 Počeem, da v srečnih lektu sem početil vse skupne, da ne so vznali na to nekaj nekaj toga. Isponjno, če bo to prišlo? Sveči sem početil na nekaj neko. OK. Zato, before starting to dirty businesses, and starting to make some kind of quantitative assessment of what we want to discuss with Costume Grade Physics, there's one other aspect I would like to enlighten, which is very important right now, since I tried to convey this idea that there are many different methodologies to test Costume Grade, and the real important point is that all of these are sort of connected at an intimate level. So I would like to talk about multi-wavelength and multi-messenger Costume Grade connections. And to do that, we have to look at what are the processes which are connected to those that will sort out to be the main component in Cosmic Race, which are electrons and protons. So I told you Cosmic Race are propagating in this dirty, so-to-speak environment, and while we do so, they leave some imprint. So for electrons there are essentially three main physical issues which are going on. From the point of view of quantum electrodynamics we are all the same, but from the point of view of energetics and the test of Cosmic Race Physics we are different. So first of all, let me discuss about electrons, how they do lose energy in a matter. So when you are in the limit in which the electron energy is not too large, we will discuss what that means. So basically M, E, V, G, V scale, there is one main mechanism through which energy is lost in electron propagation, which is Coulomb scattering. So you are propagating these electrons in a ionized medium, and what you do is to have this brainstorm radiation out of it, and pretty much in the same way as we were doing that in the atmosphere you do that along propagation in the galaxy. Okay, and then there is some cross-section in energy losses which scales linearly in energy of the electron, and with mean energy of the emitted photon as we were discussing of the order of half of the energy of the electron. The second important block is the fact that you are propagating again these electrons into a background which is filled with photons, and as we were discussing before these photons are mostly low-energy stuff, thermal components or thermal reprocessed components from the CMB to star light to reprocessed star light. So it's low-energy stuff which is eaten by electrons which in general have high energy, and then what happens is a sort of inverse process with respect to what you probe in say an accelerator in which you shoot a photon on an electron target. So instead of shooting an high-energy photon on an electron target, here you are shooting, well cosmic resources do that. We are shooting electrons on a medium which contains low-energy photon and what happens is that there is a net energy gain in photons and the electron is losing some of its energy. So there is a simple scaling that one can derive from this process which is called inverse Compton because just it's kind of reversed with the standard Compton scattering you learn the EOR QCD primer. So the scaling between the energy of the outgoing photon and the energy of the incoming photon can be understood easily. So what you have to do is to think about the scattering in the center of mass frame. In the center of mass frame essentially there is not much reshuffling of the energy of the particles. But then what you have to do is to go first from the lab frame to the center of mass frame and then go back to the lab frame. So when you go from the lab frame to the center of mass frame you have E prime energy for the lower energy photon that gets boosted to gamma factor times E then as I said the energy is sort of unchanged roughly speaking in the scattering in the center of mass frame and when you go back to the lab frame you get this extra gamma factor which makes up gamma squared E. So the energy of the outgoing photon is scaling with the square of the energy of the incoming electron and linearly with the energy of the lower energy photon. So what this does is to take a lower energy spectra and boost it up into a spectrum that has a peak in shape at, well, one quarter of the maximum energy and that's the scaling that was in lighting. As a counterpart then there is the first process which is relevant for electrons, electron cosmic rays propagating in the interstellar medium which is the emission of energy by synkrotron radiation. So as I was telling you the interstellar field is magnetized with a magnetic field of the order of the micro-gauss or so and then you have synkrotron radiation coming out of a classical view electron spiraling around the magnetic field lines. If you think about this process in terms of QED this is nothing but the same process I had before with the role of the lower energy photon played by the magnetic field. And then it doesn't come as a surprise that the scaling of the peak energy of the emitted radiation is just going with the synkrotron frequency the frequency associated to this magnetic field scaled up by, again, a gamma factor squared for the electron energy. Let's put this together. The Krabnebula is possibly the most studied cosmic ray source and because it's a bright source it's a moderative variable it's close to us and then what people do is really to calibrate their telescope to the flux you detect from the Krabnebula. And what is this flux looking like? It's looking like a two bumpy thing one low energy one picked in the infrared and then a bump here which is picked in a soft gamma rays. So we think that the Krabnebula is a source in which electrons are celebrated and escape from the Krabnebula itself an ambient which has a large magnetic field and then what it does is to emit radiation in the two processes that I just discussed. And so there is a synkrotron component emission due to the magnetic field and then an inverse component emission and this is really close to a game because when you do the calculation you find out that the synkrotron radiation you emit in this larger magnetic field is so dense that it is indeed the source of background photons that then are upscattered by inverse component by the same electrons that are escaping from the source. So this process is called synkrotron self-compton model because you see you have only one free parameter here which is the magnetic field and as you see it works beautifully although with a value of a magnetic field that is kind of large to explain on first principle. What about protons? Well, I was telling you about protons interacting with ambient material and the main feature for proton interaction is the fact that you get these adornization processes that they leave you an imprint that goes through pions and in particular the main imprint is in the channel with pi zeros because pi zero decay into two photons and then we can backtrack these photons of serving the source. So the main diagnostic of the factor high energy protons is the fact that you have a connected gamma ray component as well as a neutrino component as we will discuss in a second moment. The main feature of these is the fact that pi zero decay is again the center of mass they emit two photons that are back to back with an energy which is the mass of the pion divided by two. Then what you have to do is to make again a Lorentz transformation and then what you get is that independent of the spectrum of the incident protons you get a shape in the distribution of photons which is picked around the mass of the pi zero divided by two and this is the so-called neutral pi zero bump. OK. So do we have all these processes at work not only in the sources but along propagation? The answer is in this plot. This plot is giving you the so-called gamma ray diagnostics of what is the propagation of cosmic rays in the galaxy. So this is a plot which represents the counts that the Fermi large area telescopes as detected in the gamma ray band between 200mV and 100gV. So what you see here well point sources have been subtracted out there is just diffuser mission from the galaxy and actually that part accounts for 90% of the gamma rays that Fermi as detected in his mission. So you clearly see that this is in galactic coordinates and there is a main feature that is coming out which is the galactic plane and some high scale component here which is actually mostly local stuff. So the diagnostic through gamma rays is done in this way. If you have a theoretical model which is telling you what is the amount of protons and of electrons that are populating the halo of our own galaxy then the interactions that these protons and electrons have with the ambient medium is what is popping out in gamma rays. And as a matter of fact this is one of the pillars of the cosmic ray field because there is indeed at least a qualitative if not 100% quantitative match between the picture that I will start discussing later in this lecture and what we see in the sky. So at least at high intermediate latitudes there is very good agreement if you try to model the data with components that are connected to the emissions that I just discussed. There is the red one which is this pi zero bump. There is the inverse Compton emission which is connected to electrons and the interstellar radiation field. There is a brainstorm component. There is some component which is due to sources, point sources. You sum all them together and you find quite a spectacular match. So this is a match kind of old sky and the most inner part of this plot if you zoom in this inner part maybe there is a certain level of mismatch I will mention what we think this is connected to. Ok. Then the other diagnosis we have about adronic components is the fact that adronic components as we now been discussing at NOZA are breaking up. Ok. So if you have protons, you have adronic interaction if you have a nuclei so heavier targets, these heavier targets can interact with the ambient field and then from a given nuclear can generate a lighter daughter nuclei as a secondary component. Keep this in mind and this will be very important in few minutes. And finally there is this issue about neutrinos. So when you have interaction of protons or of heavier nucleus in such way that you get showers in these showers as we said you get pions, charged pions and the charged pions decay into first step with a new neutrino here and the second step with an anti neutrino and in electron neutrino. So that's in principle the ideal cosmic ray species that you want to treat because neutrinos don't suffer from all the issues that I have discussed before. So there is no significant neutrino horizon, right? Interaction with the starlight in background light is not important. For ultra high energy cosmic rays again the GZK cutoff is a source of neutrinos Of course there is the slight drawback of the fact that these kind of interactions are not happening because the interaction of neutrinos are suppressed and then the cross-section for scattering of a neutrino in your detector is as low as the picobar at the tab is going a little bit up when you go to the EEV scale but still is very tricky and nevertheless this has been has been addressed and the way to do it is to do it with gigantic neutrino detectors. So the largest one in the world was built the South Pole deploying strings of photo multipliers deep in the ice and forming a structure which is now 86 strings and which covers an effective area which altogether is of the size of a kilometer cube so that's the name, ice cube and what you are after is again Cherenkov light now not in the atmosphere in ice there are versions of neutrino telescopes that are built in water such as Antares and then you look for the same kind of features in water and there are essentially two kind of events that are detected this is so called an aggregate event so you have an interaction of a neutrino which electroneutrino or a town neutrino which generates bars of particles and then you are tracing up these balls on how they light up the photo multiplier in your detector if you have a muon neutrino which is interactively in your detector what you can get is a spectacular event in which a muon is generated and then again a muon is a very penetrating particle it gives up a truck which is kind of spectacular and this got interesting three years ago when there was the first announcement of the detection of extraterrestrial neutrinos so we had seen plenty of neutrinos before but they were mainly connected to the production of neutrinos in the atmosphere and in connection with cosmic ray air showers on the other end this is a kind of signal which is expected to die out when you go above in a to high energy and with this gigantic detectors it was possible to explore a frontier of energies above of the neutrinos energies above 100 TV and what came as some kind of surprise is the fact that there is a clean excess of the detective flux above this threshold which is very improbable to be connected with the atmospheric neutrino background in fact if you subtract out this atmospheric neutrino background you find a power low neutrino scaling which goes like minus 2.6 this is a number that this spectral index is a number which we will find often when we will talk about cosmic ray phenomenology so it's something that rings a bell about being due to cosmic rays and what is really spectacular is that you see you have these events that are so high in energy as the PV scale again there is a down going up going asymmetry so ice cube is looking either from events that are coming to the detector passing through the earth or for events that are coming from above these energies are energies at which neutrinos are to be stopped by passing through the earth so there is an asymmetry between up going and down going and for what regards the distribution of events there are above this threshold of 60 TV some 55 events or so and these 55 events of course have a poor statistic there is one warm spot here which is roughly consistent with the galactic center but not quite so this is in galactic coordinates and there has been also in this case some study of correlation of these events with various hypothesis and obvious counterpart identified so far but what is seems to be interesting is that this picture is a picture that has to do with flux coming from at least one of the sources so we are going to do neutrinos astronomy that's fantastic and finally the last piece of multi messenger that I cannot avoid to mention the picture that has emerged in February with the report of the detection of gravitational wave event in September last year by LIGO this event is spectacular but is an event which involves black hole black hole merging which has remarkable energetics and this is not close to us but is not really expected to have electromagnetic or adronic counterpart so it was detected with the two LIGO instruments so there is some information about where the event was localized on the sky but not very precise so with this event they sent out alert to all other kind of probes for high energy particles in the universe and there was not really any counterpart identified except for this weak claim of some coincidence with a gamma ray burst in the GMB monitor instrument in Bordom Fermi so as I said another part in electric counterpart was not really expected in this case but except if you believe in some exotic models maybe but for instance would the next event be connected to a merging involving one neutron star one neutron star would be bringing with it a large accretion disk and probably there would be some spectacular fly works coming out so the next frontier is to try to do cross correlation with this kind of messenger as well so this ends the part that I wanted to tell you about a broad picture for cosmic ray phenomenology and now I'm going to change a little bit gear and go to go from this picture to some of the pillars that are starting to give us some physical insight so maybe since I'm going to switch topic if there is some question that's a good point to ask okay there is I think there are two or three scenarios that I've been put forward all of them has to do with some kind of technical issues in a gamma reverse which I'm not sure I understand myself and definitely I won't be able to explain in few minutes so maybe this paper is a short letter not technical maybe you want to have a look at that that has to do with some resonant kind of accretion not an accretion disk some resonant accretion, a spherical shell blah blah blah yeah there is a little deep here but I think it's just one sigma away from the feet so this analysis is really triggered above 100 TV now it's some detection mode for the detector in which you are not sensitive to lower energy stuff so you you with the cuts they make you say this is completely consistent with the atmospheric neutrino background the real physical thing is of course that this is a power low is e to the minus 2.6 power low ok so let's start to have a look at doing physics or astrophysics with cosmic rays so the first important thing is this plot what is this plot this plot is a plot which demonstrates that at least what regards the lower energy tail for cosmic rays cosmic rays with energy below 10 to the 15 electron volts or so these cosmic rays are non particles that are propagating ballistic but they are rather propagating diffusively how do you understand that from this plot in this plot I'm comparing the isotope the composition that one has in galactic cosmic rays the black dots against the isotope the composition one has in ambient gas surrounding the solar system so you look at a social lines in the ambient gas and you determine that the sun is made the corona of the sun is made of these kind of elements with an abundance that follows these plots and the first site that looks very much the red dots except for two regions that have been lighted here there is a region below carbon, nitrogen and oxygen which in cosmic rays is pretty much at the same level as these elements not pretty much in this huge logarithmic scale but so striking in this huge logarithmic scale is that in comparison the abundance of berylion for instance boron in berylion is suppressed compared to this number by some six orders of magnitude and here is less pronounced but anyway dramatic elements below iron in cosmic rays have a density which is comparable to iron within an order of magnitude or so while in the sun ambient they are very much suppressed so this has to do with the fact that there is a type separation between these kind of elements and iron and these kind of elements and carbon, nitrogen, oxygen if we suppose that the ambient around the sun is a typical ambient for a star so is a typical ambient which reflects stellar nucleosynthesis so is a typical ambient in which a source is evolving and polluting is environment with its own yields and then eventually taking those yields and through some acceleration mechanism speeding out in the interstellar medium cosmic rays then you would say that these elements here which are most abundant are elements which are primary cosmic rays are cosmic rays which are synthesized in the sources and then accelerated in the sources while there is a component like this component here that was not there in the sources but a long propagation got a component and now can you get a component well you have to take into account this effect of interaction of primary cosmic rays within the stellar medium which can break up this element here and generate lighter species so once you start with the sources you have this non-democratic distribution after you propagate cosmic rays in the interstellar medium you get this more democratic distribution so we have identified two components in cosmic rays there is one component which is called primary component so for instance in that plot carbon is a primary component and we have a component which is not generated in the sources but is anyway there so is coming in as some secondary element and for instance in this plot this first open dot there is boron and boron is somehow describing the history of the propagation of this primary in the intergalactic medium and on the way to get into us so I want to sketch that this simple observation is enough to conclude what I wrote as the header of transparency that this is evidence for cosmic ray propagation in diffusive mode not in ballistic mode so so we have to go back to what I introduced previously in the morning which is the grammar the grammar X is the amount of transfer material that you get along propagation so you have some density of the medium for which you propagate you have some given track that you follow against propagation and what you are collecting is this projection of transfer material which is what I call grammar so then the scheme is the following suppose we have primary species and one secondary species I can define for these both species some kind of interaction length this is an abuse of notation because it's not really a length but this is some quantity which is tracking the grammar the conversion with respect to the grammar I just saw this interaction length for the primary component is just the mass divided by the interaction cross-section for this primary component and now obviously I will have an interaction length for the secondary component which is the mass divided by sigma for the secondary ok the matching mass is not that large so I will neglect that and then what I can do is to write an equation which describes the evolution of the density of primaries and the density of secondaries along a trajectory which I don't parameterize as a real trajectory parameterize as a grammar path so there will be a variation of NP with respect to the grammar which will be just with this definition here minus the number density of the primary species divided by this interaction length so to speak for what regards the secondary component it's density we'll have a term which is specular to that plus the fact that I'm assuming that this secondary component is generated in the break up of the primary component where once it interacts with some given material in the stellar medium so you have primary that interacts with some stuff and with generates the secondary some other stuff we are not tracking so there's some probability probability of p going into s which is just the partial cross-section for p plus stuff into s plus stuff divided by the total interaction cross-section for the primary component so I have a replenishing here of the secondary component which is p of p into s times the number density of the primary species p divided by the interaction length of p so you see I have two very simple equations which are hiding a complicated physics because I didn't tell you anything about what this path is I'm just tracking the conversion probabilities and to track the conversion probabilities is enough to track the grammar so the first question is you just solve it just np is equal to np initial times the exponential of minus x divided by p question one is in this form in which this is some kind of source function which of course depends on the grammar so the solution of this equation here is just in a form in which integrate between 0 and x in a variable x prime the source function weighted over the exponential of x prime divided by lambda s minus x divided by lambda s ok this into this this is the solution and by the way I know what what q is so I can just substitute and integrate so I have this part which does not depend on the integration variable exponential of minus x divided by lambda s and then here I have an exponential of x prime divided by lambda s minus x prime divided by lambda p so I can just integrate that that is an exponential of x prime divided by lambda p divided by 1 divided by lambda s minus 1 divided by lambda p ok this I have to integrate between x and 0 and then I just have to had up this of p into s divided by lambda p ok so then I what I do is just to substitute here and ok there is no need I write more on the blackboard what is that I have an expression of the ratio n s divided by n p which is in close form in the terms of x lambda s and lambda p and that is just ok p of p into s I have lambda s divided by p minus lambda s sorry lambda s minus lambda p and then I have an exponential of minus x divided by lambda s plus x divided by lambda p minus 1 so let me apply this formula to this picture here so I go out and take my nuclear particle physics book and there I learned that the scattering length for the CNO cycle the primary component is of the order of 6.7 grams per centimeter cube the interaction length for the secondary trio lithium beryllium boron is of the order of 10 grams per centimeter cube and the spalation probability for CNO to generate lithium beryllium boron is of the order of 35 percent then I take a real measurement of the ratio between these secondary to the primary component so that's a recent measurement by preliminary actually measurement from the AMS detector the one I was showing you earlier this morning which got the new result perfectly consistent with previous measurements and you see we are doing that game for an energy interval that corresponds to those values it's somewhere around 10 gv so I can take my ratio number of lithium beryllium boron number of carbon nitrogen, oxygen to be say 20 percent this is not very important so you see I didn't tell you how this propagation went but I quantified this ratio in terms of things that you can either measure the ratio itself or that your nuclear physics cookbook so from these numbers I can get out a value of the total grime edge that I have transverse converting primary into secondary so in numbers this comes out to be of the order 4.3 grams per centimeter cube ok so then what should I compare these two so I was sketching before that you have you have a galaxy which is shining in protons when the protons interact with the gas of the disk so the component which is doing this conversion of secondary to primary is the same component I was showing you in gamma rays localized on the disk it was the pi zero bump component localized in the disk so that is the gas disk and is something with numbers that I gave you before as a density in say mostly hydrogen which is of the order of 1 per centimeter cube it has a thickness that ok you are seeing it in the plot is is much thinner with respect to the extent of galactic halo so it has a night that is something like maybe 300 parsec or so so suppose you have that cosmic rays are traveling ballistically what would you have you would have that you have some cosmic ray primary component here and this cosmic ray primary component all is doing transfer once the thin disk of gas so I can compute the gramage from one crossing simply as what of course I raised the definition of gramage the gramage is the integral in the L of rho of L so in this case is just roughly the mass of hydrogen mass of a proton times this density of hydrogen times this thickness ok and you put in numbers and the numbers you find here is of the order of 10 to the minus 3 grams per centimeter cube so this number here is clearly inconsistent with this gramage I estimated from the conditional that I matched the abundance of secondary or primary so what is this particle doing is not transferring once the material but what is doing is probably moving on a trajectory that has very many multiple passing crossing of the gas so I can estimate what is the time that this primary component needs to propagate through the gas just by taking this to be the ratio between x which I calculated there from primary to secondary and the x that I sketched there for the one crossing case times so this is a propagation time these particles are moving with the speed of light so I have to plug in ratio that goes like this thickness divided by the speed of light so you do this computation and you find a number of 5 in 10 to the 6 years and in reality this is just the time that is spent on the fin disk in reality we think that the propagation region is really much thicker than the height of this fin disk so the global propagation time will be much larger and say order of magnitude larger and that's on average the time that the particle spends within this propagation box up to the stage where it gets to the border of the propagation box and then escape on a ballistic track so we have to find a way that discusses this grammar collection that is not on some ballistic path but is on some kind of brownian motion with an effective resilient time that is very long so what can you use to confine yourself on onto a region for a long time the trick what we think makes the propagation of cosmic rays in the galaxy diffusive is influence that ambient magnetic field have on cosmic rays so then the chapter I want to open is a chapter on in which I want to discuss a little bit about the propagation, the motion of charged particles in regular flash stochastic external magnetic field so the issue will be to see how charged particles behavior in this external environment I wrote externally in verticoma because what we really see in the end is that this system is closing up so the final picture and we are not there yet is that somehow you have acceleration of these high energy particles these acceleration of these high energy particles are creating a turbulence in the medium part of this turbulence is glued to magnetic fields and then the particles themselves resonate on these irregularities and end up on the Brownian motion that I discussed there so I there is no way I going to finish in 15 minutes this chapter but maybe I just started it and then keep going tomorrow ok, so let's start with the easy part and let's start with some ambient in which I put a large scale magnetic field b note that I'm not putting a large scale electric field because ok, we discussed all the time of highly ionized environments so whenever you create an electric gradient that's raised up by the very high conductivity that the medium has so no electric field just a large scale magnetic field and let me sketch what's going on for a particle with momentum gamma v in this magnetic field what happens if this is just a large scale say regular magnetic field so it's just some large scale b for instance, oriented in this direction what will happen is that I just have to apply Lorentz force dp over dt is equal to q then I should write the electric field but I just told you that the electric field is not phenomenologically relevant and then you have velocity orthogonal to b so if I am in this situation here what will happen is what I have some direction of my particle here what will happen is that this particle we just make an ellipse around the regular magnetic field line so for instance, if I just dab this magnetic field as something which has a zero component as a component in the z direction then the solution of this equation is just trivially the fact that in the z direction velocity is constant and in the x-y direction you have a zero frequency project the orthogonal to the direction like a cosine of omega t sine of omega t with this omega that is just a large more frequency charge of the particle be not divided by mc gamma ok so this is trivial so let's put this extra component here so on top of this regular component I plug in some perturbation and you see in the direction which is parallel to be that perturbation will not matter that much so let me assume that this perturbation is orthogonal to the regular magnetic field so perturbation is meaning that the modulus of this is much smaller than the so-called quasi linear regime so now I have this same formula here I have my b naught here and ok b over c cross b naught ok so this is the component which is acting in x, y direction and this is the component which is as I wrote it there acts on z direction ok let me make one further assumption which is the following as I told you before this is a game that is going to close up so actually these perturbations are something which is imprinted in the turbulence connected to sources themselves this perturbation will be connected to what are called of van waves these are turbulence waves which move in the solar medium and you can estimate I cannot prove it here but you can estimate that these have velocities that are of the order of the regular magnetic field component divided by a square root of the density of the ambient material over which this perturbation propagates so when I normalize these two typical values which is a magnetic field with a strength of the order of one micro Gauss and a density of Gauss which is of the order of one per centimeter cube which is what I was using before then the prefactor gets of the order of 2 in 10 to the 6 in units of centimeter per second so what you find is that these perturbations are sort of glued to the medium and they are propagating out with velocity that is much smaller than the speed of light so these are non relativistic and they are much smaller also with respect to the velocity of the cosmic rays pieces so we can go under this assumption to the static limit for these perturbations ok then what I have to do is I have these two kind of this is glued as regular field this is not really glued but slowly varying the solution of the Lorentz equation is easy and in particular I can just split p into p which is orthogonal to the magnetic field regular magnetic field and sorry p orthogonal to the magnetic field and p which is parallel to the magnetic field so for the parallel part the parallel part is the one that fills the perturbation and I just rewrite that equation projecting it out on the z component that leaves me modulus of the perpendicular velocity times and actually what I want to track is not really the quantity here but is the connected quantity which is the cosine of the angle between the direction of propagation p and the magnetic field line this is this cosine of this angle between p and b and this is the quantity which is called each angle in the cosmic ray jargon so I can now close the finger because the perpendicular motion I can just take it to be what I had in the Amperturbe case and that's just p divided by m gamma and the sine of this angle so 1 minus u squared so I get an equation in which I have why did I do this projection here, I forgot to say well I am in an environment in which I just have a magnetic field a magnetic field does not cannot accelerate a particle and then these modulus of the momentum p is constant so the equation I wrote here is an equation not for the modulus but for the pitch angle and in particular I will just have it in the form p mu t and then I have q over c is p perpendicular not that is p divided by m gamma square root of 1 minus mu squared and then I have just the x, y component that I am projecting out so I have cosine of omega t which multiplies the variation the small perturbation in the y direction minus the sign of omega t the variation in the x direction ok so that is the master equation for the so called pitch angle diffusion which is what we are going to solve tomorrow implementing what we know about the regular magnetic field which is hidden in this larmo frequency and providing a guess for what one has to assume for this stochastic perturbation perpendicular to the regular magnetic field so I think this is a good point to break