 Now, our next talk is Simulating Universes. Our speaker is Philipp Busch. 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 profit 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, I mean, 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, 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 microwave 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, 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 much, 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 wavelength. 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 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 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. So there is some structure in there. But you only see the structure because we subtracted 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 is 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 is a fit, or 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 CMV, where the CMV was emitted, and then today. And at the time of the CMV, 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 redshifting, 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's 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 I mean, 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 kind of have to see what we can actually observe with our ground-based telescopes and nowadays also satellites. And then, I mean, 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 predicts some output. And whether our output matches the observation then tells us whether we're on the right track or not. Okay, 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 try not to get too technical, but this basically is just, so we have some continuous field. And I mean, 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. Okay, and our simulations themselves will only deal with the particles. They will only see how these particles work. Okay, 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, and 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, can be, it's 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 O n squared, but we can make this much faster by using smart codes like particle mesh, we use phosphoryl transforms or tree codes and so on to get it to n log n, and then some newer codes even implement methods in O n. So just for the people that are interested in this. Okay, 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 one over D squared thing in there. And I mean, many things scale as one 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 that were 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, or that 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 the 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, turmeric, uncle and nephew wrote this paper together. And yeah, we can 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 solved for other questions. Okay, 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 micro effect around 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 antibody simulation looks like, I wanna 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, Jens Stöcker. And you basically see how in slightly under dense 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 a 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 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 on earth in Estonia from the USSR and where Doroshevich and his coworkers already did this in the 70s and then must have projected it on some screen and filmed it with some camera from the screen. And, but you already see the same structure basically as we've just seen and can jump a bit forward. So they're, 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, like 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 megaparsec. So we always have this, let's just ignore this over eight here. And one parsec is a bit more than three light years. And megaparsec is then a bit more than 3 million light years. So, and we have 500 of them on each side. As you will notice, actually, we have one gigaparsec here in this picture of the slices 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 smaller clusters or groups. You have empty regions, the voids, and you have filaments. This is where also a lot of galaxies live and which are traced then by basically these linear, 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 like thousands of megaparsec. Now we're to single megaparsec 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, you kind of 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 we 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 the abstracted data analysis kind of we're thinking. And then we want to know how these halos, what they look like and how they were formed. And to define these, there are various methods. So in the 80s, people started with what they call friends of friends, halo-finders. I also worked with them for quite some time which basically just collect like cluster opothics. I think people from machine learning will also know these algorithms as cluster-finders. And then there's another one, spherical over-density-finders which just look for over-density 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 they don't only work on the positions but they also take the full phase space so including the velocities into a count and so on. Yeah, 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 diffused 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. Okay, so what is one of the, well yeah, 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 discoveries in Navarro, Frank and White which discovered 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 R to the minus one slope in the center and then at some point in RS you go over to an R to the minus two 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 but how they should look like but that it really is that was unclear before the bigger end body simulations in the 90s and we can also, I don't have any 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 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 it really looks the same so we are on the right track there and this is also why for example these mock simulations for these bigger or for this satellite this Euclid satellite that I showed you before where 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 okay we can even compare this more quantitatively so here we have the correlation function so basically how many so I 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 a thousand 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 if there is gas in the universe there is normal matter in the universe and 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 and 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're more phenomenon that are included nowadays in most simulations but as I said time does not permit treating them okay so Eulerian hydrodynamics is the first way of treating hydrodynamics so we just discretize space this time into a grid and we have 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 and but this basically yeah as I said discretizes space but before we discretized 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 I 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 smoothes this particle and then you have some particles interact and another way that we're going to look a bit more in detail 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 you a bit like in the Eulerian hydrodynamics you let stuff flow from one cell to the other so 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 okay so just to give you a quick example 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 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 the good simulations they're still way too big to track single stars or to represent the space that actually is the supermassive black holes I mean they're huge but they're still really really tiny compared to the dimensions of the simulation so what we use are sub grid 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 actually form we just have star particles that 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 of a very active galaxy where the supermassive black hole at the center drives out these jets and emits a lot of energy and the 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 spew 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 here really reshape this galaxy okay on the other mass end of galaxies we have very massive supermassive like holes and yeah here I want to show you this video run by Di Matteo and collaborators in 2005 and while the results are not scientifically 100% up 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 Hu 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 like 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 collapse it's hot again 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 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 it's almost supernova 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 roughly at the sweet spot where we form the most stars but even there we only turn 25% of the theoretically available gas into stars okay 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 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 a simulation where this initial video came from and now I hope we maybe or could explain to you why you see what you see so here we see the 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 not 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 don't really can hold their gas you see how from the big spots the gas is also driven out in these 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 yeah and 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 saw just now and the dark matter density what we've seen for example for the the lightning 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 color of mine and this is how this 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 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 and but we also see that galaxies only trace it quite sparsely so for the most of this dark structures hidden from us and we also don't directly see the gas but we could for example observe it if we have a 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 gave 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 the structure okay 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 and body particles or hydro cells and so on and we started with 10 to 100,000 and nowadays yeah we're in the billion tens of billion range and body 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 therogite 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 but 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 our institute maybe 3 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 from 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 if the light would go through the simulation box and just record the particle data on this light cone and then we have basically simulated observation from a certain point in this simulation box they also get stronger they have more physical processes included things that I didn't talk about but 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 sub grid so in this simulation of the supernova and the skeleton I mean the star particles where I think 10 solar masses are 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 end 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 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 one point something million cores or so I forgot but anyway so we're talking about massive numbers of cores 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 other 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 Yance Yasha who used to be at my institute and is now in Stockholm does where he basically tries to in a certain sense fit N-Body simulations to our local universe so we basically calculate N-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 match really well for the most part they match really really well and then he knows from where he started so this is on a shell 100 MP around us 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 similar method with a similar goal 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 super computer 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 there were 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 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 Cosmosyn.org run by people from Potsdam the millennium database from Durham and the MPA in Garsing where I work Cosmoop I think it's in ETH and the illustrious TNG database from this illustrious collaboration also MPA and Harvard and some other institutions that are involved there and so the illustrious 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 but yeah all the interesting outcomes of these simulations and with this I want to leave you with my take home messages I hope I could yeah explain to you why cosmological simulations are really powerful tools and for cosmology and galaxy formation in these cosmologies and how we 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 illustrious and illustrious 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 yeah and if you want to know more about the physical size of these things there's going to be great talk by Sarah Conrad from Heidelberg who's going to talk about dark matter and dark energy on day 4 at 10 past 2 in Borg and yeah I'll definitely go there and see many of you there thank you 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 signal angel please the reason for the simulation results embargo sorry what is the reason for the simulation results embargo oh because I mean if you run the simulation you also want to be the first to call dibs and use the results for some time I mean they still invite people and they have these project pages where they basically say okay I want to do this with the simulation some other in the collaboration 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 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 and also factors like the different star classes I mean yeah no I mean 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 not every simulation has to do everything at the same time I mean you can have specialized simulations that look at 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 microphone 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 microphone 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 not that I know of not for any reason that I know of and of course sorry 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 sorry just to finish up this question all right microphone number three your question yeah so as you said all the particles have been scaling up all during the last decades 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 these 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 in them 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 the smaller than the largest void Mike for number one your question hi thank you for your interesting talk my question is what is the time scale at which the simulations are run meaning so you basically start the simulation from this 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 I mean sometimes people miscalculate their computing time and then they run out of computing time and then 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 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 signal a little question from the internet 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 microphone number two your question so regarding research about fitting certain simulations into our current observations would it be possible how many initial states could yield the current observations that we have 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 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 Philip that's unfortunately the last question we have time please give him a huge round of applause for that excellent talk