Grow your own planet
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Penzlin, Anna
Kimmig, Carolin
This year the Nobel prize in physics was awarded to three astronomers changing the understanding of the Universe and finding the first exoplanet. This is a good reason to dive into astronomy, numerics, and programming and to learn how modern astronomy creates the pictures and models of the reality we observe in the night sky. Let’s find out together how we can simulate the Universe and grow new planets – computationally! In all ages people have gazed at the stars and tried to grasp the dimensions of the Universe and of the teeny-tiny marble we call our planet and wondered how unique it actually is. From the ancient geeks to Johannes Kepler to modern times we slowly advanced our understanding of the sky and the laws necessary to describe the orbits and evolution of all its objects. Nowadays computational power has greatly increased. So we can further our understanding of the Universe from basic, analytically computable orbits to the challenge of turbulent gas flows – only accessible with numerical simulations. Let's go on a journey through space and compare the data we observe with breath-taking accuracy using instruments like ALMA, VLT, Gaia, and Hubble Space Telescope to numerical simulations now possible due to computer clusters, multi-core CPU and GPU-calculations. We want to explore the physics and numeric algorithms we need to comprehend the Universe and travel to the unexplained territory of problems we can not quite solve yet. We present three state-of-the-art hydrodynamics programs: PLUTO (by A. Mignone), FARGO3D (by P. Benítez Llambay and F. Masset) and AREPO (by V. Springel). All of them are free open source software and commonly used in research worldwide. Using their example, we demonstrate how hydrodynamics recreates many of the things we see in the sky, including planets. Simulations teach us how rare the formation of Earth was and show that there is no alternative planet in reach. In modern times we humans continue to gaze at the stars. Even without Planet B in sight, we are still fascinated with what we see. Numerical methods help us satisfy our thirst for knowledge and accelerate the research of the Universe.
 I have to say I'm always deeply impressed about how much we already learned about space, about the universe and about our place in the universe, our solar system. But the next speakers will explain us how we can use computational methods to simulate the universe and actually grow planets. The speakers will be Anna Penzlin. She is a PhD student in computational astrophysics in tubing. And Caroline Kimmich, she is a physics master's student at Heidelberg University. And the talk is entitled, Grow Your Own Planet, How Simulations Help Us Understand the Universe. Thank you. So hi everyone. It's a cool animation, right? And the really cool thing is that there's actually physics going on there. So this object could really be out there in space, but was created on a computer. So this is how a star is forming, how our solar system could have looked like in the beginning. Thank you for being here and that you're interested in how we make such an animation. Anna and I are researchers in astrophysics and we're concentrating on how planets form and evolve. She's doing her PhD in tubing and doing my master's in Heidelberg. And in this talk, we want to show you a little bit of physics and how we can translate that in such a way that a computer can calculate it. So let's ask a question first. What is the universe? Or what's in the universe? The most part of the universe is something we don't understand yet. It's dark matter and dark energy. And we don't know what it is yet. And that's everything we cannot see in this picture here. What we can see are stars and galaxies. And that's what we want to concentrate on in this talk. But if we can see it, why would we want to watch a computer? Well, everything in astronomy takes a long time. So each of these tiny specks you see here are galaxies, just like ours. This is how the Milky Way looks like. And we're living in this tiny spot here. And as you all know, our Earth takes one year to orbit around the Sun. Now think about how long it takes for the Sun to orbit around the center of the galaxy. It's 400 million years. And even the star formation is 10 million years. We cannot wait 10 million years to watch how a star is forming, right? That's why we need computational methods or simulations on a computer to understand these processes. So when we watch to the night sky, what do we see? Of course, we see stars and those beautiful nebulas. They are gas and dust, and all of these images are taken with Hubble Space Telescope. So there's one image that doesn't belong in there. But it looks very similar, right? This gives us the idea that we can describe the gases in the universe as a fluid. It's really complicated to describe the gas in every single particle. So we cannot track every single molecule in the gas that moves around. It's way easier to describe it as a fluid. So remember that for later. We will need that. But first, let's have a look how a star forms. A star forms from a giant cloud of dust and gas. Everything moves in that cloud. So eventually, more dense regions occur, and they get even denser. And these clumps can eventually collapse to one star. So this is how a star forms. They collapse due to their own gravity. And in this process, a disk forms, and in this disk, planets can form. So why a disk? As I said, everything moves around in the cloud. So it's likely that the cloud has a little bit of an initial rotation. As it collapses, this rotation gets larger and faster. And now you can think of making a pizza. So when you make a pizza and spin your dough on your finger, you get a flat disk, like a star, like a disk around a star. That's the same process, actually. In this disk, we have dust and gas. From this dust in the disk, the planet can form. But how do we get from tiny little dust particles to a big planet? Well, it somehow has to grow. And grow even further and compact until we have rocks. And even grow further until we reach planets. How does it grow? Well, that dust grows, we know that. At least that's what I observed when I took those images in my flat. Well, so dust can grow and grow even further and compact. But when you take two rocks, we're now at this in this stage, when you take two rocks and throw them together, you do not expect them to stick. You expect them to crash and crack into a thousand pieces. So we're standing on the proof that planets exist. How does this happen? And it's not quite solved yet in research. So this is a process that is really hard to observe, because planets are very, very tiny compared to stars. And even stars are only small dots in the night sky. Also, as I said, planets form in a disk, and it's hard to look inside the disk. So this is why we need computation to understand a process, how planets form and other astronomical processes. So let's have a look at how we simulate it on a computer. Okay. So somehow we have seen nature. It's beautiful and just like a tank of water and a bubbly fluid we already have. So now we have this bubbly fluid here in the middle demonstrated. But now we have to teach our computer to deal with the bubbly fluid, and that's way too much single molecules to simulate them, as we already said. So there are two ways to discretize it in a way that we just look at smaller pieces. One is the Lagrangian description, just like taking small bubbles or balls of material that have a fixed mass. They have a certain velocity that varies between each particle, and they have, of course, a momentum because they have a velocity and a mass. And we create a number of those particles and then just see how they move around and how they collide with each other. That would be one way. That was described last year in a very good talk. I can highly recommend to hear this talk if you're interested in this method. However, there's a second way to also describe this, not just going with the flow of the particles, but we are a bit lazy. We just box it. So we create a grid. As you see down here, in this grid, you have a certain filling level, a bit of a slope height. So what's the trend there? And then we just look for each box, what flows in, what flows out through the surfaces of this box. And then we have a volume or a mass filled within this box. And this is how we discretize what is going on in the disk. And actually, since we are usually in the system of a disk, we do not do it in this nice box way like this, but we use boxes like those because they are already almost like a disk. And we just keep exactly the same boxes all the time and then just measure what goes through the surface in these boxes. So this is how these two methods look like if you compute with both of them. So one was done by me. I'm usually using this boxing method and the other was done by my colleague. You see this, like, when you look at them at the colors, at the structure, here you have the slope inward, you have the same slope inwards here. You have even the silly structure here, the same here. But what you notice is you have these enlarged dots that are really, these are really the mass particles we saw before, these bubbles. And here you have this inner cutout. This is because when you create this grid, you have the very region at the inner part of the disk where the boxes become tinier and tinier. And while we can't compute that, so we have to cut out at some point the inner part. So here when you go to low densities, these bubbles blow up and distribute their mass over a larger area, so it's not very accurate for these areas. And here we have the problem. We can't calculate the inner area. So both methods have their pros and cons and our wallet. But now, for most, we will focus on this one. So we have this nice, actually, stream features. So again, going back to the boxes, we have to measure the flow between the boxes. This flow in physics, we call it flux. And we have a density, row one, a density, row two. And the flux is the description of what mass moves through the surface here, from one box to the next. So if we write this in math terms, it looks like this. This says the time derivative of the density, meaning the change in the change over time, so how much faster is lower you go, the velocity would be a change in time. And then this weird triangle symbol, it's called nabla, is a positional derivative. So it's like a slope. So how much, how do we change our position, actually? So if we change, look at the density over time, it should correlate to what inflow we have over position. That is what that says. So and then we have in physics a few principles that we have always to obey because it's just almost common sense. One of them is, well, if we have mass in a box, like this, the mass should not go anywhere unless someone takes it out. So if we have a closed box and mass in that box, nothing should disappear magically. We should stay. It should all stay in this box. So even if these particles jump around in our box with a certain velocity, it's the same number of particles in the end. That's again the same equation just told in math. So a second very rudimentary principle is if we have energy in a completely closed box, so for example, this nice chemicals here, and we have a certain temperature. So in this case, our temperature is low, maybe outside of around zero degree Celsius, and then we have this nice chemicals down here. And at some point they react very heavily. We suddenly end up with much less chemical energy and a lot more thermal energy. But overall, the complete energy summed up here, like the thermal and the chemical energy, also the energy of the movement and the energy of potential added up to this variable U, that should not change over time if you sum up everything because our energy is conserved within our closed box. And then the third thing is, I think you all know this, if you have like a small mass with a certain velocity, a very high velocity in this case, and it bumps into someone very large. What happens? Well, you get a very small velocity in this large body and the smaller mass stops. And the principle here is that in momentum is conserved, meaning that the velocity times the mass of one object is the same as then later for the other one, but since it's larger, this product has to be the same. That doesn't change. And we have also, like in our simulations, to obey these rules. And we have to code that in so that we have physics in them. So you say, okay, this is really simple, these rules, right? But actually, well, it's not quite as simple. So this is the Navier-Stokes equation. It's a very complicated equation. It's not completely solved. And we have here all that is marked red, other derivatives. Here we have our conservation law that was the nice and simple part. But now we have to take other physical things into accounting for pressure, accounting for viscosity, for compression. So squeezing and how sticky is our fluid and also gravity. So we have a lot of additional factors, additional physics. We also have to get in somehow. And all of these also depend somehow on the change of position or the change of time. And these derivatives aren't really nice for our computers because they, well, they don't understand this triangle. So we need to find a way to write an algorithm so that it can somehow relate with these math formula in a way that a computer likes. One of the ways to do this is, well, the simplest solution actually is just we say, okay, we have now these nasty derivatives and we want to get rid of them. So if we look just at one box now, we say that in this box, the new value for the density in this box would be the previous density plus the flux in and out times the time step over which we measured this flux. And we have to somehow get to this flux and we just say, okay, this flux now is, if we start here, the slope of this curve, the trend, so to say, where this curve is going right now, so it would look like this. So in our next time step, we would have a density down here and, well, then we do this again. We again look at this point, where's the trend going, where's the line going? And then we end up here, same here. So again, we just try to find this flux and this is the trend at this position in time. So this goes up here and then if we are here now, look at this point, it should go up here. So this is what our next trend would be. And we do this over all the times and this is how our simulation then would calculate the density for one box over different time steps. So that kind of works. So the blue curve is the analytical one, the red curve, well, it's kind of simulatized, it works, but can we do better? It's not perfect yet, right? So what we can do is we refine this a bit, taking a few more steps, making it a bit more computationally heavy, but trying to get a better resolution. So first we start with the same thing as before, we go to this point, find the trend in this point, that point, like the line would go in this direction from this point and then we go just half a step now. And now we look at this half a step to this point now and do it again, the same saying, okay, where's the trend going now, and then we take where this point would go and add it to this trend. So that would be that the average of this trend, of this exact point, and this trend, this dark orange curve. And then we go back to the beginning with this trend now and say this is a better trend than the one we had before. We now use that and go again and search the point for half a time step. And then again we do the same thing. Now we again try to find actually the trend and average it with the arrow before. So it's not exactly the trend, it's a bit below the trend because we averaged it with the arrow before. And now we take this averaging trend from the beginning to the top like this. Okay, this is already quite good, but we can still do a little bit better if we average it with our ending point. So we go here, look where's the trend going, that would go quite up like this. And we average this and this together and then we end up with a line like this. This is so much better than what we had before. It's a bit more complicated to be fair, but actually it's almost on the line. So this is what we wanted. So if we compare both of them, we have here our analytical curve. So over time in one box, this is how the density should increase. And now with both of the numerical method, the difference looks like this. So we have smaller and smaller time steps, even the Euler gets closer and closer to the curve, but actually the Runge-Kutta, this four-step process works much better and much faster, however it's a bit more computationally difficult. When we simulate objects in astronomy, we always want to compare them to objects that are really out there. So this is a giant telescope, well, consisting of a lot of small telescopes, but they can be connected and used as a giant telescope. And it takes photos of dust in the sky and this is used to take images of discs around stars and these discs look like this. So these images were taken last year and they are really cool. Before we had those images, we only had images with less resolution, so they were just blurred blobs. And we could say, yeah, that might be a disc, but now we really see the discs. And we see rings here, thin rings, and we see thicker rings over here, and even some spirally structures here, and also some features that are not really radially symmetric like this arc here. And it's not completely solved how these structures formed. And to find that out, a colleague of mine took this little object with the asymmetry here. And so this is the imagery Chester, and this is his simulation. So this is how discs looked like in the beginning, probably, and he put in three planets and let the simulation run. And so what we see here is that the star is cut out. As Anna said, we have to, so the grid cells in the inner part are very, very small and it would take a lot of time to compute them all. So that's why we are leaving out that spot in the middle. And what we see here is three planets interacting with the material in the disc. And we can see that these planets can make this thing here appear so that in the end we have something looking very similar to what we want to have or what we really observe. So we can say three planets could explain how these structures formed in this disc. It's a little bit elliptical, you see that. That's because it's tilted from our side of line. It would be round if we watched that it face on, but it's a little bit tilted. That's why it looks elliptical. So we already saw we can put planets in the gas and then we create structures. One very exciting thing that we found in the last year or two years ago, it started, but then we found more, is this system, PDS 70, in this system, for the very first time, we found a planet that was still embedded completely within the disc, so the gas and dust. Usually because the gas and dust is the main thing that creates a signal, some radiation because of heat. We only observe that and then we can't observe the planet embedded, but in this case the planet was large enough and in the right position that we actually were able to observe some signature of accretion on this planet that was brighter than the rest of the disc. Then later, just this year, just a few months ago, we actually found out, well, this is not the only object here. This is a very clearly a planet, but actually this spot here is also something. We can see it in different grains. Every picture here is a different set of grains observed. We can see this in four different, five different kinds of observations. So there is a planet here. Then there is also something, we don't know what it is yet, but it's point-like and actually creates a feature that we reproduce in different kinds of observational bands or different kinds of signals here. This is very interesting. For the first time, we actually see a planet forming right now within the disc. So a colleague of mine also is very interested in this system and started to simulate how do two planets in a disc change the dynamics of a disc. So here we have, of course, this disc is again tilted because it's not phase-on. It's like 45 degrees tilted, not like this, but like this. So he had it phase-on. This is what his simulation looks like. So there are two planets that these blobs here again, as in the simulation. Here we have a close-up. You can actually see these little boxes are actually our simulation boxes in which we have our densities. Then he just looked at how the planets would change the structure in the gas and also how the gas would interact with the planets shifting them around. It's interesting. The planets tend to clear out an area, open a gap within the disc, block a lot of gas around here, so you have a brighter ring here again, and then clearing out more and more. At some point in the simulation, he saw they get a bit jumpy. So it's very nice. You also see that the planets induce in the whole disc some kind of features, like spiral features. So a single planet will change the symmetry and the appearance of a whole disc. So the reason why the planet is staying at this point is because we're rotating with the planet. It's actually going around the disc, but the camera is rotating with the planet, so it's staying at the fixed place we put it in. But there's more. Because as I already said in the Navier-Stokes equation, we have a lot of different kinds of physics that we all have to include in our simulations. One of the things, of course, is we maybe don't have just a star in the disc. We have planets in there, and maybe two stars in there, and all of these larger bodies have also an interaction between each other. So if we have a star, every planet will have an interaction with a star, of course. But then also the planets between each other, they have also an interaction, right? So in the end, you have to take into account all of these interactions. And then also we have accretion, just looking like this. So accretion means that the gas is bound by some object. It can be the disc, the planet, or the star that takes up the mass, the dust, or the gas. And it's bound to this object. And then it's lost to the disc or the other structures, because it's completely bound to that. So the principle of this would be a simulation I did last year and published. We have here a binary star. So these two dots are stars. I kind of kept them in the same spot, but every picture will be one orbit of this binary. But since we have interactions, you actually see them rotating because of the interactions, which is other. And then also we have here a planet and here a planet. And the interesting thing was that these two planets interact in such a way that they end up on exactly the same orbit. So one starts further out, the orange one, and then very fast they go in and they end up on exactly the same orbit, if it now would play nicely. So another thing is with the accretion here, we actually see clouds from above dropping down onto the new forming star here. So all of this, what you see here would be gas, hydrogen. And it's a very early phase, so this is not completely flat. It has a lot of material and then you actually have this info from above towards the star and then the star keeps the mass. And we have to take this also into account in our simulations. Another thing we have to take into account up till now, we just cared about masses and densities. But of course, what we actually see is that stars are kind of warm, hopefully. Otherwise, temperatures here would also not be nice. And different chemicals have different condensation points. And this is also true in a system. So we start with the star temperature, at the surface of the star, we have a temperature around 4000 Kelvin. And then we go a bit into the disk and there's a point where we, for the first time, reach a point where we have any material at all because it starts to condensate and we actually have something solid like iron, for example, at 1500 Kelvin. And then if we go further in, we reach a point where we have solid water. And this is at 200 Kelvin. This is what we then would need, actually, to have a planet that also has water on it because if we don't get the water in the solid state, it will not fall onto a terrestrial planet and be bound there, right? So this is important for our earth, actually. And then if we go even further out, we have also other gases condensating to solids like CO2 or methane or things like that. And since we only get water on a planet when we have a temperature that is low enough so that the water actually forms a solid, it's important for us to think about where that is in our forming disk. Where do we start to have a planet like earth that could have some water, right? But it's not just the simple picture where we have all these nice ring structures where we have a clear line, actually. It gets more complicated because we have pressure and shocks and thermodynamics is a lot like pogo dancing, right? You crash into each other and it's all about collisions. So the gas temperature is determined by the speed of your gas molecules, like here, bouncing and crashing into each other, exchanging momentum. So there's two ways to heat up such dance. First thing is you get a large amount of velocity from the outside, like a huge kick, a shock into your system. And second way would be if we have a higher pressure, like more molecules, then also you of course have more collisions and then a higher temperature. So if you change because you have a planet now in the system, the pressure at some point, you actually get a higher temperature. So that is not then we lose this nice line because suddenly we have different pressures at different locations. And the colleague of mine also simulated this. So it starts off ninth. So this is the initial condition. We just assumed, okay, if we have no disturbance whatsoever, we have our nice planet here at one AU, so same distance as Earth to the Sun here too. But here we assume that less heat gets transferred from the surface of the disk. And here we have a planet far out like Jupiter or something. And now we actually let this planet change the structure of the disk and what happens is we found these spirals. And within these spirals, we change pressure. And with this, actually, if you see this orange everywhere where it's orange, it's hotter than the ice line. So we don't have water where it's orange. And where it's blue, we can have water. And the interesting thing is even if we put a planet out here like Jupiter, we still form these regions in the inner system where we have less water. One problem in astrophysical simulations is that we don't always know how to shape our boxes or how small these boxes have to be. So we use a trick to reshape the boxes as we need them. It's called adaptive mesh. And this is a simulation of the red fluid flowing in this direction and the blue fluid in the other one. So at the boundary, the two fluids shear and they mix up somehow. And we don't know how in advance. So we start a simulation. And as the simulation starts, we reshape those boxes here. So in the middle, we don't need much reshape because it's not that complicated here. It's just a flow. But at the boundary, we see those mixing up of the two fluids. And so we reshape the cells as we need them. This is done in an astrophysical program called ARIPO. We will later show you some more programs to use for simulations. But another simulation I want to show you first is also done with ARIPO. And it's a simulation of the universe. So from here to here, it's very big. It's 30 million light years. So each of these dots you see here is the size of a galaxy or even more. And here you can actually see that at some regions, it's very empty. So we're rotating around this universe, this simulated universe here. And these regions here are empty and we don't need a lot of boxes there. Big boxes are enough here. But in this dense regions where we have a lot of material, we need smaller boxes. And this method I showed you where we reshape the boxes as we need them is used for this simulation. So actually you see, it's all the beginning of the universe there. Basically, the initial mass collapsing to the first galaxies and first supernovae starting, very beautiful simulation. So there are different programs as I already mentioned in astrophysics. Three of them, those three are all open source. So you can download them and use them on your own machine if you like. And but there are more, a lot more. And some of them open source, some of them are not. Sometimes it's hard to get them. In the following, we will present the two, Fargo 3D and Pluto in a detailed version or more detailed version than ARIPO. Because we usually use those two for our simulations. What I want to show you with this slide is that depending on what you want to simulate, you need to choose a different program. And one thing is that in astrophysics, we sometimes call the whole program code. So if I use the word code, sorry about that, I mean the whole program. So let's have a look at Fargo 3D. It's a hydrodynamics code and what you see here is an input parameter file. There you define how the disk looks like, how much mass does it have, how big is it, and what planet. So here, a Jupiter. Do you see that? A Jupiter is put in. And we also define how big our boxes are. This program is written in C, which is quite nice because a lot of astrophysical programs are still written in Fortran. So this is good for me because I don't know any Fortran. We can run this. And what's typical for Fargo, so that's a compilation. Actually on my computer, so I don't need a fancy computer. I just did it on my small laptop. And now we run it. Now typical for Fargo, as you will see, are a lot of dots. So here. It will print out a lot of dots. And it will create at certain times some outputs. And these outputs are huge files containing numbers. So if you look at them, they are not really interesting. They just are numbers in something like a text file. So a big part of astrophysics is also to visualize the data. Not only to create it, but also to make images so that we can make movies out of them. For that, I prefer to use Python, but there are a lot of tools. But there are a lot of different tools to visualize the data. So this is actually that output, the first one we just saw. The Jupiter planet in the disk that I defined in this parameter file. And it's already started to do some spirals. And if I would have let it run further, then the spirals were more prominent. And yeah. Now we have a planet here on our computer. So we also have Pluto somehow has a bit more setup files. So what I need is three files here. Looks a bit complicated to break it down. This file defines my grid and initial values and the simulation time here. We input actually what physics do we want to need? What is our coordinate system? So do we want to have a disk or just like spherical boxes or like squared boxes? And how is the time defined? And here we then actually write a bit of code to say, okay, now how do I want a gravitational potential? So what's the source of gravity? Or what will happen at the inner region where we have this dark spot? We have somehow to define what happens if gas reaches this boundary? Is it just falling in? Is it bouncing back or something? Or is it looping through the one end to the next? And this is also something we then just have to code in. And if we then make it and let it run, it looks like this. So again, our nice thing we hopefully put in or wanted to put in, the time steps, what our boundaries were, parameters of physics, hopefully the right ones. And then nicely we start with our time steps. And if we see this, it's hooray. It worked, actually, because it's actually not quite simple usually to set up a running program, a running problem, because you have to really think about what should be the physics, what's the scale of your problem, what's the time scale of your problem, and specify this in a good way. But in principle, this is how it works. There are a few test problems that you actually want to play around with this to make it easy for the beginning. And this is how we do simulations. So as I already said, we can just start them on our laptop. So here this is my laptop. I just type dot slash Fargo 3D, and it should run, right? And then I just wait for 10 years to finish the simulations of 500 time steps or something, like 500 outputs. Well, that's not the best idea. We need more power. And both of us, for example, are using a cluster for a button written back, and that takes down our computation time by a lot, usually like a factor of maybe 20, which is a lot. So I would need on my computer maybe a year, and then I just need maybe five hours, a few days or a week on this cluster, which is usually a simulation time about a week for me. So what you see here is that we use GPUs, yes, but we do not or mostly not use them for gaming. We use them for actual science. Yeah, it would be nice to play on that, right? Yeah. That just said. So back to our Earth, actually. So can we now, we wanted to grow our own planet. We can do that. Yes, of course. Can we grow Earth? Well, Earth is a very special planet. We have a very nice temperature here, right? And we have not a crushing atmosphere like Jupiter, like a huge planet that we could not live under. We have a magnetic field that shields us from the radiation from space, and we have water, but just enough water so that we still have land on this planet where we can live on. So even if we fine tune our simulations, the probability that we actually hit Earth and have all the parameters right, it's actually tiny. It's not that easy to simulate an Earth. And there are a lot of open questions, too. How did we actually manage to get just this sip of water on our surface? How did we manage to collide enough mass or aggregate enough mass to form the terrestrial planet without Jupiter sweeping up all the mass in our system? How could we be stable in this orbit when there are seven other planets swirling around and interacting with us? All of this is open in our field of research, actually, and not completely understood. This is the reason why we still need to do astrophysics. And even in all our simulations, there is no planet B, and the Earth is quite unique and perfect for human life. So please take care of the Earth and take care of yourself and of all the other people on the Congress. And thank you for listening. And thank you to everyone who helped us make this possible and to the people who actually coded our programs with which we simulate. Thank you. Thank you for the beautiful talk and for the message at the end. The paper is open for discussion, so if you guys have any questions, please come to the microphones. I'm asking my signal, Angel. No questions right now, but microphone too, please. Yes, thank you very much. Very beautiful talk. I can agree. I have two questions. The first is you showed you are using Navier-Stokes equation, but on the one hand you have the dust disk, and on the other hand you have solid planets in it. And so are you using the same description for both, or is it a hybrid? It very much depends. This is one of the things I showed you that for Pluto we write this C file that specifies some things and about every physicist has somewhat his or her own version of things. So usually the planets, if they are large, they will be put in as a gravity source and possibly one that can accrete. And pebbles are usually then put in a different way. However, also pebbles are at the moment a bit complicated. There are special groups specializing in understanding pebbles because as we said in the beginning, when they collide usually they should be destroyed. If you hit two rocks very hard together, or two rocks together they don't stick. If you hit them hard together they're splatter around and we don't add up with bigger objects. So to explain, pebbles are small rocks or big sandstones or something like that. So bigger rocks but not very big yet. It depends on which code you use. Very short, maybe one. Do you also need to include relativistic effects or is that completely out? That's a good question. Mostly if you have a solar type system, you're in a range where this is not necessary. For example, with the binaries, if they get very close together then at the inner part of the disk that is something we could consider. And actually I know for Pluto it has modules to include relativistic physics too. Yes. Thank you. Okay, we have quite some questions so keep them short. Number one, please. Thank you. Yeah, thank you very much for your interesting talk. I think you had it on your very first slide that about 70% of the universe consists of dark matter and energy. Is that somehow considered in your simulations or do you handle this? Well in the simulations we make, we're doing planets and disks around stars, it's not considered there. In this simulation we showed you about the universe. At the beginning the blueish things were all dark matter so that was included in there. Okay, thank you. Okay, microphone three. Hi, thanks. Sorry, I think you talked about three different programs. I think Pluto, Fargo 3D and a third one. Azoring, say you're a complete beginner, which program would you suggest is like more, like if you want to learn more which one is user friendly or good to start with? I would suggest Fargo first. It's kind of user friendly, has somewhat good support and they are always also always very thankful for actual comments and additions if people actually are engaged in trying to improve on that. Because we are physicists, we're not perfect programmers and we're also happy to learn more. So yeah, Fargo I would suggest it has some easy ways of testing some systems and getting something done. And it also has a very good documentation and also a manual how to make the first steps on the Internet so you can look that up. Awesome, thank you. Let's get one question from outside from my signal angel. Thank you for your talk. There's one question from ISC. How do you know your model is good and when you can only observe snapshots? Oh, that's a good question. We have to, as we said, we're in theoretical astrophysics so there are theoretical models and these models cannot include everything. So every single process, it's not possible because then we would calculate for years. To know if a model is good, you have to... Usually you have a hypothesis or an observation that you somehow want to understand with most of the necessary physics at the stage to reproduce this image. Also from the observation, we have to take into account what our parameters should be, how dense the end of the simulation should be and things like this. So by comparing to observations, that's the best measure we can get if we kind of agree. Of course, if we do something completely wrong, then it will just blow up or we will get a horribly high density. So this is how we know physics will just go crazy if we do too large mistakes. Otherwise, we would try to compare to observations that it actually is sensible what we did. That's one of the most complicated tasks to include just enough physics that the system is represented in a good enough way but not too much that our simulation would blow up in time. Number two, please. I've got a question about the adapted grids. How does the computer decide how to adapt the grid because the data where the high density comes after making the grid? Yes. This is actually quite interesting and also not quite easy to answer question. Let me try to give a breakdown nutshell answer here. The thing is you measure and evaluate the velocities or in the flux you also evaluate the velocity. And if the velocity goes high, you know there's a lot happening. So we need a smaller grid than there. So we try to create more grid cells where we have a higher velocity. In a nutshell, this is, of course, in an algorithm a bit harder to actually achieve but this is the idea. We measure the velocities at each point and then if we measure a high velocity, we change to a smaller grid. So you can predict where the mass will go and where the densities are getting high. Exactly. Step by step. Okay. To say. Thanks. We stay with microphone too. Okay. I've got a bit of a classical question. So I guess a lot relies on your initial conditions and I have two questions related to that. So first, I guess they are inspired by observations. What are the uncertainties that you have? Be them what is the impact if you change your initial conditions like the density in the disk? Yeah. Right now, my main research is actually figuring out sensible initial conditions or parameters for a disk. If you just have an initial set of conditions and a sensible set of parameters and let it run very long, you expect a system hopefully to converge to the state that it should be in. But your parameters are, of course, very important. Here we go back to what we can actually understand from observations. What we need, for example, is the density, for example, and that is something we try to estimate from the light we see in these disks that you saw in this nice grid with all these disks. We estimate, okay, what's the average light there? What should then be the average densities of dust and gas in comparable disks? Okay. Thanks. Okay. One more at number two. Yes. Thank you for the talk. When you increase the detail on the grid in the Euler model, you have to, when you want to compute the gravitational force in one cell, you have to solve all the masses from all the other cells. So the complexity of the calculus grows quite radically at the square of the, how do you solve that? Yes, that's it. Or do you just put more CPUs? Well, that would be one way to do that. But there are ways to simplify if you have a lot of particles in one direction and they are far away from the object you're looking at. So yeah. So if you have several balls here and one ball here, then you can include all these balls or you can think of them as one ball. So it depends on, you look at, so how you define how many particles you can take together is when you look at the angle of this, of the, yeah, the big or the many particles will have from, seen from the object you're looking at. And you can define a critical angle and if it's, if an object gets smaller than this, or if a lot of objects get smaller than this angle, you can just say, okay, that's one object. So that's a way to simplify this method. And there are some, yeah, I think that's the main idea. Okay, we have another one. Do you have a strategy to check if the simulation will give a valuable solution or does it happen a lot that you wait one week for the calculation and find out, okay, it's total crash, that trash or it crashed in the time? So that also depends on the program you're using. So in Fargo, it gives these outputs after a certain amount of calculation steps. And you can already look at those outputs before the simulation is finished. So that would be a way to control if it's really working. But I think it's the same for Pluto. So you get every, you set, there's a difference between time steps and actually output steps. So and you would define your output steps not as the whole simulation, but you can look at each output step as soon as it's produced. So I usually get like 500 outputs, but I already can look at the first and second after maybe half an hour or something like that. Yeah, but it also happens that you start a simulation and wait and wait and wait and then see you put something wrong in there and well, then you have to do it again. So this happens as well. Thanks. Okay, one final question. Yeah, okay. Is there a program in which you can calculate backwards so that you don't have the starting conditions but the ending conditions and you can calculate how it had started? Not for hydrodynamics. If you go to anybody, there is a way to go backwards in time. But for hydrodynamics, the thing is that you have turbulent, almost like chaotic conditions. So you cannot really turn them back in time with anybody kind of because actually it's kind of, well, it's not analytically solved, but it's much closer than like turbulence, streams, spirals and all the things you saw in the simulations. Okay, I guess that brings us to the end of the talk and of the session. Thank you for the discussion and of course, thank you guys for the presentation.
 I have to say I'm always deeply impressed about how much we already learned about space,  about the universe and about our place in the universe, our solar system.  But the next speakers will explain us how we can use computational methods to simulate  the universe and actually grow planets.  The speakers will be Anna Penzlin.  She is a PhD student in computational astrophysics in tubing.  And Caroline Kimmich, she is a physics master's student at Heidelberg University.  And the talk is entitled, Grow Your Own Planet, How Simulations Help Us Understand the Universe.  Thank you.  So hi everyone.  It's a cool animation, right?  And the really cool thing is that there's actually physics going on there.  So this object could really be out there in space, but was created on a computer.  So this is how a star is forming, how our solar system could have looked like in the  beginning.  Thank you for being here and that you're interested in how we make such an animation.  Anna and I are researchers in astrophysics and we're concentrating on how planets form  and evolve.  She's doing her PhD in tubing and doing my master's in Heidelberg.  And in this talk, we want to show you a little bit of physics and how we can translate that  in such a way that a computer can calculate it.  So let's ask a question first.  What is the universe?  Or what's in the universe?  The most part of the universe is something we don't understand yet.  It's dark matter and dark energy.  And we don't know what it is yet.  And that's everything we cannot see in this picture here.  What we can see are stars and galaxies.  And that's what we want to concentrate on in this talk.  But if we can see it, why would we want to watch a computer?  Well, everything in astronomy takes a long time.  So each of these tiny specks you see here are galaxies, just like ours.  This is how the Milky Way looks like.  And we're living in this tiny spot here.  And as you all know, our Earth takes one year to orbit around the Sun.  Now think about how long it takes for the Sun to orbit around the center of the galaxy.  It's 400 million years.  And even the star formation is 10 million years.  We cannot wait 10 million years to watch how a star is forming, right?  That's why we need computational methods or simulations on a computer to understand these  processes.  So when we watch to the night sky, what do we see?  Of course, we see stars and those beautiful nebulas.  They are gas and dust, and all of these images are taken with Hubble Space Telescope.  So there's one image that doesn't belong in there.  But it looks very similar, right?  This gives us the idea that we can describe the gases in the universe as a fluid.  It's really complicated to describe the gas in every single particle.  So we cannot track every single molecule in the gas that moves around.  It's way easier to describe it as a fluid.  So remember that for later.  We will need that.  But first, let's have a look how a star forms.  A star forms from a giant cloud of dust and gas.  Everything moves in that cloud.  So eventually, more dense regions occur, and they get even denser.  And these clumps can eventually collapse to one star.  So this is how a star forms.  They collapse due to their own gravity.  And in this process, a disk forms, and in this disk, planets can form.  So why a disk?  As I said, everything moves around in the cloud.  So it's likely that the cloud has a little bit of an initial rotation.  As it collapses, this rotation gets larger and faster.  And now you can think of making a pizza.  So when you make a pizza and spin your dough on your finger, you get a flat disk, like  a star, like a disk around a star.  That's the same process, actually.  In this disk, we have dust and gas.  From this dust in the disk, the planet can form.  But how do we get from tiny little dust particles to a big planet?  Well, it somehow has to grow.  And grow even further and compact until we have rocks.  And even grow further until we reach planets.  How does it grow?  Well, that dust grows, we know that.  At least that's what I observed when I took those images in my flat.  Well, so dust can grow and grow even further and compact.  But when you take two rocks, we're now at this in this stage, when you take two rocks  and throw them together, you do not expect them to stick.  You expect them to crash and crack into a thousand pieces.  So we're standing on the proof that planets exist.  How does this happen?  And it's not quite solved yet in research.  So this is a process that is really hard to observe, because planets are very, very tiny  compared to stars.  And even stars are only small dots in the night sky.  Also, as I said, planets form in a disk, and it's hard to look inside the disk.  So this is why we need computation to understand a process, how planets form and other astronomical  processes.  So let's have a look at how we simulate it on a computer.  Okay.  So somehow we have seen nature.  It's beautiful and just like a tank of water and a bubbly fluid we already have.  So now we have this bubbly fluid here in the middle demonstrated.  But now we have to teach our computer to deal with the bubbly fluid, and that's way too  much single molecules to simulate them, as we already said.  So there are two ways to discretize it in a way that we just look at smaller pieces.  One is the Lagrangian description, just like taking small bubbles or balls of material  that have a fixed mass.  They have a certain velocity that varies between each particle, and they have, of course,  a momentum because they have a velocity and a mass.  And we create a number of those particles and then just see how they move around and  how they collide with each other.  That would be one way.  That was described last year in a very good talk.  I can highly recommend to hear this talk if you're interested in this method.  However, there's a second way to also describe this, not just going with the flow of the  particles, but we are a bit lazy.  We just box it.  So we create a grid.  As you see down here, in this grid, you have a certain filling level, a bit of a slope  height.  So what's the trend there?  And then we just look for each box, what flows in, what flows out through the surfaces  of this box.  And then we have a volume or a mass filled within this box.  And this is how we discretize what is going on in the disk.  And actually, since we are usually in the system of a disk, we do not do it in this  nice box way like this, but we use boxes like those because they are already almost like  a disk.  And we just keep exactly the same boxes all the time and then just measure what goes through  the surface in these boxes.  So this is how these two methods look like if you compute with both of them.  So one was done by me.  I'm usually using this boxing method and the other was done by my colleague.  You see this, like, when you look at them at the colors, at the structure, here you  have the slope inward, you have the same slope inwards here.  You have even the silly structure here, the same here.  But what you notice is you have these enlarged dots that are really, these are really the  mass particles we saw before, these bubbles.  And here you have this inner cutout.  This is because when you create this grid, you have the very region at the inner part  of the disk where the boxes become tinier and tinier.  And while we can't compute that, so we have to cut out at some point the inner part.  So here when you go to low densities, these bubbles blow up and distribute their mass  over a larger area, so it's not very accurate for these areas.  And here we have the problem.  We can't calculate the inner area.  So both methods have their pros and cons and our wallet.  But now, for most, we will focus on this one.  So we have this nice, actually, stream features.  So again, going back to the boxes, we have to measure the flow between the boxes.  This flow in physics, we call it flux.  And we have a density, row one, a density, row two.  And the flux is the description of what mass moves through the surface here, from one  box to the next.  So if we write this in math terms, it looks like this.  This says the time derivative of the density, meaning the change in the change over time,  so how much faster is lower you go, the velocity would be a change in time.  And then this weird triangle symbol, it's called nabla, is a positional derivative.  So it's like a slope.  So how much, how do we change our position, actually?  So if we change, look at the density over time, it should correlate to what inflow we  have over position.  That is what that says.  So and then we have in physics a few principles that we have always to obey because it's just  almost common sense.  One of them is, well, if we have mass in a box, like this, the mass should not go anywhere  unless someone takes it out.  So if we have a closed box and mass in that box, nothing should disappear magically.  We should stay.  It should all stay in this box.  So even if these particles jump around in our box with a certain velocity, it's the  same number of particles in the end.  That's again the same equation just told in math.  So a second very rudimentary principle is if we have energy in a completely closed box,  so for example, this nice chemicals here, and we have a certain temperature.  So in this case, our temperature is low, maybe outside of around zero degree Celsius, and  then we have this nice chemicals down here.  And at some point they react very heavily.  We suddenly end up with much less chemical energy and a lot more thermal energy.  But overall, the complete energy summed up here, like the thermal and the chemical energy,  also the energy of the movement and the energy of potential added up to this variable U, that  should not change over time if you sum up everything because our energy is conserved  within our closed box.  And then the third thing is, I think you all know this, if you have like a small mass  with a certain velocity, a very high velocity in this case, and it bumps into someone very  large.  What happens?  Well, you get a very small velocity in this large body and the smaller mass stops.  And the principle here is that in momentum is conserved, meaning that the velocity times  the mass of one object is the same as then later for the other one, but since it's larger,  this product has to be the same.  That doesn't change.  And we have also, like in our simulations, to obey these rules.  And we have to code that in so that we have physics in them.  So you say, okay, this is really simple, these rules, right?  But actually, well, it's not quite as simple.  So this is the Navier-Stokes equation.  It's a very complicated equation.  It's not completely solved.  And we have here all that is marked red, other derivatives.  Here we have our conservation law that was the nice and simple part.  But now we have to take other physical things into accounting for pressure, accounting for  viscosity, for compression.  So squeezing and how sticky is our fluid and also gravity.  So we have a lot of additional factors, additional physics.  We also have to get in somehow.  And all of these also depend somehow on the change of position or the change of time.  And these derivatives aren't really nice for our computers because they, well, they don't  understand this triangle.  So we need to find a way to write an algorithm so that it can somehow relate with these math  formula in a way that a computer likes.  One of the ways to do this is, well, the simplest solution actually is just we say, okay, we  have now these nasty derivatives and we want to get rid of them.  So if we look just at one box now, we say that in this box, the new value for the density  in this box would be the previous density plus the flux in and out times the time step  over which we measured this flux.  And we have to somehow get to this flux and we just say, okay, this flux now is, if we  start here, the slope of this curve, the trend, so to say, where this curve is going right  now, so it would look like this.  So in our next time step, we would have a density down here and, well, then we do this  again.  We again look at this point, where's the trend going, where's the line going?  And then we end up here, same here.  So again, we just try to find this flux and this is the trend at this position in time.  So this goes up here and then if we are here now, look at this point, it should go up here.  So this is what our next trend would be.  And we do this over all the times and this is how our simulation then would calculate  the density for one box over different time steps.  So that kind of works.  So the blue curve is the analytical one, the red curve, well, it's kind of simulatized,  it works, but can we do better?  It's not perfect yet, right?  So what we can do is we refine this a bit, taking a few more steps, making it a bit more  computationally heavy, but trying to get a better resolution.  So first we start with the same thing as before, we go to this point, find the trend in this  point, that point, like the line would go in this direction from this point and then  we go just half a step now.  And now we look at this half a step to this point now and do it again, the same saying,  okay, where's the trend going now, and then we take where this point would go and add  it to this trend.  So that would be that the average of this trend, of this exact point, and this trend,  this dark orange curve.  And then we go back to the beginning with this trend now and say this is a better trend  than the one we had before.  We now use that and go again and search the point for half a time step.  And then again we do the same thing.  Now we again try to find actually the trend and average it with the arrow before.  So it's not exactly the trend, it's a bit below the trend because we averaged it with  the arrow before.  And now we take this averaging trend from the beginning to the top like this.  Okay, this is already quite good, but we can still do a little bit better if we average  it with our ending point.  So we go here, look where's the trend going, that would go quite up like this.  And we average this and this together and then we end up with a line like this.  This is so much better than what we had before.  It's a bit more complicated to be fair, but actually it's almost on the line.  So this is what we wanted.  So if we compare both of them, we have here our analytical curve.  So over time in one box, this is how the density should increase.  And now with both of the numerical method, the difference looks like this.  So we have smaller and smaller time steps, even the Euler gets closer and closer to the  curve, but actually the Runge-Kutta, this four-step process works much better and much  faster, however it's a bit more computationally difficult.  When we simulate objects in astronomy, we always want to compare them to objects that  are really out there.  So this is a giant telescope, well, consisting of a lot of small telescopes, but they can  be connected and used as a giant telescope.  And it takes photos of dust in the sky and this is used to take images of discs around  stars and these discs look like this.  So these images were taken last year and they are really cool.  Before we had those images, we only had images with less resolution, so they were just blurred  blobs.  And we could say, yeah, that might be a disc, but now we really see the discs.  And we see rings here, thin rings, and we see thicker rings over here, and even some  spirally structures here, and also some features that are not really radially symmetric like  this arc here.  And it's not completely solved how these structures formed.  And to find that out, a colleague of mine took this little object with the asymmetry  here.  And so this is the imagery Chester, and this is his simulation.  So this is how discs looked like in the beginning, probably, and he put in three planets and  let the simulation run.  And so what we see here is that the star is cut out.  As Anna said, we have to, so the grid cells in the inner part are very, very small and  it would take a lot of time to compute them all.  So that's why we are leaving out that spot in the middle.  And what we see here is three planets interacting with the material in the disc.  And we can see that these planets can make this thing here appear so that in the end  we have something looking very similar to what we want to have or what we really observe.  So we can say three planets could explain how these structures formed in this disc.  It's a little bit elliptical, you see that.  That's because it's tilted from our side of line.  It would be round if we watched that it face on, but it's a little bit tilted.  That's why it looks elliptical.  So we already saw we can put planets in the gas and then we create structures.  One very exciting thing that we found in the last year or two years ago, it started, but  then we found more, is this system, PDS 70, in this system, for the very first time, we  found a planet that was still embedded completely within the disc, so the gas and dust.  Usually because the gas and dust is the main thing that creates a signal, some radiation  because of heat.  We only observe that and then we can't observe the planet embedded, but in this case the  planet was large enough and in the right position that we actually were able to observe some  signature of accretion on this planet that was brighter than the rest of the disc.  Then later, just this year, just a few months ago, we actually found out, well, this is  not the only object here.  This is a very clearly a planet, but actually this spot here is also something.  We can see it in different grains.  Every picture here is a different set of grains observed.  We can see this in four different, five different kinds of observations.  So there is a planet here.  Then there is also something, we don't know what it is yet, but it's point-like and actually  creates a feature that we reproduce in different kinds of observational bands or different  kinds of signals here.  This is very interesting.  For the first time, we actually see a planet forming right now within the disc.  So a colleague of mine also is very interested in this system and started to simulate how  do two planets in a disc change the dynamics of a disc.  So here we have, of course, this disc is again tilted because it's not phase-on.  It's like 45 degrees tilted, not like this, but like this.  So he had it phase-on.  This is what his simulation looks like.  So there are two planets that these blobs here again, as in the simulation.  Here we have a close-up.  You can actually see these little boxes are actually our simulation boxes in which we  have our densities.  Then he just looked at how the planets would change the structure in the gas and also how  the gas would interact with the planets shifting them around.  It's interesting.  The planets tend to clear out an area, open a gap within the disc, block a lot of gas  around here, so you have a brighter ring here again, and then clearing out more and more.  At some point in the simulation, he saw they get a bit jumpy.  So it's very nice.  You also see that the planets induce in the whole disc some kind of features, like spiral  features.  So a single planet will change the symmetry and the appearance of a whole disc.  So the reason why the planet is staying at this point is because we're rotating with  the planet.  It's actually going around the disc, but the camera is rotating with the planet, so it's  staying at the fixed place we put it in.  But there's more.  Because as I already said in the Navier-Stokes equation, we have a lot of different kinds  of physics that we all have to include in our simulations.  One of the things, of course, is we maybe don't have just a star in the disc.  We have planets in there, and maybe two stars in there, and all of these larger bodies have  also an interaction between each other.  So if we have a star, every planet will have an interaction with a star, of course.  But then also the planets between each other, they have also an interaction, right?  So in the end, you have to take into account all of these interactions.  And then also we have accretion, just looking like this.  So accretion means that the gas is bound by some object.  It can be the disc, the planet, or the star that takes up the mass, the dust, or the gas.  And it's bound to this object.  And then it's lost to the disc or the other structures, because it's completely bound  to that.  So the principle of this would be a simulation I did last year and published.  We have here a binary star.  So these two dots are stars.  I kind of kept them in the same spot, but every picture will be one orbit of this binary.  But since we have interactions, you actually see them rotating because of the interactions,  which is other.  And then also we have here a planet and here a planet.  And the interesting thing was that these two planets interact in such a way that they  end up on exactly the same orbit.  So one starts further out, the orange one, and then very fast they go in and they end  up on exactly the same orbit, if it now would play nicely.  So another thing is with the accretion here, we actually see clouds from above dropping  down onto the new forming star here.  So all of this, what you see here would be gas, hydrogen.  And it's a very early phase, so this is not completely flat.  It has a lot of material and then you actually have this info from above towards the star  and then the star keeps the mass.  And we have to take this also into account in our simulations.  Another thing we have to take into account up till now, we just cared about masses and  densities.  But of course, what we actually see is that stars are kind of warm, hopefully.  Otherwise, temperatures here would also not be nice.  And different chemicals have different condensation points.  And this is also true in a system.  So we start with the star temperature, at the surface of the star, we have a temperature  around 4000 Kelvin.  And then we go a bit into the disk and there's a point where we, for the first time, reach  a point where we have any material at all because it starts to condensate and we actually  have something solid like iron, for example, at 1500 Kelvin.  And then if we go further in, we reach a point where we have solid water.  And this is at 200 Kelvin.  This is what we then would need, actually, to have a planet that also has water on it  because if we don't get the water in the solid state, it will not fall onto a terrestrial  planet and be bound there, right?  So this is important for our earth, actually.  And then if we go even further out, we have also other gases condensating to solids like  CO2 or methane or things like that.  And since we only get water on a planet when we have a temperature that is low enough so  that the water actually forms a solid, it's important for us to think about where that  is in our forming disk.  Where do we start to have a planet like earth that could have some water, right?  But it's not just the simple picture where we have all these nice ring structures where  we have a clear line, actually.  It gets more complicated because we have pressure and shocks and thermodynamics is a lot like  pogo dancing, right?  You crash into each other and it's all about collisions.  So the gas temperature is determined by the speed of your gas molecules, like here, bouncing  and crashing into each other, exchanging momentum.  So there's two ways to heat up such dance.  First thing is you get a large amount of velocity from the outside, like a huge kick, a shock  into your system.  And second way would be if we have a higher pressure, like more molecules, then also you  of course have more collisions and then a higher temperature.  So if you change because you have a planet now in the system, the pressure at some point,  you actually get a higher temperature.  So that is not then we lose this nice line because suddenly we have different pressures  at different locations.  And the colleague of mine also simulated this.  So it starts off ninth.  So this is the initial condition.  We just assumed, okay, if we have no disturbance whatsoever, we have our nice planet here at  one AU, so same distance as Earth to the Sun here too.  But here we assume that less heat gets transferred from the surface of the disk.  And here we have a planet far out like Jupiter or something.  And now we actually let this planet change the structure of the disk and what happens  is we found these spirals.  And within these spirals, we change pressure.  And with this, actually, if you see this orange everywhere where it's orange, it's hotter  than the ice line.  So we don't have water where it's orange.  And where it's blue, we can have water.  And the interesting thing is even if we put a planet out here like Jupiter, we still form  these regions in the inner system where we have less water.  One problem in astrophysical simulations is that we don't always know how to shape our  boxes or how small these boxes have to be.  So we use a trick to reshape the boxes as we need them.  It's called adaptive mesh.  And this is a simulation of the red fluid flowing in this direction and the blue fluid  in the other one.  So at the boundary, the two fluids shear and they mix up somehow.  And we don't know how in advance.  So we start a simulation.  And as the simulation starts, we reshape those boxes here.  So in the middle, we don't need much reshape because it's not that complicated here.  It's just a flow.  But at the boundary, we see those mixing up of the two fluids.  And so we reshape the cells as we need them.  This is done in an astrophysical program called ARIPO.  We will later show you some more programs to use for simulations.  But another simulation I want to show you first is also done with ARIPO.  And it's a simulation of the universe.  So from here to here, it's very big.  It's 30 million light years.  So each of these dots you see here is the size of a galaxy or even more.  And here you can actually see that at some regions, it's very empty.  So we're rotating around this universe, this simulated universe here.  And these regions here are empty and we don't need a lot of boxes there.  Big boxes are enough here.  But in this dense regions where we have a lot of material, we need smaller boxes.  And this method I showed you where we reshape the boxes as we need them is used for this simulation.  So actually you see, it's all the beginning of the universe there.  Basically, the initial mass collapsing to the first galaxies and first supernovae  starting, very beautiful simulation.  So there are different programs as I already mentioned in astrophysics.  Three of them, those three are all open source.  So you can download them and use them on your own machine if you like.  And but there are more, a lot more.  And some of them open source, some of them are not.  Sometimes it's hard to get them.  In the following, we will present the two, Fargo 3D and Pluto in a detailed version  or more detailed version than ARIPO.  Because we usually use those two for our simulations.  What I want to show you with this slide is that depending on what you want to simulate,  you need to choose a different program.  And one thing is that in astrophysics, we sometimes call the whole program code.  So if I use the word code, sorry about that, I mean the whole program.  So let's have a look at Fargo 3D.  It's a hydrodynamics code and what you see here is an input parameter file.  There you define how the disk looks like, how much mass does it have, how big is it,  and what planet.  So here, a Jupiter.  Do you see that?  A Jupiter is put in.  And we also define how big our boxes are.  This program is written in C, which is quite nice because a lot of astrophysical programs  are still written in Fortran.  So this is good for me because I don't know any Fortran.  We can run this.  And what's typical for Fargo, so that's a compilation.  Actually on my computer, so I don't need a fancy computer.  I just did it on my small laptop.  And now we run it.  Now typical for Fargo, as you will see, are a lot of dots.  So here.  It will print out a lot of dots.  And it will create at certain times some outputs.  And these outputs are huge files containing numbers.  So if you look at them, they are not really interesting.  They just are numbers in something like a text file.  So a big part of astrophysics is also to visualize the data.  Not only to create it, but also to make images so that we can make movies out of them.  For that, I prefer to use Python, but there are a lot of tools.  But there are a lot of different tools to visualize the data.  So this is actually that output, the first one we just saw.  The Jupiter planet in the disk that I defined in this parameter file.  And it's already started to do some spirals.  And if I would have let it run further, then the spirals were more prominent.  And yeah.  Now we have a planet here on our computer.  So we also have Pluto somehow has a bit more setup files.  So what I need is three files here.  Looks a bit complicated to break it down.  This file defines my grid and initial values and the simulation time here.  We input actually what physics do we want to need?  What is our coordinate system?  So do we want to have a disk or just like spherical boxes or like squared boxes?  And how is the time defined?  And here we then actually write a bit of code to say, okay, now how do I want a gravitational  potential?  So what's the source of gravity?  Or what will happen at the inner region where we have this dark spot?  We have somehow to define what happens if gas reaches this boundary?  Is it just falling in?  Is it bouncing back or something?  Or is it looping through the one end to the next?  And this is also something we then just have to code in.  And if we then make it and let it run, it looks like this.  So again, our nice thing we hopefully put in or wanted to put in, the time steps, what  our boundaries were, parameters of physics, hopefully the right ones.  And then nicely we start with our time steps.  And if we see this, it's hooray.  It worked, actually, because it's actually not quite simple usually to set up a running  program, a running problem, because you have to really think about what should be the physics,  what's the scale of your problem, what's the time scale of your problem, and specify this  in a good way.  But in principle, this is how it works.  There are a few test problems that you actually want to play around with this to make it easy  for the beginning.  And this is how we do simulations.  So as I already said, we can just start them on our laptop.  So here this is my laptop.  I just type dot slash Fargo 3D, and it should run, right?  And then I just wait for 10 years to finish the simulations of 500 time steps or something,  like 500 outputs.  Well, that's not the best idea.  We need more power.  And both of us, for example, are using a cluster for a button written back, and that takes  down our computation time by a lot, usually like a factor of maybe 20, which is a lot.  So I would need on my computer maybe a year, and then I just need maybe five hours, a few  days or a week on this cluster, which is usually a simulation time about a week for me.  So what you see here is that we use GPUs, yes, but we do not or mostly not use them  for gaming.  We use them for actual science.  Yeah, it would be nice to play on that, right?  Yeah.  That just said.  So back to our Earth, actually.  So can we now, we wanted to grow our own planet.  We can do that.  Yes, of course.  Can we grow Earth?  Well, Earth is a very special planet.  We have a very nice temperature here, right?  And we have not a crushing atmosphere like Jupiter, like a huge planet that we could not  live under.  We have a magnetic field that shields us from the radiation from space, and we have water,  but just enough water so that we still have land on this planet where we can live on.  So even if we fine tune our simulations, the probability that we actually hit Earth and  have all the parameters right, it's actually tiny.  It's not that easy to simulate an Earth.  And there are a lot of open questions, too.  How did we actually manage to get just this sip of water on our surface?  How did we manage to collide enough mass or aggregate enough mass to form the terrestrial  planet without Jupiter sweeping up all the mass in our system?  How could we be stable in this orbit when there are seven other planets swirling around  and interacting with us?  All of this is open in our field of research, actually, and not completely understood.  This is the reason why we still need to do astrophysics.  And even in all our simulations, there is no planet B, and the Earth is quite unique  and perfect for human life.  So please take care of the Earth and take care of yourself and of all the other people  on the Congress.  And thank you for listening.  And thank you to everyone who helped us make this possible and to the people who actually  coded our programs with which we simulate.  Thank you.  Thank you for the beautiful talk and for the message at the end.  The paper is open for discussion, so if you guys have any questions, please come to the  microphones.  I'm asking my signal, Angel.  No questions right now, but microphone too, please.  Yes, thank you very much.  Very beautiful talk.  I can agree.  I have two questions.  The first is you showed you are using Navier-Stokes equation, but on the one hand you have the  dust disk, and on the other hand you have solid planets in it.  And so are you using the same description for both, or is it a hybrid?  It very much depends.  This is one of the things I showed you that for Pluto we write this C file that specifies  some things and about every physicist has somewhat his or her own version of things.  So usually the planets, if they are large, they will be put in as a gravity source and  possibly one that can accrete.  And pebbles are usually then put in a different way.  However, also pebbles are at the moment a bit complicated.  There are special groups specializing in understanding pebbles because as we said in the beginning,  when they collide usually they should be destroyed.  If you hit two rocks very hard together, or two rocks together they don't stick.  If you hit them hard together they're splatter around and we don't add up with bigger objects.  So to explain, pebbles are small rocks or big sandstones or something like that.  So bigger rocks but not very big yet.  It depends on which code you use.  Very short, maybe one.  Do you also need to include relativistic effects or is that completely out?  That's a good question.  Mostly if you have a solar type system, you're in a range where this is not necessary.  For example, with the binaries, if they get very close together then at the inner part  of the disk that is something we could consider.  And actually I know for Pluto it has modules to include relativistic physics too.  Yes.  Thank you.  Okay, we have quite some questions so keep them short.  Number one, please.  Thank you.  Yeah, thank you very much for your interesting talk.  I think you had it on your very first slide that about 70% of the universe consists of  dark matter and energy.  Is that somehow considered in your simulations or do you handle this?  Well in the simulations we make, we're doing planets and disks around stars, it's not considered  there.  In this simulation we showed you about the universe.  At the beginning the blueish things were all dark matter so that was included in there.  Okay, thank you.  Okay, microphone three.  Hi, thanks.  Sorry, I think you talked about three different programs.  I think Pluto, Fargo 3D and a third one.  Azoring, say you're a complete beginner, which program would you suggest is like more, like  if you want to learn more which one is user friendly or good to start with?  I would suggest Fargo first.  It's kind of user friendly, has somewhat good support and they are always also always very  thankful for actual comments and additions if people actually are engaged in trying to  improve on that.  Because we are physicists, we're not perfect programmers and we're also happy to learn more.  So yeah, Fargo I would suggest it has some easy ways of testing some systems and getting  something done.  And it also has a very good documentation and also a manual how to make the first steps  on the Internet so you can look that up.  Awesome, thank you.  Let's get one question from outside from my signal angel.  Thank you for your talk.  There's one question from ISC.  How do you know your model is good and when you can only observe snapshots?  Oh, that's a good question.  We have to, as we said, we're in theoretical astrophysics so there are theoretical models  and these models cannot include everything.  So every single process, it's not possible because then we would calculate for years.  To know if a model is good, you have to...  Usually you have a hypothesis or an observation that you somehow want to understand with most  of the necessary physics at the stage to reproduce this image.  Also from the observation, we have to take into account what our parameters should be,  how dense the end of the simulation should be and things like this.  So by comparing to observations, that's the best measure we can get if we kind of agree.  Of course, if we do something completely wrong, then it will just blow up or we will get a  horribly high density.  So this is how we know physics will just go crazy if we do too large mistakes.  Otherwise, we would try to compare to observations that it actually is sensible what we did.  That's one of the most complicated tasks to include just enough physics that the system  is represented in a good enough way but not too much that our simulation would blow up  in time.  Number two, please.  I've got a question about the adapted grids.  How does the computer decide how to adapt the grid because the data where the high density  comes after making the grid?  Yes.  This is actually quite interesting and also not quite easy to answer question.  Let me try to give a breakdown nutshell answer here.  The thing is you measure and evaluate the velocities or in the flux you also evaluate  the velocity.  And if the velocity goes high, you know there's a lot happening.  So we need a smaller grid than there.  So we try to create more grid cells where we have a higher velocity.  In a nutshell, this is, of course, in an algorithm a bit harder to actually achieve but this  is the idea.  We measure the velocities at each point and then if we measure a high velocity, we change  to a smaller grid.  So you can predict where the mass will go and where the densities are getting high.  Exactly.  Step by step.  Okay.  To say.  Thanks.  We stay with microphone too.  Okay.  I've got a bit of a classical question.  So I guess a lot relies on your initial conditions and I have two questions related to that.  So first, I guess they are inspired by observations.  What are the uncertainties that you have?  Be them what is the impact if you change your initial conditions like the density in the  disk?  Yeah.  Right now, my main research is actually figuring out sensible initial conditions or parameters  for a disk.  If you just have an initial set of conditions and a sensible set of parameters and let it  run very long, you expect a system hopefully to converge to the state that it should be  in.  But your parameters are, of course, very important.  Here we go back to what we can actually understand from observations.  What we need, for example, is the density, for example, and that is something we try  to estimate from the light we see in these disks that you saw in this nice grid with  all these disks.  We estimate, okay, what's the average light there?  What should then be the average densities of dust and gas in comparable disks?  Okay.  Thanks.  Okay.  One more at number two.  Yes.  Thank you for the talk.  When you increase the detail on the grid in the Euler model, you have to, when you want  to compute the gravitational force in one cell, you have to solve all the masses from  all the other cells.  So the complexity of the calculus grows quite radically at the square of the, how do you  solve that?  Yes, that's it.  Or do you just put more CPUs?  Well, that would be one way to do that.  But there are ways to simplify if you have a lot of particles in one direction and they  are far away from the object you're looking at.  So yeah.  So if you have several balls here and one ball here, then you can include all these  balls or you can think of them as one ball.  So it depends on, you look at, so how you define how many particles you can take together  is when you look at the angle of this, of the, yeah, the big or the many particles will  have from, seen from the object you're looking at.  And you can define a critical angle and if it's, if an object gets smaller than this,  or if a lot of objects get smaller than this angle, you can just say, okay, that's one  object.  So that's a way to simplify this method.  And there are some, yeah, I think that's the main idea.  Okay, we have another one.  Do you have a strategy to check if the simulation will give a valuable solution or does it happen  a lot that you wait one week for the calculation and find out, okay, it's total crash, that  trash or it crashed in the time?  So that also depends on the program you're using.  So in Fargo, it gives these outputs after a certain amount of calculation steps.  And you can already look at those outputs before the simulation is finished.  So that would be a way to control if it's really working.  But I think it's the same for Pluto.  So you get every, you set, there's a difference between time steps and actually output steps.  So and you would define your output steps not as the whole simulation, but you can look  at each output step as soon as it's produced.  So I usually get like 500 outputs, but I already can look at the first and second after maybe  half an hour or something like that.  Yeah, but it also happens that you start a simulation and wait and wait and wait and  then see you put something wrong in there and well, then you have to do it again.  So this happens as well.  Thanks.  Okay, one final question.  Yeah, okay.  Is there a program in which you can calculate backwards so that you don't have the starting  conditions but the ending conditions and you can calculate how it had started?  Not for hydrodynamics.  If you go to anybody, there is a way to go backwards in time.  But for hydrodynamics, the thing is that you have turbulent, almost like chaotic conditions.  So you cannot really turn them back in time with anybody kind of because actually it's  kind of, well, it's not analytically solved, but it's much closer than like turbulence,  streams, spirals and all the things you saw in the simulations.  Okay, I guess that brings us to the end of the talk and of the session.  Thank you for the discussion and of course, thank you guys for the presentation.
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