Simulating Universes
Busch, Philipp
In this talk I want to present the computational undertakings in the field of cosmological structure formation and galaxy formation. Here, sometimes gigantic simulations help us to unravel the processes that led to the Universe that we can see today. I will give a short overview of our current understanding of the evolution of the Universe, the history and techniques of the simulations and their current state and future.
 Now, our next talk is simulating universes. Our speaker is Philipp Bülsch. He's a PhD student at the Max Planck Institute. He used to study at Potsdam at the Leibniz Institute. And as quite a few of you, he's also an angel at the Congress. He's going to speak about how astrophysics profited from improvements in computational power and what the current understanding of the universe is for this perspective. Please welcome him for a huge round of applause. Hi, so thanks everyone for coming. And thanks for the organizers for giving me the chance to talk about this. Actually, last Congress, I heard some very interesting talks in this room. And I thought, why not give a talk about an aspect of science that completely relies on huge computers and couldn't be done otherwise? And to show you where we are going to end up at the end of the talk, I want to show you this video. This is the modern cosmological simulation, including gas physics and everything run by a collaboration of astrophysicists from the US and Germany and some other countries. And basically, I hope at the end of the talk, you'll be able to understand what you're seeing here and why it's there. OK. And to get there, as this is a simulation, we need to simulate universes. I couldn't have given this talk without learning a lot from different people. First of all, I want to mention the top row, my former and current supervisors in Garching and Potsdam, few friends and colleagues of mine in the second row who helped me prepare this talk and some more colleagues that provided me with material for this talk. And yeah, science is a group effort, so I couldn't have done it without them. Before I really come to the simulations, we first have to talk about what we are simulating. And so I have to give you a quick introduction into cosmology, which is the science of the development of the universe as a whole. So this is a certain sense, a neighboring or speciality of astrophysics. And there's also going to be a lot of astrophysics in the talk, although we're not going to go very deep into this part. So let's dive right in. This is, in our community, a very famous plot by the Planck collaboration. Planck is a satellite that measures the cosmic micro-ref background, which I'm going to come to in a second. And this basically has it all in there. Everything that we know or that we think to know or do know to a large degree, but how the universe developed, is in this plot. We are here today. And because light has a finite speed, we look away, and we look into the past. Because light from for the way took some time to reach us. And so we look all the way to the past. And of course, we can't look all the way to the Big Bang, but that's where our story starts. And so we have this Big Bang event, which I guess all of you have heard about. And afterwards, we have a phase of rapid expansion, in which actually quantum mechanical fluctuations are blown up to macroscopic sizes. And it's these fluctuations, which perturb an initially homogeneous universe, and which then bring the structure that we see today, galaxies, and so on. And after this very rapid expansion, the universe still expands. And as it expands, it cools down. And particles start to form. There's still a lot of light in there, so a lot of photons, which interact with these particles. And some of these particles are what we call dark matter. And they don't interact with these light particles, while the rest is the normal matter that we know. So basically, protons, neutrons, and later on electrons. And they do interact with light. And because they do interact with light, although they attract each other gravitationally, they do not form structure yet. But dark matter, because it's decoupled from the photons, can already start forming structure. And that's one of the hints why there has to be something like dark matter. Because if there wouldn't be dark matter, there wouldn't have been enough time today to see any structure in the universe as something like galaxies and so on. OK, then stuff, the universe further expands. The contents further cool down. And at one point, the universe is so big and so dilute that the normal matter and photons stop interacting with each other. And at that point, the photons can just fly freely. And at some point later on, reaching us, after being redshifted by a lot of match, redshifted is so the wavelength increases. Red light has a longer wavelength. So we call this redshifting. And that basically happens because the universe is expanding under the light as it travels to us. And because of this redshift, it reaches us as cosmic microwave radiation, the cosmic microwave background. But at this point, it's not a microwave yet. It's a shorter wave thing. Anyway, the dark matter has already formed structure. The gas streams into the structure and starts forming stars and galaxies. And more and more structure forms, the longer the universe exists. So it's stuff further clumps. And it becomes less and less homogeneous. And this is this dark matter structure in purple. But the structure we actually see are the galaxies. And the galaxies inhabit this rich dark matter structure in basically just as tracers. So we don't see the full structure like that. But we only see some light bulbs, if you want to say, on this tree or on this network of dark matter structure. OK. Now, this is a picture or a depiction of the cosmic microwave background. And so this is a full-sky map. This is basically all around us. This was measured by Planck. Again, this is from 2013. So it's a satellite that basically measures how the cosmic microwave radiation reaches us. And it can calculate what's called a black body temperature or a black body temperature for each point. But that's not really important. What I want to show you here, so there is some structure in there. But you only see the structure because we subtract it, a value 100,000 times bigger than the variations. So for the most part, the cosmic microwave background is one temperature. But there are tiny fluctuations. As I show down here, it's 0.001% variation on this one temperature. And these variations are very close to what mathematicians will call a Gaussian random field. And this was predicted this way. This was predicted by our cosmological model. Whether there are some tiny deviations, actually an interesting current question. But because it's a Gaussian random field, there's one statistic that describes it fully in a statistical sense. And that's the power spectrum. So basically, how strong are the fluctuations on a given scale? And it's not really important that you understand why this curve looks this way. What is important here, and which I would like you to see, is that in red, we see the data points. We see what we measure from this map. And in green, as a fit, is a cosmological model with six free parameters, only six. And these six free parameters give us a predicted power spectrum that fits these data points to this degree of accuracy. So the green line is the mean value, and then the green area is basically uncertainty on this level. And unfortunately, this works so well. People would love if it wouldn't work so well, because then there would be more to talk about. But for the last 30 years, it has worked really well. And people are trying to break it. And Sarah Conrad is going to give a talk about how people might find some problems in there, and what can be done, or what other avenues can be explored on day four at 2 PM or 2 10 PM. So I would definitely also check this talk out and learn more about this. OK, from this fit, we get the following makeup of the universe once at the time of the CMB, where the CMB was emitted, and then today. And at the time of the CMB, there was emitted atoms and dark matter, which don't really change in absolute amount, but in relative amount, where the most part of the universe they emit neutrinos and photons. And because of the expansion of the universe and the red shifting, they decrease in basically energy content. And atoms and dark matter still stay the same. But then there's something weird called dark energy, which drives the accelerated expansion, as we know since the late 90s of the universe, and which, again, Sarah Conrad will also talk much more in depth about. OK, so far, I mostly talked about gravity only, and I talked a bit about gas flowing. And that also sets the stage for our simulations. The most important thing we have to talk about is gravity. And we can't do simulations of the universe without gravity. The second thing is hydrodynamics. And we can already do quite good simulations without hydrodynamics. But in the end, if you want to look at the smaller scales, we need hydrodynamics. And then there are many more things, radiation, and many more things that might also appear later on in the talk, but they're not that important. And I don't have the time to actually talk about how we incorporate them in simulations. So well, the first question, I guess, is why do we do simulations at all? And yes, there are a lot of analytical models, but they only take us so far. And we have a problem. The things in space are pretty big. So we can't really set them up in a lab. And so if we want to play around with things, we have to see what we can actually observe with our ground-based telescopes, and nowadays also satellites. And then we do have a large amount of other physical theories. That we know about. And so we might have some idea how these things work in space. And then we can calculate what they should do, which is our simulation. And then we see whether they actually do that. And our simulation itself takes some input. And then we have some algorithm that is inspired by physics, which basically incorporates our physical laws. And then predict some output. And whether our output matches the observation, then tells us whether we're on the right track or not. OK. But while we need one more step for simulations, we need to discretize our problems. And this is something that will appear over and over in this talk. That's why I'm putting it here. Otherwise, I don't turn it up to get too technical. But this basically is just so we have some continuous field. And to describe this field, we will discretize it into a finite amount of elements. And for example, we can just use particles of the same mass if we interpret this as a density field. And then where it's denser, so where it's darker, we have more particles per unit area. And where it's less dense, we have less particles per unit area. OK. And our simulations themselves will only deal with the particles. They will only see how these particles work. OK. So I talked about how dark matter doesn't interact with light. And because it doesn't interact with light, so it doesn't do electromagnetic interactions, it also doesn't collide with itself as normal matter does. So we have a collisionless system, which is only influenced by gravity. And it's a good approximation to just say everything in the universe is just something like dark matter. It's just collisionless, only gravitationally influenced matter. And we'll see where this takes us. And the problem that this is is called the n-body problem. That's why these simulations are called n-body simulations. And basically, it's just the question, how do these n-bodies, so these particles, for example, that only interact via gravity, how do they behave over time? And we all know from high school physics, we have some Newton's gravitational law. And we don't need GR at this point, because we're far from the limits where GR would be of any relevance to us. But we basically have to see how n-particles act on these n-particles. And as I've written down here, just because, I mean, in the end, we're at a technology and computer-focused Congress, usually this calculation would scale as n squared. But we can make this much faster using smart codes, like particle mesh, we use phosphoryl transforms, or tree codes, and so on, to get to n log n. And then some newer codes even implement methods in ON, so just for the people that are interested in this. OK, then let's get to an early example of this, because people have been trying to solve this problem for quite some time, even before they had computers. And this is more for the hacker and tinkering part of the audience, because Mr. Holmberg here, Eric Holmberg, in 1941 also tried to solve this problem. And he mostly was concerned with this 1 over d squared thing in there. And I mean, many things scale as 1 over d squared, for example, the light intensity from a light bulb. So he set up a system of little elements with a light bulb and a photoreceptor. And those were his particles. And then he basically measured how much light from the other particles were reaching every given particle and could, this way, evolve the system. And he actually got pretty good results with that. So and with a lot of student work, of course, because there was a lot of manual work back then. But so he has two galaxies. Actually, a problem that we'll revisit, I mean, it's often used in this field of study. And we'll see later on. But we have two galaxies. And as they cross or came close to each other and interacted, they formed these tidal tails you see here. And this is a picture from a real galaxy taken with a Hubble Space Telescope. And this is how actually galaxy looks like. I mean, this is pure work of gravity and, yeah, Newtonian dynamics. And then when people had computers, they revisited this problem, Tumor and Tumor, Uncle and Nephew wrote this paper together. And, yeah, we again see these tidal tails. Yeah, and even nowadays, some people look at simulations like that, not necessarily for the tidal tails, because it's kind of soft, but for other questions. OK, but we're actually interested in the whole universe, right? So we look at cosmological in-body simulations. And we don't start with the galaxies here, but we actually start with the power spectrum. So what we're actually doing, we're not simulating our universe, because in the end, the cosmic microwave background is billions of light years away, because it was billions of years ago. So we just create an initial density field with the same statistic, with the same power spectrum. So with the same amount of fluctuations on different scales as we measure in our universe. And while nowadays, you can do maybe, you come a bit closer, as I will show in the end of the talk, to our universe, that is what we do for the most part. And just to give you a feeling how this such an in-body simulation looks like, I want to show you this quick video, which is just a 2D simulation. So we're not in 3D yet. We're just 2Ds, because then it's easier to understand. This was done by a colleague of mine, Jan Stikker. And he's basically sitting there, and he's basically seeing how in slightly underdense regions, the particles flow out. And where you had these slight over densities, the particles flow in. And then at some point, they meet each other down here, for example, and they flow through each other, and they cross. And we get this system of filaments and nodes. And remember this first video? We also had this system of filaments and nodes. Of course, in 3D, it's a bit different, because after one crossing, you get some two-dimensional structure. You get a sheet. And then after second crossing, only you get a filament, because then you have collapsed two dimensions, and you're left with one dimension. And then when you collapse it in more dimensions, then, for example, down here, also, now we collapse two dimensions in 2D, and three dimensions, and we collapse three dimensions, you get what we call halos. And halos are the birthplace of galaxies, because they are the densest dark matter structures. And there, the gas flows in, and then the galaxies, both stars and the galaxies that make up these, and the stars that make up the galaxies form in there. Sorry. Yeah, but we're also not the first to do this, of course. I mean, people in the 70s already did this. And this is a video that a colleague of mine unearthed in Estonia from the USSR, and where Doroshevich and his co-workers already did this in the 70s, and then must have projected it on some screen and filmed it with some camera from the screen. But you already see the same structure, basically, as we've just seen. And you can jump a bit forward. So if you jump here, they also did the same problem, basically, that we just showed as a toy example. And I mean, that's, by now, what, 41 years ago? And they even had quite realistic cosmological density fields, but I mean, in 2D here, but nevertheless. So what I'm working with still, despite this having been run in 2005, but there's just a lot of information in there that we can still investigate, is the Millennium Simulation, which is very important for the field, because at the time, it was the largest simulation, and it was very influential in the development. And this uses a bit more than 10 billion particles in 2005. And each particle represents something like a billion solar masses. So one solar mass is one sun, and a billion of them is one particle. And we have 10 billion particles in the simulation. And the box is 500 mega-parsec. So we always have this over 8 here. And one parsec is a bit more than three light years. And mega-parsec is then a bit more than 3 million light years. And we have 500 of them on each side. As you will notice, actually, we have one giga-parsec here. In this picture of the slices is because the people did a very smart trick of basically unfolding this box for this picture so that it doesn't repeat. But then this video shows us a flight into this thing, into the simulation, and we'll see how much structure is actually resolved. And at this point, so this is actually a good nice place to stop, here you can see a lot of things already. So you see this network, which is called the Cosmic Web. And you see the nodes in there. This is where large clusters of galaxies form. And here are smaller clusters or groups. You have empty regions, the voids. And you have filaments. This is where also a lot of galaxies live, which are traced then by basically these linear arrangements of galaxies. And then let's jump forward a bit. So now we're zooming into this thing. And we still see structure, right? We started with thousands of mega-parsec. Now we're single mega-parsec, and there's still structure. And that is, to me, at least absolutely fascinating that we can see that much in a simulation. Nowadays, of course, computers get bigger. Simulations get bigger. This is from last year. It's one of the biggest that I know of. It's a two trillion particle simulation, so two with 12 zeros. And this is used for a future satellite mission, basically, to have some data that you can already analyze before the mission is running and to learn how to analyze the data from this mission. And again, here you see these little density peaks, the halos. And that's a very useful abstraction because they are the birthplace of galaxies. And I already told you some of these things. So halos are these gravitationally collapsed dark matter objects. And we really would like to know a lot about halos. And they're basically the core outcome of these simulations, the core result of these simulations to know about how the halos are distributed, how they look like, and so on. Because how a halo looks like and how it was formed tells us about the galaxy that was formed in there. And so here, I just chose this picture because it nicely shows this process of going from a part of the density field with all these density peaks in here. And then we separate it into a main halo and a lot of subhalos. And then basically, we're mostly interested in this abstracted picture. Of course, not necessarily in a plot, but in an abstracted data analysis, kind of with thinking. And then we want to know what they look like and how they were formed. And to define these various methods, so in the 80s, people started with what they call friends of friends halo finers. I also worked with them for quite some time, which basically just collect cluster opothics. I think people from machine learning will also know these algorithms as cluster finders. And then there's another one, spherical overdensity finers, which just look for overdensity peaks or density peaks and then grow spheres around them until they reach a certain minimum density and stop. But modern halo finders, for example, Rockstar by Peter Beruzzi, they're much more complex and don't only work on the positions, but they also take the full phase space, including the velocities into account and so on. But I also told you that we're interested in how the halos form. And that is encoded in here. And this is what's called a merger tree, basically, because halos don't form just from creating diffuse material, but they also form from halos merging. And this is what we see here. So this halo today was formed from all these different halos. And I mean, you see all these little halos here, basically, which at some point in time, so this is time looking backwards from today, merged with this halo and make up this halo. OK, so what is one of the most prominent and most important outcomes of these simulations that we didn't know about before, actually, is what's called the NFW profile. After, the discoverer is Navarro, Frank, and White, which discovered it in 1996 in simulations. And this is very remarkable because they found that no matter the mass of the halo, all the density profiles are basically how the density evolves as you go outwards can be described to a very good degree with two parameters, this RS and rho, and R is basically how far out you are. And so you have a R2 to the minus 1 slope in the center, and then at some point at RS, you go over to an R2 to the minus 2 slope, and you have some normalization factor. And that's actually quite remarkable. And this has also been tested with observations and has worked very well so far. Of course, there's slight deviations in certain cases, but it's a very good model. And it was not theoretically predicted before. I mean, people had ideas about how they should look like, but that it really is that was unclear before the bigger n-body simulations in the 90s. And we can also, I don't have time to talk about how, but we can populate these dark matter only simulations, spite not having gas in there, with galaxies through using these merger trees and the masses of the halos and so on. So just through this dark matter information, which basically represents dark matter and gas, we can populate them with galaxies, and then compare these galaxy populations with real observations of galaxies. And in the top left part of this plot, we see real observations. So people going out there, taking the telescopes, measuring positions of galaxies in distance and on the sky. And we can do this in the simulation. This is in the millennium simulation and do it in the same fashion. And we see there's not a big difference. I mean, it really looks the same. So we are on the right track there. And this is also why, for example, these MOC simulations for these bigger, or for this satellite, this Euclid satellite that I showed you before, why they do these simulations. Because basically you can do this analysis already in simulations to then do the analysis later on with the real data. OK. We can even compare this more quantitatively. So here we have the correlation function. So basically how many, so take a certain kind of galaxy in this case and look how many other galaxies this kind, or how many other objects I expect at a certain radius. So we have the radial distance here. This is this. But it doesn't really matter what it shows in detail. What I want to show you is that the dots are the measured values from the very important SDSS survey. And in red, we have different kinds of populating the simulation with galaxies. But it works really well, even if we split galaxies into red and blue. And if we go to different masses, so this is a factor of 1,000 in mass between here and here. So this works really well. But still, I mean, we're treating everything as a collisionless fluid. And that's not really right. So there is gas in the universe. There is normal matter in the universe. We're living testament of that. So we are going to hydrodynamic simulations because we need hydrodynamics at some point because we actually want to know how the gas behaves. And these hydrodynamic simulations, for us today, they're only going to have these four ingredients. So apart from gravity, of course, and gravity is still in there, it's still the most important part. We need to model the hydrodynamics. We need to see how we form stars in there because that's in the end what we see and how we treat the supermassive black holes because it's in the center of galaxies because it turns out they're actually quite important to what we see in these galaxies and how the stars and the supermassive black holes act back on their host galaxies and how they form them. And they are more phenomenon that are included nowadays in most simulations, but as I said, time does not permit treating them. OK, so Eulerian hydrodynamics is the first way of treating hydrodynamics. So we just discretize space this time into a grid. And because we have some regions where we need more spatial resolution than in others, we have nested hierarchy of grids in there. And there are codes today that still use them, or not still use them, but that do use them, for example, Ramses and Enzo, two codes that are very important in the field. But this basically, yeah, as I said, discretizes space. But before we discretize mass, we can also do this for hydrodynamics. We basically divide our gas up into particles or moving cells. And so the first way of dealing with this that did this was, it's called smooth particle hydrodynamics. I think many people will know this by now if they used blender or something like this. They think they also have this in there. Many other fields use this. So basically, you have a particle that represents a certain amount of gas. And then you have some kernel function which smooths this particle. And then you let these smooth particles interact. And another way that we're going to look a bit more in detail at in a second, or just give a little example of, is an unstructured mesh, where you have these generator points. Then you calculate a Voronoi tessellation. Then you know which cells are neighboring each other. And then a bit like in the Eulerian hydrodynamics, you let stuff flow from one cell to the other. But you basically refine or derefine your grid to keep the cells at roughly the same mass. And then there are new techniques which have particles, again, which look similar and which are then called meshless methods, because they don't really have these cells and meshes. But yeah, they just look the same. OK. So just to give you a quick example of how this looks like, on the left is a very bad resolution example where you can actually see the cells using this technique here in the middle, this moving mesh, which is also used in the simulations that I'm going to show you further on, and that I showed you in the first video. And just to give you a feeling of what this looks like. So we have a flow to the right and a flow to the left. You can see this as cool and this as hot. And we see the cells in the center are very square. And they move with the flow. And at the surface, they deform. And you see how the stuff mixes in the cells and how the cells flow with the fluid. And this way, you basically, this makes it often advantageous as compared to Eulerian hydrodynamics. And then if you don't do this with a bad resolution, but with a quite good resolution, and this is pretty much the same problem with a little bit different initial condition, but we see we get very nice results. We get a very nice Kelvin-Helmholtz instability, which is the standard test of hydrodynamical codes with these two fluids flowing through each other or by each other. And we see the level of details and 40 C's that we can track with this. OK, so this is hydrodynamics. We hope we have a good handle on that. Then what about stars and supermassive black holes? Problem is we can't resolve them. I mean, particles are still, I mean, even in good simulations, there's still way too big to track single stars or to represent the space that actually is the supermassive black hole. I mean, they're huge, but they're still really, really tiny compared to the dimensions of the simulation. So what we use are subgrid models, which are effective models, which basically tell us how the processes that we cannot resolve behave and how they act back on the scales that we do resolve. And so instead of resolving how all these single stars in this forming star cluster in the Andromeda galaxy, that's where this picture's from, actually form, we just have star particles, which represent sometimes millions, sometimes thousands of stars. And then we have models, how basically these, when these stars explode, how they feed back energy and momentum into the surrounding gas. The same happens for supermassive black holes. So here we have a multi-frequency composite image of a very active galaxy, where the supermassive black hole at the center drives out these jets and emits a lot of energy. Because, I mean, black holes do eat, but they're very messy eaters. So when they eat, the material that falls in gets heated a lot, it radiates. And also a lot of the materials actually spin out again and imparts momentum on the surrounding gas. And how the supernova feedback looks like. I want to show you in this video, run by Chayu Hu from NPA at the time now in New York. And this gives you a face-on density map of a dwarf galaxy. And cut through this galaxy, and we see stars forming, and then exploding, and forming these low-density bubbles as they drive out the gas. And this is most important in small galaxies and dwarf galaxies, because they're not massive enough to really keep all the gas in. And they're the potential well. So the gravitational potential is weak enough that these supernovas can really do a lot of damage. And as we see, it really reshaped this galaxy. On the other mass end of galaxies, we have very massive supermassive thick holes. And yeah, here I want to show you this video run by DiMatteo and collaborators in 2005. And while the results are not scientifically 100% to date now, but they're still very close to what's actually happening. And so we have two very massive galaxies, of which we can see the gas here, with the hue representing the temperature and the color, the density, if I remember correctly, interact. So fly by each other. That actually, remember the tidal tails that I showed you before? That's what's forming there right now. So we see these tidal tails, and we have supermassive thick holes at the centers of these two galaxies. And at one point, they start eating a lot of this gas, which is driven on them as part of this collision. And it starts heating up, and we already see some outflows there. And then at some point, they really start releasing a lot of energy and driving out the gas. And if there's no gas, if there's no cool gas, which can form stars, which can gravitation collapse, it's hot again. And remember, as talked about in the early universe, then we can't really form stars. And this also inhibits star formation in very massive galaxies. And we didn't always know that we needed these two processes, but observations told us that very massive and very low mass galaxies don't form a lot of stars. And what we see here is actually the mass of stars divided by the mass of the dark matter halos of the system. So as a proportional to the mass of normal matter in the universe divided by the matter of the universe. So basically, this is a question, how much available gas in the universe is actually turned into stars in galaxies? And we see that here, we see the mass of the galactic system, so dark matter halo plus the galaxy inside, but it's mostly just the dark matter halo. And we see that at the low mass end, stellar feedback, so mostly supernovae, really decreases this amount of gas that is formed into stars, the proportional one, and at the high mass end. And here, these colorful curves are observations. This red and black one is an older simulation, which actually doesn't get this top end perfectly right. But we'll see a video of the refined model, which does much better than this. But nonetheless, we see this trend already here. And we in our galaxy, the Milky Way, live here in the roughly at the sweet spot where we formed the most stars. But even there, we only turn 25% of the theoretically available gas into stars. OK. I told you that nowadays, galaxy simulation, or these cosmological hydrodynamic simulations, do much better. And so I want to show you some results from the illustrious TNG. This is from the illustrious simulation, the illustrious TNG, because apparently people like Star Trek do much better. And this is just a little gallery of all the different kinds of galaxies they form. And they look pretty realistic. And if you look at the other two, they look pretty realistic. And at some point, we can also look at another talk at more quantitative floods, but also quantitatively, they do much better. And that's actually the simulation where this initial video came from. And now I hope we could explain to you why you see what you see. So we have a very large gas density and temperature. In this cosmological hydrodynamic simulation, we see the gas flowing into dark matter halos that formed. And into this cosmic web structure formed by the dark matter. We see that you don't see as many little bright spots as you saw in the dark matter simulation when we just showed these density maps, because the small galaxies can hold their gas. The big spots, the gas is also driven out in these winds from the feedback. And you see things merging and forming bigger and bigger lumps. And here, we actually see something like a cluster of galaxies form. But it's still, of course, a bit hard to envision how this looks like in starlight. So let's look at this in a bit more quantitative fashion. Here, we just have some slice projected into 2D with three panels, the gas density, what we've saw just now, and the dark matter density, what we've seen, for example, for the Millennium simulation before, and actually the stars. So this is what you would see if you could look out with your telescope and see very faint objects. And this again from the illustrious TNG simulation. And this is run by Dylan Nelsen, a colleague of mine. He did these very nice figures. And so let's run them for a bit. We see how the dark matter structure forms. And then the gas follows this already much more structured dark matter. And then we see over here how stars created. And sometimes you can even see, let's maybe go back to the beginning of the video, you can see how these single stellar particles pop up here. And later on, there's enough star formation that you don't see these single events anymore. And yeah, we see how this structure forms. And this already looks a bit like, if you remember, this plot from the very beginning with these actual galaxy surveys. We see this web structure. But we also see that galaxies only trace it quite sparsely. So for the most of this dark structure is hidden from us. And we also don't directly see the gas. But we could, for example, observe it if we have very powerful light sources behind it and then see how, as the light pierces through the gas, is changing its properties. And dark matter, for example, we can see if we maybe someone else has said, give a talk at some point about this here. Gravitational lensing, how basically the gravitational force of the dark matter bends the light around it and distorts the galaxy images that are behind this structure. So what are people doing nowadays? So what's happening at the moment in this field? Of course, things get bigger. Things always get bigger with computers. So we started here in the 90s, before we had a few. So this is the number of resolution elements. So particles or cells or something like this. So antibody particles or hydrocells and so on. And we started with 10 to 100,000. And nowadays, yeah, we're in the billion, tens of billion range. Inbodies simulations were always faster because just calculating gravity is much faster than also doing all these other calculations. But they actually track each other quite well. This is from a publication by Gannel in 2014. So we don't have the most recent developments on here. But as things get bigger, they also get much harder to save. So the millennium simulation uses roughly 300 gigabytes per snapchat just for a particle data. Then if you have data products, it gets much bigger. And we have 64 snapshots. So that's roughly 18 therabytes that we need to save if we want to keep it. This Euclid flagship simulation, I calculated if you would save it as the millennium simulation, of course, you can trick a bit. And then it would be 60 terabytes per snapshot. If we have 60 snapshots, this would be 3.6 petabyte, which, I guess, is not. I mean, yes, I think we can save it at our institute, maybe three times or so. But then our storage is full. So the solution is we don't really save everything. So we produce these halo catalogs that I talked about before. So we look for the halos on the fly and write those things out and how they merge into each other and so on. And we only record data on a light cone. Because I mean, you saw this before when I showed you this plot in the beginning of the history of the universe. As the light reaches us, it basically light from further way places reaches us later. So we see into the past as we look out. And so basically, we record on a light cone as if the light would go through the simulation box and just record the particle data on this light cone. And then we have basically a simulated observation from a certain point in this simulation box. OK, they also get stronger. They have more physical processes included, things that I didn't talk about. For example, radiation, magnetic fields are already included in the illustrious TNG and illustrious simulation. Cosmic rays, dust, stars produce dust, and dust couples gas and radiation. And in the end, there's a lot more processes that we can follow, which also increase computational complexity. And as we increase our resolution, we decrease what we have to consider a sub-grid. So in this simulation of the supernova and the skeleton, I mean, the star particles were, I think, 10 solar masses or so. And in other simulations, they would have to be thousands or hundreds of thousands of solar masses and so on. So sometimes you actually resolve single stars in this very high, so the very massive stars you would resolve as a single particle in these simulations. And they become faster because, but I mean, this being faster is then translated into we make them bigger, so they're as slow as before, because we have the same lifetime as a researcher, but we now have more computational time. And we also include more things in them. But of course, also the codes get faster. As I told you about before, I mean, when we talked about this n-body problem, there are faster and faster methods, and the codes become just much more efficient. And we also have new codes that maybe solve certain problems in a more specialized but fast way. But as computers become bigger, scaling becomes more of a problem because we don't just use one core in the beginning or maybe a few hundred or a few thousand. But now we come into the scale where, so I talked once about running something on the Tianhe computer, so I think that's 1.0 million cores or so. I forgot. But anyway, so we're talking about massive numbers, of course, that have to work together. And so scaling becomes a major concern. And so right now, most of these simulations are programmed in this typical MPI open MP paradigm, where you have MPI for the inter-process communication, and then on a node, you have open MP threads that do most of the work, sometimes just MPI with one process per core, but people move away from there and work with computer scientists and specialists from big HPC vendors to get faster and better algorithms into these simulations. And as they become faster, there's one more thing that I wanted to show you. We can actually do interesting things with them. And this is something that Yan Siashev, who used to be at my institute and is now in Stockholm, does what he basically tries to, in a certain sense, fit in-body simulations to our local universe. So we basically calculate in-body simulation in a quick way and then perturbs the initial conditions in such a way that he comes closer and closer to the real outcome. And here on the right, you see in dark his simulated density field, and in red actually galaxies from a real galaxy survey. And they match really well. OK, there are some parts where they don't really match, but for the most part, they match really, really well. And then he knows from where he started. So this is on a shell 100 megaparsec around us. And so this way, he can unravel the initial conditions of our own universe. And there are also other groups that do similar undertakings, for example, in Potsdam and in a different way, but with a similar goal. Yeah, and I think also for this audience, quite interesting, this field is becoming increasingly open, but it's already quite open in the sense that the codes are to a large degree public. Some parts of the codes are not necessarily public, but a lot of the big codes try to be as public as they deem possible. So you can just go to GitHub or whatever and just look for these codes and run simulations yourself. They have some small working examples, and you can toy around with them. I mean, you don't really have a supercomputer, but you can still do some nice little exercises. The simulation results are often made public. So they actually want you to use the data. I mean, you as a scientist now that produces relevant citations. And that really helps make the simulations known and gets more value out of the simulations because more people can actually work on them. And here, again, I want to give the millennium simulation as an example. So in 2018, I'm still working on this. This was run in 2005 when I turned 14. And today, or the last time I checked, that there were 974 publications that used the data from the simulation for this publication. I mean, some of them were just on the simulation, some compared it with others. But yeah, I think that's a pretty impressive number. And yeah, it's really interesting. And you can also look at those things yourself. I mean, they're on the web in the end. Sometimes you have to register and maybe tell them why you want to look at these things. So there's cosmosyn.org run by Pippin Potsdam, the millennium database from Durham and the MPA in Garsing where I work. Cosmoop, I think it's in ETH. And the Elastos TNG database from this Elastos collaboration, also MPA and Harvard and some other institutions that are involved there. And so the Elastos TNG was actually publicly released on the 14th of December. So it's pretty new on the web now. But you can look at the halo catalogs and you can look at all the interesting outcomes of these simulations. And with this, I want to leave you with my take home messages. I hope I could explain to you why cosmological simulations are really powerful tools and for cosmology and galaxy formation in these cosmologies and how they predict also some previously unknown things that we, for example, this NFW profile that we didn't really know about before. And also, they're quite robust in terms of the gravity. And also, I mean, we've seen there was some evolution still between, for example, Elastos and the Elastos TNG. But they're also getting better and better in this respect. And they're huge computational undertakings. And they're very nice examples of how science and its results can be made public and the way to get to these results as well. And if you want to know more about the physical size of these things, there's going to be a great talk by Sarah Conrad from Heidelberg, who's going to talk about dark matter and dark energy on day four at 10 past 2 in Borg. And yeah, I'll definitely go there and I hope I'll see many of you there. Thank you. Thank you, Philipp. If you would like to leave at this point, please do that very quietly so that people can still enjoy the Q & A. If you would like to ask a question, please line up in the microphones in the room. We have a question from the internet, the simulation results embargo. Sorry? What is the reason for the simulation results embargo? Because if you run the simulation, you also want to be the first to call dibs and use the results for some time. They still invite people, but they have these project pages where they basically say, okay, I want to do this with the simulation, some other in the cover, color operation wants to do this. Other project with simulation, and that's basically that you just want to reap the fruits of your own labor. Alright, thanks. Thank you. My phone number two. Yeah, as far as I understood, these simulations are not as granular as to predict the behavior of individual stars or are they? Okay. How far along will it approximately be until this is possible and also factors like the different classes, star classes of the H.R.R.S.R. diagram? Yeah, no. I mean, there are, so there was something that I had in the talk that I threw out again. So there are, of course, simulations that simulate how star clusters form. So there are simulations even that simulate how a single star evolves in 3D and how it explodes as a supernova. But I think it's not the, it's not really, not every simulation has to do everything at the same time. I mean, you can have specialized simulations that look on a certain length scale and then use the information and that's also what people try to do, to use information from that length scale then in a model that you can basically use as a separate model in larger simulations, for example. Thank you. Please try to limit your questions to a single sentence. Michael, for number one, please. Hi, and thank you. Of all the particles in our physical universe, having mass, is every particle able to interact with every other particle? No. Thanks. Michael, for number four. So in all your simulations, is there kind of sometimes a steady state that simulation goes to and then just doesn't go any further in terms of changes or is it always changing? No, I don't think so because I mean, you have an accelerated expansion, so. Well, it could be that it reaches equilibrium for some reason or the other. So it doesn't matter. It's not that I know of, not for any reason that I know of. And of course, sorry, so just for the question right now, I mean, yeah, it doesn't interact via all interactions. Of course, if it has mass, it will interact via gravity. Yeah, sorry, just to finish up this question. All right. Michael, for number three, your question. Yeah, so as you said, the models have been scaling up all during the last decade. Are there actually questions that could be answered by just a bigger model? So does it really make sense to go bigger and bigger all the time? It improves your statistics. Basically, you get more extreme environments. So basically, if you have a bigger box, so for example, the smaller hydrodynamic simulations often don't have very massive clusters in them just because clusters are very massive clusters of galaxies are rare. And then sometimes you form one and then if you're lucky with your initial conditions, but you can't really predict that because you haven't run the simulation yet. And then sometimes you don't. And so bigger boxes basically help you to get all these different environments sampled and the same for the largest voids and so on. You don't have the largest voids in a small box because sometimes your box is smaller than the largest void. Michael, for number one, your question. Hi, thank you for your interest in talk. My question is what is the time scale at which the simulations are run? Meaning, so you basically start the simulation from these image of the temperature scan, right? And then you run it for, I don't know how much. So could it be that we just run compared to the life of the universe, the simulation for like a very tiny? No, no, no, no. So you run it. So you don't run it. A, you don't run directly from this image because in the beginning you can do analytical approximations. But then at some point those break down and then you have to really do these calculations. But then you usually run them until today. So also this video that I showed you, it runs from when the universe, so just the video shows you the part of the simulation that runs from when the universe was a fifth of its current volume and then until today basically. That's what you usually, I mean sometimes people miscalculate their computing time and then they run out of computing time and they don't get there. That's always a bit annoying. But some simulations are even constructed that way because they're not interested in today. They're only interested in the high redshift universe, meaning the old universe. So for example, just, yeah, the process of how the first stars and galaxies form and then you don't really want it to run that far down because you have enough simulations showing that part. All right. Single individual question from the internet. No, my question from the internet is, is it possible to simulate backwards instead of changing star parameters until they match what we observe in our universe? Not so, not no. Okay. Thank you. Mike from number two, your question. Yeah. So regarding research about fitting certain, you know, like simulations into our coding of current observations, would it be possible, how many initial states could yield the current observations that we have? Like not only the sheer number, but because that's probably infinite, but could two completely different initial states like completely random and having no connection whatsoever yield the same state like converge? The exact same? No, I mean, two completely different initial states converging into our, you know, into some state after the simulation that closely resembles our current observations. Or do they have some common pattern? Well, I mean, if the large scale fluctuations are very different than no, I don't think so. But it's a good question. I might have to think about this. All right. Thank you, Phillip. That's unfortunately the last question we have time. Please give him a huge round of applause for that excellent talk.
 Now, our next talk is simulating universes.  Our speaker is Philipp Bülsch.  He's a PhD student at the Max Planck Institute.  He used to study at Potsdam at the Leibniz Institute.  And as quite a few of you, he's also an angel at the Congress.  He's going to speak about how astrophysics profited  from improvements in computational power  and what the current understanding of the universe  is for this perspective.  Please welcome him for a huge round of applause.  Hi, so thanks everyone for coming.  And thanks for the organizers for giving me the chance  to talk about this.  Actually, last Congress, I heard some very interesting talks  in this room.  And I thought, why not give a talk about an aspect of science  that completely relies on huge computers  and couldn't be done otherwise?  And to show you where we are going to end up  at the end of the talk, I want to show you this video.  This is the modern cosmological simulation,  including gas physics and everything  run by a collaboration of astrophysicists from the US  and Germany and some other countries.  And basically, I hope at the end of the talk,  you'll be able to understand what you're seeing here  and why it's there.  OK.  And to get there, as this is a simulation,  we need to simulate universes.  I couldn't have given this talk without learning  a lot from different people.  First of all, I want to mention the top row, my former and current  supervisors in Garching and Potsdam,  few friends and colleagues of mine in the second row who  helped me prepare this talk and some more colleagues that  provided me with material for this talk.  And yeah, science is a group effort,  so I couldn't have done it without them.  Before I really come to the simulations,  we first have to talk about what we are simulating.  And so I have to give you a quick introduction  into cosmology, which is the science of the development  of the universe as a whole.  So this is a certain sense, a neighboring or speciality  of astrophysics.  And there's also going to be a lot of astrophysics in the talk,  although we're not going to go very deep into this part.  So let's dive right in.  This is, in our community, a very famous plot  by the Planck collaboration.  Planck is a satellite that measures the cosmic micro-ref  background, which I'm going to come to in a second.  And this basically has it all in there.  Everything that we know or that we think to know or do  know to a large degree, but how the universe developed,  is in this plot.  We are here today.  And because light has a finite speed, we look away,  and we look into the past.  Because light from for the way took some time to reach us.  And so we look all the way to the past.  And of course, we can't look all the way to the Big Bang,  but that's where our story starts.  And so we have this Big Bang event, which I guess  all of you have heard about.  And afterwards, we have a phase of rapid expansion,  in which actually quantum mechanical fluctuations  are blown up to macroscopic sizes.  And it's these fluctuations, which perturb an initially  homogeneous universe, and which then bring the structure  that we see today, galaxies, and so on.  And after this very rapid expansion, the universe still  expands.  And as it expands, it cools down.  And particles start to form.  There's still a lot of light in there,  so a lot of photons, which interact with these particles.  And some of these particles are what we call dark matter.  And they don't interact with these light particles,  while the rest is the normal matter that we know.  So basically, protons, neutrons, and later on electrons.  And they do interact with light.  And because they do interact with light,  although they attract each other gravitationally,  they do not form structure yet.  But dark matter, because it's decoupled from the photons,  can already start forming structure.  And that's one of the hints why there  has to be something like dark matter.  Because if there wouldn't be dark matter,  there wouldn't have been enough time today  to see any structure in the universe  as something like galaxies and so on.  OK, then stuff, the universe further expands.  The contents further cool down.  And at one point, the universe is so big and so dilute  that the normal matter and photons  stop interacting with each other.  And at that point, the photons can just fly freely.  And at some point later on, reaching us,  after being redshifted by a lot of match,  redshifted is so the wavelength increases.  Red light has a longer wavelength.  So we call this redshifting.  And that basically happens because the universe is  expanding under the light as it travels to us.  And because of this redshift, it reaches us  as cosmic microwave radiation, the cosmic microwave background.  But at this point, it's not a microwave yet.  It's a shorter wave thing.  Anyway, the dark matter has already formed structure.  The gas streams into the structure  and starts forming stars and galaxies.  And more and more structure forms,  the longer the universe exists.  So it's stuff further clumps.  And it becomes less and less homogeneous.  And this is this dark matter structure in purple.  But the structure we actually see are the galaxies.  And the galaxies inhabit this rich dark matter structure  in basically just as tracers.  So we don't see the full structure like that.  But we only see some light bulbs, if you want to say,  on this tree or on this network of dark matter structure.  OK.  Now, this is a picture or a depiction  of the cosmic microwave background.  And so this is a full-sky map.  This is basically all around us.  This was measured by Planck.  Again, this is from 2013.  So it's a satellite that basically measures  how the cosmic microwave radiation reaches us.  And it can calculate what's called a black body temperature  or a black body temperature for each point.  But that's not really important.  What I want to show you here, so there is some structure in there.  But you only see the structure because we subtract it,  a value 100,000 times bigger than the variations.  So for the most part, the cosmic microwave background  is one temperature.  But there are tiny fluctuations.  As I show down here, it's 0.001% variation  on this one temperature.  And these variations are very close to what mathematicians  will call a Gaussian random field.  And this was predicted this way.  This was predicted by our cosmological model.  Whether there are some tiny deviations,  actually an interesting current question.  But because it's a Gaussian random field,  there's one statistic that describes it fully  in a statistical sense.  And that's the power spectrum.  So basically, how strong are the fluctuations  on a given scale?  And it's not really important that you understand  why this curve looks this way.  What is important here, and which I would like you to see,  is that in red, we see the data points.  We see what we measure from this map.  And in green, as a fit, is a cosmological model  with six free parameters, only six.  And these six free parameters give us a predicted power  spectrum that fits these data points  to this degree of accuracy.  So the green line is the mean value,  and then the green area is basically uncertainty on this  level.  And unfortunately, this works so well.  People would love if it wouldn't work so well,  because then there would be more to talk about.  But for the last 30 years, it has worked really well.  And people are trying to break it.  And Sarah Conrad is going to give a talk about how people might  find some problems in there, and what can be done,  or what other avenues can be explored on day four at 2  PM or 2 10 PM.  So I would definitely also check this talk out  and learn more about this.  OK, from this fit, we get the following makeup of the universe  once at the time of the CMB, where the CMB was emitted,  and then today.  And at the time of the CMB, there  was emitted atoms and dark matter, which don't really  change in absolute amount, but in relative amount,  where the most part of the universe  they emit neutrinos and photons.  And because of the expansion of the universe  and the red shifting, they decrease in basically energy  content.  And atoms and dark matter still stay the same.  But then there's something weird called dark energy,  which drives the accelerated expansion,  as we know since the late 90s of the universe,  and which, again, Sarah Conrad will also  talk much more in depth about.  OK, so far, I mostly talked about gravity only,  and I talked a bit about gas flowing.  And that also sets the stage for our simulations.  The most important thing we have to talk about is gravity.  And we can't do simulations of the universe without gravity.  The second thing is hydrodynamics.  And we can already do quite good simulations  without hydrodynamics.  But in the end, if you want to look at the smaller scales,  we need hydrodynamics.  And then there are many more things, radiation,  and many more things that might also  appear later on in the talk, but they're not that important.  And I don't have the time to actually talk about how  we incorporate them in simulations.  So well, the first question, I guess,  is why do we do simulations at all?  And yes, there are a lot of analytical models,  but they only take us so far.  And we have a problem.  The things in space are pretty big.  So we can't really set them up in a lab.  And so if we want to play around with things,  we have to see what we can actually  observe with our ground-based telescopes,  and nowadays also satellites.  And then we do have a large amount of other physical theories.  That we know about.  And so we might have some idea how these things work in space.  And then we can calculate what they should do,  which is our simulation.  And then we see whether they actually do that.  And our simulation itself takes some input.  And then we have some algorithm that  is inspired by physics, which basically incorporates  our physical laws.  And then predict some output.  And whether our output matches the observation,  then tells us whether we're on the right track or not.  OK.  But while we need one more step for simulations,  we need to discretize our problems.  And this is something that will appear over and over  in this talk.  That's why I'm putting it here.  Otherwise, I don't turn it up to get too technical.  But this basically is just so we have some continuous field.  And to describe this field, we will discretize it  into a finite amount of elements.  And for example, we can just use particles of the same mass  if we interpret this as a density field.  And then where it's denser, so where it's darker,  we have more particles per unit area.  And where it's less dense, we have less particles per unit area.  OK.  And our simulations themselves will only deal with the particles.  They will only see how these particles work.  OK.  So I talked about how dark matter doesn't interact with light.  And because it doesn't interact with light,  so it doesn't do electromagnetic interactions,  it also doesn't collide with itself as normal matter does.  So we have a collisionless system,  which is only influenced by gravity.  And it's a good approximation to just say everything  in the universe is just something like dark matter.  It's just collisionless, only gravitationally influenced  matter.  And we'll see where this takes us.  And the problem that this is is called the n-body problem.  That's why these simulations are called n-body simulations.  And basically, it's just the question,  how do these n-bodies, so these particles, for example,  that only interact via gravity, how do they behave over time?  And we all know from high school physics,  we have some Newton's gravitational law.  And we don't need GR at this point,  because we're far from the limits where GR  would be of any relevance to us.  But we basically have to see how n-particles act on these n-particles.  And as I've written down here, just because, I mean,  in the end, we're at a technology and computer-focused  Congress, usually this calculation would scale as n squared.  But we can make this much faster using smart codes,  like particle mesh, we use phosphoryl transforms,  or tree codes, and so on, to get to n log n.  And then some newer codes even implement methods in ON,  so just for the people that are interested in this.  OK, then let's get to an early example of this,  because people have been trying to solve this problem for quite  some time, even before they had computers.  And this is more for the hacker and tinkering part  of the audience, because Mr. Holmberg here, Eric Holmberg,  in 1941 also tried to solve this problem.  And he mostly was concerned with this 1 over d squared thing  in there.  And I mean, many things scale as 1 over d squared,  for example, the light intensity from a light bulb.  So he set up a system of little elements  with a light bulb and a photoreceptor.  And those were his particles.  And then he basically measured how much light  from the other particles were reaching every given particle  and could, this way, evolve the system.  And he actually got pretty good results with that.  So and with a lot of student work, of course,  because there was a lot of manual work back then.  But so he has two galaxies.  Actually, a problem that we'll revisit,  I mean, it's often used in this field of study.  And we'll see later on.  But we have two galaxies.  And as they cross or came close to each other and interacted,  they formed these tidal tails you see here.  And this is a picture from a real galaxy  taken with a Hubble Space Telescope.  And this is how actually galaxy looks like.  I mean, this is pure work of gravity and, yeah,  Newtonian dynamics.  And then when people had computers,  they revisited this problem, Tumor and Tumor,  Uncle and Nephew wrote this paper together.  And, yeah, we again see these tidal tails.  Yeah, and even nowadays, some people  look at simulations like that, not necessarily  for the tidal tails, because it's kind of soft,  but for other questions.  OK, but we're actually interested in the whole universe,  right?  So we look at cosmological in-body simulations.  And we don't start with the galaxies here,  but we actually start with the power spectrum.  So what we're actually doing, we're not  simulating our universe, because in the end,  the cosmic microwave background is billions of light years  away, because it was billions of years ago.  So we just create an initial density field  with the same statistic, with the same power spectrum.  So with the same amount of fluctuations  on different scales as we measure in our universe.  And while nowadays, you can do maybe, you come a bit closer,  as I will show in the end of the talk, to our universe,  that is what we do for the most part.  And just to give you a feeling how this such an in-body  simulation looks like, I want to show you this quick video, which  is just a 2D simulation.  So we're not in 3D yet.  We're just 2Ds, because then it's easier to understand.  This was done by a colleague of mine, Jan Stikker.  And he's basically sitting there,  and he's basically seeing how in slightly underdense regions,  the particles flow out.  And where you had these slight over densities,  the particles flow in.  And then at some point, they meet each other down here,  for example, and they flow through each other, and they cross.  And we get this system of filaments and nodes.  And remember this first video?  We also had this system of filaments and nodes.  Of course, in 3D, it's a bit different,  because after one crossing, you get some two-dimensional structure.  You get a sheet.  And then after second crossing, only you get a filament,  because then you have collapsed two dimensions,  and you're left with one dimension.  And then when you collapse it in more dimensions,  then, for example, down here, also,  now we collapse two dimensions in 2D,  and three dimensions, and we collapse three dimensions,  you get what we call halos.  And halos are the birthplace of galaxies,  because they are the densest dark matter structures.  And there, the gas flows in, and then the galaxies,  both stars and the galaxies that make up these,  and the stars that make up the galaxies form in there.  Sorry.  Yeah, but we're also not the first to do this, of course.  I mean, people in the 70s already did this.  And this is a video that a colleague of mine  unearthed in Estonia from the USSR,  and where Doroshevich and his co-workers already did this  in the 70s, and then must have projected it on some screen  and filmed it with some camera from the screen.  But you already see the same structure, basically,  as we've just seen.  And you can jump a bit forward.  So if you jump here, they also did the same problem, basically,  that we just showed as a toy example.  And I mean, that's, by now, what, 41 years ago?  And they even had quite realistic cosmological density  fields, but I mean, in 2D here, but nevertheless.  So what I'm working with still, despite this having  been run in 2005, but there's just a lot of information  in there that we can still investigate,  is the Millennium Simulation, which  is very important for the field, because at the time,  it was the largest simulation, and it was very influential  in the development.  And this uses a bit more than 10 billion particles in 2005.  And each particle represents something  like a billion solar masses.  So one solar mass is one sun, and a billion of them  is one particle.  And we have 10 billion particles in the simulation.  And the box is 500 mega-parsec.  So we always have this over 8 here.  And one parsec is a bit more than three light years.  And mega-parsec is then a bit more than 3 million light years.  And we have 500 of them on each side.  As you will notice, actually, we have one giga-parsec here.  In this picture of the slices is because the people did  a very smart trick of basically unfolding this box  for this picture so that it doesn't repeat.  But then this video shows us a flight into this thing,  into the simulation, and we'll see how much structure is  actually resolved.  And at this point, so this is actually a good nice place  to stop, here you can see a lot of things already.  So you see this network, which is called the Cosmic Web.  And you see the nodes in there.  This is where large clusters of galaxies form.  And here are smaller clusters or groups.  You have empty regions, the voids.  And you have filaments.  This is where also a lot of galaxies live,  which are traced then by basically these linear arrangements  of galaxies.  And then let's jump forward a bit.  So now we're zooming into this thing.  And we still see structure, right?  We started with thousands of mega-parsec.  Now we're single mega-parsec, and there's still structure.  And that is, to me, at least absolutely fascinating  that we can see that much in a simulation.  Nowadays, of course, computers get bigger.  Simulations get bigger.  This is from last year.  It's one of the biggest that I know of.  It's a two trillion particle simulation, so two with 12 zeros.  And this is used for a future satellite mission, basically,  to have some data that you can already  analyze before the mission is running  and to learn how to analyze the data from this mission.  And again, here you see these little density peaks, the halos.  And that's a very useful abstraction  because they are the birthplace of galaxies.  And I already told you some of these things.  So halos are these gravitationally  collapsed dark matter objects.  And we really would like to know a lot about halos.  And they're basically the core outcome of these simulations,  the core result of these simulations  to know about how the halos are distributed,  how they look like, and so on.  Because how a halo looks like and how it was formed  tells us about the galaxy that was formed in there.  And so here, I just chose this picture  because it nicely shows this process of going  from a part of the density field with all these density  peaks in here.  And then we separate it into a main halo and a lot of subhalos.  And then basically, we're mostly interested  in this abstracted picture.  Of course, not necessarily in a plot,  but in an abstracted data analysis, kind of with thinking.  And then we want to know what they look like  and how they were formed.  And to define these various methods,  so in the 80s, people started with what  they call friends of friends halo finers.  I also worked with them for quite some time, which basically  just collect cluster opothics.  I think people from machine learning  will also know these algorithms as cluster finders.  And then there's another one, spherical overdensity finers,  which just look for overdensity peaks or density peaks  and then grow spheres around them until they reach  a certain minimum density and stop.  But modern halo finders, for example, Rockstar by Peter  Beruzzi, they're much more complex  and don't only work on the positions,  but they also take the full phase space,  including the velocities into account and so on.  But I also told you that we're interested in how the halos form.  And that is encoded in here.  And this is what's called a merger tree, basically,  because halos don't form just from creating diffuse material,  but they also form from halos merging.  And this is what we see here.  So this halo today was formed from all these different halos.  And I mean, you see all these little halos here, basically,  which at some point in time, so this  is time looking backwards from today,  merged with this halo and make up this halo.  OK, so what is one of the most prominent and most important  outcomes of these simulations that we didn't know about  before, actually, is what's called the NFW profile.  After, the discoverer is Navarro, Frank, and White,  which discovered it in 1996 in simulations.  And this is very remarkable because they  found that no matter the mass of the halo,  all the density profiles are basically  how the density evolves as you go outwards  can be described to a very good degree with two parameters,  this RS and rho, and R is basically how far out you are.  And so you have a R2 to the minus 1 slope in the center,  and then at some point at RS, you go over to an R2 to the minus 2  slope, and you have some normalization factor.  And that's actually quite remarkable.  And this has also been tested with observations  and has worked very well so far.  Of course, there's slight deviations in certain cases,  but it's a very good model.  And it was not theoretically predicted before.  I mean, people had ideas about how they should look like,  but that it really is that was unclear before the bigger  n-body simulations in the 90s.  And we can also, I don't have time to talk about how,  but we can populate these dark matter only simulations,  spite not having gas in there, with galaxies  through using these merger trees and the masses of the halos  and so on.  So just through this dark matter information, which  basically represents dark matter and gas,  we can populate them with galaxies,  and then compare these galaxy populations  with real observations of galaxies.  And in the top left part of this plot,  we see real observations.  So people going out there, taking the telescopes,  measuring positions of galaxies in distance and on the sky.  And we can do this in the simulation.  This is in the millennium simulation  and do it in the same fashion.  And we see there's not a big difference.  I mean, it really looks the same.  So we are on the right track there.  And this is also why, for example,  these MOC simulations for these bigger,  or for this satellite, this Euclid satellite  that I showed you before, why they do these simulations.  Because basically you can do this analysis already  in simulations to then do the analysis later  on with the real data.  OK.  We can even compare this more quantitatively.  So here we have the correlation function.  So basically how many, so take a certain kind of galaxy  in this case and look how many other galaxies this kind,  or how many other objects I expect at a certain radius.  So we have the radial distance here.  This is this.  But it doesn't really matter what it shows in detail.  What I want to show you is that the dots  are the measured values from the very important SDSS survey.  And in red, we have different kinds  of populating the simulation with galaxies.  But it works really well, even if we split galaxies  into red and blue.  And if we go to different masses,  so this is a factor of 1,000 in mass between here and here.  So this works really well.  But still, I mean, we're treating everything  as a collisionless fluid.  And that's not really right.  So there is gas in the universe.  There is normal matter in the universe.  We're living testament of that.  So we are going to hydrodynamic simulations  because we need hydrodynamics at some point  because we actually want to know how the gas behaves.  And these hydrodynamic simulations, for us today,  they're only going to have these four ingredients.  So apart from gravity, of course, and gravity is still in there,  it's still the most important part.  We need to model the hydrodynamics.  We need to see how we form stars in there  because that's in the end what we see  and how we treat the supermassive black holes  because it's in the center of galaxies  because it turns out they're actually quite important to what  we see in these galaxies and how the stars and the supermassive  black holes act back on their host galaxies  and how they form them.  And they are more phenomenon that are included nowadays  in most simulations, but as I said,  time does not permit treating them.  OK, so Eulerian hydrodynamics is the first way  of treating hydrodynamics.  So we just discretize space this time into a grid.  And because we have some regions where  we need more spatial resolution than in others,  we have nested hierarchy of grids in there.  And there are codes today that still use them,  or not still use them, but that do use them,  for example, Ramses and Enzo, two codes that  are very important in the field.  But this basically, yeah, as I said, discretizes space.  But before we discretize mass, we  can also do this for hydrodynamics.  We basically divide our gas up into particles  or moving cells.  And so the first way of dealing with this that did this was,  it's called smooth particle hydrodynamics.  I think many people will know this by now  if they used blender or something like this.  They think they also have this in there.  Many other fields use this.  So basically, you have a particle  that represents a certain amount of gas.  And then you have some kernel function  which smooths this particle.  And then you let these smooth particles interact.  And another way that we're going to look a bit more in detail  at in a second, or just give a little example of,  is an unstructured mesh, where you have these generator points.  Then you calculate a Voronoi tessellation.  Then you know which cells are neighboring each other.  And then a bit like in the Eulerian hydrodynamics,  you let stuff flow from one cell to the other.  But you basically refine or derefine your grid  to keep the cells at roughly the same mass.  And then there are new techniques  which have particles, again, which look similar and which  are then called meshless methods,  because they don't really have these cells and meshes.  But yeah, they just look the same.  OK.  So just to give you a quick example of how this looks like,  on the left is a very bad resolution example  where you can actually see the cells using this technique here  in the middle, this moving mesh, which is also used  in the simulations that I'm going to show you further on,  and that I showed you in the first video.  And just to give you a feeling of what this looks like.  So we have a flow to the right and a flow to the left.  You can see this as cool and this as hot.  And we see the cells in the center are very square.  And they move with the flow.  And at the surface, they deform.  And you see how the stuff mixes in the cells  and how the cells flow with the fluid.  And this way, you basically, this  makes it often advantageous as compared to Eulerian hydrodynamics.  And then if you don't do this with a bad resolution,  but with a quite good resolution, and this is pretty much  the same problem with a little bit different initial condition,  but we see we get very nice results.  We get a very nice Kelvin-Helmholtz instability,  which is the standard test of hydrodynamical codes  with these two fluids flowing through each other or by each  other.  And we see the level of details and 40 C's  that we can track with this.  OK, so this is hydrodynamics.  We hope we have a good handle on that.  Then what about stars and supermassive black holes?  Problem is we can't resolve them.  I mean, particles are still, I mean, even in good simulations,  there's still way too big to track single stars  or to represent the space that actually  is the supermassive black hole.  I mean, they're huge, but they're still really, really tiny  compared to the dimensions of the simulation.  So what we use are subgrid models,  which are effective models, which basically tell us  how the processes that we cannot resolve behave  and how they act back on the scales that we do resolve.  And so instead of resolving how all these single stars  in this forming star cluster in the Andromeda galaxy,  that's where this picture's from, actually form,  we just have star particles, which represent sometimes  millions, sometimes thousands of stars.  And then we have models, how basically these,  when these stars explode, how they feed back energy and momentum  into the surrounding gas.  The same happens for supermassive black holes.  So here we have a multi-frequency composite image  of a very active galaxy, where the supermassive black hole  at the center drives out these jets  and emits a lot of energy.  Because, I mean, black holes do eat,  but they're very messy eaters.  So when they eat, the material that falls in gets heated a lot,  it radiates.  And also a lot of the materials actually  spin out again and imparts momentum on the surrounding gas.  And how the supernova feedback looks like.  I want to show you in this video,  run by Chayu Hu from NPA at the time now in New York.  And this gives you a face-on density map of a dwarf galaxy.  And cut through this galaxy, and we see stars forming,  and then exploding, and forming these low-density bubbles  as they drive out the gas.  And this is most important in small galaxies and dwarf  galaxies, because they're not massive enough  to really keep all the gas in.  And they're the potential well.  So the gravitational potential is weak enough  that these supernovas can really do a lot of damage.  And as we see, it really reshaped this galaxy.  On the other mass end of galaxies,  we have very massive supermassive thick holes.  And yeah, here I want to show you this video run by DiMatteo  and collaborators in 2005.  And while the results are not scientifically 100%  to date now, but they're still very close to what's  actually happening.  And so we have two very massive galaxies, of which  we can see the gas here, with the hue representing  the temperature and the color, the density,  if I remember correctly, interact.  So fly by each other.  That actually, remember the tidal tails  that I showed you before?  That's what's forming there right now.  So we see these tidal tails, and we  have supermassive thick holes at the centers  of these two galaxies.  And at one point, they start eating a lot of this gas,  which is driven on them as part of this collision.  And it starts heating up, and we already  see some outflows there.  And then at some point, they really  start releasing a lot of energy and driving out the gas.  And if there's no gas, if there's no cool gas,  which can form stars, which can gravitation collapse,  it's hot again.  And remember, as talked about in the early universe,  then we can't really form stars.  And this also inhibits star formation  in very massive galaxies.  And we didn't always know that we needed these two processes,  but observations told us that very massive and very low mass  galaxies don't form a lot of stars.  And what we see here is actually the mass of stars  divided by the mass of the dark matter halos of the system.  So as a proportional to the mass of normal matter  in the universe divided by the matter of the universe.  So basically, this is a question, how much available gas  in the universe is actually turned into stars in galaxies?  And we see that here, we see the mass of the galactic system,  so dark matter halo plus the galaxy inside,  but it's mostly just the dark matter halo.  And we see that at the low mass end,  stellar feedback, so mostly supernovae,  really decreases this amount of gas  that is formed into stars, the proportional one,  and at the high mass end.  And here, these colorful curves are observations.  This red and black one is an older simulation, which actually  doesn't get this top end perfectly right.  But we'll see a video of the refined model, which  does much better than this.  But nonetheless, we see this trend already here.  And we in our galaxy, the Milky Way,  live here in the roughly at the sweet spot  where we formed the most stars.  But even there, we only turn 25% of the theoretically  available gas into stars.  OK.  I told you that nowadays, galaxy simulation,  or these cosmological hydrodynamic simulations,  do much better.  And so I want to show you some results from the illustrious  TNG.  This is from the illustrious simulation, the illustrious TNG,  because apparently people like Star Trek do much better.  And this is just a little gallery  of all the different kinds of galaxies they form.  And they look pretty realistic.  And if you look at the other two,  they look pretty realistic.  And at some point, we can also look  at another talk at more quantitative floods,  but also quantitatively, they do much better.  And that's actually the simulation  where this initial video came from.  And now I hope we could explain to you  why you see what you see.  So we have a very large gas density and temperature.  In this cosmological hydrodynamic simulation,  we see the gas flowing into dark matter halos that formed.  And into this cosmic web structure formed by the dark matter.  We see that you don't see as many little bright spots  as you saw in the dark matter simulation  when we just showed these density maps,  because the small galaxies can hold their gas.  The big spots, the gas is also driven out  in these winds from the feedback.  And you see things merging and forming bigger and bigger lumps.  And here, we actually see something  like a cluster of galaxies form.  But it's still, of course, a bit hard to envision  how this looks like in starlight.  So let's look at this in a bit more quantitative fashion.  Here, we just have some slice projected into 2D  with three panels, the gas density, what we've  saw just now, and the dark matter density, what we've seen,  for example, for the Millennium simulation before,  and actually the stars.  So this is what you would see if you could look out  with your telescope and see very faint objects.  And this again from the illustrious TNG simulation.  And this is run by Dylan Nelsen, a colleague of mine.  He did these very nice figures.  And so let's run them for a bit.  We see how the dark matter structure forms.  And then the gas follows this already much more structured  dark matter.  And then we see over here how stars created.  And sometimes you can even see, let's maybe  go back to the beginning of the video,  you can see how these single stellar particles pop up here.  And later on, there's enough star formation  that you don't see these single events anymore.  And yeah, we see how this structure forms.  And this already looks a bit like, if you remember,  this plot from the very beginning  with these actual galaxy surveys.  We see this web structure.  But we also see that galaxies only trace it quite sparsely.  So for the most of this dark structure is hidden from us.  And we also don't directly see the gas.  But we could, for example, observe it  if we have very powerful light sources behind it  and then see how, as the light pierces through the gas,  is changing its properties.  And dark matter, for example, we can  see if we maybe someone else has said,  give a talk at some point about this here.  Gravitational lensing, how basically the gravitational  force of the dark matter bends the light around it  and distorts the galaxy images that  are behind this structure.  So what are people doing nowadays?  So what's happening at the moment in this field?  Of course, things get bigger.  Things always get bigger with computers.  So we started here in the 90s, before we had a few.  So this is the number of resolution elements.  So particles or cells or something like this.  So antibody particles or hydrocells and so on.  And we started with 10 to 100,000.  And nowadays, yeah, we're in the billion,  tens of billion range.  Inbodies simulations were always faster  because just calculating gravity is much faster  than also doing all these other calculations.  But they actually track each other quite well.  This is from a publication by Gannel in 2014.  So we don't have the most recent developments on here.  But as things get bigger, they also get much harder to save.  So the millennium simulation uses roughly 300 gigabytes  per snapchat just for a particle data.  Then if you have data products, it gets much bigger.  And we have 64 snapshots.  So that's roughly 18 therabytes that we need to save  if we want to keep it.  This Euclid flagship simulation, I calculated  if you would save it as the millennium simulation,  of course, you can trick a bit.  And then it would be 60 terabytes per snapshot.  If we have 60 snapshots, this would be 3.6 petabyte, which,  I guess, is not.  I mean, yes, I think we can save it at our institute,  maybe three times or so.  But then our storage is full.  So the solution is we don't really save everything.  So we produce these halo catalogs that I talked about before.  So we look for the halos on the fly  and write those things out and how they  merge into each other and so on.  And we only record data on a light cone.  Because I mean, you saw this before when  I showed you this plot in the beginning of the history  of the universe.  As the light reaches us, it basically  light from further way places reaches us later.  So we see into the past as we look out.  And so basically, we record on a light cone  as if the light would go through the simulation box  and just record the particle data on this light cone.  And then we have basically a simulated observation  from a certain point in this simulation box.  OK, they also get stronger.  They have more physical processes included,  things that I didn't talk about.  For example, radiation, magnetic fields  are already included in the illustrious TNG  and illustrious simulation.  Cosmic rays, dust, stars produce dust,  and dust couples gas and radiation.  And in the end, there's a lot more processes  that we can follow, which also increase  computational complexity.  And as we increase our resolution,  we decrease what we have to consider a sub-grid.  So in this simulation of the supernova and the skeleton,  I mean, the star particles were, I think, 10 solar masses or so.  And in other simulations, they would  have to be thousands or hundreds of thousands  of solar masses and so on.  So sometimes you actually resolve single stars  in this very high, so the very massive stars  you would resolve as a single particle in these simulations.  And they become faster because, but I mean,  this being faster is then translated into we make them  bigger, so they're as slow as before,  because we have the same lifetime as a researcher,  but we now have more computational time.  And we also include more things in them.  But of course, also the codes get faster.  As I told you about before, I mean,  when we talked about this n-body problem,  there are faster and faster methods,  and the codes become just much more efficient.  And we also have new codes that maybe solve certain problems  in a more specialized but fast way.  But as computers become bigger, scaling  becomes more of a problem because we don't just  use one core in the beginning or maybe a few hundred  or a few thousand.  But now we come into the scale where,  so I talked once about running something on the Tianhe  computer, so I think that's 1.0 million cores or so.  I forgot.  But anyway, so we're talking about massive numbers,  of course, that have to work together.  And so scaling becomes a major concern.  And so right now, most of these simulations  are programmed in this typical MPI open MP paradigm, where  you have MPI for the inter-process communication,  and then on a node, you have open MP threads that  do most of the work, sometimes just MPI with one process  per core, but people move away from there  and work with computer scientists and specialists  from big HPC vendors to get faster and better algorithms  into these simulations.  And as they become faster, there's  one more thing that I wanted to show you.  We can actually do interesting things with them.  And this is something that Yan Siashev, who  used to be at my institute and is now in Stockholm,  does what he basically tries to, in a certain sense,  fit in-body simulations to our local universe.  So we basically calculate in-body simulation  in a quick way and then perturbs the initial conditions  in such a way that he comes closer and closer  to the real outcome.  And here on the right, you see in dark  his simulated density field, and in red actually galaxies  from a real galaxy survey.  And they match really well.  OK, there are some parts where they don't really match,  but for the most part, they match really, really well.  And then he knows from where he started.  So this is on a shell 100 megaparsec around us.  And so this way, he can unravel the initial conditions  of our own universe.  And there are also other groups that  do similar undertakings, for example, in Potsdam  and in a different way, but with a similar goal.  Yeah, and I think also for this audience, quite interesting,  this field is becoming increasingly open,  but it's already quite open in the sense  that the codes are to a large degree public.  Some parts of the codes are not necessarily public,  but a lot of the big codes try to be as public  as they deem possible.  So you can just go to GitHub or whatever  and just look for these codes and run simulations yourself.  They have some small working examples,  and you can toy around with them.  I mean, you don't really have a supercomputer,  but you can still do some nice little exercises.  The simulation results are often made public.  So they actually want you to use the data.  I mean, you as a scientist now that produces relevant citations.  And that really helps make the simulations known  and gets more value out of the simulations  because more people can actually work on them.  And here, again, I want to give the millennium simulation  as an example.  So in 2018, I'm still working on this.  This was run in 2005 when I turned 14.  And today, or the last time I checked,  that there were 974 publications that  used the data from the simulation for this publication.  I mean, some of them were just on the simulation,  some compared it with others.  But yeah, I think that's a pretty impressive number.  And yeah, it's really interesting.  And you can also look at those things yourself.  I mean, they're on the web in the end.  Sometimes you have to register and maybe tell them  why you want to look at these things.  So there's cosmosyn.org run by Pippin Potsdam,  the millennium database from Durham and the MPA in Garsing  where I work.  Cosmoop, I think it's in ETH.  And the Elastos TNG database from this Elastos collaboration,  also MPA and Harvard and some other institutions  that are involved there.  And so the Elastos TNG was actually  publicly released on the 14th of December.  So it's pretty new on the web now.  But you can look at the halo catalogs  and you can look at all the interesting outcomes  of these simulations.  And with this, I want to leave you with my take home messages.  I hope I could explain to you why cosmological simulations are  really powerful tools and for cosmology and galaxy  formation in these cosmologies and how they predict  also some previously unknown things that we, for example,  this NFW profile that we didn't really know about before.  And also, they're quite robust in terms of the gravity.  And also, I mean, we've seen there was some evolution still  between, for example, Elastos and the Elastos TNG.  But they're also getting better and better in this respect.  And they're huge computational undertakings.  And they're very nice examples of how science and its results  can be made public and the way to get to these results as well.  And if you want to know more about the physical size  of these things, there's going to be a great talk by Sarah  Conrad from Heidelberg, who's going  to talk about dark matter and dark energy on day four  at 10 past 2 in Borg.  And yeah, I'll definitely go there  and I hope I'll see many of you there.  Thank you.  Thank you, Philipp.  If you would like to leave at this point, please do that very  quietly so that people can still enjoy the Q & A. If you would  like to ask a question, please line up in the microphones  in the room.  We have a question from the internet,  the simulation results embargo. Sorry? What is the reason for the simulation results embargo?  Because if you run the simulation, you also want to be the first to call dibs and use  the results for some time. They still invite people, but they have these project pages  where they basically say, okay, I want to do this with the simulation, some other in the  cover, color operation wants to do this. Other project with simulation, and that's basically  that you just want to reap the fruits of your own labor.  Alright, thanks. Thank you. My phone number two. Yeah, as far as I understood, these simulations  are not as granular as to predict the behavior of individual stars or are they? Okay. How  far along will it approximately be until this is possible and also factors like the different  classes, star classes of the H.R.R.S.R. diagram? Yeah, no. I mean, there are, so there was  something that I had in the talk that I threw out again. So there are, of course, simulations  that simulate how star clusters form. So there are simulations even that simulate how a single  star evolves in 3D and how it explodes as a supernova. But I think it's not the, it's  not really, not every simulation has to do everything at the same time. I mean, you can  have specialized simulations that look on a certain length scale and then use the information  and that's also what people try to do, to use information from that length scale then in  a model that you can basically use as a separate model in larger simulations, for example.  Thank you. Please try to limit your questions to a single sentence. Michael, for number  one, please. Hi, and thank you. Of all the particles in our physical universe, having  mass, is every particle able to interact with every other particle? No. Thanks. Michael,  for number four. So in all your simulations, is there kind of sometimes a steady state  that simulation goes to and then just doesn't go any further in terms of changes or is it  always changing? No, I don't think so because I mean, you have an accelerated expansion,  so. Well, it could be that it reaches equilibrium for some reason or the other. So it doesn't  matter. It's not that I know of, not for any reason that I know of. And of course, sorry,  so just for the question right now, I mean, yeah, it doesn't interact via all interactions.  Of course, if it has mass, it will interact via gravity. Yeah, sorry, just to finish up  this question. All right. Michael, for number three, your question. Yeah, so as you said,  the models have been scaling up all during the last decade. Are there actually questions  that could be answered by just a bigger model? So does it really make sense to go bigger  and bigger all the time? It improves your statistics. Basically, you get more extreme  environments. So basically, if you have a bigger box, so for example, the smaller hydrodynamic  simulations often don't have very massive clusters in them just because clusters are  very massive clusters of galaxies are rare. And then sometimes you form one and then if  you're lucky with your initial conditions, but you can't really predict that because  you haven't run the simulation yet. And then sometimes you don't. And so bigger boxes basically  help you to get all these different environments sampled and the same for the largest voids  and so on. You don't have the largest voids in a small box because sometimes your box  is smaller than the largest void. Michael, for number one, your question. Hi, thank  you for your interest in talk. My question is what is the time scale at which the simulations  are run? Meaning, so you basically start the simulation from these image of the temperature  scan, right? And then you run it for, I don't know how much. So could it be that we just  run compared to the life of the universe, the simulation for like a very tiny? No, no,  no, no. So you run it. So you don't run it. A, you don't run directly from this image  because in the beginning you can do analytical approximations. But then at some point those  break down and then you have to really do these calculations. But then you usually run  them until today. So also this video that I showed you, it runs from when the universe,  so just the video shows you the part of the simulation that runs from when the universe  was a fifth of its current volume and then until today basically. That's what you usually,  I mean sometimes people miscalculate their computing time and then they run out of computing  time and they don't get there. That's always a bit annoying. But some simulations are even  constructed that way because they're not interested in today. They're only interested in the high  redshift universe, meaning the old universe. So for example, just, yeah, the process of  how the first stars and galaxies form and then you don't really want it to run that  far down because you have enough simulations showing that part.  All right. Single individual question from the internet.  No, my question from the internet is, is it possible to simulate backwards instead of  changing star parameters until they match what we observe in our universe? Not so, not  no. Okay. Thank you. Mike from number two, your question.  Yeah. So regarding research about fitting certain, you know, like simulations into our  coding of current observations, would it be possible, how many initial states could yield  the current observations that we have? Like not only the sheer number, but because that's  probably infinite, but could two completely different initial states like completely random  and having no connection whatsoever yield the same state like converge?  The exact same? No, I mean, two completely different initial  states converging into our, you know, into some state after the simulation that closely  resembles our current observations. Or do they have some common pattern?  Well, I mean, if the large scale fluctuations are very different than no, I don't think  so. But it's a good question. I might have to think about this.  All right. Thank you, Phillip. That's unfortunately the last question we have time. Please give  him a huge round of applause for that excellent talk.
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Now, our next talk is simulating universes. Our speaker is Philipp Bülsch. He's a PhD student at the Max Planck Institute. He used to study at Potsdam at the Leibniz Institute. And as quite a few of you, he's also an angel at the Congress. He's going to speak about how astrophysics profited from improvements in computational power and what the current understanding of the universe is for this perspective. Please welcome him for a huge round of applause. Hi, so thanks everyone for coming. And thanks for the organizers for giving me the chance to talk about this. Actually, last Congress, I heard some very interesting talks in this room. And I thought, why not give a talk about an aspect of science that completely relies on huge computers and couldn't be done otherwise? And to show you where we are going to end up at the end of the talk, I want to show you this video. This is the modern cosmological simulation, including gas physics and everything run by a collaboration of astrophysicists from the US and Germany and some other countries. And basically, I hope at the end of the talk, you'll be able to understand what you're seeing here and why it's there. OK. And to get there, as this is a simulation, we need to simulate universes. I couldn't have given this talk without learning a lot from different people. First of all, I want to mention the top row, my former and current supervisors in Garching and Potsdam, few friends and colleagues of mine in the second row who helped me prepare this talk and some more colleagues that provided me with material for this talk. And yeah, science is a group effort, so I couldn't have done it without them. Before I really come to the simulations, we first have to talk about what we are simulating. And so I have to give you a quick introduction into cosmology, which is the science of the development of the universe as a whole. So this is a certain sense, a neighboring or speciality of astrophysics. And there's also going to be a lot of astrophysics in the talk, although we're not going to go very deep into this part. So let's dive right in. This is, in our community, a very famous plot by the Planck collaboration. Planck is a satellite that measures the cosmic micro-ref background, which I'm going to come to in a second. And this basically has it all in there. Everything that we know or that we think to know or do know to a large degree, but how the universe developed, is in this plot. We are here today. And because light has a finite speed, we look away, and we look into the past. Because light from for the way took some time to reach us. And so we look all the way to the past. And of course, we can't look all the way to the Big Bang, but that's where our story starts. And so we have this Big Bang event, which I guess all of you have heard about. And afterwards, we have a phase of rapid expansion, in which actually quantum mechanical fluctuations are blown up to macroscopic sizes. And it's these fluctuations, which perturb an initially homogeneous universe, and which then bring the structure that we see today, galaxies, and so on. And after this very rapid expansion, the universe still expands. And as it expands, it cools down. And particles start to form. There's still a lot of light in there, so a lot of photons, which interact with these particles. And some of these particles are what we call dark matter. And they don't interact with these light particles, while the rest is the normal matter that we know. So basically, protons, neutrons, and later on electrons. And they do interact with light. And because they do interact with light, although they attract each other gravitationally, they do not form structure yet. But dark matter, because it's decoupled from the photons, can already start forming structure. And that's one of the hints why there has to be something like dark matter. Because if there wouldn't be dark matter, there wouldn't have been enough time today to see any structure in the universe as something like galaxies and so on. OK, then stuff, the universe further expands. The contents further cool down. And at one point, the universe is so big and so dilute that the normal matter and photons stop interacting with each other. And at that point, the photons can just fly freely. And at some point later on, reaching us, after being redshifted by a lot of match, redshifted is so the wavelength increases. Red light has a longer wavelength. So we call this redshifting. And that basically happens because the universe is expanding under the light as it travels to us. And because of this redshift, it reaches us as cosmic microwave radiation, the cosmic microwave background. But at this point, it's not a microwave yet. It's a shorter wave thing. Anyway, the dark matter has already formed structure. The gas streams into the structure and starts forming stars and galaxies. And more and more structure forms, the longer the universe exists. So it's stuff further clumps. And it becomes less and less homogeneous. And this is this dark matter structure in purple. But the structure we actually see are the galaxies. And the galaxies inhabit this rich dark matter structure in basically just as tracers. So we don't see the full structure like that. But we only see some light bulbs, if you want to say, on this tree or on this network of dark matter structure. OK. Now, this is a picture or a depiction of the cosmic microwave background. And so this is a full-sky map. This is basically all around us. This was measured by Planck. Again, this is from 2013. So it's a satellite that basically measures how the cosmic microwave radiation reaches us. And it can calculate what's called a black body temperature or a black body temperature for each point. But that's not really important. What I want to show you here, so there is some structure in there. But you only see the structure because we subtract it, a value 100,000 times bigger than the variations. So for the most part, the cosmic microwave background is one temperature. But there are tiny fluctuations. As I show down here, it's 0.001% variation on this one temperature. And these variations are very close to what mathematicians will call a Gaussian random field. And this was predicted this way. This was predicted by our cosmological model. Whether there are some tiny deviations, actually an interesting current question. But because it's a Gaussian random field, there's one statistic that describes it fully in a statistical sense. And that's the power spectrum. So basically, how strong are the fluctuations on a given scale? And it's not really important that you understand why this curve looks this way. What is important here, and which I would like you to see, is that in red, we see the data points. We see what we measure from this map. And in green, as a fit, is a cosmological model with six free parameters, only six. And these six free parameters give us a predicted power spectrum that fits these data points to this degree of accuracy. So the green line is the mean value, and then the green area is basically uncertainty on this level. And unfortunately, this works so well. People would love if it wouldn't work so well, because then there would be more to talk about. But for the last 30 years, it has worked really well. And people are trying to break it. And Sarah Conrad is going to give a talk about how people might find some problems in there, and what can be done, or what other avenues can be explored on day four at 2 PM or 2 10 PM. So I would definitely also check this talk out and learn more about this. OK, from this fit, we get the following makeup of the universe once at the time of the CMB, where the CMB was emitted, and then today. And at the time of the CMB, there was emitted atoms and dark matter, which don't really change in absolute amount, but in relative amount, where the most part of the universe they emit neutrinos and photons. And because of the expansion of the universe and the red shifting, they decrease in basically energy content. And atoms and dark matter still stay the same. But then there's something weird called dark energy, which drives the accelerated expansion, as we know since the late 90s of the universe, and which, again, Sarah Conrad will also talk much more in depth about. OK, so far, I mostly talked about gravity only, and I talked a bit about gas flowing. And that also sets the stage for our simulations. The most important thing we have to talk about is gravity. And we can't do simulations of the universe without gravity. The second thing is hydrodynamics. And we can already do quite good simulations without hydrodynamics. But in the end, if you want to look at the smaller scales, we need hydrodynamics. And then there are many more things, radiation, and many more things that might also appear later on in the talk, but they're not that important. And I don't have the time to actually talk about how we incorporate them in simulations. So well, the first question, I guess, is why do we do simulations at all? And yes, there are a lot of analytical models, but they only take us so far. And we have a problem. The things in space are pretty big. So we can't really set them up in a lab. And so if we want to play around with things, we have to see what we can actually observe with our ground-based telescopes, and nowadays also satellites. And then we do have a large amount of other physical theories. That we know about. And so we might have some idea how these things work in space. And then we can calculate what they should do, which is our simulation. And then we see whether they actually do that. And our simulation itself takes some input. And then we have some algorithm that is inspired by physics, which basically incorporates our physical laws. And then predict some output. And whether our output matches the observation, then tells us whether we're on the right track or not. OK. But while we need one more step for simulations, we need to discretize our problems. And this is something that will appear over and over in this talk. That's why I'm putting it here. Otherwise, I don't turn it up to get too technical. But this basically is just so we have some continuous field. And to describe this field, we will discretize it into a finite amount of elements. And for example, we can just use particles of the same mass if we interpret this as a density field. And then where it's denser, so where it's darker, we have more particles per unit area. And where it's less dense, we have less particles per unit area. OK. And our simulations themselves will only deal with the particles. They will only see how these particles work. OK. So I talked about how dark matter doesn't interact with light. And because it doesn't interact with light, so it doesn't do electromagnetic interactions, it also doesn't collide with itself as normal matter does. So we have a collisionless system, which is only influenced by gravity. And it's a good approximation to just say everything in the universe is just something like dark matter. It's just collisionless, only gravitationally influenced matter. And we'll see where this takes us. And the problem that this is is called the n-body problem. That's why these simulations are called n-body simulations. And basically, it's just the question, how do these n-bodies, so these particles, for example, that only interact via gravity, how do they behave over time? And we all know from high school physics, we have some Newton's gravitational law. And we don't need GR at this point, because we're far from the limits where GR would be of any relevance to us. But we basically have to see how n-particles act on these n-particles. And as I've written down here, just because, I mean, in the end, we're at a technology and computer-focused Congress, usually this calculation would scale as n squared. But we can make this much faster using smart codes, like particle mesh, we use phosphoryl transforms, or tree codes, and so on, to get to n log n. And then some newer codes even implement methods in ON, so just for the people that are interested in this. OK, then let's get to an early example of this, because people have been trying to solve this problem for quite some time, even before they had computers. And this is more for the hacker and tinkering part of the audience, because Mr. Holmberg here, Eric Holmberg, in 1941 also tried to solve this problem. And he mostly was concerned with this 1 over d squared thing in there. And I mean, many things scale as 1 over d squared, for example, the light intensity from a light bulb. So he set up a system of little elements with a light bulb and a photoreceptor. And those were his particles. And then he basically measured how much light from the other particles were reaching every given particle and could, this way, evolve the system. And he actually got pretty good results with that. So and with a lot of student work, of course, because there was a lot of manual work back then. But so he has two galaxies. Actually, a problem that we'll revisit, I mean, it's often used in this field of study. And we'll see later on. But we have two galaxies. And as they cross or came close to each other and interacted, they formed these tidal tails you see here. And this is a picture from a real galaxy taken with a Hubble Space Telescope. And this is how actually galaxy looks like. I mean, this is pure work of gravity and, yeah, Newtonian dynamics. And then when people had computers, they revisited this problem, Tumor and Tumor, Uncle and Nephew wrote this paper together. And, yeah, we again see these tidal tails. Yeah, and even nowadays, some people look at simulations like that, not necessarily for the tidal tails, because it's kind of soft, but for other questions. OK, but we're actually interested in the whole universe, right? So we look at cosmological in-body simulations. And we don't start with the galaxies here, but we actually start with the power spectrum. So what we're actually doing, we're not simulating our universe, because in the end, the cosmic microwave background is billions of light years away, because it was billions of years ago. So we just create an initial density field with the same statistic, with the same power spectrum. So with the same amount of fluctuations on different scales as we measure in our universe. And while nowadays, you can do maybe, you come a bit closer, as I will show in the end of the talk, to our universe, that is what we do for the most part. And just to give you a feeling how this such an in-body simulation looks like, I want to show you this quick video, which is just a 2D simulation. So we're not in 3D yet. We're just 2Ds, because then it's easier to understand. This was done by a colleague of mine, Jan Stikker. And he's basically sitting there, and he's basically seeing how in slightly underdense regions, the particles flow out. And where you had these slight over densities, the particles flow in. And then at some point, they meet each other down here, for example, and they flow through each other, and they cross. And we get this system of filaments and nodes. And remember this first video? We also had this system of filaments and nodes. Of course, in 3D, it's a bit different, because after one crossing, you get some two-dimensional structure. You get a sheet. And then after second crossing, only you get a filament, because then you have collapsed two dimensions, and you're left with one dimension. And then when you collapse it in more dimensions, then, for example, down here, also, now we collapse two dimensions in 2D, and three dimensions, and we collapse three dimensions, you get what we call halos. And halos are the birthplace of galaxies, because they are the densest dark matter structures. And there, the gas flows in, and then the galaxies, both stars and the galaxies that make up these, and the stars that make up the galaxies form in there. Sorry. Yeah, but we're also not the first to do this, of course. I mean, people in the 70s already did this. And this is a video that a colleague of mine unearthed in Estonia from the USSR, and where Doroshevich and his co-workers already did this in the 70s, and then must have projected it on some screen and filmed it with some camera from the screen. But you already see the same structure, basically, as we've just seen. And you can jump a bit forward. So if you jump here, they also did the same problem, basically, that we just showed as a toy example. And I mean, that's, by now, what, 41 years ago? And they even had quite realistic cosmological density fields, but I mean, in 2D here, but nevertheless. So what I'm working with still, despite this having been run in 2005, but there's just a lot of information in there that we can still investigate, is the Millennium Simulation, which is very important for the field, because at the time, it was the largest simulation, and it was very influential in the development. And this uses a bit more than 10 billion particles in 2005. And each particle represents something like a billion solar masses. So one solar mass is one sun, and a billion of them is one particle. And we have 10 billion particles in the simulation. And the box is 500 mega-parsec. So we always have this over 8 here. And one parsec is a bit more than three light years. And mega-parsec is then a bit more than 3 million light years. And we have 500 of them on each side. As you will notice, actually, we have one giga-parsec here. In this picture of the slices is because the people did a very smart trick of basically unfolding this box for this picture so that it doesn't repeat. But then this video shows us a flight into this thing, into the simulation, and we'll see how much structure is actually resolved. And at this point, so this is actually a good nice place to stop, here you can see a lot of things already. So you see this network, which is called the Cosmic Web. And you see the nodes in there. This is where large clusters of galaxies form. And here are smaller clusters or groups. You have empty regions, the voids. And you have filaments. This is where also a lot of galaxies live, which are traced then by basically these linear arrangements of galaxies. And then let's jump forward a bit. So now we're zooming into this thing. And we still see structure, right? We started with thousands of mega-parsec. Now we're single mega-parsec, and there's still structure. And that is, to me, at least absolutely fascinating that we can see that much in a simulation. Nowadays, of course, computers get bigger. Simulations get bigger. This is from last year. It's one of the biggest that I know of. It's a two trillion particle simulation, so two with 12 zeros. And this is used for a future satellite mission, basically, to have some data that you can already analyze before the mission is running and to learn how to analyze the data from this mission. And again, here you see these little density peaks, the halos. And that's a very useful abstraction because they are the birthplace of galaxies. And I already told you some of these things. So halos are these gravitationally collapsed dark matter objects. And we really would like to know a lot about halos. And they're basically the core outcome of these simulations, the core result of these simulations to know about how the halos are distributed, how they look like, and so on. Because how a halo looks like and how it was formed tells us about the galaxy that was formed in there. And so here, I just chose this picture because it nicely shows this process of going from a part of the density field with all these density peaks in here. And then we separate it into a main halo and a lot of subhalos. And then basically, we're mostly interested in this abstracted picture. Of course, not necessarily in a plot, but in an abstracted data analysis, kind of with thinking. And then we want to know what they look like and how they were formed. And to define these various methods, so in the 80s, people started with what they call friends of friends halo finers. I also worked with them for quite some time, which basically just collect cluster opothics. I think people from machine learning will also know these algorithms as cluster finders. And then there's another one, spherical overdensity finers, which just look for overdensity peaks or density peaks and then grow spheres around them until they reach a certain minimum density and stop. But modern halo finders, for example, Rockstar by Peter Beruzzi, they're much more complex and don't only work on the positions, but they also take the full phase space, including the velocities into account and so on. But I also told you that we're interested in how the halos form. And that is encoded in here. And this is what's called a merger tree, basically, because halos don't form just from creating diffuse material, but they also form from halos merging. And this is what we see here. So this halo today was formed from all these different halos. And I mean, you see all these little halos here, basically, which at some point in time, so this is time looking backwards from today, merged with this halo and make up this halo. OK, so what is one of the most prominent and most important outcomes of these simulations that we didn't know about before, actually, is what's called the NFW profile. After, the discoverer is Navarro, Frank, and White, which discovered it in 1996 in simulations. And this is very remarkable because they found that no matter the mass of the halo, all the density profiles are basically how the density evolves as you go outwards can be described to a very good degree with two parameters, this RS and rho, and R is basically how far out you are. And so you have a R2 to the minus 1 slope in the center, and then at some point at RS, you go over to an R2 to the minus 2 slope, and you have some normalization factor. And that's actually quite remarkable. And this has also been tested with observations and has worked very well so far. Of course, there's slight deviations in certain cases, but it's a very good model. And it was not theoretically predicted before. I mean, people had ideas about how they should look like, but that it really is that was unclear before the bigger n-body simulations in the 90s. And we can also, I don't have time to talk about how, but we can populate these dark matter only simulations, spite not having gas in there, with galaxies through using these merger trees and the masses of the halos and so on. So just through this dark matter information, which basically represents dark matter and gas, we can populate them with galaxies, and then compare these galaxy populations with real observations of galaxies. And in the top left part of this plot, we see real observations. So people going out there, taking the telescopes, measuring positions of galaxies in distance and on the sky. And we can do this in the simulation. This is in the millennium simulation and do it in the same fashion. And we see there's not a big difference. I mean, it really looks the same. So we are on the right track there. And this is also why, for example, these MOC simulations for these bigger, or for this satellite, this Euclid satellite that I showed you before, why they do these simulations. Because basically you can do this analysis already in simulations to then do the analysis later on with the real data. OK. We can even compare this more quantitatively. So here we have the correlation function. So basically how many, so take a certain kind of galaxy in this case and look how many other galaxies this kind, or how many other objects I expect at a certain radius. So we have the radial distance here. This is this. But it doesn't really matter what it shows in detail. What I want to show you is that the dots are the measured values from the very important SDSS survey. And in red, we have different kinds of populating the simulation with galaxies. But it works really well, even if we split galaxies into red and blue. And if we go to different masses, so this is a factor of 1,000 in mass between here and here. So this works really well. But still, I mean, we're treating everything as a collisionless fluid. And that's not really right. So there is gas in the universe. There is normal matter in the universe. We're living testament of that. So we are going to hydrodynamic simulations because we need hydrodynamics at some point because we actually want to know how the gas behaves. And these hydrodynamic simulations, for us today, they're only going to have these four ingredients. So apart from gravity, of course, and gravity is still in there, it's still the most important part. We need to model the hydrodynamics. We need to see how we form stars in there because that's in the end what we see and how we treat the supermassive black holes because it's in the center of galaxies because it turns out they're actually quite important to what we see in these galaxies and how the stars and the supermassive black holes act back on their host galaxies and how they form them. And they are more phenomenon that are included nowadays in most simulations, but as I said, time does not permit treating them. OK, so Eulerian hydrodynamics is the first way of treating hydrodynamics. So we just discretize space this time into a grid. And because we have some regions where we need more spatial resolution than in others, we have nested hierarchy of grids in there. And there are codes today that still use them, or not still use them, but that do use them, for example, Ramses and Enzo, two codes that are very important in the field. But this basically, yeah, as I said, discretizes space. But before we discretize mass, we can also do this for hydrodynamics. We basically divide our gas up into particles or moving cells. And so the first way of dealing with this that did this was, it's called smooth particle hydrodynamics. I think many people will know this by now if they used blender or something like this. They think they also have this in there. Many other fields use this. So basically, you have a particle that represents a certain amount of gas. And then you have some kernel function which smooths this particle. And then you let these smooth particles interact. And another way that we're going to look a bit more in detail at in a second, or just give a little example of, is an unstructured mesh, where you have these generator points. Then you calculate a Voronoi tessellation. Then you know which cells are neighboring each other. And then a bit like in the Eulerian hydrodynamics, you let stuff flow from one cell to the other. But you basically refine or derefine your grid to keep the cells at roughly the same mass. And then there are new techniques which have particles, again, which look similar and which are then called meshless methods, because they don't really have these cells and meshes. But yeah, they just look the same. OK. So just to give you a quick example of how this looks like, on the left is a very bad resolution example where you can actually see the cells using this technique here in the middle, this moving mesh, which is also used in the simulations that I'm going to show you further on, and that I showed you in the first video. And just to give you a feeling of what this looks like. So we have a flow to the right and a flow to the left. You can see this as cool and this as hot. And we see the cells in the center are very square. And they move with the flow. And at the surface, they deform. And you see how the stuff mixes in the cells and how the cells flow with the fluid. And this way, you basically, this makes it often advantageous as compared to Eulerian hydrodynamics. And then if you don't do this with a bad resolution, but with a quite good resolution, and this is pretty much the same problem with a little bit different initial condition, but we see we get very nice results. We get a very nice Kelvin-Helmholtz instability, which is the standard test of hydrodynamical codes with these two fluids flowing through each other or by each other. And we see the level of details and 40 C's that we can track with this. OK, so this is hydrodynamics. We hope we have a good handle on that. Then what about stars and supermassive black holes? Problem is we can't resolve them. I mean, particles are still, I mean, even in good simulations, there's still way too big to track single stars or to represent the space that actually is the supermassive black hole. I mean, they're huge, but they're still really, really tiny compared to the dimensions of the simulation. So what we use are subgrid models, which are effective models, which basically tell us how the processes that we cannot resolve behave and how they act back on the scales that we do resolve. And so instead of resolving how all these single stars in this forming star cluster in the Andromeda galaxy, that's where this picture's from, actually form, we just have star particles, which represent sometimes millions, sometimes thousands of stars. And then we have models, how basically these, when these stars explode, how they feed back energy and momentum into the surrounding gas. The same happens for supermassive black holes. So here we have a multi-frequency composite image of a very active galaxy, where the supermassive black hole at the center drives out these jets and emits a lot of energy. Because, I mean, black holes do eat, but they're very messy eaters. So when they eat, the material that falls in gets heated a lot, it radiates. And also a lot of the materials actually spin out again and imparts momentum on the surrounding gas. And how the supernova feedback looks like. I want to show you in this video, run by Chayu Hu from NPA at the time now in New York. And this gives you a face-on density map of a dwarf galaxy. And cut through this galaxy, and we see stars forming, and then exploding, and forming these low-density bubbles as they drive out the gas. And this is most important in small galaxies and dwarf galaxies, because they're not massive enough to really keep all the gas in. And they're the potential well. So the gravitational potential is weak enough that these supernovas can really do a lot of damage. And as we see, it really reshaped this galaxy. On the other mass end of galaxies, we have very massive supermassive thick holes. And yeah, here I want to show you this video run by DiMatteo and collaborators in 2005. And while the results are not scientifically 100% to date now, but they're still very close to what's actually happening. And so we have two very massive galaxies, of which we can see the gas here, with the hue representing the temperature and the color, the density, if I remember correctly, interact. So fly by each other. That actually, remember the tidal tails that I showed you before? That's what's forming there right now. So we see these tidal tails, and we have supermassive thick holes at the centers of these two galaxies. And at one point, they start eating a lot of this gas, which is driven on them as part of this collision. And it starts heating up, and we already see some outflows there. And then at some point, they really start releasing a lot of energy and driving out the gas. And if there's no gas, if there's no cool gas, which can form stars, which can gravitation collapse, it's hot again. And remember, as talked about in the early universe, then we can't really form stars. And this also inhibits star formation in very massive galaxies. And we didn't always know that we needed these two processes, but observations told us that very massive and very low mass galaxies don't form a lot of stars. And what we see here is actually the mass of stars divided by the mass of the dark matter halos of the system. So as a proportional to the mass of normal matter in the universe divided by the matter of the universe. So basically, this is a question, how much available gas in the universe is actually turned into stars in galaxies? And we see that here, we see the mass of the galactic system, so dark matter halo plus the galaxy inside, but it's mostly just the dark matter halo. And we see that at the low mass end, stellar feedback, so mostly supernovae, really decreases this amount of gas that is formed into stars, the proportional one, and at the high mass end. And here, these colorful curves are observations. This red and black one is an older simulation, which actually doesn't get this top end perfectly right. But we'll see a video of the refined model, which does much better than this. But nonetheless, we see this trend already here. And we in our galaxy, the Milky Way, live here in the roughly at the sweet spot where we formed the most stars. But even there, we only turn 25% of the theoretically available gas into stars. OK. I told you that nowadays, galaxy simulation, or these cosmological hydrodynamic simulations, do much better. And so I want to show you some results from the illustrious TNG. This is from the illustrious simulation, the illustrious TNG, because apparently people like Star Trek do much better. And this is just a little gallery of all the different kinds of galaxies they form. And they look pretty realistic. And if you look at the other two, they look pretty realistic. And at some point, we can also look at another talk at more quantitative floods, but also quantitatively, they do much better. And that's actually the simulation where this initial video came from. And now I hope we could explain to you why you see what you see. So we have a very large gas density and temperature. In this cosmological hydrodynamic simulation, we see the gas flowing into dark matter halos that formed. And into this cosmic web structure formed by the dark matter. We see that you don't see as many little bright spots as you saw in the dark matter simulation when we just showed these density maps, because the small galaxies can hold their gas. The big spots, the gas is also driven out in these winds from the feedback. And you see things merging and forming bigger and bigger lumps. And here, we actually see something like a cluster of galaxies form. But it's still, of course, a bit hard to envision how this looks like in starlight. So let's look at this in a bit more quantitative fashion. Here, we just have some slice projected into 2D with three panels, the gas density, what we've saw just now, and the dark matter density, what we've seen, for example, for the Millennium simulation before, and actually the stars. So this is what you would see if you could look out with your telescope and see very faint objects. And this again from the illustrious TNG simulation. And this is run by Dylan Nelsen, a colleague of mine. He did these very nice figures. And so let's run them for a bit. We see how the dark matter structure forms. And then the gas follows this already much more structured dark matter. And then we see over here how stars created. And sometimes you can even see, let's maybe go back to the beginning of the video, you can see how these single stellar particles pop up here. And later on, there's enough star formation that you don't see these single events anymore. And yeah, we see how this structure forms. And this already looks a bit like, if you remember, this plot from the very beginning with these actual galaxy surveys. We see this web structure. But we also see that galaxies only trace it quite sparsely. So for the most of this dark structure is hidden from us. And we also don't directly see the gas. But we could, for example, observe it if we have very powerful light sources behind it and then see how, as the light pierces through the gas, is changing its properties. And dark matter, for example, we can see if we maybe someone else has said, give a talk at some point about this here. Gravitational lensing, how basically the gravitational force of the dark matter bends the light around it and distorts the galaxy images that are behind this structure. So what are people doing nowadays? So what's happening at the moment in this field? Of course, things get bigger. Things always get bigger with computers. So we started here in the 90s, before we had a few. So this is the number of resolution elements. So particles or cells or something like this. So antibody particles or hydrocells and so on. And we started with 10 to 100,000. And nowadays, yeah, we're in the billion, tens of billion range. Inbodies simulations were always faster because just calculating gravity is much faster than also doing all these other calculations. But they actually track each other quite well. This is from a publication by Gannel in 2014. So we don't have the most recent developments on here. But as things get bigger, they also get much harder to save. So the millennium simulation uses roughly 300 gigabytes per snapchat just for a particle data. Then if you have data products, it gets much bigger. And we have 64 snapshots. So that's roughly 18 therabytes that we need to save if we want to keep it. This Euclid flagship simulation, I calculated if you would save it as the millennium simulation, of course, you can trick a bit. And then it would be 60 terabytes per snapshot. If we have 60 snapshots, this would be 3.6 petabyte, which, I guess, is not. I mean, yes, I think we can save it at our institute, maybe three times or so. But then our storage is full. So the solution is we don't really save everything. So we produce these halo catalogs that I talked about before. So we look for the halos on the fly and write those things out and how they merge into each other and so on. And we only record data on a light cone. Because I mean, you saw this before when I showed you this plot in the beginning of the history of the universe. As the light reaches us, it basically light from further way places reaches us later. So we see into the past as we look out. And so basically, we record on a light cone as if the light would go through the simulation box and just record the particle data on this light cone. And then we have basically a simulated observation from a certain point in this simulation box. OK, they also get stronger. They have more physical processes included, things that I didn't talk about. For example, radiation, magnetic fields are already included in the illustrious TNG and illustrious simulation. Cosmic rays, dust, stars produce dust, and dust couples gas and radiation. And in the end, there's a lot more processes that we can follow, which also increase computational complexity. And as we increase our resolution, we decrease what we have to consider a sub-grid. So in this simulation of the supernova and the skeleton, I mean, the star particles were, I think, 10 solar masses or so. And in other simulations, they would have to be thousands or hundreds of thousands of solar masses and so on. So sometimes you actually resolve single stars in this very high, so the very massive stars you would resolve as a single particle in these simulations. And they become faster because, but I mean, this being faster is then translated into we make them bigger, so they're as slow as before, because we have the same lifetime as a researcher, but we now have more computational time. And we also include more things in them. But of course, also the codes get faster. As I told you about before, I mean, when we talked about this n-body problem, there are faster and faster methods, and the codes become just much more efficient. And we also have new codes that maybe solve certain problems in a more specialized but fast way. But as computers become bigger, scaling becomes more of a problem because we don't just use one core in the beginning or maybe a few hundred or a few thousand. But now we come into the scale where, so I talked once about running something on the Tianhe computer, so I think that's 1.0 million cores or so. I forgot. But anyway, so we're talking about massive numbers, of course, that have to work together. And so scaling becomes a major concern. And so right now, most of these simulations are programmed in this typical MPI open MP paradigm, where you have MPI for the inter-process communication, and then on a node, you have open MP threads that do most of the work, sometimes just MPI with one process per core, but people move away from there and work with computer scientists and specialists from big HPC vendors to get faster and better algorithms into these simulations. And as they become faster, there's one more thing that I wanted to show you. We can actually do interesting things with them. And this is something that Yan Siashev, who used to be at my institute and is now in Stockholm, does what he basically tries to, in a certain sense, fit in-body simulations to our local universe. So we basically calculate in-body simulation in a quick way and then perturbs the initial conditions in such a way that he comes closer and closer to the real outcome. And here on the right, you see in dark his simulated density field, and in red actually galaxies from a real galaxy survey. And they match really well. OK, there are some parts where they don't really match, but for the most part, they match really, really well. And then he knows from where he started. So this is on a shell 100 megaparsec around us. And so this way, he can unravel the initial conditions of our own universe. And there are also other groups that do similar undertakings, for example, in Potsdam and in a different way, but with a similar goal. Yeah, and I think also for this audience, quite interesting, this field is becoming increasingly open, but it's already quite open in the sense that the codes are to a large degree public. Some parts of the codes are not necessarily public, but a lot of the big codes try to be as public as they deem possible. So you can just go to GitHub or whatever and just look for these codes and run simulations yourself. They have some small working examples, and you can toy around with them. I mean, you don't really have a supercomputer, but you can still do some nice little exercises. The simulation results are often made public. So they actually want you to use the data. I mean, you as a scientist now that produces relevant citations. And that really helps make the simulations known and gets more value out of the simulations because more people can actually work on them. And here, again, I want to give the millennium simulation as an example. So in 2018, I'm still working on this. This was run in 2005 when I turned 14. And today, or the last time I checked, that there were 974 publications that used the data from the simulation for this publication. I mean, some of them were just on the simulation, some compared it with others. But yeah, I think that's a pretty impressive number. And yeah, it's really interesting. And you can also look at those things yourself. I mean, they're on the web in the end. Sometimes you have to register and maybe tell them why you want to look at these things. So there's cosmosyn.org run by Pippin Potsdam, the millennium database from Durham and the MPA in Garsing where I work. Cosmoop, I think it's in ETH. And the Elastos TNG database from this Elastos collaboration, also MPA and Harvard and some other institutions that are involved there. And so the Elastos TNG was actually publicly released on the 14th of December. So it's pretty new on the web now. But you can look at the halo catalogs and you can look at all the interesting outcomes of these simulations. And with this, I want to leave you with my take home messages. I hope I could explain to you why cosmological simulations are really powerful tools and for cosmology and galaxy formation in these cosmologies and how they predict also some previously unknown things that we, for example, this NFW profile that we didn't really know about before. And also, they're quite robust in terms of the gravity. And also, I mean, we've seen there was some evolution still between, for example, Elastos and the Elastos TNG. But they're also getting better and better in this respect. And they're huge computational undertakings. And they're very nice examples of how science and its results can be made public and the way to get to these results as well. And if you want to know more about the physical size of these things, there's going to be a great talk by Sarah Conrad from Heidelberg, who's going to talk about dark matter and dark energy on day four at 10 past 2 in Borg. And yeah, I'll definitely go there and I hope I'll see many of you there. Thank you. Thank you, Philipp. If you would like to leave at this point, please do that very quietly so that people can still enjoy the Q & A. If you would like to ask a question, please line up in the microphones in the room. We have a question from the internet, the simulation results embargo. Sorry? What is the reason for the simulation results embargo? Because if you run the simulation, you also want to be the first to call dibs and use the results for some time. They still invite people, but they have these project pages where they basically say, okay, I want to do this with the simulation, some other in the cover, color operation wants to do this. Other project with simulation, and that's basically that you just want to reap the fruits of your own labor. Alright, thanks. Thank you. My phone number two. Yeah, as far as I understood, these simulations are not as granular as to predict the behavior of individual stars or are they? Okay. How far along will it approximately be until this is possible and also factors like the different classes, star classes of the H.R.R.S.R. diagram? Yeah, no. I mean, there are, so there was something that I had in the talk that I threw out again. So there are, of course, simulations that simulate how star clusters form. So there are simulations even that simulate how a single star evolves in 3D and how it explodes as a supernova. But I think it's not the, it's not really, not every simulation has to do everything at the same time. I mean, you can have specialized simulations that look on a certain length scale and then use the information and that's also what people try to do, to use information from that length scale then in a model that you can basically use as a separate model in larger simulations, for example. Thank you. Please try to limit your questions to a single sentence. Michael, for number one, please. Hi, and thank you. Of all the particles in our physical universe, having mass, is every particle able to interact with every other particle? No. Thanks. Michael, for number four. So in all your simulations, is there kind of sometimes a steady state that simulation goes to and then just doesn't go any further in terms of changes or is it always changing? No, I don't think so because I mean, you have an accelerated expansion, so. Well, it could be that it reaches equilibrium for some reason or the other. So it doesn't matter. It's not that I know of, not for any reason that I know of. And of course, sorry, so just for the question right now, I mean, yeah, it doesn't interact via all interactions. Of course, if it has mass, it will interact via gravity. Yeah, sorry, just to finish up this question. All right. Michael, for number three, your question. Yeah, so as you said, the models have been scaling up all during the last decade. Are there actually questions that could be answered by just a bigger model? So does it really make sense to go bigger and bigger all the time? It improves your statistics. Basically, you get more extreme environments. So basically, if you have a bigger box, so for example, the smaller hydrodynamic simulations often don't have very massive clusters in them just because clusters are very massive clusters of galaxies are rare. And then sometimes you form one and then if you're lucky with your initial conditions, but you can't really predict that because you haven't run the simulation yet. And then sometimes you don't. And so bigger boxes basically help you to get all these different environments sampled and the same for the largest voids and so on. You don't have the largest voids in a small box because sometimes your box is smaller than the largest void. Michael, for number one, your question. Hi, thank you for your interest in talk. My question is what is the time scale at which the simulations are run? Meaning, so you basically start the simulation from these image of the temperature scan, right? And then you run it for, I don't know how much. So could it be that we just run compared to the life of the universe, the simulation for like a very tiny? No, no, no, no. So you run it. So you don't run it. A, you don't run directly from this image because in the beginning you can do analytical approximations. But then at some point those break down and then you have to really do these calculations. But then you usually run them until today. So also this video that I showed you, it runs from when the universe, so just the video shows you the part of the simulation that runs from when the universe was a fifth of its current volume and then until today basically. That's what you usually, I mean sometimes people miscalculate their computing time and then they run out of computing time and they don't get there. That's always a bit annoying. But some simulations are even constructed that way because they're not interested in today. They're only interested in the high redshift universe, meaning the old universe. So for example, just, yeah, the process of how the first stars and galaxies form and then you don't really want it to run that far down because you have enough simulations showing that part. All right. Single individual question from the internet. No, my question from the internet is, is it possible to simulate backwards instead of changing star parameters until they match what we observe in our universe? Not so, not no. Okay. Thank you. Mike from number two, your question. Yeah. So regarding research about fitting certain, you know, like simulations into our coding of current observations, would it be possible, how many initial states could yield the current observations that we have? Like not only the sheer number, but because that's probably infinite, but could two completely different initial states like completely random and having no connection whatsoever yield the same state like converge? The exact same? No, I mean, two completely different initial states converging into our, you know, into some state after the simulation that closely resembles our current observations. Or do they have some common pattern? Well, I mean, if the large scale fluctuations are very different than no, I don't think so. But it's a good question. I might have to think about this. All right. Thank you, Phillip. That's unfortunately the last question we have time. Please give him a huge round of applause for that excellent talk.
and what the current understanding of the bring the structure that we see today, galaxies, bit closer, as I will show in the end of the fascinating that we can see that much in a basically tell us how the processes that we gas density and temperature. In this cosmological want to give the millennium simulation as an cosmology and galaxy formation in these And they're huge computational undertakings. And