 155, correct. Good morning and good afternoon everyone. Welcome to our Latin American webinar of physics, number 155. My name is Walter Tangarife. I work at Loyola Chicago. I need my pleasure today to host Dr. Rebecca Lin, who is going to give a very exciting seminar about detecting dark matter inside our planet. Dr. Rebecca Lin finished in 2017, her PhD at University of Melbourne in Australia. And then moved to Cambridge, where she was a post-doc at the MIT Center for Theoretical Physics until 2020, when she moved for a year as a post-doc to Slack in Stanford. And then in 2021, she joined Stanford officially as a staff scientist. And she's been there ever since. Today, she will give us a seminar on detecting the dark matter that our planet can capture. And I encourage you, everyone, to ask your questions on the YouTube channel. And we will be happy to answer it, to ask these questions to Rebecca at the end of her talk. And also remember to subscribe to our channel, to social media in Facebook, YouTube, and Twitter, or X. And so people keep posted on the upcoming seminars. So without further ado, it's a pleasure to introduce Rebecca. Thank you, and you can take it away. Great, thanks very much for the introduction. And thanks a lot for having me here today, part of your seminar series. It's really a pleasure to be here. Now I'll just share my slides. All right, you can see that all just fine? Yeah, great. OK, so today, I'm going to tell you all about how we can detect dark matter that might be seeing already inside the Earth. So this talk today will be based on a couple of papers. The first one is based on work with Yuri Spurnoff, who's at Liverpool. And the second part of the talk, we based on work with Anna Wormdass and Noah Karinsky, who are both at Salk. All right, so just to set the stage of why I care about what I'm going to tell you about today and kind of what the angle of my research is coming at this problem is, overall, we know that dark matter makes up most of the matter of the universe, but we have really almost no idea about what its fundamental nature is. So the overarching goal of my research is to find what dark matter is and really to think about what are the new ways we can try to find out what sort of new ways haven't we thought of before. And usually, I'm thinking about what new searches we can do with astrophysical systems. And I think astrophysical systems are particularly interesting, or at least, in my opinion, a lot of fun, because they're very diverse, so they're all very different. And we really have a lot of different astrophysical systems. So some are very big, some are very dense. And overall, this allows us to probe timescales that are much longer than anything we could do on Earth. We can probe much higher energies. We can really do a lot with them. The other part of what I usually think about is how when we have these new searches, we can actually execute them. So often, this involves using astrophysical data sets to try and discover new particles. And this is particularly because really the wealth of different astrophysical data sets that we're going to have in the next few years really have quite a lot. But particularly in the talk today, I'm going to focus on a little bit closer to home, which is how this can kind of come together with searches we can do on Earth. So as an outlet for the talk today, I'll start first with discussing how dark matter can be captured in different celestial objects, including our own Earth, which is how this works, what sort of signatures might we expect. Then I'll tell you about how we can derive how dark matter sits once it's actually inside these objects. So what are the distributions of like, how does dark matter distribute itself once it's captured? Then for the second part of the talk, I'll focus on the implications for some searches that we already have. But in particular, I want to highlight a new search strategy that we can use with quantum devices on Earth to detect this dark matter that's built inside the Earth. Okay. So the general picture of how dark matter is captured in any star or planet, including our own Earth, is that we have stars and planets peppered throughout the galactic halo. And assuming dark matter interacts with the standard model particles, dark matter can come into contact with the star or planet. It can scatter, it can lose energy, and it can come gravitationally captured. And over time, more and more dark matter particles can build up inside stars and planets. And if dark matter is the type of dark matter that annihilates, what can happen is once you start building up this population, the particles can really build up in quite a dense region and find each other and start annihilating. So as this dark matter annihilates, the thing that happens next depends on the particle physics scenario you're considering. But under the assumption that dark matter annihilates quite promptly, so it annihilates to either a short-lived mediator, a one that's not produced with a very large boost, the decay products or the annihilation products are produced inside the star or the planet. So this is the assumption that this is the decay length, so that the boost is the gamma, see your speed of light, tower is the lifetime. So the decay length of this mediator that you produce is less than the radius of the object. The products are produced on the inside. And in that case, things like neutrinos can get out because they're quite weakly interacting. Or what can happen is these products can be absorbed by the star or the planet and this temperature can increase. And this is something we can see potentially in infrared, but it depends on the star or the planet that you're considering. Another scenario is if you annihilate to a particle that's more long-lived or produced with a large boost, so again, the boost, speed of light, times the lifetime of the mediator is larger than the radius of the object, the annihilation products can get out. And if they can get out, we can detect them. So you can make, for example, gamma rays and we can look for these gamma ray telescopes. So these are just a few examples of the classes of signatures that you can have, the dark matter in stars or planets. But really the range of observables that we do have is much broader than this. And it really is quite broad. So for annihilating dark matter, we can have this heating or neutrino production for short-lived mediators, gamma rays for long-lived mediators as I just discussed. But there are other cases too, so dark matter doesn't have to annihilate. If dark matter doesn't annihilate, you can build up even more particles inside stars and planets. So some examples of the signatures you have in that case is you can have the creation of a black hole from over accumulation. So just you make too much and you have so much dark matter that actually the whole thing then just collapses and then you destroy stars and planets. And we know they exist, so usually it just gives you a constraint. You can have other things like changes in the heat flow from just changing the distribution of dark matter inside stars, usually is what people have thought about in that context. And we can also change how stars evolve. So if you just put stars in a very dark matter dense environment, they evolve in a different way, which is kind of neat. The point overall that I wanna make is that these are highly detectable effects. So this isn't just like here's some hypothetical class of signatures that we're never gonna see them. We can see these and we have seen, well, we've at least done the searches for these for a number of these already. So they're highly detectable, we can find them. But what actually drives these signatures often are the dark matter distributions once it's inside. So if you get a different answer for how dark matter sits inside a star or the planet, you're gonna get a different theoretical prediction for the dark matter signatures. So the distributions are important. And that's what I wanna talk about now. How do we actually calculate those? So there are two different regimes you can think about. You can think about having strong interactions. So when I say strong, I don't mean like QCD sort of strong. I just mean that you have the bulk of the dark matter caption is how we usually think about the strong, strong enough sort of interactions of the dark matter. And this case really you have a short mean free path. So this means that you just think about when dark matter scatters, how long does it actually take to fully thermalize? So just what is the average distance is traveling? So this will depend on, for the mean free path will depend on the number density, the standard model particles that it comes across and also the scattering cross section between dark matter and the standard model. So dark matter thermalizes pretty much immediately if you have a big enough cross section and it doesn't, you know, it has this short mean free path regime. And we call this being in local thermal equilibrium which is pretty much you have the temperature or the dark matter has the temperature of its surrounding standard model particles. The other regimes if you have weaker interactions usually if you wanna say it's weak would say that the mean free path is about the size of the object. So you're scattering once or less roughly as the dark matter passes through the object. And in this case you would have non-local thermalization which is as you scatter you'd pick up some temperature in one location by from scattering standard model particles. And you travel really far without interacting again because you have weak interactions pretty long mean free path and you'll go somewhere else where there's a different temperature. So you end up getting a totally different scaling with the temperature compared to this fairly strong interaction case. But you have approximately the temperature of the local particles. So the case that I'm gonna focus on is this relatively strongly interacting regime where you're in local thermal equilibrium. So there are these two different cases I'm just gonna zoom in on what happens for the dark matter distribution in this top case. Okay, so in this relatively strongly interacting regime what are the effects on the dark matter distribution? So the first one is the most obvious one and it's super easy to deal with it's just gravity. So I don't think I even have to define what's in this equation. We see this back in high school. So really just dark matter particles go inside the star of the planet. It's gonna feel the gravitation well and be drawn towards the core of the object. So that one's pretty easy. Not too hard to try and model what happens then. One that's a little bit more tricky is what the effect of the standard model temperature gradient is. So what I mean in that case is if you think about the star in the core it's quite hot and as you go towards the surface it cools. So we end up having a gradient, the temperature. Hotter in the center, cooler on the outside. So how does that affect how dark matter distributes itself under the presence of a temperature gradient of what happens? So it turns out this is a kind of non-trivial problem. This has been thought of actually a lot in the literature and I'll get to comparing with some other results shortly. But when trying to understand this problem we went back just to kinetic gas theory. So what happens when you put two gases together you can think about even in a box how they diffuse through each other if you have a temperature gradient. And there's actually a really nice example of this problem for just two generic gases. Well, not totally generic but two different gases in Lando and Lyft sheets. So Lando and Lyft sheets are probably already knows these are just absolutely classic textbooks. There's an excellent example of how to calculate this for a dilute gas in trying to diffuse through a background gas. And this is the problem we wanna think about in our case because the amount of dark matter that's in a star or planet is much lower than the amount of standard model. So even when it's accumulated a lot it's still pretty negligible compared to all the standard model matter that's in them. So the dilute gas is the dark matter and it's gonna just try and diffuse through a background gas. So how does this work? So we think about our temperature gradient and if we assume the dark matter is in roughly local semi-equilibrium that approximately has the same distribution as the background but not the same. So the reason for that is so we can write just like a sort of Maxwell distribution a nice sort of thermal distribution of the particles and along the temperature gradient we're gonna perturb the dark matter distribution. So you can think about it the dark matter sitting there it's thermalized it's still moving around has some thermal motion bumps into the standard model particles. And if it goes up just a little bit further you can hit a higher temperature and then it can eventually it's gonna diffuse back to its equilibrium position. On the lower end it can also kind of bump down get some cooler particles and be more on the cooler side. So really you just have a small perturbation along the temperature gradient away from being this nice sort of Maxwell distribution. So we have a Maxwell distribution plus some small perturbation in the direction of the temperature gradient. Now to try and figure out what the distribution is we can think about how these perturbations work. You can think about them in terms of a collision operator. So the dark matter particles come around they can hit the standard model particles. So this NSM, so this is the collision operator. The NSM is the standard model number density that we have from the star of the planet and it's gonna hit me have some velocity and we're gonna primatize it as the sum function. So just G for now is just some function G as a function of velocity and the position R. And same we also just the way we primatize it cos theta with the angle of the scattering and this sigma T here is what we call the transport cross section. So you can just think about it as you have your scattering with some cross section with some number of particles, some velocity and some function that will describe how this interaction works effectively. So you can also write this collision operator simply as being the time derivative of this function F. So this F here is just the dark matter distribution. So if we take the change in time with that and just take the total derivative, we get something that looks like this. So we're still taking with respect to the position R how this F is changing, this is the same cos theta and we have some velocity. So it's just two ways of trying to describe what's happening, have me write this in two different ways. So to solve how much this is changing what the distribution will look like, we wanna solve for what this function G is and once we get this function G, this is gonna tell us how much is changing along the gradient. So this is effectively just how much do we change the caring about this delta F. And once we have that, we wanna think about how much dark matter is passing through a given shell. So when I say shell, it's like an imaginary sort of like slice through the sphere of the object. And when you're in equilibrium, the amount of dark matter particles passing through any given shell should be zero. So dark matter particles can move in one direction, you're getting perturbed along with the temperature gradient, they can move back in another direction the other way. But we want just that the net through a given shell, the flux is zero and that will be equilibrium. We had net movement in one shell that wouldn't be equilibrium. So we try and just solve for what this G is, we'll get some flux going through a given shell from this. And then we just wanna set this flux to zero effectively. It's qualitatively doing. So there's a bunch of the calculation details in the middle. I'm not gonna show you a boy with all of them. But from just setting this flux through a given shell to zero, you get an expression that looks like this. So the N chi is the dark matter number density distribution. T is the standard model temperature, which is approximately the dark matter temperature as well. This mu here is the ratio of the dark matter mass to the standard model matter mass and the star. And if you can just solve this for N chi, this will give you the distribution. So we see that the scaling of the dark matter density with temperature looks something like this. So this N chi LTE, LTE is local thermal equilibrium. This is the strongly interacting regime. This is how the distribution will go once you just solve this top equation here. On the bottom, this is just a normalization constant. The core temperature is T zero. So again, just where to normalize it. And this shows you that the N chi, the dark matter number density distribution is always like the temperature of the standard model temperature, the celestial object to this power here. So this power might look kind of, why am I showing this to you? But you can get some physical intuition of what happens in this problem. So this mu, again, remember, this is the ratio of the dark matter mass to the standard model mass. So the interesting thing you actually see here, and this is true for any light dilute gas that's trying to diffuse through a background gas, is that the distribution you get off the gas is not the same as the background, even though you're in equilibrium. Some of these are surprising and this actually was somewhat surprising to us. We were trying to think physically, how do you understand why this is actually what happens when you put two gases together? But you can kind of understand this, thinking about some limiting cases. So first of all, the thermal velocity of the particles go like roughly the square root of the temperature divided by their mass. So you can think that if you have very light particles, they, for a fixed temperature, move pretty fast. So they have some thermal motion, something like this. And if you're putting lots of these particles that kind of move like this in a dense area, what can happen is they can get stuck actually longer than heavier particles would in the same sort of regions. So if you're heavier particle, your thermal motion is slower. And what actually ends up happening is that the light gas spends more time in regions where the temperature is high, relative to the heavy, if the particles were heavy. So it's not true that overall, all the gas is in a region where the temperature is high. They still prefer to move out of these high temperature regions. But it's kind of an interesting result that the scaling for the light dark matter is that it prefers compared to the background to be pushed more into, more time into the high temperature regions. So for the heavy particles, heavy dark matter particles, the density is just proportional to the inverse of the temperature. So that is pretty much the same as the background. But not for the light particles, they get put into a different distribution. Okay, so there I was telling you only about what happens when you have particles under a temperature gradient from just kinetic gas theory. But now we can consider both at once. And actually the temperature gradient by itself is much harder, putting them together is not so good. So really just to help kind of hammer in how this works, I'm gonna show you pretty much the same calculation which is an additional term. This additional term will correspond to gravity. So again, we start with some temperature gradient then we're gonna perturb the dark matter distribution along this temperature gradient. We write the collision operator just as before, but when we take the total derivative, so this D F D T, because we also will have some acceleration in there, the total derivative is gonna give you this extra term. So it is V, remember it's just like D R D T. So to change the position with time, and we can also then do the square. So D D squared R D T squared. So the second derivative of that and that will give you the acceleration. So this effectively then includes an external force before we didn't have one either. And then you just push through the calculation as before. We say there's some flux that can move through a given shell. We want the net amount of the flux to be zero if we're in equilibrium. So we just solve for what the function G is, we then find how much is moving through set to zero. We get a similar expression as before, but now we have this additional term, there's a force because it's allowed to have this, not the way we set up the problem with the total derivative having this acceleration term. And then if you just solve it, you get how the distribution looks for dark matter in a relatively arbitrary celestial object. So we can actually see physically a few terms here. So this first one is concentration diffusion. This middle one is thermal diffusion. So if we turned off the temperature gradient, we wouldn't have this kappa here. So this kappa is a thermal diffusion coefficient. So we wouldn't get this extra scaling that we see at all. And then we have just simply gravity. So we have this force here being M chi times G, G is gravitational acceleration. So we can see these are the main effects that we expect to impact dark matter in a star or planet. And this expression here, we found actually managed to reproduce golden refilled. So a calculation like this from a different sort of angle was done a long time ago back in 1990. So we could reproduce from first principles in kinetic gas theory, the same sort of result that they have. So that's how it looks in equilibrium. But the thing that we actually really want, we want to think about a detectable signatures is we want the present time dark matter distribution. So an equilibrium framework assumes dark matter ejection in the distant past, and there's been enough time for the dark matter particles to go into equilibrium. But the ones that have just entered in the surface coming from outer space and going into the surface of, for example, the earth won't be in equilibrium yet. So how do we include the fact that we have a continuous source injection of dark matter particles at the surface? So this is what we wanted to include. So we have some flux of dark matter particles coming in from space. And that looks something like this. So we have this, the velocity dispersion of dark matter in the halo is v chi. We have in the brackets here, a term that's gravitational focusing. So that goes like the escape velocity with the object divided by the dark matter halo dispersion squared. So you can see if you had a really high escape velocity, you get more of a boost from gravitational focusing. And of course we also care about how much dark matter there is. So root chi is just the amount of dark matter in the local region of the star on the planet. M chi is the dark matter mass, and f cap is the fraction of dark matter particles that are captured. So in here, we're kind of, we're including if dark matter capture is very efficient or not. So if everything's captured at f cap one, it's not, it's something less than one. So this is just generically how we can think about the flux of dark matter particles moving into the object. But also then once it's gone inside from flux conservation in a given shell, once it starts moving in, it's gonna go like through a given shell, number of dark matter particles times the diffusion velocity. So the dark matter that comes in, it's diffusing at some speed, so it goes through. And through a given shell, it will be the ratio of the radius of that little shell versus this capital R, which is the radius of the whole object. So you can imagine dark matter is moving through these little shells at a given time and roughly because you have, roughly as the dark matter is coming in, it's changing over time, but it's not changing a lot. So based on this, we can try and get the full dark matter distribution. So the diffusion velocity equation looks like this expression that I showed you before, but this time we don't wanna say the flux in a given shell was necessarily zero. So we still wanna keep this diffusion velocity on the outside. And based on that really from, but I was saying about a certain amount of flux coming in by, and then this approximate conservation through all shells, we get this new dark matter source term. So for the full dark matter distribution today, this is a first order differential equation that will give you how the distribution looks, including this source term for the constant ejection. Because it's a first order differential equation, we also need some more information to solve it. And that's actually that part's quite simple. So we can just enforce the total number of dark matter particles that's captured by the celestial object gives you, well, we can do the integral of the distribution and just check it's normalized to give you the right number of particles effectively. So we know how the capture works. We can just normalize it appropriately. So with that condition, this can fully solve and fully give you the distribution of dark matter in arbitrary celestial objects. And what we find to rule is that you can have what we called floating dark matter. So it's in some sort of quasi equilibrium where constantly there's some amount of dark matter particles coming in at the surface and there's an equilibrium distribution which is still the dominant distribution. But overall, you can have quite large abundances at the surface of stars and planets. So I'm gonna show you results for that in just a second of how we can some example objects. But just briefly, I wanted to mention some other distribution considerations. So first of all, we also have to think about evaporation of dark matter. And this is just the fact that when the dark matter particles come in, they get some thermal kick from interacting with the sand water particles. And if they get too much of a kick that they can overcome the gravitational barrier to get out, they will just leave. So as dark matter becomes lighter, it cares less or gravity is not pulling on it as much and it can get out more easily. So this is something we call likely evaporation mass and this will set the lower end of where our sensitivity will be because the distribution just won't be there if the particles are all left. But this really depends a lot on the particle physics model where you would cut off this evaporation process. So we actually discussed that in the paper early this year how this can really change a lot with your particle physics model. So for the purposes of the plots I'm about to show you, I'll just assume contact interactions because it's the simplest case, but you should check out this paper if you're curious about how this can be much lower than the cases I'm about to show you. The other thing that we consider is non-annihilating dark matter. So when dark matter goes into these distributions, if it annihilates too much, then you'll just deplete the large densities that are possible. But we did check in fact, actually for P-wave annihilation, you're okay. But if you have S-wave annihilation, you're gonna deplete more than the results that we show you. So probably the simplest way to think is that the results I show you are either P-wave annihilation, so suppressed annihilation or no annihilation really at all. The last thing I wanted to note is that diffusion is very fast. So the timescale where dark matter particles diffuse into the equilibrium position, for most the sort of parameter space we're considering is like order years. So very quick. That means that usually it will go into equilibrium and not be so worried about other effects that might perturb the distribution. All right. So now here's an example of how the distributions look. This is the sun at quite large cross sections. They don't have to be this large, it's just an example case. So on the y-axis, we have the number density of dark matter particles. And this is as a function of the radius. So one, this is the surface of the sun. So what you can see is that while at the core, there are really a lot of dark matter particles and it's where the bulk of them are. Still as you move towards the surface, you can see that the distribution is not negligible. It's still, it might be a little bit, a few orders of magnitude weaker than what you see at the core, but there's still a lot of it there. Just quite interesting. And notice how the lighter the dark matter particles are, the more kind of flat the distribution's going. And you can think about this as being really an interplay of gravity and thermal diffusion. As your lighter overall, you just end up kind of going more flat, which is nice. If you have lighter particles, you can get more at the surface, kind of broadly speaking. And what you see with these solid lines and dashed lines, the difference in our calculation where we include this source injection term of the surface, and then the classic calculation of golden refold from 1990, where it was only the equilibrium distribution. So you see particularly these dashed lines, I look like this two GV dark matter mass case. This case here, you see that as the dark matter particles are coming in, when it's heavier, it's kind of getting more blocked up at the surface. So the source injection term is more important in that case. And five GV, you see actually a really big difference. If you hadn't included the fact that dark matter kept getting injected at the surface, the answer you would get is actually quite drastically different, particularly how many still sit at the surface. And you also see it for this light dark matter case, it doesn't make as much of a difference. So the dashed and the solid are roughly on top of each other. Keep in mind though, the wax is just passive, but at least clearly the change isn't as big in that case. And you can think about that really just as the light dark matter particles are diffusing very quickly. So they pretty quickly getting into the equilibrium distribution, but also that when the particles are lighter, they less want to go into the core. So when the particles are heavy, the equilibrium distribution is always close to the core because gravity is just pulling them in because they're heavier. And the light case, that's less true. It's just part of why you see this difference in the scaling of mass. Okay. And here are some of the surface distributions look. So you can see really, but distribution can be very high. If you were thinking about something like a usual 0.4 GB per centimeter is cubed as the local dark matter abundance, it's actually much higher when you consider what the population is that's already in there. So this can potentially give you some really interesting different type of signals. The other interesting case is the Earth. We actually did a bunch of cases in the paper. You can check it out if you're interested, but only show you the Earth as the other case here. In this case, again, you see for lighter dark matter particles, you go more towards the surface. You're gonna go more flat. And as the dark matter mass becomes heavier, you more readily sink into the core as gravity pulls you in more. And then you also see this source injection term that comes even more important as you go heavier as the bigger discrepancy here. And here are how the densities can look in the Earth. So sitting right now at the surface of our Earth can be something that looks like this, assuming dark matter isn't massively annihilating. At the surface, we could have like above 10 to the 13 particles per centimeter cubed right now. So that's something like 40 or so magnitude larger than our usual 0.4 GB per centimeter cubed. One thing I also wanted to note is that this wasn't the first time people thought about the fact you could have some surface abundance of dark matter particles. You're actually a bunch of papers that thought about that. So here's a couple of examples here, but previously the papers just hadn't considered all these effects altogether. So you know, thermal diffusion, the source injection term all written that sort of sort of consistent way. We find in any case distributions can really be quite large, particularly on the Earth. So as soon as you see a plot like this, this is very intriguing. We're on Earth. Can we see this? So there's definitely implications there. So overall new signatures are possible. So dark matter annihilation products can maybe be detected for generic models. So what I mean by that is before I was talking about this dark matter annihilation closer to the core or maybe being boosted outside with some longer lived mediating particles, really this can move the boundary between the other heating search or directs, you know, a standalone product search like with gamma rays. Simply because well, if you think about where the dark matter is annihilating it really does have a full distribution. So we can kind of move the particles get out while they're being produced inside. But the one I wanted to focus on for the rest of the talk is direct detection. So what can we do there? What is large surface abundance on the Earth? Can we see it? That's pretty large, pretty large density. So this is part of work with Anna Vandas, Noah Kerinsky, that's Slack. And if you want to think about the implications, the first question is, well, can we just do this with direct detection already? Can we just take the experiments that we have and then just crank up the dark matter density and get some amazing results? Unfortunately, we can't do that. And the reason for this is that this population that sits inside the Earth is very different to what we can call the halo dark matter. So when I say halo dark matter, I'm gonna refer to that as meaning the incoming dark matter. So dark matter that's sitting out in a galactic halo and comes into the Earth. Now, the one that's usually coming in at us, the Earth, the halo, that velocity distribution peaks around 270 kilometers per second. So it's quite fast. But in this case of the thermal population inside the Earth, it's quite slow. So it's less than the escape velocity of the Earth, because it has to stay bound in the Earth, which is less than about 11 kilometers per second. That's for most of it to not leave. One of it's even more slowly moving than that. But what this means is that if you wanted to detect this using some sensor on Earth, you would need thresholds that are really low, like something like 0.05 EV. And this is so low that our regular direct detection experiments won't be able to help us. And this is way below the threshold of anything they can do. So they just wouldn't see it. It wouldn't show up. So in that sense, we wouldn't get to take advantage of the fact that this distribution has such a high number density, because it just wouldn't be detectable, which just wouldn't give you enough energy deposition to actually see it. So what that means is that we would need some new detector, something that we haven't thought about yet to detect dark matter. And very importantly, we need something that has a very low threshold. If it has the threshold, the regular direct detection can't use it. And really moving towards these lower thresholds, direct detection experiments has been a really key direction for field at the moment. So direct detection, it starts kind of getting weaker and weaker as we quite quickly, as we start trying to look at sub-GV dark matter particles. So there is a push overall in the field to understand what's happening in this sort of regime. And one thing that we point out that's actually helpful in this direction, not just for our thermalized population, just more broadly for direct detection techniques, is using these devices that we call a low-quasi-particle density devices. So what does that mean? Well, just from the title, I guess, we want low densities of quasi-particles. And I guess I'll explain how that fits in the dark matter in a second. But such devices actually have been investigated a lot recently because they have an important role in existing and emerging technologies. So for example, they're important for radiation detectors. You don't want large backgrounds of quasi-particles showing up in your detectors. Also, it's really important for quantum computing. So if we start having large backgrounds of quasi-particles, it's just gonna wreck what we're trying to do. So overall, people are trying to develop devices with these low backgrounds. And overall, their performance will be limited by quasi-particle excitations. This is what I mean by having problems at the background. Now this works is that if you're, particularly if you're superconducting, you have cooper pairs sitting everywhere in your superconductor. And if you break the cooper pairs, you have quasi-particle excitations inside the object. And this will then limit the performance of these devices. And studies of these devices are well and truly underway. I'll get to a second how this works for dark matter. But what we could find, this was the lowest quasi-particle device, single quasi-particle device that exists in the literature. And this I thought was, it's very interesting sort of setup. How this works is so you have in your superconductor here, you'll have some cooper pairs. So this I guess is supposed to be. And if you have something else come inside and deposit energy, so you could think of, for example, for Sonomall cases like cosmic rays or just other backgrounds, if you have anything that comes in and disturbs these cooper pairs, they'll break. And what this device wants to do is it wants to measure the charge on this detector. So what can happen is if you break these cooper pairs, you can have charges sitting on this island and then they can tunnel through to another metal here. So there's just some chemical potential difference between the two. So we'll just tunnel out. And that will leave, you'll see charges appearing on the island to change as the quasi-particles are tunneling through. So this little plot at the bottom is showing what they found. How long could they go without seeing these charges effectively appearing on the island? So they have charged flips of plus one minus one as they're kind of tunneling out. And they wanted to look for what's the longest period where they didn't see anything happening. So nothing was coming in, messing this up, breaking the cooper pairs. And if it was free of any quasi-particles for a long time, so apparently seconds is a long time. This is like the lowest of background device we could have effectively. Okay. And what's the important with these devices as well is they have a very low thresholds because the threshold is just set as they could prepare binding energy. So we're looking at really like milliev, very, very low. Thankfully for us low enough to see dark matter potentially in these devices. So if you think about the traditional direct detection you have some recoil from dark matter. So really it's just like dark matter comes in, bumps off the target, look for the recoil and dark matter leaves. And you know if you saw the recoil you might say have you saw dark matter. In this case, if we want to think about how the background, sorry how the thermalized dark matter distribution actually sits, there's lots of it, the number density is really high. So it hits very frequently. So the background suppose, sorry the detector's supposed to be the blue dots and these moving, quickly moving black dot things at the dark matter. So there's lots of dark matter in there and this large surface abundance and it's just bumping around a lot with the detector but it's bumping it much kind of slowly, more slowly. And what we want is these bumps really to break these Cooper pairs that are in this quantum device. And if it breaks the Cooper pairs we should see charge flips on the island and as they were moving out we would register plus minus flips. And if we want to then actually do the calculation by how dark matter actually is appearing in these devices we can convert a possible production rate inside this device to some power density. So we just say what's the dark matter power density that we would expect as it goes in. And overall what this will allow was really just a probe of the stabilized dark matter population that needs these really low thresholds. So there's Cooper pair binding energies are perfect for us but this also means we should be able to probe very light dark matter just coming in from the halo. So not using the one that's the population that's in the earth but the ones just coming in from the surface with low enough densities but faster velocities. And if you just go lighter in general you need lower thresholds. All right. So just before I show you the plots because we were thinking about this power density you actually could see this from super CDMS as well the experimental setup is totally different but super CDMS actually measured the power density as a background sort of calibration mission but it wasn't used yet for limits. So we're also going to include that in our results. So here are how our sensitivities look. So on the y-axis we have the scattering rate of the dark matter particles with the standard model particles in the earth. This is a spin independent scattering rate. On the x-axis we have the dark matter mass. Now what we show are the colored regions. So there's a few different devices you can use and there's a few different dark matter populations you can search for. So this thermalized population that sits inside the earth that's this blue region here. And we've made these like low threshold devices you can probe anything in this region. So anything above the bottom of this blue line. So what actually happens here is while you have good sensitivity to this region this solid line here on the left is truncating the limit just because of evaporation. So assuming only contact interactions but in that case the sensitivity is actually really good and we found this sensitivity could go pretty far down in the primary space even further to the left for the thermalized population but the dark matter particles just leave. So if you wanted to go to really light masses you don't see them with contact interactions. But as I mentioned earlier, depending on the model this can go more to the left. We're just showing you the first time an example case with contact interactions. And what you see in this top region here this orange one is what we call quasi particle that the device I just was telling you about. And this one here is for the halo dark matter. So for the halo dark matter the dark matter that's just coming in at the surface not the one that's thermalized inside. For that one you don't care about evaporation because it comes into the surface it hits the surface of the earth it goes in a little bit maybe it gets kicked back out but we still see the signature as it comes still detected at the surface. And that's the sort of sensitivity we get under some model assumptions you can have a look in our paper if you're curious about that model on the modeling side of the experiment. And in this case we see really that the sensitivity is pretty far down. So we're going to any V scale here. And we also have from this magenta region where we can get from super CDMS CDB using its power density machines which weren't used before in the context of dark matter. And we could in principle go higher up to higher cross sections that we're showing here. But we also then are restricted somewhat by the atmospheric overburden at some point. And we have to think about then what point you're actually going to not just thermalize in the atmosphere and then still get down to the higher velocity. Okay. So what we find is that we have the strongest lab based experiments and some of the parameters space. So these gray regions are other existing experiments that we have at the moment. So all the ones on the right side here are types of direct detection experiments. So UG is underground a bunch of these are for surface experiments. But notice that they have a ceiling at the top here. And this is just again from the dark matter particle has to get in with a high enough speed otherwise it just thermalizes with the overburden. So we don't have that problem if we're really a surface looking for thermalized dark matter anyway in some cases up here. So we can actually go above the sensitivity of some of these experiments with big cross sections. And so halo cross sections we see that we're going into regions where we only have astrophysical bounds. So they're bounced from Milky Way satellites to the Lime and Alpha and the CMB which are shown as these dotted lines here. But they're much easier to get around than lab-based experiments. So I don't get around in the sense that we want to ignore them so we don't want to show them here. But there are a few cases where these bounds weren't to fly and our bounds will apply. So first of all just because we have a direct measure in the lab they're just more robust. So our systematic uncertainties are much lower. But also cases where you have for example a subconfrontant of dark matter when I say subconfrontant I mean the relic abundance is not fully explained by the population you're considering. Then actually you'd find that these limits can actually disappear as soon as your subconfrontant the dark matter is very, very low. So if you order tens of percent I think of the full dark matter abundance these two at least are not really there. And for these other cases too they kind of scale in such that the thermalized component actually can be the dominant bound you get here. The other thing is that we've shown to pretty big cross sections and as soon as you get above about 10 to minus 30 centimeters squared there's issues with the bond approximation which is just how to do the scaling with the mass number of the target. So really once you start going to such big cross sections usually you want to think about what's the dark matter particle physics model that sets up here because just how everything goes can really change. We weren't interested in that and the purpose is this paper. We just highlight though if you're really interested in figuring out what happens in here usually it's better to actually pick a specific particle physics model. And overall going forward better sensitivities will definitely be possible. So there's a few ways we expect this can happen. So we can push into not just the new astrophysical well not the parameter space just we have astrophysical bounds but we do think we can move into this region here with these types of devices. So one thing is just really doing better systematic studies. So these devices are very new some of these quantum devices and really just haven't been studied properly. If you want to see if you look at some of the plots we don't have any nice systematic error bars in a lot of these. So really they have to be studied better for us to start making more robust statements who we do understand them better we can have some sensitivity moving a bit further down and of course maybe we can optimize for better detector materials better actual devices themselves and overall we think some stronger sensitivity might be possible. Okay. So to summarize the dark matter distributions are important for signals in different stars and planets really because the distribution can drive how your signal your theoretical prediction for the dark matter signal looks. So what we did on the first part of the talk was to arrive the general framework for how the dark matter distribution looks and that was including thermal diffusion effects, gravity and the non equilibrium dark matter component. So we considered the case where you have dark matter goes into equilibrium but also there was this source injection term which can give you particularly for heavier dark matter particles quite large extra amounts of dark matter at the surface that you wouldn't have realized was there if you only took the traditional equilibrium approach. So we find overall that you can have quite large surface abundances particularly for light dark matter. So if a light dark matter and we saw the profiles kind of start going a bit more flat or more peak towards the surface and in that case you can have, for example with the earth more than about 14 orders of magnitude higher than the dark matter heat load density that we have. So then really the question is right but how can we find this? There's a huge number of dark matter particles just sitting in that surface and we should think about how can we detect that? So I gave you this example case of a new search using these low quasi-particle density devices and we set the first limits now using those devices on this thermalized population and we think that there will be improvement that's possible in the future as well. So I think overall there's lots of implications that extend past the earth and past these particular devices but I think that's a whole not the topic for another day but overall there are a lot of implications from thinking about how can some large surface abundance of dark matter particles be detected? So that leaves us with plenty of new opportunities hopefully to find dark matter sometime in the future. So that's all I wanted to say. Thanks a lot for your attention. All right, thank you very much. Rebecca for this amazing talk. So now we are opening the floor for questions. If you have any question and you're watching through the YouTube channel please write your questions on the chat and we'll be happy to read the question for you and meanwhile you do that let's start with any questions from people who are in the Zoom meeting. So, okay Roberto, you go ahead. Okay, first of all, very nice to talk Rebecca. So I have a couple of questions. The one, the first one is about the, when you present the amount of dark matter that is present at earth in terms of the, you have a graph about the, and the number density diversions, the radius with respect to the earth's radius. This one? There is a, I mean, is any particular effect why at 1GV is kind of increasing at the border? A little tick. Yeah, it's not tick, it's just the simulation or- No, that's a great question. So there's a few other pictures like that too. Maybe it's not as obvious because it's kind of zoomed out. There's a kind of tick up in the middle here as well. And these are just coming from actually the density or the standard model profiles. So for the earth, it's actually kind of rigid. So, you know, you have the core and then it drops very quickly. So you have parts of the core, the mantle, the crust and because of this really the change in the standard model, number density changes very quickly. So that's the main reason that, and also for the temperature too. So for the temperature profiles, they drop very quickly between the layers of the earth. So what you're seeing here actually is with the layer of the crust and the mantle. So it switches over actually, and that's in here as well, I think. You can see something, yeah, a little bump in here as well. So it's just, this has to do with the standard model profiles of the earth. Oh, okay. That is very interesting, the fact, because in the sun is kind of, everything is more smooth, let's say. Yeah, it doesn't pick up as much, right? Yeah, exactly. It's kind of you can, yeah, as you explained with the 5GV and 600 MeV, yeah, it's kind of natural the smoothness of the profile. Yeah, so I have another question about the quasi-particle device. Yeah. This is, because when you presented the, kind of the spin-dependent cross section versus the mass of that matter, would you have any signals from the neutrino wall as well in the device? I mean, could neutrinos also trigger the signal in the apparatus, I mean, in the same case of the other? Yeah, I think you probably want even lowest thresholds, right? Probably than this, to be saying that. Also for them, the cross sections are not this big, I think is probably more the point. So these are pretty big-ish cross sections. So if you took, and this what, to actually get these sensitivities here, the two things that matter, we need the scattering cross section, but also the number density. So in here, you know, we have this 10 to the 14 also per centimeter cubes number density with a pretty large scattering rate. So if you applied this to neutrinos, you would have, I think importantly, you would have much lower scattering rates. Oh yeah, that's true. I think that's probably the main answer of why we see this. Yeah. Yeah, and the- I think it's more lower than, yeah. That doesn't go down that far. Yeah, this is the other question because of the, I didn't understand, I mean, if this type of detector can be scalable to like, for instance, Xenon, that you can go to tons and tons and then lower and lower the value of the cross section. I mean, the sensitivity of the apparatus. And yeah, I don't know if it is, if you can comment how before this first phase, how do you increase the sensitivity of the apparatus? Good question. So with these devices, they don't have volume scaling in the same way as the conventional direct detection experiments because it's gonna get bigger, the backgrounds get worse. That's just kind of not the same setup. It doesn't have typical volume scaling. But what we can do and some things we're thinking about now, but first of all, you can think about something that's, some detector material that's optimized for these sort of low energy depositions. So for these, like the main one in here, we're using aluminium and that's what that device was that I was talking about before. And that's just because first of all, that's what that device was, but also aluminium in general, we think about that, it's been very well characterized as a detector material. So there's lots of data on thinking about how do we do, how do we think about how the energy is deposited with quasi-particles in that. So it could be that actually when you look at the, the other types of materials, they can be more optimized for this type of detection. And actually we find that the aluminium is not necessarily the best one you could use. So really thinking about other detector materials could help us a lot for moving forward. I think that's one of the key things, I think for both of these actually at the moment. Okay, thank you, Rebecca. Thanks for the questions. Yol. Thank you. So I have to make this very quick because I have to go to a lecture in five minutes. So I was wondering if this floating dark matter could be measurable with these gravimeters that the satellites measuring the gravitational field within the planet. I don't know about neither the resolution of these things nor the amount of the relative change in density given by this floating dark matter. So I don't know if this is a real question or not, but I just understand that for instance, I don't know which space agency plans to do this on Jupiter, right? Measure the gravitational field to get an idea of the inner densities of Jupiter. So I don't know if this could be sensitive enough for the density that you're having here. Yeah, that's a great question. My guess is that it wouldn't be sensitive. And the reason I would say that is just that while these distributions are really large, they're still not large compared to the standard model number density. So they're quite low. That said, I don't know what the precise sensitivity, like one parting what that experiment works to that you're saying. So if it really is sensitive, so I think it would have to be like one parting 10 or was a magnitude though, make sure that was. Because I mean, if we look at the case of the earth, for example, like the best case here, this is still multiple orders of magnitude below the standard model number density in the atmosphere. So you'd have to have really, really good sensitivity. So my guess is not, but I don't know how sensitive those devices are. Thanks. Great thought though. It's interesting to think about. Thank you. Thanks for the talk. Thanks for the talk. All right. We have a question from the YouTube channel. Basia and Diaz asked, what about the uncertainties of what the earth is made of internally? I understood that you have assumed some scattering cross-section, but I guess that should vary in principle and the same for other planets. That's right. So in the case of the earth here, this plot is assuming purely oxygen and there's a lot of oxygen in the earth, but that's not technically everything that's there. But we did actually check in this paper what happened if we tried to change the modeling a little bit. So if we took the same sort of density profile, for example, the earth, but then try and put actually, what are the dominant elements in each layer of the earth? And then we actually found that the answer didn't change very much in that case. I think that what could change the answer more though is if the density profile were very different. In the case of the earth, we kind of know with some uncertainty how it steps down as we go through each layer. So there would be some uncertainty there. But in case of the earth, we kind of know roughly what to expect within our own planet. In the paper, we did look at some other objects and we thought that you could probably do this more broadly. In that case, it could change a lot from if you think you might accept planets, for example, because we don't know very well, very robustly what their interiors are, and there'd be some variation. But the way to do it better going forward would be, okay, how well can we actually measure or predict what these density profiles actually would be? But in terms of the elemental composition, it didn't make a huge difference. At least taking some reasonable range of parameters, that is. Okay, thank you. I guess they will hear the answer in a few seconds. I have another question about these low threshold detection experiments. So let's say that you have a signal that corresponds to some recoil or some breaking of the cooper pairs that will give you a particular energy that could correspond to a low velocity dark matter particle which is one of the floating dark matter particles on earth. But it could also correspond to a very light dark matter particle with high velocity coming from the halo. Is there a way to distinguish which of the two cases would that signal be? That's a great question. So in principle, with the device itself, there's no directional information. So you couldn't use that. So while we show the halo and the thermalized one here, there's some rate where they can end up being the same. So to set this, again, it's the, we're thinking about the number density in the cross section effectively in the kinematics. And it can be that as you're pointing out actually that these can kind of overlap. And I actually am not sure, well, actually, sorry, there's one way potentially you could tell. And that's for the thermalized case, you'd have to take your detector and put it at different depths in the earth. So for the ones, if you're thinking about like Gran Sasso for example, when you go much further underground versus really truly more of a surface run, you couldn't principle see something. I'm not sure within the uncertainties or what we expect at this stage though, you could actually distinguish. But I think if we saw a signal going forward and we were trying to figure out what's happening, that potentially is a way you could do it because the density does change as a function of the radius. But we'd also need to get our uncertainties low enough to know the difference. All right, and I have a few questions, but just getting out of the earth, because I know that you have worked on this for other compact objects. Yep. So if I had two compact objects that are in a binary system, so they are emitting gravitational waves and each of these objects has some dark matter that is floating around. But as they rotate, it might be that the distribution, there is an offset between the center of mass of the compact object and the center of mass of the dark matter distribution, right? Is there any possible signal in the gravitational wave function that these guys are emitting that could tell us, ah, I mean, the mass distribution of these two objects, it's weird. And they might be because there is some floating mass, dark matter mass in it. Yeah, that's a great question. So actually, I have written a paper in the past actually thinking about the title love numbers. So it's really, you can think about like the, or like the in spiral, if there's some sort of like friction as the particles are moving together, sorry, as the two objects are kind of in spiraling. And people have thought about this actually for a long time, maybe going back at least another 10 years. And in this case, actually, usually the focus was on if you had a dark matter distribution and it kind of got puffed out. So you can get this if you have repulsive interactions. So in our case, these are just contact interactions purely. But as soon as you start putting in sort of additional types of interactions or longer range interactions, the case we were considering was work with Juno Kuhn and her student, Michael. And in that case, what you could get was that out extending out actually quite far into the atmosphere, you could get past the atmosphere, even you could get these dark matter components. And in that case, actually, you would expect that as you look at the in spiral, you would actually see a difference. So I'm not sure if we have this contact interaction case, that would be enough to get a large signal because the distribution in the case, we looked at these repulsive interactions, they were extending pretty far out. But it's potentially possible. But if you could do this, isn't it also something you do with a future gravitational wave experiment? Probably not any time soon, I guess. But you'd have to probably do the calculation to make for sure. All right, Robert, do you have any other questions? Yes, but it's very short about the device. Is there any limitation in the, I mean, kind of the runtime of the device? In the sense, is it would be possible to be sensitive for, for example, for annual modulation or signals that would depend of the, I mean, if you'd like to separate the signal from the halo, from the one that is thermalized at Earth, let's say, thinking in that... The halo one, you see the modulation, the other one is just thermalized and sits there already. Yeah, potentially you could do that because you do get a slight difference in the rates with the season. That's true. But again, once you put the systematics on, I'm not sure how well they're resolving. Yeah, of course it's going to be very small. Usually it's very small to signal that makes it challenging. Yeah, sure. Right, so I'm not sure because we didn't actually check what the set, the problem is with all these devices is really there's no good systematics yet. So while we show you something here, we really emphasized in the work that we need better systematic studies and we wanted to try and emphasize this is an interesting direction for people to think about as opposed to this is the most robust thing we really have. So in terms of even trying to do the annual modulation, that's a great point. And it is in principle the way you could tell them apart, but we probably want some good error bars first before we start doing that sort of thing. Okay, thanks for the answer. All right, I think that this brings us to the end of this webinar. Thank you very much, Dr. Rebecca Lin for this amazing seminar. It was very entertaining and very interesting. To all who are watching, remember that you can subscribe to our YouTube channel and to our Twitter and Facebook accounts so that you are always informed about the upcoming events. And to all who watch, thank you very much for joining us and I hope that you can still watch the other webinars that we are broadcasting every two weeks. Thank you again, Rebecca, and have a great rest of the day. And to all of you who are watching or who will watch, have a rest of the day as well. Thank you and bye.