 Okay, hello everyone and welcome to our 33rd episode webinar of the series of the Latin American webinars on physics. My name is Alejandro de la Puente. I am currently a science and technology fellow at the National Science Foundation and I will be your host today. Our speaker today is Aaron Vincent. He's currently a fellow at the Imperial College in London. Before that, Aaron received his PhD in McGill University, went on to do a first postdoc at Valencia and then a second postdoc in Nuremberg College. We're happy to have Aaron here with us today and he'll present a talk on dark matter in the sun and after the webinar, after his talk is over, we'll open the floor for discussions among the panelists here that are present and also you can ask your questions to the Twitter with the hashtag law op and also through the question and answer system embedded in the Google Hangouts system. So with that, I leave the floor to Aaron and thank you Aaron for joining us and I hope you all enjoy today's talk. Alright, so thank you very much for the invitation to give the talk. Thank you so much for the nice introduction. Let me share my screen. So I think we still see your face that I have on the room. Okay, now you are, I've clicked, now I see yours and now I'm going to take that off. Okay, you should be good to go Aaron. Alright, if everyone can see my slides, that's great. So as Alejandro said, I will be talking about dark matter in the sun, more specifically some recent work, mainly with Pat Scott, who's a fellow here at Imperial College as well, as well as some work with Aldo Saganelli and a few other people more recently. So I'll just start with dark matter. So we have extraordinary gravitational evidence for dark matter. And in particular, so ranging from the sizes of galaxies, clusters of galaxies, large scale structure here in the middle, collisions of galaxy clusters, all the way up to the CMB, that's providing this near incontrovertible evidence that dark matter exists. It's about 85% of the matter in the universe. And it is composed of something like a fundamental particle. Now all the evidence so far has been gravitational, but we have a lot of hints that the relationship between dark matter and the standard model is more than gravitational. So there should be some connection at the particle physics level between the dark sector here on the left hand side and the standard model sector here on the right. So this is the main motivation behind what we're doing here. So let me just set up direct detection experiment, which relies on these standard model dark matter interactions at the particle level. So as we fly around the galaxy, the sun is moving about 220 kilometers per second with respect to the galactic halo of dark matter particles. Of course, the Earth is orbiting around them. And what one normally does is you take a set of nuclei, normally heavier particles, since they're more sensitive to the canonical heavier wimps that people have theorized over the years. You put that underground to get rid of any possible source of radiation, especially from cosmic rays, and then you wait until the dark matter from the halo smacks one of your nuclei and produces a signal from the recoil of that nucleus. So that can be ionization. It could be a phonon. It could be some kind of singulation, et cetera. So this is more sensitive to heavy particles, and it's more sensitive to fast particles. Since a faster particle from the Milky Way halo will give a faster recoil, or a larger energy recoil, that is easier to reconstruct from a ground-based experiment. Now I'm going to argue that the sun is also a direct detection experiment. It's flying around the center of the galaxy the same rate as the underground labs. And it has a much larger mass, so it's under the 30 kilograms. If you compare that to the paltry 370 kilograms of lux, you see that you have essentially a free, very, very, very large dark matter detector. Now it's 73% hydrogen, 25% helium, 2% heavy elements, but that can still be important since the dark matter nucleus or the coherent scattering of something with the nucleus cross section goes as the number of nucleons squared. So obviously you can't measure the recoil of a solar atom or a solar nucleus as the dark matter strikes it, but you can do something tricky, which is if a dark matter particle comes in, collides with the nucleus, say hydrogen or helium, or maybe something heavier. If the transfer of kinetic energy is such that the final kinetic energy of this dark matter particle is smaller than the local escape velocity from the sun, then that dark matter particle becomes gravitationally bound, and now it lives inside the sun. Now over four and a half billion years you have a very large exposure, which means that you can have a fairly large accumulation of dark matter particles inside the sun. There are, as I mentioned, several differences with respect to an earth-based direct detection experiment, and these mainly come out in the kinematics. So in the lab you're sensitive to these large recoils, large incoming velocities, since those give you a large signal inside a detector, whereas in the solar case you sort of want the opposite. You want a slower moving particle, or you're sensitive to lower momentum transfers than you would be in the lab, since these would give you these slowdowns of these guys that would eventually bind them to the gravitational potential of the sun. So in other words you're probing different kinematic ranges, either in terms of velocity or momentum transfer, which is what a cross-section in the end depends on. So you're more sensitive to lighter dark matter since you're scattering with a lighter nucleus and kinematic matching means that you scatter optimally with something that's about the same mass, and you're also sensitive to different kinds of couplings. So the population of dark matter in the sun is a very simple equation. The change in number of CHI particles in the sun, CHI being whatever my dark matter is, is proportional to the capture rate minus the annihilation rate if the dark matter self-annihilates as it accumulates in the center as it scatters down to its sort of ground state near the center of the sun, minus the evaporation rate. An evaporation just means that if a nucleus hits the dark matter particle and gives it kinetic energy that's large enough to escape the gravitational potential of the sun, obviously it will leave, and this is much easier for much, much lower masses just because a given transfer of kinetic energy gives you a much larger velocity if your target dark matter particle is much lighter. So this is just to illustrate that the capture rate, so the rate at which you scatter to a velocity lower than the escape velocity, the equation for this looks a lot like the rate for direct detection experiments if you're familiar with those. So there's an integral over the cross-section, the dark matter nucleus cross-section here, over the momentum, this integral, sorry, this is integral over recoil energies, this is here in the solar case, and there's an integral over the velocity distribution of the dark matter times the cross-section inside the Milky Way. So integral over the velocity distribution in the solar case since your velocity distribution is changing as the dark matter goes into the sun, you need to compensate for the acceleration due to gravity, but apart from that conceptually it's very, very similar. So if enough dark matter is then accumulated inside the sun, then at some point heat transport from these dark matter particles become important, so the same scattering mechanism that let that capture happen also leads to transfer of heat. So if you look at a nucleus or a photon inside the core of the sun, well the mean free path is very, very tiny, so heat transport generally happens on a very local level, but if you look at the dark matter since it's very weakly interacting, then it can travel a much longer distance. So its mean free path is much, much longer meaning that it can get a kick from a very, very hot nucleus in the center of the sun, travel outside to a colder region at a higher radius, and deposit that energy thereby conducting heat. So this is an idea that dates back to the first solar crisis that was eventually solved by solar neutrinos. So this is something that people have been thinking about since the 1980s. So what you need to do in order to efficiently transfer heat is you need to capture rate, you need an accumulation of dark matter particles that's much, much larger than the annihilation rates in the evaporation rate. So for evaporation that effectively means a certain threshold in the dark matter mass around a few GeV, although I'll come back to that at the end. And for the annihilation rate, well that means you could have some asymmetric dark matter particle, for example, or an asymmetry between the capture of dark matter and anti dark matter particles. So in this case, conduction will change the temperature profile inside the sun, which also reflects the other state variables of the sun. So the pressure is a function of the radius, the density, the sound speed, the convective zone radius, etc. So then how do I actually measure these minute effects? Because I can only capture one part in 10 to the 10 at most of the solar mass in dark matter. This is the absolute maximum just based on the local density of dark matter. So the obvious probes of the sun, the things that you don't want to mess up are the mass of course, the age of the sun to produce the kind of star that we see, the radius at the end, the luminosity, these are extremely well measured. And if you're a solar model in which you've incorporated this extra dark matter, doesn't reproduce these, then you've obviously messed up. A little less obvious, but measurable, are the neutrinos. So the PP neutrinos, these are the lowest energy neutrinos from the basic fusion process, that's constrained by the overall luminosity of the sun. So the number of fusion events is directly related to the luminosity that we observe in photons at the end. But there are other byproducts of the PP chain that are very, very sensitive to the temperature. For example, the boronate and neutrino flux goes as something like temperature of the core to the power of 25. So a very, very tiny change in the temperature of the core means that you can actually get an order one change in the flux of these neutrinos that are measured at Earth. These are measured to within a few percent, although the theory error on those, because of this giant exponent, is still order maybe tens of percent. And finally, heliosysmology is a very, very accurate probe of the structure of the sun. So what you do is you look at the oscillation modes on the surface of the sun, and you invert those, doing a sort of a spherical Fourier transform to give you the properties, so the pressure and the density and the sound speed of the sun, of the solar interior as a function of the radius. And the different modes that you see at the surface of the sun probe effectively different depths. So all of these go into a solar model. So to actually get these observables out, you need to model things properly. So what you do is you input a chemical composition, a mass, of course, the size of your star that you want to produce, the age at which you want to stop the evolution, and obviously the physics of the star. You pop that into a solar model, you evolve your star from zero age to today, and you get all these different outputs. Now, the input I want to talk about more closely is the chemical composition. So the way this is measured, so this is an input, you need to measure the chemical composition of the sun before you can simulate it to see if your model is behaving correctly, is from, so the propagation of photons from the solar interior from the surface in which the optical depth is no longer infinite to, or sorry, no longer zero, through the photosphere where these photons interact with the various elements, produce absorption and emission lines, and then onward to the Earth where they're observed. So the formation of these lines crucially depends on the structure, the three-dimensional structure of the photosphere, as well as its chemical composition. So the elemental abundance that you infer from looking at the sun depends very sensitively on how you're modeling the surface of the sun. Now, around 2004, people upgraded from basic one-dimensional models to some more complete 3D models of the photosphere with a better understanding of how all of these lines are formed. And what happened was the elemental abundances that we used to think were correct were actually revised downward by about 10%, as much as 30% for some elements. And the impact of this was that if you lower the metallicity, this would say that the abundance of these elements with respect to hydrogen, if you lower the overall metallicity, you're changing the mean molecular weight and you're changing the entire equation of state. You're changing the way in which the solar structure behaves. So the upshot of this is that when you plot the sound speed as a function of radius, this is the plot on the right-hand side here, you find that, and then when you compare that to those heliostereosmological observations I was talking about, you find that while the old abundances inferred using sort of the crude model of the photosphere gave a pretty good description of the sound speed. So that's the blue line here. The revised abundances, which actually appear to be correct, give a very, very discrepant description of the sound speed. This is the residual I'm plotting here. More importantly, if you look at the precision heliostereosmological observables that give you a probe of the core, so these are observables constructed with the frequency of oscillations that are meant to eliminate systematic errors and to really probe the core, you get a massive discrepancy between the observations, which are the points here, and the predictions of the standard solar model, which is in red. Now, if you look at the residuals at the very bottom, you can see that we're not close at all. So in some sense, you could say if you make a fit, the standard solar model is excluded at about 6 sigma, which sounds insane. So then if I go back to dark matter, then there are two motivations, really. One is, well, discovering the properties of dark matter. And the second one, which also will let me motivate or let motivate me, but with an eye on the first, is addressing this solar composition problem. Because it was noticed quite early that if you lower the opacity in the inner layers of the sun, this can alleviate the problem. So you're smoothing the density gradient. You're smoothing the temperature gradient in the sun from the core towards the outer layers. And the change in opacity looks a lot like more heat conduction. So let's look a bit closer at heat transport by dark matter in the sun. So there are two regimes. If I imagine my interactions are very, very weak. So I have a super weakly interacting particle. Then, well, I have a very long mean free path, but it's very difficult to actually deposit any energy anywhere. So I have a very weakly conducting particle. Now, so I tune that cross-section up, and I make the dark matter very strongly interacting. Well, then it's stuck, essentially. So it can deposit a lot of energy, but it's not going very far with it. So it turns out there is a very nice little Goldilocks zone in between this non-local, so-called Knudsen regime and the local thermal equilibrium regime in which my dark matter is stuck. And if I plot the transported energy as a function of the cross-section, then there's this peak here, this Knudsen peak, in which the energy transport is both efficient and long range. So the next thing to do is to sort of calculate this. The isothermal case, this non-local transport case, is actually fairly easy to calculate, since it's like you have a dark matter cloud that's in a gravitational potential that's in weakly interacting with a heat path. So it's sort of a very basic thermodynamic supply. And in the end, I get a luminosity that is proportional to the difference between the local stellar temperature and the overall dark matter temperature. On the other side, it's a little more difficult because we suddenly have a collisional system that is very difficult to disentangle from the stellar physics. Fortunately, Boltzmann, and specifically Golden Routhout, developed this formalism in 1990 to solve a Boltzmann equation in the limit where you have a weakly interacting particle that's very diffuse with respect to your background stellar gas. So when the collision term here on the right-hand side is equal to 0, that's just the thermal Maxwell-Boltzmann distribution. And when it's not equal to 0, that's when you get conduction. So Golden Routhout came out with a formal solution. This looks like a mess, but the only thing to notice is that you have a nice, calculable expression as a function that gives you the number density of dark matter as a function of the radius, so the fluffiness of the dark matter cloud, if you will, that's inside the core of the sun. And a luminosity, which is proportional to the temperature gradient. And then this actually only really depends on two parameters when it comes to actually calculating with respect to the dark matter itself. One is this alpha, which is a molecular transport coefficient that just tells you how fluffy your cloud of dark matter is as it accumulates in the sun. And the second guy is kappa, and this is a thermal conductivity. So for each collision, how efficient is the heat transfer, really? And these only depend on one single parameter, which is called mu, which is the mass of the dark matter with respect to the mass of the nucleus. And the average nuclear mass, of course, is a local thing. So you can extend these guys for a mixture of different nuclei as you get in the sun in a fairly straightforward way. So if you crank the little machine and go through the calculation, then when the smoke clears, you get this sort of behavior. So for an increasing molecular, so for an increasing dark matter mass divided by the nuclear mass, you wind up with a fluffier dark matter cloud as a function of mu. And on the conduction side, for larger masses, you get a larger conduction rate. So these are dimensionless coefficients here. So if you look here, alpha is just the term that's fighting the gravitational potential. And if you look at the luminosity, well, the entire luminosity is proportional to this conduction coefficient kappa. So there's a very intuitive way to do that. So then to put together your weekly and strongly interacting regimes, you sort of interpolate between the two. This is based on numerical studies from the 90s. In order to get the full conduction as a function of the mean-free path. So then you can plot the efficiency of conduction, that's the color scale, versus the mass and the cross section. And you can see right away that you're sort of in trouble. So the optimal region is quite large with respect to what's allowed by direct detection experiments. And the masses are quite low. So you can start to worry about evaporation. You can start to worry about your particles just flying out. Nonetheless, if you stick this into simulations, you can alleviate the solar composition problem. In fact, you can get a very, very nice, nicely behaved solar model with the exception of what's going around the core. You get these very, very big spikes. So something's not quite right in the core. This is a bit weird, but here we go. So the extension of this result led us to, logically, was to look at cross sections that were not the simple billiard ball cross sections, spin-independent or spin-dependent, that people always look at. Rather, if you generically compute a cross section in some particle physics process, you get some function of the center of mass, energy, and some function and also of the transferred momentum, which, in the non-relativistic case, which we're looking at, just turns into a function of the relative velocity or the transferred momentum, the non-relativistic transferred momentum. So for concreteness, we just looked at two different parameterizations. The first being the relative velocity to some power of n times some normalization cross section. And the second being the transferred momentum to some power n. We're looking at n to the minus 2, n squared, n to the 4. The reason we have to pick some specific functional forms of the cross section is that we want to put this into a solar simulation to actually get some numerical results at the end. So then you need to recompute the capture rate as well as the conduction coefficients. But that's sort of more sticking these guys into the sausage machine and doing that calculation carefully. So once again, when the smoke clears, you wind up with some interesting conclusions. So for v to the minus 2 or q to the minus 2 proportional cross sections, you wind up with sort of a fluffier core. This alpha coefficient becomes larger. And conversely, for positive powers of v and q, you wind up with a suppression of the efficiency of conduction, especially at low dark matter masses. Conduction coefficient sort of goes the other way. So you get a more efficient conduction of heat for these negative powers. And you get a less efficient conduction of heat per per collision, on average per collision, for positive powers of v and q. So to actually test this numerically, what we did is combine this dark stars code, which is a sort of WIMP dark matter capture annihilation heat transport code that was developed a few years ago for constant cross-section dark matter with Garstek, which is a very high precision solar simulation code that's been used extensively by the solar physics community, into a monster called Darkstek, which combines all of the advantages of both of these and tries to minimize the drawbacks, except for execution time, which I won't talk about too much. But nonetheless, so you get some modifications in the capture rate as you include these non-standard q squared or q to the minus 2 v squared v to the minus 2 v to the 4 cross-sections. And you also get, more interestingly, a modification of the location of this peak in the efficiency of conduction for the different dark matter models. So this looks like a mess, but I think the takeaway from these plots is that the peak of efficiency is a function of cross-section and also as a function of mass moves around quite a lot. So several CPU years later, here are some of the results. So if I look at the sound speed, this is the residual sound speed with respect to observation. The standard solar model is this spiky guy out here. And once I start to add different dark matter different types of interactions, well, I can move around and load this to the extent where it can be very, very good. So the modeling error is this blue thing and the heliocysmological error or observational error is this green thing and the sound speed. So the sound speeds look, well, better. But then if I look at what's happening in the core, I realize that I can do much, much, much better than the standard solar model. So the standard solar model was up here very, very far away from anything to do with reality. Now once I've added dark matter, I can actually get inside the one sigma band. So I can get a dark matter model that is actually reproducing what's going on in the core of the sun, which is quite extraordinary. So you can get amazing improvements, but there are other constraints. I should say we're suppressing the production of neutrinos, but these are still within error. So this is still within error of the observed neutrino production rates. So I can look at direct detection experiments at very low masses. There have been a couple. And you see right away that for spin independent cross sections, the region of interest, the thing that solves the solar abundance problem, is very, very far, is quite excluded by these direct detection experiments. You can do the same exercise for spin dependent cross sections, though. And then you are doing much better because the region of interest is now not so tightly constrained by these experiments. And then if I look at the cross section versus mass, I see that there are still regions. It's starting to be quite tight, but there are still some regions in which direct detection experiments do not exclude some of these fits that give these amazing improvements to the standard solar model. So if you look at the standard solar model, it's order 280 up here, and these fits are down at 100. So even though they're not amazing fits for about 30 degrees of freedom, there's still a delta chi squared of order 100. So I've highlighted here, this is the same table as before, but just highlighting the models that are allowed by direct detection experiments. So the p squared of the solar standard model is around 10 of the minus 12. And even though it's not this p value of order 1 that we had for the model that's now excluded by direct detection experiments, we're still doing amazingly better than the standard solar model. So since I only have 10 slides left, but I have minus 2 minutes, I'll go fairly quickly over the rest of this. But feel free to ask me questions a little later. Just very quickly, what could these models be? Well, for this v squared thing, so these are the best fit models to evade the direct detection constraints, I know I can produce a v squared cross section with a simplified model that looks a little like this with a vector mediator. But this also leads to another term, which we would have seen. Q to the minus 2, well, something like a long range force, long range mediator, could produce this sort of model. And well, v squared, if you have any ideas, please let me know because I'm very confused by what this could be. So on the long range force side, this has been studied quite a while. So we actually, so this was some work by a master's student, Ben Gittenby, who's now a PhD student, who looked at dipole and anapole interactions between dark matter and nuclei. So he looked at these actual more realistic realizations of these dark matter models. You recompute these alpha and capicoe coefficients, and once again, you can get very, very good fits, likewise with the small frequencies. Unfortunately, these are for cross sections for values of the electric and magnetic dipole moments that are disfavored by direct detection experiments. Nonetheless, you see there's a very good improvement in the center with respect to the constant cases. Now finally, in my remaining minus four minutes, I'll say a little bit about evaporation because this is something that I've been working on mainly with Giorgio Buzoni, Andrea de Simone in Pat Scott, who's here. So as I mentioned, if the dark matter is very light and gets kicked in the center, it requires enough velocity to overcome the local escape velocity, you'll deplete the number of dark matter particles in the sun very quickly. So this has been done by Golden 1990 for the constant cross-section case. And the lower the thing that people repeat at conferences and cocktail parties is that anything below a massive 4GV will evaporate and will have zero effect in the sun. And this is not quite true. What actually happens is something like this. So as a function of the mass and the cross-section, as you go to larger cross-section, the sun becomes optically thick in the same way as before. And the evaporation will become suppressed. As your interactions get weaker on the other hand, the evaporation, again, is suppressed just because you get so few of these different kicks. And this will, of course, depend on the form of the cross-section. What's very nice to notice is that this behavior is very similar to the conduction behavior, even though the formalism to actually produce this is completely different. So as a function of radius, you have an optically thin part of the sun that's closer to the surface. And as you go towards the core, you'll have a more optically thick. So even if you do get that kick from the center of the core, if you're above a certain cross-section, then it doesn't really matter, because you will scatter with someone else on the way out of the sun. It looks very different for the different models. This is quite interesting. But the upshot at the end of the day is this. So the little dotted, so these are the same plots as I showed you before, some of the same plots I showed you before, but then the dotted lines, things to the left of these dotted black lines are excluded by evaporation. So you can see it's not just a cut-off for a GV now. It's actually something that's more complicated than that. And the other thing to realize is that in this region here, so here we've overshot, the dark matter has produced too much of an effect. So it could be that by adding evaporation, these weren't added in the simulation. This is just overlaid on the simulation plot. We can suppress the amount of dark matter, but still get the benefits of conduction. So this is something that we want to, that we'll be pursuing in the near future. So I finally reached the end. So to summarize, so can we solve the solar composition problem, which has been a problem for over a decade, which solar physicists have been trying to alleviate for over a decade. Can we solve it with asymmetric dark matter, with the accumulation and conduction of dark matter and the sun? Well, we can make it better, but constraints are starting to squeeze it. There's still some unanswered questions of what happens when you add evaporation in properly. And the other question is, well, are these ad hoc parametrizations that we're using realistic? So we could upgrade and go to a more quantum mechanical effective operator approach in which the nuclear response functions are also considered correctly. And this doesn't make a difference for most models, but for a few, you do get some drastic changes. This is something I haven't mentioned, but it's quite interesting. And then if you really don't believe in dark matter, there's still something going on, since we're still observing a very, very nice improvement here. And finally, we can also apply this to other stars and look at say regions where there's a lot of dark matter. Maybe we can do something with asterisisomology or with some future observations of stars in dark matter environments to actually constrain or detect the presence of dark matter there. So I'll stop there. Thank you very much. Thank you, Aaron, for such a wonderful talk. Now I would, you finished right on time. Perfect, thank you. Now I would like to open the floor for questions. I'm gonna get some questions for the audience here, present life in this webinar. And then we'll open up for questions through the question and answer mechanism in Google Hangouts and then some of those submitted through Twitter. So with that, let me hear some of the questions that you guys have for Aaron. I'm gonna start with one from the audience here that's been watching life. So one of the questions by Roberto, it's what about the interaction with leptons? It's in the case where you have leptophilic dark matter. So that's kind of interesting. So if it was a year ago, I would have said, there's no chance, right? So if you, your dark matter comes in next into a nucleus, you have a chance of slowing down that dark matter, right? And capturing it in the gravitational potential of the sun. If your dark matter comes in, hits an electron, chances are the electron will bounce off, the dark matter will keep going, right? The momentum transfer will just not be enough. So that means that you need to reduce the mass of the dark matter enough to be able to efficiently scatter. Now that in turn means that you're capturing, 500 KV scale dark matter, which means you are going to evaporate very, very quickly. And so maybe you could figure out a way to capture and suppress the evaporation rate quite well. It's not something I've thought about too carefully, but it would be a possible little. But I think that's the thing that would kill you if something kills you is the evaporation rate from such a light dark matter particle. Okay. I have a quick question. One of your conclusions, when you say what if the dark matter scenario is ruled out, but then you say afterwards, we still see any improvement anyway. So can you rule out dark matter and what do you mean with that? Just rule out dark matter over a whole wide range of masses or I didn't understand that bullet. Oh, all I meant is that in these simulations, we are adding dark matter. And this is giving heat conduction in a very, very specific way that say changing the opacities doesn't. Okay. And the dark matter seems to give a very, very good fit to the solar observations whereas changing the opacities in some ad hoc way doesn't really do that. So if there's something mathematically going on, that could be interesting. I don't know. Can I have a quick for Marco? Yeah. Can you hear me? Yeah. So some questions about the formalism. So basically the formalism comes from Raffelt and collaborated, right? So they were considering a cross section which is basically constant as a function of the radius. Instead, the fact that you introduce a moment to a velocity dependence means the cross section changes around there for different radius, basically, right? So is that capture just changing this parameter's alpha and K or there is something more? Which is because there are a second related question is that as you explained, there are two regimes. One is where solution is analytic and the other one were not. And basically interpolate between these two regimes. Right. So I suppose that interpolation comes from this formalism developed by Raffelt and Gould. So again, this was for a constant cross section. Is that changing in your case or do you expect something different? So there are two questions there and the answer to those two questions are different. When it comes to just the local thermal equilibrium calculations, here we go. So the change in the Gould and Raffelt formalism, this is a change in alpha and kappa, right? And the cross section comes in, the velocity or the momentum difference comes in here, right? Where you have the collision operator. The collision operator is proportional to the cross section. And when you do this averaging over F naught, which is the thermal distributions, that's when you see the interaction between the velocity and the actual kinematics is going on inside the sun. So I think that is very, very solid. Now, that's the LTE, local thermal equilibrium conduction rates. Now, when it comes to that matching between the Knudsen, the non-local, and the LTE formalism, what they did I think was very generic. It was just a statement as a function of the mean free path and the thrones and particles and I see what happens. But this is something that I've been meaning to do for quite a while is to see how generic that actually is, that matching is. And obviously this was done in 1990 and it would be good to have some understanding of the Knudsen transition that's based on more modern computation than a simulation on a desktop computer in the 1990s. So you expect some little change for different interactions, let's say? I think there would be. The only way to do it is actually to do the simulation. I think it's important. It's important to actually go and look at that, yeah. Thank you. We have another question from Roberto and he's asking what you can elaborate more about this effect in other stars. So it would be effectively, I mean, it's effectively the same thing overall. So the problem is obviously other stars are far away, so it's much more difficult to get any kind of heterosystemological observables from them just because they're so far away. Nonetheless, we're starting to be able to do astroesysmology, so heliosysmology on other stars, in particular, so there was a nice series of papers by Jaldi Casaneos, I think, Elidio Lopez, where they're looking at suppression of convective cores. So if you have a convective core in a star, that's because you have quite a large temperature gradient and then you change the temperature gradient near the center. So is to erase the transition between hydrostatic, so as to basically erase the convective core, then the oscillations that you see on the surface of the star will be completely different because you don't have a boundary. It's telling you the star has a convective core. So you can erase those guys actually by dark matter conduction. Now the challenge is finding a star that we can observe this effect more sensitively than what's going on in the sun and maybe if we can get closer to the galactic center, we could start to grow larger dark matter populations so we'd have a better chance of actually seeing this in other stars. And I think Sergio has a question also, he's part of the panel as well. Yeah, I have, hi, can you hear me? Yeah. So I have a couple of questions. So in all this, you are assuming you need a symmetric dark matter, right? Ideally, yeah. So how much do you come free on that? So another way, how big could be the annihilation cross-section for this steel to work? So we haven't looked at that directly. You need to suppress it enough that you, I mean, you don't want to lose an auto infraction of your population. So like a thermal cross-section is definitely ruled out for this. Thermal cross-section definitely doesn't work. Okay. And okay, so you mentioned that in the code that you are using is a full evolution star code, right? Yeah. And but usually the computations in this business are done with a fixed picture. So how is the evolution, how much the evolution matters? How much does it matter for the computation? Sorry, what do you mean? I mean, in the sand, so you take into account the evolution of the sandstorm from the beginning to now. So the composition changes. So how much does that matter when you compute the capture rates and all of that? That the fact that you have different composition of hydrogen, helium, or different elements along the history of the sun. Well, I mean, in the early stages, your radius is going to be changing. So you'll... Yeah, everything. I mean, how much the evolution matters in the computation? That's not something I've looked at very closely, actually. It would be worth looking at since there's potentially a big time saver. Yeah. Certainly you see models that just fail to age. Well, it's also a matter of a scale, right? So what is the accumulation time if the prison composition is long enough or not compared to the calibration time and all that? So I don't know. I don't have an idea of how much evolution matters. Well, yeah. Well, the thing is here, you're not reaching an equilibrium in the sense of the dark matter because you're constantly accumulating dark matters. Yeah. In this case, yes. The effect of the conduction increases with time. It would be a slightly different rate of increasing, right? Exactly, yeah, yeah. So if you just artificially popped in some dark matter at the end, I don't think you would get the same kind of result. And one further question. In these plots that you were showing, I think it was the speed of sound as a function of metallicity, I think. As a function of the radius? Yeah, as a function of the radius. So what is, is there anything special about 0.6, 0.7? Well, 0.7 is the convective zone. So the peak has to do with that. So the peak is right below the transition, right? So the, above the, inside the convective zone, so this is the mixed portion. And this peak is right below. So this is the temperature gradient. That's what's going on right below the convective zone. So is that because the gradient is higher and it's very sensitive to a little change which moves that peak? Yeah, the little, yeah. So if you have tiny, tiny changes in the gradient here, you're moving the radius of the convective zone by an observable amount. So then the entire structure will shift sort of to accommodate that. That being said, if we understood this peak here, we would be very, very far on the way to actually solving this all. It's like all these models just shift a little bit or reduce the overall normalization but the shape is pretty much the same no matter what the model you use. Certainly there's some systematic thing that we don't understand with this peak here. Yeah, I agree. Okay. And yes, one further comment. Someone asked at the beginning about leptophilic. Leptophilic, if I might add just a comment on that. No, please. There was a work some years ago where they, I mean it was just barely touching on that and definitely the capture rate is lower but an earlier magnitude in general. So but in principle you could indeed capture with electrons. And yeah, actually I'm working on that and in a matter of, soon I will have results. Have you looked at conduction? Not yet. That could be interesting. Now we have only worked on the capture a bit more in detail of what they did but actually it works. It works. Is less efficient than nucleons? But it's still, it is efficient enough. No need. No. Okay, so thank you Adam for the answers. Thanks Oju. So Aaron, I have a question or maybe, I don't know if it is, but maybe other people in the panel can correct me if it is wrong. I guess when you are asking for a process that is Q out of four, maybe that is related by circuit scatters, no? With two gamma five in the, I'm not sure because this circuit scatter is like quite that matter and those are very suppressed that you cannot look it in. I think I forgot to mention on this specific page. I need a spin dependent interaction. So the scalar would give you a spin independent scattering rate. No, so the scalar. I know, yeah, true, true, true. Yeah, yeah, all is gonna give you. No, in principle you can have a spin dependent but it's through loops. So, but this means that your dependence in momentum is gonna be, you know, gonna be something fixed like Q to the four or something like that. It's too precious. Suspect the dominant process is still going to be spin independent. That's all. And then as soon as you have that process dominating you're producing, you're ruled out by direct detection. Yeah, so I just used a very transfer sort of question with respect to the one of the questions from Sergio that he was talking about. Oh, you mentioned that if you put your son and suddenly you put a lot of that matter the output is gonna be not the same that you obtained. So I was wondering what happened with the presence of clumps or other type of over densities in which the sun could at some point pass through. I mean, if you start to enter, maybe not the sun because it doesn't have a sound. Well, I mean, it depends when, if I trade my constant accumulation of dark matter through four billion years with a bunch of spikes over four billion years it's probably about the same. If I have one spike at the very end, it's, you know. Maybe it's gonna be more sensitive but then also you need to capture. Yeah, I don't have a very good intuition to what would happen at what stage of the solar revolution. Okay, thanks. I'm very nice talk, by the way. I don't know if someone else has questions. Yeah, there's no more questions in the Google question and answer session but is there any questions in Twitter? No. Anyway, if there isn't any more questions I wanna thank Aaron for participating in the Latin American webinars in physics. We can then tell you how many people view this life and obviously this will be online for eternity. So you can always go and check from a month from today and you can see how many people have watched and eventually you'll get a thousand and then hopefully you'll get a million one day. I know I always check mine. Anyway, so thanks for joining us today and I'm going to now say goodbye and then look forward to the next webinar in the near future. Thank you so much. Yeah, thank you very much.