthesis to tell you that there are many signature and we can use those experiments the other thing I wanted to tell you is I told you the dark matter can produce cosmic ray or fine but then those cosmic rays eventually can arrive to us pass through the atmosphere interact with protons in the atmosphere and eventually you will see a shower which arrive on the ground so what is interesting then is that if it's true then you think well I can basically have a number of experiments to look for either the gamma rays or the cosmic rays on from the ground and so you have here important experiments Hess was looking for gamma rays it's magic and very test but CTA is looking really for cosmic ray and for the showers and you have another one looking at high energy cosmic ray which is basically Hawk the Hawk experiment which is in Mexico and you have a number of experiments basically looking at very high energy cosmic rays so in principle we're covering basically all interest in range if that matter is heavy and in fact we're not doing that only from the ground we're also looking at cosmic ray which are so I told you in the yellow there should be a dark matter and you listen to produce the cosmic ray then in principle if you send a if you have basically a telescope in space or satellite then you should be able to to see them so one of them is AMS02 which you see here and the logo is on the left it's on the ISS so it's basically installed there on the ISS and this experiment tried to see anti-matter mostly so if they try to measure positrons but also anti-potoms which has been possibly produced by the dark matter when you're in space you can also look so you can have a satellite look and you're searching for gamma rays and so that's the case for example of a Fermi satellite and light is basically the experiment on Fermi and this is one of the maps that they've done so they basically map the the galaxy in gamma rays and they found a number of sources like I said the municipal missiles and they found other objects and then the question is when you have those precise maps the question is is there any anomalies or not so let me just go now to the results the first of all one one important thing is you can look in the Milky Way and you can look in objects where you think there is not so much ordinary matter and more dark matter and the reason why you do you want to do that is that in this case you don't expect so many if you don't have so much ordinary matter then you shouldn't have too many gamma rays from ordinary matter so if you see gamma rays from those objects which are mostly dominated by dark matter then it is it is a signature of dark matter so their primary target because in principle it's a clean signature you don't expect gamma rays from those objects because there is there are not so many stars there's not so much binding matter in it so if you found gamma rays there it's a very good indication that the dark matter is perhaps annihilating all we came so there are several experiments looking at them but it was quite astonishing so first of all you have to find those objects which is not an easy thing the experiment desk found several and well I guess everyone has their preferred satellite you see the small magini cloud and the large magini cloud those ones are big in the end and they contain a lot of ordinary matter so they're not the objects you really want to look at although people people obviously study them but you can see on this there is one of them is called reticulum 2 this one is a primary target for dark matter searches and there are a few which are looked at but reticulum 2 is very interesting because it really doesn't contain many many stars and you don't really expect a lot of gamma rays here is the result so by looking at those targets plus Fermi which I just showed you with a map of gamma rays and stacking the result basically people are able to constrain the dark matter and in particular it's a probability I mean the probability that in any any legs this is the result you see the plot which is sigma v versus the dark matter mass you see lots of curves which correspond to the different objects but if you combine them all you obtain the thickest black line which is line at the bottom and that line I'm sorry and you can see the horizontal line which is dashed which correspond to a thermal relative density so an annihilation cross section of about 310 to minus 26 and you can see that the dark line cut through this relative density line and so in a sense this analysis is excluding and this was in this was earlier but this analysis is excluding thermal dark matter if the dark matter has a mass up to in this case 10 gv I'm sorry 100 gv so very powerful tool because if you if you say well dark matter is thermal it has we know basically as I show you it could be an EV but it has to be basically in a range where it has minimum of an EV up to maybe TV and already here the Fermi the Fermi results tell you and you can extend them to a lower mass but they can tell you already dark matter is not a thermal candidate between one and another gv forget it so it's a it was a very strong I mean very important milestone I think somehow it's not been celebrated enough but for me it was a sort of turn an important turn in the community I'll show you more plots but just to show you that all of those results are essentially is fluided thermal dark matter if a dark matter is smaller is lighter than 100 gv so it's it's a very I mean indirect detection is a very powerful method and a very important method to look for dark matter now we're hoping to do the same with our experiments including hope which I mentioned and then with CTA I think that would be a game changer just to to finish off because I think I don't have so much time but just to show you the confusion that you can have between dark matter and astrophysical source so Fermi provides this beautiful map and the data could be analyzed by other people not just by the collaboration so it happens that Dan Hooper and he's a good enough actually looked at the data and they realized so they're not part of a collaboration they realized that actually looking at the data there is an anomaly which is around from 1 to 10 gv they realized that this anomaly was basically fitting I mean you could have explained it with a dark matter and the editing into solar model particles so excess of gamma ray in the range in the gv range and can be fitted by a dark matter in that range so if you want to have a spare factor of public shape you need something like you need a dark matter mass of 10 gv let's say so shows that percentually the dark matter can be light I mean light still but then I show you the constraints they had to do now because we know that in fact by stacking with a dwarf galaxy it's really hard to make it survive but Dan always found a way to I think to make it survive I think he's still thinking that could be dark matter however a lot of people have said well could we explain this with a millisecond pulsar for example and when they've done I'm not showing you plots here but you have to distribute you don't know where they are you have to distribute them in some ways and see that could actually fit the excess and the answer is yes I mean there's been a lot of controversy so yes no yes no depending on the effort but I think there is quite good evidence that it I mean it's very likely that this excess is due in fact to probably a population of mini pulsar in the center of the galaxy the other thing is what they observe other groups but so one related to Dan was some what do you call Fermi bubbles so Fermi it happens that Fermi has some figure of light basically some bubbles in gamma rays now funnily enough you see those bubbles in x-rays you see them in in radio or so and I think you see them in in our frequency so most translates some phenomena but at first which may be also related to perhaps the central black hole or something else another astrophysical source but at the beginning also people were saying oh maybe this is a dark matter again I don't think that would be true but there was a lot of controversy and I think now people have admitted that it's more related to to astrophysical sources there are funny things sometimes I just wanted to show you now the spectrum of gamma ray for the Milky Way extend up to 100 TV and again it's correlated with this figure of 8 at the big I mean at the center who knows what it is maybe dark matter maybe something else then when we looked at other objects like an NGN so central is a again we see an excess in this case again you see this this curve could be millisecond pulsar could be dark matter that works too so we never know and that's only because the mechanism by which you would observe a dark matter is the production of electronic positrons and so it's the same mechanism for millisecond pulsars so the moment you have this you can explain any anomaly if there is one maybe more fun I wanted to show you something a bit surprising so I mentioned that I liked or I showed that you can you can you can find a counter example to a limit and then in this case you can propose a movie dark matter if you want and that is the same time and I was doing this work an experiment so a satellite called integral and an experiment on this article called SPI reported new results from the number of positrons in the galactic center and in fact they actually map those positron distribution you can see the map here I should also add the reference to the to the experimental paper but what you can see here is that this map seems like center on the galactic center fairly spherical and so it tells you that potentially the positrons are well located in the galactic center but it's so correlated to the highest density of dark matter in the galactic center what what happens here is you don't see really the map of positrons you see you see basically the positrons annihilating with the electron and when they do that they form positronium the positronium is either decayed into either two photons or three photons the two photons is basically a line again so it's five it tries the mass of the electron so it's 511 kV all the three photons give you a continuum and that continuum is basically it's less than 511 kV but what they see what they I mean the map I show you here is really the 511 kV and so you know that there is antimatter in the galactic center more more than that you know that this antimatter is actually positron and more than that you know that for this positronium to happen the positrons might be at very low energy and so as I was proposing mv dark matter the natural thing to say is well it annihilates and produce positrons annihilates positrons and electron and there is almost no energy so you can produce 511 kV line and of course if it's true then the positrons that you should see so the gamma rays you should see in less respect should be correlated with the distribution of dark matter and that was exactly the case so this this was in 2003 and this was you know very surprising and very exciting because suddenly it's like oh maybe dark matter is like and maybe we found it through this but again the question is can it be explained by astrophysical sources or not now the funny thing about this one is no one could prove anything so we still we still don't know the origin of this line I personally now believe it's not dark matter but I couldn't really exclude it completely and it may actually I mean no one no astrophysical sources that people really know explain the emission either so very puzzly the best explanation is actually nucleosynthesis from the stars within the center it's probably a likely explanation but I don't think there is any consensus either on that so very interesting problem so the thing I wanted to show you is that and this was exciting but this is also very controversial if you have dark matter in a galaxy then in principle it should be accreted by a black hole and then the question is will he actually be the density is the density going to increase or not so it's it's not about the dark matter being absorbed by a black hole or anything like this it's just the density there is a question of all the matter around and the density of dark matter should increase eventually and if it does that and if a dark matter annihilates then it will produce some gamma rays and eventually produce radio emission so what happened is that you have a black hole and you have a shadow of a black hole which you see but there is a light last last trajectory where basically you can see the light you can still see some light and what happened is that this is basically announced now because of a presence because the dark matter may annihilate so this is a funny funny work actually but what is interesting is you can make prediction and in fact now we are improving this prediction and we're working with people from with i mean the ht who make who observe now the black hole so our prediction was was before the observation and we would see basically if they can put limits on the dark matter accretion or actually they can even observe it so this would be very exciting now i think i'm exceeding my time so i guess and tomorrow i'll do a direct detection and a bit of energy and then the cosmology wrapping up everything i'd say an answering question sounds good so maybe it's a good moment to stop the recording and now we switch to the q and a