 It's always a great pleasure to come to the ICTP. And my talk title is Galaxy Clusters as TeleAlpscopes. And then I'd like to kind of tell you about some work I've been doing with the variety of collaborators over probably the last couple of years now. And let me also thank the sponsors or my people who fund me. But before I start properly, I also want to just give you a break on how we are doing this. I think it's a great opportunity Felly yn gwybod, mae'n mynd i wneud i'r holl bach o'r holl bach. Felly, mae gennym ni'n holl bach o'r holl meddwl sydd fath o'r holl bach, gyda'u hefyd penedig o'r moll fath o'r holl ym lŷ. Felly, mae hi'n meddwl amcofio, mae'n modd o'r holl bach o'r holl ym mhaith. Felly'n meddwl amcofio, mae'n meddwl, ac mae'n meddwl merth yn mwygoed, rechyd i yn meddwl yr holl, i'n meddwl i'r holl meddwl mewn meddwl, a why it should be studied. Having inserted that, I will now return to the main part of the talk. Okay, so this is work that I've done over the last couple of years. It involves a variety of topics unified by the idea that string theory is something that is important and what someone should be able to think about possible observational consequences of it and how it can connect to observations. So what's in this talk, we mostly based on things from these papers which are done with these people and this is what they look like in case you want to, some of whom are here, in case you want to offer them a job. And it's all about basically thinking about axion-like particles and how they can manifest themselves obfistatiously. So although the contents of this talk will be reasonably phonological, at half time the string theorist, so I want to basically motivate why in the context of string theory axion-like particles are something which are good to think about. Okay, so if you think that string theory might be actually the one true theory of the world at the smallest possible scales, then in the great tradition of science, one wants to think about how this can manifest its statement, could manifest itself observationally. And one approach to this is to try and get back to the standard model, reproduce the standard model and think about what might lie beyond the standard model. One difficulty with this is that it's certainly become abundantly clear that there are many, many ways of getting things which look at least approximately like the standard model in string theory. There are many, many different corners of string theory where you can compactify and it's not at all clear which one would be the right one to go down. So if you want to try and get back to the standard model, you're faced with an abundance of options and it's entirely unclear which is the right way to go. So in this respect, my attitude is that it's more useful to think about the most generic features of a compactification. The fact, things that if the statement that the world has extra dimensions is really a true statement about the world, what are the most generic consequences of this fact? And one of the generic consequences of this fact is that the existence of extra dimensions leads to the existence of of moduli and axions. So basically gravitationally coupled particles that arise from the geometry of the extra dimensions. Such moduli and axions arise very generically, much of their physics in terms of their effective actions is rather universal across compactifications and so these represent one of the most natural and universal targets to go for. This talk is going to be about axions. If you read papers on axions, the nomenclature has become confusing or confused in that the word axian means several different things to several different people. Okay, so the traditional string theory usage is that any particle where there's an exact shift symmetry, basically theta goes to theta plus two pi, you move around in the circle and you come back to exactly the same point in the Hilbert space is an axian. There's a more recent usage which is in the context of monogamy, which is where you have particles that in a sense would be axions were not for some other features of the compactification and these are, so these do not have a fundamental shift symmetry. You move through two pi, you are back at a different point in the Hilbert space but they still get called axions and finally there's the usage which I'm going to really adopt here which is that the word axian, the axian is reserved for the QCD axian. The particle that solves the strong C problem, the strong CP problem and all these other types of particles, particularly the first type of particles that are called axions in string theory are called axian-like particles. So this is an element which I'm going to adopt here and the talk is then going to be about axian-like particles. Why to think about them from a morphological point of view? Well, they're fun. They're one of the best-motivated ways of extending the standard model. You're moving at 90 degrees to the directional thinking about basically colliders at the TV scale. There's no immediate technological obstructions. You can probe the far UV using rather low energy experiments. There's various interesting hints. So for all these and many others, they're both good and fun things to think about. In terms of the Lagrangian that this talk is basically going to focus about, so this is basically the standard out Lagrangian. So what we have here is we have electromagnetism. We have a scalar at the out. So as we're expanding about the minimum of the potential, in principle, there can be a mass term, although in practice I'm going to treat this as zero. So this would complete to a sinusoidal potential, but we're just looking around the minimum here. And then there's the real guts of this, which is the coupling of the out to electromagnetism. So this is, of course, a dimension five coupling. So it's suppressed by an explicit mass scale. And this coupling can be rewritten conveniently as basically ae.b, suppressed by a mass, by a large mass scale. And just from the outset, so I'm going to basically assume that the out mass is zero in this talk, although everything I say can go through with a mass assuming the mass is less than around 10 to the minus 12 electron volts. If you wonder what this scale is, it corresponds to the plasma frequency, i the effective mass of the photon in the side galaxy clusters. Direct bounds on this coupling basically say that M has to be bigger than around two times 10 to the 11, 11 GF. And beyond that, it's actually open. The basic phonology of alps is simple, which is a good thing for a simple person like myself. So it's that alps convert to photons in coherent magnetic fields. If you have a magnetic field which is transverse to the direction of motion of the out, there's a finite probability that that out will convert to a photon. And in an appropriate small angle limit, this conversion probabilities goes with the square of the magnetic field, the square of the coherence length and inversely with the square of the coupling. So in this game, if you want to win, you want big fields that are coherent over large distances and obviously you want the coupling to be as less, at least impressive as possible. And these basic simple features determine the phonology of alps. Okay, so this is probably a slide that's not easy to take in real time, but going beyond the small angle approximation, so there's basically two oscillation angles. The physics of how this is worked out is very similar to that of neutrino oscillations. So there's basically two angles that determine out photon. Solation is one called theta and one called delta. And for typical astrophysical values of the parameters, I've given numerical values for both theta and delta here. Theta is basically always small, essentially, whereas delta can come out of the small angle regime. Given the physics that what you like is big magnetic fields over big distances, there's really two things that can immediately come to your mind. Okay, so one is that you try and go to look for get very big magnetic fields. And the other thing is to get very big distances. So the very big magnetic fields is, you think, basically LHC test magnet. So this is the principle of the CAST experiment at CERN, where you have something like an LHC magnet, 10 Tesla magnetic field extending over about 10 meters. You can work out the virtual probability. Astrophysical parameters, you have micro-gauss magnetic fields. So a gauss is 10 to the minus four of a Tesla, coherent over roughly kiloparsec scales. And if you do the numbers, what you see is, you know, there's no real, I don't have any kind of intuitive thing for seeing this in advance of doing the numbers, but basically astrophysical sources are overwhelmingly better by a factor of something like 10 to the 18. So if you've got something like a relativistic out, or a relativistic, moving around, then the conversion probability for out to photon is something like a factor of 10 to the 18 better in something like a galaxy or a galaxy cluster than it is passing through an LHC test magnet. And what this says is that if you're interested in basically converting out to photons and the phenology of outs, astrophysical sources are extremely good places to think about this physics. Okay, so then this leads me to the second part of the talk, which is about galaxy clusters. Okay, so as I said, I'm a string theorist and in string theory 101, one thing you'll indoctrinate it into is the fact that string theory is a theory of everything. And so as it's a theory of everything, it's a particular theory of galaxy clusters. So this next part of the talk, I'm now going to discuss the string theory of galaxy clusters. Okay, so here are pretty pictures of some clusters. So these are tasting, shaking the Charm Direct-Stray Telescope. So this one is the most famous one. This is, you'll recognise immediately, it's the bullet cluster and the separation of the dark matter with the hot gas. So the distinctive thing of cluster is what you'll see is you'll see the many kind of background galaxies which emit basically optically and then you'll see the diffuse haze of the hot gas. Cluster is around 90% hot glass and they emit copiously in X-rays. So clusters are the largest virulised structures in the universe, typically about a megaparsec across 100 to 1,000 galaxies. The baryonic matter is 90% in the gas, the whole cluster is 90% dark matter and they'll suffused by basically this mini-tylionic plasma which has temperatures of the X-ray temperatures and emits copiously through thermal breadth drug. The point of most relevance to this talk is the fact that this plasma is magnetised. So there's a micro-gauce scale magnetic field that exists throughout clusters. This field is measured empirically through Faraday rotation measurements and it's got a typical coherent scale or reversal scale of around one to 10 kiloparsecs. So you've basically got a region of space which is roughly kind of a megaparsec across and is kind of filled with micro-gauce magnetic field. And it goes into various kind of frontiers of particle physics. So this is really kind of a large magnetic field over large volumes frontier and this is optimal for the physics of ALPS. Okay, so just to make this a little more here. So there is one cluster I'm going to focus on in particular. This is the Coma cluster. So this is quite a famous cluster because it's both kind of reasonably bright, reasonably nearby. It's about 100 megaparsecs away. So this is it invisible. So you see what you see is all the galaxies. This is it in X-rays. So again, so you see basically this characteristic diffuse glow in X-ray energies. And this is it in gamma rays. So the scale of this is basically 10 degrees by 10 degrees and the Coma cluster itself is a degree by a degree roughly. So if you look at this central degree scale roughly there in here and you can look very hard and you can keep on looking very, very hard and you won't see a thing because clusters have never been detected in gamma rays. So despite original hopes, Fermi has failed to detect a single cluster, a diffuse emission from a single cluster in gamma rays. Okay, so the relevance of clusters to here to this talk is the fact that because I've got relatively large magnetic fields over relatively large, they are efficient converters of alts to phytox. And in this respect, the fact that the magnetic field is 10 to the minus four of a, sorry, 10 to minus 10 of a Tesla is relatively weak is more than compensated by a coherence length that is expressed in kind of GEV units, partial physics units is as a numerical value of 10 to the 34, which you then get to put in the numerator of the equation and square. And just looking at the sums, what you see is that if you've got a relativistic Alp with extra energies, then it's passing through a cluster, its conversion probability is for coupling values that are something like two orders of magnitude above where the current bounds are. The conversion probability is as large as something like 10 to the minus three. Now, while that might not sound large, if you convert this to a rate of basically converting energy to light, you'll realise this is a rate of conversion of energy to light which is 1000 times more efficient than the sun. And if you put it like that, you can see that this is then something that you can then seriously think about going to look for and seeing whether you could do something interesting with it. Okay, so this slide is just to scare you and to show you that we did some real work. So what we've done in more detail is then we've looked at basically the best fit models for the magnetic field of the Coma cluster, which have been determined by various radio astronomers and just propagated Alps through them. So this is basically a multi-scale Cormigore spectrum with these have been done on the sort of numerically on a 2000 cubed grid. And we've basically propagated Alps through this to look at their conversion probabilities. Okay, so let's just show you the plots. Okay, so the impact parameter is just the distance from the centre of the cluster here. So what you see is that for sort of x-ray energies, then the conversion probabilities end up is around 10 to the minus three. So this is for a coupling strength of 10 to the 13 jev and then at lower energies, the coupling, the conversion probability falls off rather dramatically. I'm not going to particularly focus on this in this talk, but this is something you can understand through looking at the oscillation angles that are involved. So this is one of the first main points I want to make in this talk is that galaxy clusters are very efficient out-photon converters. Even for coupling strengths that are up to two or three orders of magnitude belong beyond where the current observation limits are, out-photon conversion can be significant. And which direction is this, I might don't want to take this in, is that it should be clear then that even if you have any primary population of Alps, now where that comes from is another question, but if you have any primary population of relativistic Alps, you can get quite a significant photon signal and if you have a significant photon signal, you can see it. And so then in the next part of the talk I want to basically describe an application of this. Okay, so in our work we've basically, there's been two or three applications we've been really looking at. So the original one, which is the most stringy, which is based on the general unistring cosmology, the universe passes through a moduli dominated epoch early in the universe, is the idea that there's a primordial cosmic Alp background which comes from moduli decays at the time of reheating. Their decays can produce Alps, the Alps propagate through the universe today, they turns out they have extra energies today and they convert into photons and they have the possibility of explaining this long-standing anomaly in the X-ray spectrum of galaxy clusters called the cluster soft access. Another one where you can take it is by looking because clusters emit copiously in X-rays and clusters are also extremely well measured in X-rays, you can actually use basically back photon Alp conversion to I think basically improve the bounds on our parameter space. So that's something we're doing at the moment. But where I want to take this talk is to think about is the three and a half KV which I'm sure you've heard of because this was certainly a very hot topic last year. Okay, so to then talk about the three and a half KV line. So I want to give some basic observational review and then explain what else they have to do. Okay, so as I'm sure you know, this story started last year with two papers that appeared on the archive within a week or two of each other, one from a group at Harvard, which is this top one, and then one from a group a mixture of Leiden and Lausanne. And they both reported basically an unidentified line in X-ray line at energies of approximately three and a half KV. The first one from basically clusters and the second one from a mixture of the outskirts of the Perseus cluster and also from Andromeda galaxy. So this is one of the pretty pictures from the NASA publicity shot. So this is the center of the Perseus cluster and this is showing spectrum with this kind of excess emission around three and a half. Okay, so the first thing to say about this is this is a small signal on a large background. It is obviously manifestly obvious that if you look at these plots, you can clearly see the red line going along here and the blue lines, the blue lines of background, it's completely obvious to see there's a red line here and this is an excess at large statistical significance. Yeah, okay, so okay. Yeah, but we know on these things we shouldn't really trust our eyes. The Higgs discovery is also a small signal on a large background and what this means is one needs to be careful and do the statistics carefully and worry about such a background and the various ways you could make a signal. Okay, so what do these original papers have? Okay, so the most detailed analysis, I think it's fair to say, came in the paper by Bulgur Chal. So their main thing was they had a stacked sample of 73 clusters where they basically stacked the X-ray spectrum of clusters as a different redshift and appropriately shifting them back to the rest frame. So there are two instruments on X and M Muton, the MOS and the PN cameras. So they saw the signal with both the MOS and the PN camera basically on all this sample. To check that it wasn't one single anomalous cluster or something throwing the signal, they split it up into the Perseus cluster, which is the brightest X-ray cluster in the sky and the combination of Coma and Ophiuchus and Centaurus, which are also three nearby bright clusters and then all remaining 69. And they found the signal again in each of these sub-samples. For the case of Perseus, where the signal was strongest, they reconfirmed it with deep observations with the archival Chandra observations, both with both the Assis S and Assis I cameras on Chandra. In none overlapping observations, the other paper by Byarski et al, they found the line in the outskirts of the Perseus cluster, whereas the Bulbul observations were at the centre of the cluster. So they found it with both, again, the XMM cameras, XMOS and PN, and they also found the line in M31, which is the Andromeda galaxy. Okay, so these were the original papers in terms of significance counting and chi-squared per degree of freedom. That I've shown here. In terms of things like the Look Elsewhere effect. Okay, so the Look Elsewhere effect basically means you can cross out any one of these lines. So you can take, or you can say that N should be 2 rather than 1. So basically, you can cross out any one of these lines to say that you can find a line somewhere. But once you've found a line somewhere, obviously that somewhere is fixed and you know where you should look at everywhere else. So each of these rows is basically independent observations. And what you see is definitely something that means you should pay attention to this. Okay, how to evaluate this. So this is my take on this. Okay, so it's a plus that is seen by four independent instruments. It's a plus that's seen by two independent collaborations. It's a plus that the collaborations are not solely kind of BSM theorists. Why is this? If you're extra astronomers, then there's a much higher price to be paid to declaring that you've seen anomaly and it might possibly be dark matter than if you are a theorist. And in particular, if you look at someone like say, Maxi Markovic who has written something like 200 papers on X-ray astronomy of galaxy clusters and then in the 201st paper, you say, well actually there's this unidentified line and I'm willing to speculate about dark matter. It doesn't mean it's right, but it does mean that it deserves to have attention paid. So the line's absent in basically some 16 megaseconds of blank sky observations. Okay, what are the negatives? It's a small signal. It's only 1% above the continuum. There are extra atomic lines at similar energies. There are detector backgrounds. Small wiggle in the effect of air and you'd worry might mimic the signal. This is counted to some degree by this, but these are certainly things one has to be worried about. And in the original paper, due caution was generally offered. Okay, so since these papers, there's been a variety of work on this topic. So basically, there's been none observations in Dwarf Siroidal's stacked galaxies. Milky Way Centre's unclear. There's this series of papers that I commend to anyone who is a connoisseur of the comment on reply on comment on style of scientific writing. And there's also been observations with Suzaku, which is the other main x-ray satellite, which has seen the line in Perseus, not in Coma Virgo or Ophiapas. And the other comment to make which is important, which is important where I'm going, is that the line in Perseus is clearly is strongest in the centre of the cluster and the line in Perseus and Perseus is a much stronger signal than in other. Okay, so in terms of the kind of, the right to interpret this, so the clear first claim belongs to basically models of sterile and neutrino dark matter, because these were the only models that were really talking about x-ray lines in advance of the actual observations. Now, why should one not just go with sterile and neutrinos is that on face value, the data is inconsistent. So sterile and neutrino just decays directly to a photon. Parameter in the sterile and neutrino model is basically the sine squared to theta, which just says basically how fast it decays. And if you look at the numbers in this column, you'll see that basically the strength of the decays are basically incompatible or face value incompatible with dark matter decaying directly to photons. In particular, the stack samples of clusters which give a kind of pretty high strong determination of this. Yeah, there's claims in the abstract claiming to basically exclude this value of something like 11 sigma through the stacked galaxy observations. Whereas if you look at the Perseus cluster, it is consistently the case that Perseus produces a much stronger signal. And the center of the Perseus cluster even more so produces a much stronger signal than coming from the stacked samples and clearly a much stronger signal than anything involving galaxies. Okay, now you can say whether this 11 sigma is really a 11 sigma or not, but it's certainly clear that if you take this data at face value, dark matter decaying directly to photons is in trouble. Okay, so taking the data at face value, what are the challenges for any BSM explanation? Okay, the first point is that clusters are special. The signal is stronger in clusters than it's in galaxies. It hasn't showed up in the stacked sample of galaxies. It is present in clusters. There's only one galaxy which has been observed in, which is Andromeda M31. The Milky Way Center I think is a special case because it's not very unclear what's happening there. And that's the very sort of special in the region. There's also nearby or cool core or nearby and cool core clusters are special. So cool core clusters are precisely that where the core of the cluster is cool. This just happens over time through radiative cooling because the signal is stronger in both Perseus cluster which is both nearby and cool core. And it's also stronger in the stacked coma for the Uccasin Centaurus sample than it is in for more distant galaxies, for more distant clusters. And why I want to talk about Alps is I want to focus on an explanation which I think can explain all these features which is where diamata decays not directly to a photon but to an ALP, a three and a half KV ALP plus something else. So relativistic ALP with energies of three and a half KV followed by ALP photon conversion in the astrophysical field. Okay, so the basic proposal is then the diamata decays to a three and a half KV ALP and then this three and a half KV ALP converts to a photon in the magnetic field. So what this basically implies is that the signal will then trace both the diamata distribution obviously and the astrophysical magnetic field. This can then explain this data because clusters are special because they're the best ALP converters in the universe. They're much bigger than galaxies but they've got a comparable magnetic field. So their conversion rates are much higher. Nearby clusters are special because telescopes can only look at very small parts of the sky. So pointed at a nearby cluster, the telescope could only fit the center of the cluster in its field of view. Cool core clusters such as Perseus are special because both observationally and theoretically they have much larger magnetic fields at the center of the cluster. So at the center of the Perseus cluster the magnetic field might be around say 25 microgauce whereas a typical cluster magnetic field would be a few microgauce. And finally, M31 is special because it's an edge-on spiral galaxy and it's with an unusually coherent regular magnetic field. The advantage of being edge-on is that if something diamata decays in the center of the galaxy it passes through the disk of the galaxy. So through the entire coherent magnetic field which then maximizes conversion compared to a face-on decay where you just come straight out of the plane of the galaxy and don't really see any magnetic field. Okay, so yeah, among clusters Perseus is special. Ofiaca, Centauros, and Coma these are also nearby, so you can see the central regions. And so again you can expect stronger signals for these. We can quantify the differences between cool core and non-cool core clusters. So this might work with Andy Powell who's in the audience. So I'll just show you some plots as I'm kind of running out of time. So this is non-cool core cluster. So the point to take is basically the cool core clusters have a much higher spike in signal at the center of the cluster because they have this spike in the magnetic field. Okay, for the future, one of the fun things about this is there's, you know, there's both lots of data and the data situation is going to get a lot better. So first of all, all these observations have been with archival observations. There's something like 15 years of archival data sitting there and analysis of some of it is in process. For example, Bulbwrthwell are currently analysing stacked archival suzarko observations of galaxy clusters. There's also been recently an approval also of a very deep greater than one mega-second ex-emmusion observation of the draco dwarf galaxy. So observation data taking has actually started for this. So it's probably going to be a result on this by the end of the year. So this will give a pretty decisive test of the sterol neutrino interpretation of the three and a half KV line. Early next year, Astra-H, the next generation X-ray satellite is by the Japanese Space Agency is flying and this will offer a decisive test of the dark matter interpretation of this line. Through basically it will have unprecedented energy resolution for X-rays in space. X-rays in space. So this is Astra-H. So this is flying in about six months. So kind of hope it works because I won't talk about history but microchelorimus is in space but let's hope this one works. The SKA is going to also give unprecedented improvements in the ability to determine magnetic fields in clusters which is if you're interested in alps is something that will tell you about alphoton conversion. This is coming online over the next 10 years. And so we've got S-Astra-H, the SKA and even the longer term future, Athena has been approved by ESA. So Athena is the next next generation X-ray satellite and that's been approved by ESA for the 2028 large class mission launch slot. So click lose. Clusters are great if you're interested in alps. Alphoton conversion is highly efficient in clusters. For the three and a half KV line, I think this dark matter to alps photon scenario is basically a promising and distinctive explanation that can explain the observed morphology and over the next one, 10, 20 years there's a variety of new satellites and instruments that basically guarantee to be coming online. Thank you. Questions? Yes, so you were trying in the last part where you were discussing the gamma line and so in the case of the alps explanation you can explain all the difference in these parameters practically from differences of the magnetic fields or you have to take it as a free parameter. So you can explain the fact that the signal is stronger and perseus than it is in other clusters. You can explain because the magnetic field in the centre of perseus is much larger than typical. For M31, so the fact that as it is, it's an edge on spiral means you expect a much stronger signal for M31 than for typical galaxies. For taking an actual value and saying, why is it this as opposed to say a factor of too high? You would need to know the magnetic field very precisely. So that's hard to be in terms of say qualitatively, why is the signal stronger here than it is here? And what are the perspectives to have a better estimate of the magnetic fields? So ultimately SKA, depending on kind of, how appealing working out magnetic fields are to the broader astronomical community. So existing radio telescopes could give you better information. It's just a matter of, are astronomers willing to spend time? How long are they putting pointing telescopes at clusters? I think a related question. So you showed us several different clusters which have different properties, but for all of them the line is at 3.5 kV. And your process of alps seems to depend on the properties of the cluster like size, magnetic fields. And it's an explanation by for, even for different clusters, the line is always at 3.5 kV and not at different energies. So the proposal is that the original, so that this would be coming from dark matter decay, but you would have dark matter decays instead of like dark matter decays to a photon plus something else. You would have dark matter decays to an alt plus something else. So the fact that the energy of the alt was 3.5 kV would just be fixed ultimately by what the mass of the dark matter particle is. And this I have no prior. But then, yeah, so the fact is always that 3.5 kV would come from the mass of dark matter. Is there any alternative explanation from particle physics? So there is somebody involving kind of... Okay, so there's a huge number of models which are basically dark matter decays directly to photons. And those are just exactly the same behaviour as they're on neutrinos. There are some ideas involving basically dark matter kind of bumping together, so-called excited dark matter. I mean, I think there's a... I don't think they'd be able to provide a reason of what say why, for example, andromeda would be special as opposed to other galaxies or why perseus should be so much more stronger than other clusters. I mean, they can give, I think, different behaviour between... They can say broadly why clusters should be stronger than galaxies. I don't think there'd be sort of a good explanation for why, say, perseus is much stronger than other clusters or why M31 is so special among galaxies. Okay, so...