 Okay, hello, my name is Alejandro de la Puente. I'll be your host today and welcome to another edition of your Latin American webinars in physics. Today we have a really awesome speaker. His name is Joseph Bramante. Joseph Bramante is gonna talk to us about dark kinetic heating of neutron stars. Really interesting topic. Before we start, I'm gonna like to tell you that you can, after the webinar, you can ask your questions through the question and answer module in your YouTube page. Or you can ask him also through social media using the hashtag L-A-W-O-P. So Joseph is a graduate from the University of Hawaii. He did one of his postdocs in my alma mater, oh, not my alma mater, but where I did my PhD in the University of Notre Dame. And now he's currently doing another postdoc at Perimer Institute, which is an awesome place to work. And it's a lot of fun, I hear. He will tell us about future measurements of infrared emission from nearby neutron stars that can be used as a largely model on the pan and probe of dark matter. He will tell us a lot more about that. So with that, I'd like to welcome you to this edition of the Latin American webinars in physics and I hope you enjoy it. So thank you, Joseph, and welcome to this family of physics enthusiasts. Thanks for the wonderful introduction, Alejandro. And thank you everyone for tuning in or joining in on the webinar. If you do have questions at any time during the webinar, I don't know if you can type them in and I can see them, but I'll be looking. And hopefully it will make sense. So I guess I have to share my screen now, so I'll do that. Then I'll put that's working. Is that working? Can you guys see this? That's perfect, thank you. Great. Okay, so today I'm going to be talking to you about dark matter heating nearby neutron stars to barbecue temperatures, because actually the temperature of that dark matter would heat nearby neutron stars to, is about 1700 Kelvin, which is about the temperature of an industrial barbecue. So as Alejandro says, I'm at Perimeter Institute and this is the Latin American webinar. This is based mostly on a recent paper I put on the archive with Masha Bayaktar, Shirley Lee, Tim Linden, and Nirmal Raj, all really excellent postdocs and grad students who I worked with on this project and I'm very fortunate to have been able to work with. So first I'm going to give you a lightning review of weekly interacting dark matter. So weekly interacting dark matter is sort of this dark particle, it could be a particle, it could be a wave, it could be some other matter distribution, but anyways, there's something in the galaxies that's causing stars to move faster around the center of galaxies than we would naively expect if there weren't any sort of dark substance there. And this is called dark matter. We can also tell that there's dark matter when we look at cosmological observables and we plot the sort of initial seed perturbations that give you the structures that we see in our universe. If we study those very carefully, we also see an imprint of dark matter there. And so the simplest explanation for these, oh, excuse me, skip two. So the simple explanation here is that something like a fifth of the energy density of the universe is cold, collisionless dark matter. And this has been known since about the 1930s. Hold on one second, I'm just going to hide this annoying thing. Now I'll get back to my slides. Okay, and back to my slides. Great. There's something called the WIMP miracle, which is that if you try to figure out what dark matter is, there's an incredibly simple model that seems to just work. And this very simple model is that dark matter could plausibly interact with standard model particles or the sort of particles we know about and have detected already through exchange of a weak boson, which is one of the four forces, the weak force is mediated by what we call the W and the Z bosons. And it turns out that if you have a dark particle with a wide range of masses, anywhere from the mass of the proton up to something like 10,000 times the mass of the proton, and it couples to the standard model or it exchanges forces with the standard model through this weak force or through this W or Z boson. Then it turns out this sort of dark matter model immediately gives you exactly what we see, which is a relic abundance of dark matter that would give you about a fifth of the energy density of the universe. And it does that sort of automatically if you just start the universe off in a very hot dense state and then you cool it down, this dark matter will what we call freeze out to the right relic abundance and give us the dark matter we see today in our universe. So people have been very inspired by this weekly interacting dark particle. But there's a bit of a problem and that is that if you calculate how much that weekly interacting dark particle should hit into detectors on earth that we've been setting up while we're keenly excited to find this dark particle. If you just calculate that very simple standard model or simple, it's not the standard model, simple dark matter WIMP cross section for scattering off of terrestrial experiments. It looks like for a lot of the parameter space we were interested in for a lot of the dark matter masses that we thought dark matter could be there. It's excluded. So here what I'm showing you is a plot of the dark matter nucleon. So this is like a neutron or a proton cross section and that's the y-axis in units of centimeters squared. So the cross section for scattering off of neutrons or protons versus the mass of the dark matter particle. And it looks like experiments like Luxe and Panda X which are these vats of xenon underground and also CDMS, which is that light green line and also Crest which is a tungsten calcium oxygen crystal which is that dark green line. All these bounds are sort of in tension with the simplest dark matter candidate. And you could ask, does this mean that we should give up on this very standard, very exciting, very in principle simple dark matter model and the answer is maybe no, maybe the dark matter is just hiding and we need new detectors to find all the WIMPs. So today I'm going to talk to you about a new way we could look for dark matter and we could probe a lot of the sorts of dark matters that wouldn't quite follow the exact rubric I've been talking about and would also be very motivated but could be hiding because they're just much harder to probe than this typical WIMP dark matter candidate. So there'll be a few lessons. One will be the importance of being semi-relativistic and abundant. So in the early universe, dark matter was semi-relativistic when it was in its thermal bath state freezing out to the observed relic abundance. It was also incredibly abundant back then. The next lesson will be that neutron stars can act as nature's dark matter accelerators and that's actually we'll find out not just an analogy, but literally true. And the third thing will be that the final step to sort of making this new detection regime, I'm going to introduce a reality is that we have to bring our astrophotography friends and astrophysical friends to our backyard dark matter barbecue and I'll explain what that is when I get there. Okay, so occasionally maybe I'll click away from the screen and just check if there are any questions. Okay, no questions yet. Okay, great, so. All right, so first let me review really quickly how you find dark matter. So the first step is to just look at a ball of secluded stuff. So if I just look at a ball of secluded stuff and I want it to be secluded so I don't see other things, radioactive decays and cosmic rays hitting this ball of stuff. So I secluded it and one example is liquid xenon. So this is what Lux, Panda X and xenon which are direct detection experiments, that's what they use. And so dark matter in the Milky Way, I know has about the same velocity as all the other stars in the Milky Way simply from very basic physical considerations of very ultram for instance. So I know how fast the dark matter is moving and I know how much dark matter there is for a given dark matter mass. And so I'm just sitting with this ball of stuff in space waiting for it to hit that ball. And it turns out that the number of events I expect will fall off as one over the dark matter mass. And that can be understood very simply as a consequence of I know how much mass there is of dark matter in the galaxy. If the dark matter is less massive there'll be more particles around and I'll expect more events. If the dark matter is more massive there'll be fewer particles around and I'll expect fewer events. And so the rate for events as I'm staring at this ball falls off as one over the dark matter mass. There's also a minimum mass for detecting dark matter for a given detector. And this is because my detector in practice is only sensitive to sort of this minimum recoil energy. So if I set the dark matter as kinetic energy in the halo one half mxvx squared to be greater than or equal to that minimum recoil energy which tends to be around three kv or kv in the xenon experiments just as an example. It turns out that the minimum dark matter mass that actually has enough kinetic energy to excite that much energy and be detected is around six gv or six times the proton mass. And so if I'm doing a very simple analysis I can immediately solve for what the cross-section bound is using that rate formula on the left side of the slide. And that can give me the cross-section if I'm thinking about a dark matter candidate that's roughly the mass of my nucleus and that'll actually give me the largest cross-section because then I'll have the largest reduced mass for those of you who are kinematic aficionados. And then I see that the bound creeps up as one over mx as I go to higher masses and this is simply because the rate is falling off. And then I see that there's this sort of exponential swoop on the left side of that center bound point. And that's because I have this minimum mass that my detector is actually sensitive to. So this is how you typically find dark matter at direct detection experiments. Okay, so we talked about WIMPs before and we talked about these bounds that were being set up by various direct detection experiments. But one thing I didn't mention is that these are really what we would call a spin-independent WIMP. And that simply means that you have this nucleus, this assemblage of protons and neutrons. So carbon, for instance, that's 12 of them. Anyways, well, 24. Anyways, so yes. So you see this assemblage of neutrons and protons. You wait around for a dark matter particle to hit it, but if the dark matter particle can actually interact with every nucleon inside of a nucleus, it actually has a larger cross-section and can be detected more easily than if not. So for spin-independent WIMPs, the lesson is simply that I can scatter with every neutron and proton in my nucleus and I get these big deep bounds that I showed you before. For spin-dependent WIMPs, the story changes a little bit. These guys actually can only interact with the nucleus as a whole and they can't interact with every little nucleon inside the nucleus because they're coupling actually to the spin of these particles. And the neutrons and protons inside of the nuclei, most of their spins cancel each other. So we're left with just some fraction of spin leftover and that's actually what the dark matter's coupling to. And so this is what's called a spin-dependent dark matter candidate. And in this case, heavy nuclei aren't working as well to give me as much oomph as they did in the spin-independent case. And so you can see that this bounding line in green is not ruling out as much of my typical WIMP dashed line parameter space as it otherwise was. There's also a distinction between what I've been talking about so far, which is elastic dark matter where a dark matter particle comes in, it hits a nucleus, gives the nucleus a bunch of recoil energy and then the dark matter goes back out into space and something else called inelastic dark matter. And inelastic dark matter is a dark matter model where instead of simply scattering from one dark matter state to the same dark matter state, you can only scatter from one dark matter state to a heavier dark matter state. So for those of you familiar with inelastic scattering of say, electrons off of neutrons or protons, the story there is that you're exciting the neutron or the proton into a sort of higher energy excited state, but you could still have the process where you hit the neutron and it just gets a lot of recoil energy and it's still a neutron. In this case, for inelastic dark matter, the sort of process where the X1 or the lightest dark matter state comes in and the lightest dark matter state goes out, that process is simply forbidden at tree level. And so the only way to scatter is if you have enough energy to turn the lighter state into the heavier state, because otherwise you can't exchange the boson. And there's a loop correction, exception to that, which I'll talk about a little bit later, but to leading order, this is true. So some work I did recently with Graham Cribs, Adam Martin and Patty Fox was simply to point out that direct detection experiments could actually do much better in searching for these inelastic dark matter candidates if they looked at higher recoil energies. So a little bit earlier, we talked about how there's this minimum recoil energy they have to look for in order to find the dark matter. It turns out that when you have inelastic dark matter, as we just talked about, there's sort of this minimum recoil energy you have to pump through the system in order to create the heavier dark matter particle. But that tells you that actually you should start looking at much higher recoil energies than the experiments typically look at. So in this plot, you can see that Xenon experiments typically only analyze up to 30 KB. But if I had a dark matter candidate where the splitting between the lighter state X1 and the heavier state X2 was around 300 KV, I'd have to start looking at recoil energies of about 120 KV in order to see this at all. Okay. And so let me give you an example of a dark matter model that does this sort of thing. And this is actually just the Higgseno. And for those of you who don't know, the Higgseno is a very standard dark matter candidate in the minimal supersymmetric standard model. So a very well-motivated, very well-studied model in physics. And what's happening is while at tree level, I could exchange a Z boson, and this is the diagram in the lower left of the slide, and scatter from X1 to X2 and have an incredibly large typical WIMP, 10 to the minus 39 centimeter squared cross-section. Because after I diagonalize my Higgseno mass matrix and I mix my Higgseno a little bit with binos and winos, I get a mass splitting that's of order a GEV. And remember before we were talking about inelastic mass splittings of hundreds of KV, and now we're talking about GEV, which is a thousand times larger. Because I get this mass splitting between my two latest Higgseno states, which were H1 and H2 to begin with, and now are mostly still Higgseno-like states, but have a small mass splitting between them. Well, actually it's a large mass splitting without a GEV. Some ball on the scales we're talking about is these dark matter masses would be about a TEV or even a thousand times beyond a GEV. If this happens, I simply can't get enough recoil energy in my dark matter scattering about direct detection experiments. And in that case, instead of this tree level process being how I scatter with nucleons, instead I have this loop level process shown on the right here. And actually this loop level process is very difficult to calculate for a number of reasons. And so far there's sort of a loose upper bound on what the cross section could be and it's 10 to the minus 48 centimeters squared or perhaps well beyond what any direct detection experiment will be able to achieve in the near future. So as we were doing this project, we got really excited because we were looking at Crest data. So right here I'm showing you actual honest to goodness data from a direct detection experiment, the Crest experiment. And here we have recoil energies between zero and 120 KEV. And they had these four events at very high recoil energies and no events at lower recoil energies, which is a very characteristic signal of an inelastic dark matter candidate. So we got very excited because maybe we'd found the dark matter or the first hints of the dark matter since four events really isn't enough to claim a true discovery. But anyways, these four events were exactly where you might expect them to be if you had a Higgseno with a mass building between your Higgsena states of about 200 KEV. So we found this and we were very excited but being good physicists, good phenomenologists, we analyzed this a little bit further and we looked at other experiments and we found that PICO, which is this bubble chamber experiment, which instead of looking for the energy deposited in individual events, simply looks for an event to cause this huge bubble cascade and decompress the entire chamber. Because of that, it can't actually, you know, reject events or not analyze high recoil events. So it actually naturally has to be, you have to do the analysis with up to MEV recoil events. And so PICO 60, we were able to use their results to set a bound on inelastic dark matter that excludes above 200 KEV mass split inelastic dark matter. And so our Crest Higgseno sadly was rolled out by a PICO result and was probably just background events. But a lesson we learned is that if you want to find inelastic dark matter better, you should simply analyze up to higher recoil energies. And so on the right slide here, I'm showing you how searches at Crest and Lux and Panda X and Xenon could be improved simply by analyzing the data they already have and will have at higher recoil energies. And you can see that instead of getting out to something like Delta equals 180 KEV for Higgseno type cross sections, I can get out to 300 KEV, which is a substantial improvement. But really, if you remember from before, for Higgsenos, we want to be able to probe inelastic mass splitings up to a GV. And that's a lot more. So it's kind of a tall order. Great. So I could say, based on all these things I've been saying, what would be my ideal direct detector? So if I could build a direct detector from scratch in any possible configuration, what would I make it? If I could just make a magical direct detector? So the first thing is that I'd want to probe mass scales more evenly. So you might have noticed in those bound plots I showed you that the best bounds were around 100 GV or 100 times the mass of the proton. This is simply because most nuclei have masses around 100 times the mass of the proton or 100 GV. And this is why we get the best bounds on dark matter around the weak scale. There's this coincidence between the mass of xenon and the mass of weak bosons. So it'd be great if I could actually probe mass scales between a GV and say a PV roughly evenly. The next thing I would want is to have a sensitivity without requiring nuclear coherence. So we saw that there was a difference in the sensitivity of spin independent versus spin dependent dark matter searches. So I'd want to be able to probe spin dependent dark matter and I'd want to not so much be relying on these nuclei with tons of nucleons in them which helps increase the scattering rate for dark matter off of my fiducial mass. The last thing is if I could, if I'm asking for anything I want, maybe I could accelerate dark matter to the speed of light. This would allow me to have a lot of initial kinetic energy. So for all these inelastic dark matter models that I'm not probing, I'd be able to upscatter quite a bit more if I were moving at the speed of light instead of a thousandth the speed of light which is how fast dark matter in the halo moves. Okay, so just to focus our minds a little bit before I talk about what I'm going to talk about which is my ideal direct detector. I'm going to talk about a dark matter heated astronaut. So if we think about how many times an astronaut out in space could be hit by dark matter, right now you could hit the astronaut about once per year and that's because the current direct detection limits on dark matter scattering about at the hundred kilogram year level. So for a hundred kilogram astronaut, we could hit the astronaut once per year. So if I figure out what the luminosity of the astronaut or the radiation coming off the astronaut from that dark matter heating, what that would be, I would have L, which is my luminosity, equal to one event per year times the mass of carbon, we'll say the astronauts mostly made of carbon, times the speed of the dark matter in the halo squared. And this gives me roughly the energy I'm putting in per unit time. And I set that equal to four pi times the radius of the astronaut squared times the Stefan Boltzmann constant times the temperature of the astronaut to the fourth. And I solve for the temperature of the astronaut and I get 75 micro-pelvin, which isn't very much. So I'd have a very cold astronaut if this is the only source of heat for the astronaut. But I should point out, I didn't do this calculation as precisely as I could have. So while I use the dark matter's speed in the halo, Vx squared, I could have used Vx bar squared, which is not only the dark matter speed in the halo, but the extra speed boost the dark matter gets from the astronaut's gravitational potential. So the speed that the dark matter gets from the astronaut's gravitational potential will just be two G mass of the astronaut divided by radius of the astronaut. Now in the case of a dark matter heated astronaut, this is a very small correction to the speed of the incoming dark matter on the order of 81 microns per second. So the dark matter's coming in at something like 200 kilometers per second. So I don't care about that small correction, it doesn't matter. But in the case of neutron stars, it really does matter. So you can think of neutron stars as nature's dark matter accelerators. And that's not just lip service, they really do accelerate dark matter. And they really are nature's dark matter accelerators. So if I just calculate what the escape velocity is of a neutron star, I know that a dark matter particle far away in the halo that falls into the neutron star's gravitational well is going to be accelerated up to that escape velocity, simply by conservation of energy or many other ways you could prove that. So the escape velocity of the neutron star is 0.7 times the speed of light. So I wanted my ideal direct detector to accelerate dark matter to the speed of light. And indeed, it looks like a neutron star does that, which is great. So if I think about my neutron star as a secluded ball in space, it has an interior with a fiducial mass of 10 to the 57 GED or 10 to the 57 times the mass of the proton, which is the mass of both a neutron star and our sun. And it has a composition of neutrons to protons to electrons of about 10 to one to one. So even though these are called neutron stars, they actually have some protons and electrons in them as well. Okay. So now I should explain to what dark kinetic heating is. So dark kinetic heating is very simple. So dark matter is gravitationally accelerated to 0.7 times the speed of light by the neutron star. Then it scatters and rescatters against neutrons, electrons and protons inside the neutron star. This heats the neutron star up and results in black body emission. So you might ask, okay, great. You know, I get this black body emission from neutron star heating, from dark matter heating the neutron star, but is that going to be noticeable? Is the neutron star already going to be so hot that this is a small effect? And I can't really notice that dark matter is heating it up. And the answer is that no, actually this will be a pretty big effect for most of the neutron stars in the Milky Way that are around us that we could find. So after about 100 million years, neutron stars would emit as black bodies with effective temperatures much less than 1,000 Kelvin. That has some dependence on what the actual crust of the neutron star is made of, but for the most part and for the accuracy we care about here, it's true. It's also true that most neutron stars or all stars really in the Milky Way are older than a billion years. And at that time, the effective temperature of the neutron star as viewed by us would be much less than 100 Kelvin, or around 100 Kelvin. It could actually be less depending on what the exact composition is of the neutron star, whether it has a super fluid interior or not. You can compare that with the maximum kinetic energy I could put into it from dark matter sweeping through that neutron star and that temperature is 1750 Kelvin. Now that may not seem like a big temperature difference, but actually because energy density goes like temperature to the fourth, this ends up being a huge difference between 1750 Kelvin and even 1,000 Kelvin, but also a huge difference between 1750 Kelvin and 100 Kelvin. And so yes, you can indeed notice this effect if you have telescopes that are good enough. So if I want to find a neutron star nearby, I can look for it by looking for pulsars. Now pulsars are simply neutron stars, but pulsars are a neutron star that has this radio beam that sweeps past and pulses light at us. So you can find neutron stars simply by looking for this radio beam, which can tell you exactly where these pulsars are. And this plot is very confusing and has a lot of data on it. And if you guys have questions about afterwards, I'm happy to talk about it. But right now, all I'm showing you is that the sort of pulsars that or pulsars slash neutron stars, same thing that we need are enclosed in this green box and there are plenty sort of candidates that are old enough and have the right characteristics in the pulsars we know with one exception, which is that we haven't yet found a pulsar that's quite close enough to use next generation telescopes to find dark kinetic heating, although we're very close. So the closest we found a neutron star to us is about 80 parsecs. And really we'd want to find an neutron star somewhere between 10 and 50 parsecs from Earth where we expect there should be a few hundred pulsars in order to do this measurement. So I have a few strategies I've proposed for how you can find dark kinetic heating. And the first is what I like to call the backyard neutron star barbecue. So this is a fine one or two pulsars with fast SCA and CHIME, which are radio telescopes, next generation, wonderful radio telescopes. Fast is already online. CHIME will be online this summer. SCA, which is a square kilometer array will be on probably five or so years from now. And so if you find a few pulsars within 50 parsecs from Earth, then you can use the James Webb Space Telescope, which is this huge eight meter wide telescope that we're going to send into space next year and is going to give us the best infrared sensitivity of any telescope ever when it comes online. Another option is using the 30 meter telescope, which should also come online in the next five years. James Webb should actually be online in the next two years. So that's faster. So if I ask how long do I need to point one of these telescopes at a nearby pulsar in order to see dark kinetic heating if it's there, I can ask what these two sigma or the minimum significance integration times are. For James Webb Space Telescope, if I have dark matter that's heating the neutron star simply by hitting it like we've been talking about, then I would need 10 to the five seconds for a pulsar that's 10 parsecs away. And this scales like a distance of the pulsar to the fourth. I didn't talk about the dark matter annihilating in the star, but it's also possible that after it deposits its kinetic energy in the star that it also annihilates in the star. And that's actually what people had considered before the study I recently put out is the annihilation heating. Kinetic heating is nice because it's more general. It applies whether or not your dark matter annihilates and yeah, it makes the whole analysis much simpler and perhaps convinces you that you're probing most dark matter candidates using this. Anyways, getting on track a little bit. The 30 meter telescope does a little bit better for kinetic only heating, but it does a lot better for annihilation heating. And the reason is that a 30 meter telescope for kinetic heating would be probing in infrared wave vans and those are shrouded on earth by zadiacal light. Whereas if there was annihilation heating in a pulsar the temperature would be much greater and would shift the central frequencies to optical frequencies, which are much easier to probe with telescopes on earth because there's less of a background in our atmosphere to those wave vans. The other option is a long-term brace. So astronomers have had proposals and it does seem feasible to make a 100 meter telescope. So the 30 meter telescope is unsurprisingly 30 meters wide. So right now I'm talking about 100 meter telescope, which in the astronomical community is known as an owl or an overwhelmingly large telescope. And that one could get two sigma unknown pulsars. So those pulsars about 80 to 150 parsecs away that I can already point out to you in the sky if you ask me to. Those can find those in 100 hours, which is a reasonable telescope integration time, although it is asking them to point at it for quite a bit of time. And this is really an excellent task for the next generation telescopes that will undoubtedly be built to image the atmospheres of exoplanets. So yeah. Okay, so now I'm going to go over, well, actually I'm gonna pause for one moment just to make sure that no questions showed up in a little chat box. Nope, looks like we're good, so I will continue on. Okay, so next we'll talk about dark matter capture and we'll finish off by showing the sensitivity curves you would get from dark kinetic heating. First I'd like to just explain to you the basic parametrics of what sensitivity the neutron star has to a dark matter nucleon scattering cross-section. So if I think about the dark matter passing through the star, I can define the fraction of dark matter captured as the minimum of one, or of the sigma nx divided by sigma sat, which is the scattering cross-section off of nucleons divided by what I'm going to define as a saturation cross-section. So the saturation cross-section is just the cross-section at which any dark matter passing through the neutron star is going to get captured unless its kinetic energy is also going to get captured. So the reason that the fraction of dark matter captured can only be up to one is because I can't capture more dark matter than I'm putting in. So that explains the form of that function. Okay, so now I'm looking at the mean free path. So this is just the very basic expression for what the mean free path is of a particle moving through a medium of density n. So if I have a particle moving through a medium of density n, then the path I expected to travel before it scatters is simply one divided by n, where n is the number of density of scattering sites in that medium times sigma, whereas sigma is the cross-section for scattering off of those sites in that medium. And what I find is that my star will be opaque to dark matter if the total cross-section of the star, which is pi r squared, just the area of the star, divided by the number of scattering sites, which is here, the number of neutrons in the star, which is about 10 to the 57, if that quantity is less than the scattering cross-section for dark matter on nucleons, then that tells me that every dark matter particle that is moving through the star will get captured. And so I can think about three different mass limits to figure out what that saturation cross-section is, because it changes a little bit depending on what dark matter mass I'm thinking about. So in order for dark matter to get captured in the star, it has to lose its halo-kinetic energy, which is about 10 to the minus six times the mass of the dark matter. So that's just 1 1,000th the speed of light squared times the mass of the dark matter. So for dark matter between masses of GV and a PV, I can compare the dark matter's halo-kinetic energy, 10 to the minus six times Mx, to the energy lost in a single scattering event, which is roughly the reduced mass of the nucleon dark matter system, which is this mu Nx, times the velocity of the dark matter squared. So for GV to PV, that reduced mass is simply going to be one GV, because it'll be the mass of the neutron. And we already said that the speed the dark matter has coming into the neutron star is roughly 0.7 or roughly order one. So altogether, I get roughly a GV of recoil energy for dark matter. If it has a mass between GV and a PV, about a GV of recoil energy is transferred. And that's much more than its halo-kinetic energy. So long as its mass is below a PV, which is 10 to the six GV. And once I get above masses of a PV, that GV of recoil energy isn't quite enough to capture it. But for between GV and PV, that's enough to capture it. For dark matter masses less than a GV, there's this phenomenon called polyblocking, which I'm going to move very quickly through, but you can ask me about it later, if you like. And this simply means that because of quantum effects, only a fraction of the neutrons in the neutron star can actually scatter with the dark matter. And so I get the scattering of the dark matter off of the star suppressed by one over the dark matter mass. And this tells me that for lower masses, my sensitivity curve will have a linear slope upward. So I'll be less sensitive as one power of the dark matter mass. For dark matter much heavier than a PV, I entered into what I call the multi-scatter regime. And I actually wrote a whole paper on this with Antonio Delgado and Adam Martin this year. And for these dark matter masses, as we said, one GV of energy deposited is not enough to capture it in the star's gravitational well. And so I need to keep scattering many, many times inside of the neutron star in order to get captured. Set the number of times I'm scattering times the recoil energy equal to its halo-kinetic energy. And I can figure out that the saturation cross-section in this case is going to be proportional to the mass of the dark particle. But then that's actually enough to exactly figure out what this curve will look like because I already knew that the normalization of this curve was this two times 10 to the minus 45 centimeters squared or the saturation cross-section for dark matter masses between a GV and a PV. And so I can immediately figure out where that sensitivity curve flies. Okay. And now I've come to a plot I really, really like. So this plot shows you the sensitivity that neutron stars would have to dark matter. So if I found a neutron star that I convinced myself was very old and wasn't heated by anything else, which we could talk about how to do that and had a temperature of 1750 Kelvin, I'd be sensitive to dark matter with masses between a few KV all the way up to here. I'm showing 10 to the 11 GV, but actually it extends far beyond that. And I'd be sensitive at cross-sections that are over a lot of the parameter space well beyond what's being probed in direct detection experiments like Lux and Panda X. The other thing to keep in mind is because I'm scattering off of individual neutrons, the sensitivity here is the same for spin-independent and spin-dependent dark matter. So in this red curve, I've plotted the spin-dependent limit on dark matter scattering and this sensitivity curve applies equally to spin-independent and spin-dependent dark matter models. The other cool thing is I can do a little bit better than 1750 Kelvin with next generation telescopes. I can actually get maybe down to 1,000 Kelvin if I actually find a pulsar 10 parsecs away. So this would actually get well below any planned direct detection experiment over a large part of the parameter space. Okay, so that's enough for this plot. We can come back to it later if you guys want. This plot, this slide is a little bit busy. So let me take you through it quite slowly. So this slide essentially answers the question, let's say I find a neutron star and I think it might be heated by the dark matter, how do I start verifying that? So in this plot up to the right, which seems kind of busy, on the y-axis we have the mass of a neutron star and on the x-axis we have the radius of a neutron star. So neutron stars come in a number of varieties. They have a number of different masses and corresponding radii. Typically we find them to have between one and two solar masses. So lying between the one and two on the y-axis and various considerations, including the number of neutron stars that we've imaged thermally and other measurements we've made of neutron stars and simulations we've done of their interiors all seem to indicate that the neutron star parameter space should roughly lie inside of this green region. So if I know my neutron star, sort of mass radius relationship is going to lie inside this green region, eventually if I start seeing dark matter heating neutron stars is going to get a wide distribution of neutron stars between one and two solar masses. And this tells me actually that the heating of those neutron stars is going to have a spread. So for kinetic heating, which here is shown in the red lines, that spread of luminosities is a factor of something like two. So for the bottom dash dotted red line, we have 1.2 nanogenskies, which is just a unit of flux from a neutron star 10 parsecs away. We have between 1.2 and 2.8 nanogenskies for all the neutron stars we would find that were just heated by dark matter kinetic energy. Oh, excuse me, that one is for kinetic energy and annihilation. So in that case, we get the red lines. For the blue lines, we get the blue lines if you just have dark matter kinetic heating and there we get a factor of between 0.2 and 1.2 nanogenskies, which is more like a factor of 10 to 15 or something like that, around 10. Well, actually it's more like 15. But anyways, the point is simply this. The point is that if I had something that was just heated kinetically, I'd be able to see a difference in my neutron star temperatures across a population of neutron stars than I would if it was also heated by annihilation. Now, if you directly measure the mass of neutron stars, which you consider doing if you found one in a binary system, or if you could actually resolve how large it is which gives you some information about what its mass is, those are other ways that you could actually maybe do this analysis I'm talking about a little bit more simply. Okay. The last thing I'll show you before concluding is Hyxenos. So before we talked about this model of inelastic dark matter, that's incredibly hard to probe. And it's incredibly hard to probe because we can't scatter the lightest state up to the heaviest state. But it turns out because we have a GV of recoil energy for scattering dark matter off of neutrons and protons in a neutron star, we could actually probe these Hyxenos quite well using neutron stars. And so this is just showing you the parameter space of the MSSM. So on the x-axis here, we have M2, which is the Weno mass on the y-axis. We have M1, which is the Beno mass. And so we have four panels here which take a bunch of different supersymmetry parameters and sort of scan over all of them. So this dashed new line with a little V or new next to it. That shows you the neutrino floor or essentially the ultimate reach of future direct detection experiments. And what you see is that the parameter space accessible to neutron stars, which lies above the blue and red lines indicated the direction is indicated with arrows. So that would all be probed actually with the first observation or non-observation of dark kinetic heating of neutron stars. So these two parameter spaces are very complimentary. So essentially neutron stars could probe almost all of the Hyxenoparameter space that future direct detection experiments would not probe. All right, so my conclusions. So dilute in elastics, independent and actually a lot of other weekly interacting massive particles and non-weekly interacting massive particles would all be probed by dark kinetic heating of neutron stars. This is because the dark matter is actually semi-relativistic and that's actually its natural state when it's freezing out in the early universe which is an interesting connection to make. And infrared telescopes will be really great for finding exoplanets and finding out their properties but they can also find dark matter. So that's it for me. And now I guess I'll take your questions. Thank you very much. Hold on. Sorry. No problem. Okay, we already have one. Thank you so much. Yeah, yeah, of course. Yeah, that was mine. That was mine because I was, I got a little confused about... Anyway, thank you so much for the webinar and we're just going to move to the question and answer session. First we'll take some questions from people here and then we'll see if there are questions in the YouTube thing. But my first question I guess is, I got a little confused. So the dark kinetic heating, it's the heating you will get from a dark matter particle scattering inside the neutron star and eventually being released and then accelerated, right? Okay, so yeah, a very basic physics question to ask is where is the energy for this coming from? The answer is that there's a gravitational potential energy difference between the dark matter far away from the neutron star and next to the neutron star. So that's where the energy is coming from. And then yes, so the dark matter falls into the neutron star and then it hits neutrons and protons in the neutron star and then it excites them. And then that energy gets circulated through the neutron star actually very efficiently. And the neutron star then emits that energy as a black body. So it's all these individual dark matter particles hitting neutrons or protons or electrons inside the neutron star and that kinetic energy rapidly thermalizing inside the neutron star and then being emitted as light. So that's the whole process. Does that answer that? Okay, that's the light you will detect with the arrays, with the telescope arrays. That's the light you will detect with these next generation telescopes. And so how would you probe then the capturing process, dark matter capturing? Because those velocities will be much lower, right? That's just dark matter moving through the neutron star, right, like the halo. So now you're asking a question about direct detection, like how I then find this same dark matter at direct detection experiments or? No, I'm asking that you went over, you went over also the process of dark matter being captured in the neutron star. Yeah. So the point is, if dark matter is lighter than about a GV in mass, then after it hits the neutron star once, it's done. And it's actually deposited all its kinetic energy. If it's any heavier than a GV, then actually the process is it hits the neutron star once. And if it's gravitationally bound to the neutron star after that first hit, then it'll circle back in an orbit and keep hitting the neutron star until it's deposited all of its kinetic energy. But if it doesn't get captured, if it only deposits so little kinetic energy into the neutron star that it can still reach escape velocity and get out of the neutron star's gravitational potential, then it's not going to heat up the neutron star as much as I'm saying. So that's why I was showing you what you need to capture the dark matter, because that's what's important. Because if the dark matter is captured, then you're guaranteed that all the kinetic energy gets into the neutron star. Got it. So that's why that's important, yeah. Okay, and then I guess the last question I have is how fine tune are these models of one GEV splittings of Hexeno one, Hexeno two? No, that's the super standard case. So that's if your Wino and Bino parameters are right at the weak scale, TV each. That gives you GEV splittings. And then those splittings go down and to get them down to where we could see them at direction detection experiments like 500 KV, you actually have to raise those Bino and Wino masses all the way up to 10 to seven GEV. I think you could argue that's actually the fine tuned case. Okay, I see. All right, thank you. And anyone else would like to ask a question here in the audience? Yeah, hi, hello, can you hear me? Yeah, I can hear you. Yeah, about the Hexeno, I mean, if you make, if you put the other parameters relatively close, you could get to higher splittings, mass splittings, right? Yeah. So in that case, is it hopeless or can you still? Oh, I see. So actually, no. Okay, there's an additional complication that I didn't really have time to go over, which is that actually for such low masses, for M1 and M2 really around a TV or lower, next generation direct detection detectors, we'll actually already find that dark matter. The reason is that they're the mixing between the Hexeno and the Bino and Wino is large enough that you actually get sort of the mostly Hexeno mass eigenstate, it can act also like a Bino or a Wino. And this gives you a larger cross-section than we're talking about. And so actually you can find those anyway. So that parameter space, a lot of that parameter space is already ruled out by the direct detection experiments. And I think any of it that isn't ruled out will be in the next few years. So that parameter space we can also tackle. Right, and I have another brief question. I didn't understand in the case where you have this 1700 KVM Kelvin temperature. Is that like an equilibrium temperature? I mean, that's the black body temperature. So if you've had a black body spectrum and you asked me what temperature do I plug into that to get the neutron star spectrum right? That's the 1750 Kelvin. Right, right. What I mean is like the neutron star would be losing energy because it's... Oh yeah, yeah, yeah. So I mean, that's the equilibrium temperature if there's dark matter in the halo and all of it scatters with the neutron star, yeah. Right, okay. So I mean, but that's actually sort of a dark matter model independent statement in the sense that it doesn't matter what my dark matter mass is. The kinetic energy it has as it's moving through the neutron star is the same. Simply because the energy density of dark matter is the same across all these different models. So that's why that temperature is the same no matter which dark matter model I'm thinking about. Anyone else want to ask? Yeah, yeah, I have a couple of questions for Joseph. First of all, Joseph, very nice with the slides. I'd like to look at the style. Yeah, I have a couple of questions. So one question is regarding can you also put some constraint or kind of sensitivity with respect with scattering with electrons? Because also this is that's kind of most of the direction also they are pointing to electron Yeah. Required energy between electrons and dark matter in these cases. So it turns out because there are about a 10th as many you can simply take the sensitivity curves I showed you and we're doing a paper that properly inspects this question, but I can tell you basically how it works. I take the sensitivity curves I show you and you shift them up by one order of magnitude. So if you compare that to direct detection experiments searching for electrons scattering it actually does a lot, lot better. At low masses it does better than in order of magnitude above. And this is because the degenerate momentum of the electrons in the neutron star is lower than the degenerate momentum of the neutrons. And so there you're not as polyblocked as you were with the neutrons. And so there are lies for the low mass region and a lie about a factor of two above the sensitivity curve I showed you. And then for the GB to PB region it would be a factor of an order of magnitude above this. So yeah. Ah yeah, so it's awesome. The other question is like what about the, is it possible to trace the evolution of the neutron star in this case? Kind of the H error diagram, but for neutron stars. I mean, I would expect because this kinetic hitting, dark kinetic hitting is more relevant for older neutron stars. So there you could see some kind of deviation with respect to a whole population or something like that. I don't know how is this. Yeah, you're exactly correct. That's exactly what we're looking for. We're looking for, you know, typical stellar cooling curves look like this, but then if there's an additional source of heating in this case dark kinetic heating or dark annihilation heating, it flattens out if it's a constant heat source. And so that's exactly, if you're thinking about a diagram that looks like that, that's exactly what we're looking for here. I've just tried to phrase it a bit more simply that, you know, oh, if you see neutron stars this hot when they're very old, then, you know, yeah, but it is that steady state temperature that the dark matter is giving it. Ah, that's cool. So in principle, but I don't know if this effect would modify also the pulsation rate of the if it is a pulsar in this instance. Oh. Yeah, because there are different effects at the end because how the neutron star lose angular momentum is is not true. Typically, especially for these old guys, they're losing, they're simply radiating like a dipole in free space. So if I just like put a magnetic dipole, like literally one of these magnets you can buy in free space and just like spun it around, then it's emission and EM in electromagnetic waves is what's slowing down these older pulsars. So I don't expect this very low level of heating because this is a very low level of heating compared to neutrons, well, compared to pulsars that we've seen that are much hotter that don't seem to be affected by their heat. I don't expect this low level of heating to affect how it's spinning or pulsing, but it's always possible. They're very complicated systems. Yeah, yeah, yeah, that's for sure. Yeah, mostly my faith in this whole setup is that, you know, this very basic thermodynamics, you know, energy in and energy out has to balance. Which is what we're talking about. Yeah, so, I mean, yeah. No, yeah, yeah, it's a little bit, yeah, thank you. I think, oh, thanks, sorry. I think you published a paper, or maybe, yeah, I think it was you that capturing of dark matter inside neutron stars and then gravitationally collapsing. Yeah, yeah, so, sorry. How much overlap is there between these dark matter candidates and those dark, well, obviously there's our bosons and the former ones are bosons, right? So we need to just kind of become a boson and condensate them. Yeah, so actually those models you can do, it's fermions as well, and also very heavy fermions and heavy bosons. But yeah, so the idea there is it's possible to collect enough dark matter into a neutron star. If it can't annihilate with itself, that you form a small black hole inside the neutron star. Then that small black hole at first very gradually and then at the end very explosively sucks up all the neutron star fluid into itself. So it's not so much gravitationally collapsing the neutron star as it is creating a tiny black hole at its center and then having that black hole grow until it consumes the neutron star. But that's all exactly correct what you said. Those models are a subset of dark kinetic heating models, mostly because dark kinetic heating works with almost any dark matter model. It's very hard to construct a dark matter model that wouldn't dark kinetically heat the pulsar. In fact, you could flip this around and I like to flip this around. You could say that in a sense, while you often talk about things that are complementary to direct detection experiments, if you get this up and running, then direct detection experiments will complement this. Because this will actually apply to all these inelastic and spin dependent and weird models and actually strongly interacting dark matter models that no one really talks about and I don't have time to get into. Yeah, those are fascinating. I have one question from the audience that's not here. It's just from the YouTube chat. It's from Maria Angel Asperes Garcia. Her question is how about in homogenize in the temperature profile for young neutron stars? Is there, would they be possible? So Maria is a researcher who does dark matter neutron stars more. She's been up in the game longer than I have. So I have to be very careful when trying to answer this question, which is very good work. So let me think about this. Okay, so I mean, I guess I would say naively and again, I would caution, perhaps I haven't understood the question as well as I should. I don't worry about the young neutron stars because I'm only looking for the old neutron stars. So I think there are in homogeneities and temperature profiles for young neutron stars that have been observed. Some people think that's because if I'm thinking about a particular pulsar that's quite famous, the sort of poles of the neutron star where it seemed to be heated to much higher X-ray temperatures than sort of the most, the rest of the neutron star which is more an optical and the theory there was it had recently accreted a ton of baryons and those would sort of follow the magnetic field lines and heat the tops of the neutron star more than the center. That's one example of in homogeneously heated young neutron stars that I know of that could be what's being referenced. And I mean, actually that does get to a very good point which is that if you find neutron stars that are very old or you think are very old and you think they've been heated by dark matter, one test you could do to make sure they weren't heated by baryons is looking for this sort of inhomogeneous heating and if you don't, if you see only sort of a homogeneous black body spectrum from all points on the pulsar and then you'd be safer but I will be writing Maria an email to make sure I understood the question later. But yes, thank you for the question. Okay, I have one question. So I was wondering about dark matter self interactions. So if you have sizable self interaction you can also capture dark matter with this. So the self interactions I've played around with with regards to those black hole forming models because it can change whether or not you form black holes or how long it takes to form black holes in a neutron stars. In terms of actually capturing the dark matter I think the main thing will be what scattering cross section is off of nucleons. There's some self interacting dark matter models I've recently become aware of where maybe, no, that doesn't make sense. So I don't wanna say it. Yeah, I'm not sure. You could maybe come up with a model where that's true. I don't know about it yet though. Oh, oh, oh, sorry. Okay, nevermind. I think I understand the question now. So if you collect a bunch of dark matter inside of the neutron star, then you could ask, can I capture more dark matter using that dark matter? Exactly, self capture. Yeah, yeah, I understand that. That sometimes is true. Sort of at the limits of the parameter space we're thinking about. You already need the neutron star almost to be opaque to the dark matter. So to almost capture every dark matter particle that's coming through the star to begin with. And that limit, it doesn't matter so much what the dark matter inside is doing for capturing because you're already in the limit where you're capturing every dark matter particle that moves through it. But yes, as we get to lower and lower cross sections in the future, as we probe lower and lower cross sections you're exactly right. You could think about models where you're doing a little bit better at capturing the dark matter than you naively expect because of the dark matter particles we've already captured. Absolutely, that's a good point. Okay, thanks. Great. Well, thank you Joe. In the interest of time, we're gonna end the talk here. If you have other questions, I can get them to Joe at some point. Well, thank you Joe for this wonderful talk and thanks for joining the Latin America. I hope you found this experience pretty cool. That's another way to kind of spread your research around the world in a very, very cool way. So with that, thank you all for watching the webinar and I will see you next time. Okay, thank you everyone. Thank you for watching and thanks. Yeah, it was great. Bye.