I love the way in which the Nice model takes what looks like a small problem, the eccentricities of Jupiter, Saturn, Uranus, and Neptune, realizes that it's not a small problem after all. And spins the solution into a profound story of how the solar system might very well have evolved. We're going to tell a similar story today, and I would say this one is significantly less secure. The problem that then Nice model solves, the problems that the Nice model solves, were big problems that are clearly there in the solar system, eccentricities, cause of Late Heavy Bombardment. The problem that this next one solves is one that might be a problem, and it might not be a problem at all. But let's talk about what the problem is and what the solution is. The problem is Mars is too small. What do I mean by Mars is too small? What I mean is that if you try to simulate the formation of the terrestrial planets using these processes that we've talked about, thus sticking together to form planetesimals. Planetesimals eventually growing up to become oligarchs for a long period of time as the oligarchs finally combine together to form terrestrial planets. If you take those processes and use the disco material that we think the sun had, you don't get Mars. What do you get instead? Well, here's a set of simulations where this has been attempted and we're looking at semimajor axis down here of the final planet and mass in Earth mass is up here. And, of course, here's the Earth, 1 AU, one earth mass, sitting right here. Here is Venus. Here is Mercury. Here is Mars. Now we do have a lack of large objects out through here and that's of course because Jupiter is preventing large things from forming out there. But we also have a lot of large objects through here. These are Planets that we don't have in our solar system. Something around the distance of Mars but the mass of something closer to the Earth. These simulations do give something about the mass of Venus about the mass of Earth. Mercury is small. But Mercury is we know had a giant impact that cause problems to it. And the other thing that this simulation show is a lot of medium Mars-sized objects actually scattered out further in the solar system where we don't have those either. So what's the story? Why do we not have a large object right here where Mars is. This is called the Mars problem. Why do I say this is only maybe a problem? Well, it's certainly an interesting problem but these things are still caustic, you cannot use these simulations to predict precisely what our planets should end up like. You can use these simulations to predict the range of things that our planet should end up like, and it's true. We don't really have anything in the right range in through here and certainly not in the right range in through here. But there's just a lot of chance involved. Maybe we just got lucky or unlucky, depending on how you want to think about it at Mars, maybe not. May be this is a real Mars problem. Let's go on th assumption as a problem and let's think about ways to solve it. Once a solution is found in a sort of simulations by Hansen in 2009, around the same year. Which was, you might have felt the solutions would be well, I'll just make a last mass with masses. Let's use the same sort of plot which is on the major axises. Now we have mass on a log scale so it looks a little bit different. Here's one Earth mass up here. Tenth of an earth mass, hundredth of an earth mass and again you have Mercury, Venus, Earth and Mars. What was found was that if you just had less material out through here, it still didn't work. You still got those objects. More massive objects scattered out of the asteroid belt, you still had a more massive Mars. What you really needed to do was confine all of the disk to a fairly small annulus. And that annulus was something like .7 to 1 Au. If you confine all of the disk into this annulus. What happens is the oligarchs grow and when they become their isolation mass, they start to eventually gravitationally interact and they spread out. They scatter each other around. Not only that they scatter each other around, but some of them gets scattered so far out that they never interact. With other oligarchs, and that is the origin of these objects out through here. They are single oligarchs that got scattered out into the outer part of the disk beyond where all the other oligarchs are. And they are left in place. A really cool thing about this idea is that one of the things that we've known about Mars for a while is that it appears that the accretion time scale of Mars is short. Something like maybe short as 1.5 million years. This comes from things like if you remember the discussion of half mean tungsten dating of the of the formation of form of the earth and some more recent work also. This is a much shorter time scale than it took the, we think 100 million years of these objects to form. For a while this 1.5 million years was a complete mystery. How could it be? We thing that it takes 100 million years to form terrestrial planets, and yet mars appeared so comparatively early in the history of the solar system. Well this could be the solution. It could just be an oligarch that got scattered out there never to interact again. The big planets forming through here. The Venus size things, the Earth size things. More or less the same pattern in through here and more or less in these region through here. Pretty cool. This is a solution to the Mars problem but it doesn't really tell you anything. It tells you, if the disk were like this, this would solve the Mars problem. Why the heck would the disc be like this. A solution to this has now been termed the grand. Tack model, I don't know where they come up with this names. And this is one that was recently published by Welsh Shuttle in Nature. And everything I'm going to show you now on this from that model. It starts out with a several interesting questions. One question is, we know that hot Jupiters exist, and we even think we know why hot Jupiters exist. We think they exist because stars here something like Jupiter starts to form, and there's still a disk of gas and dust around it. And Jupiter starts to eat up all the gas that's around it, and makes a gap in the disk. There's gas inside, there's gas outside, and there's not gas in the middle. The gas inside and the gas outside both cause torques on Jupiter, which could cause Jupiter's Jupiter to move. In the short version of the story there's so much mass outside here that the torques on the outside here push inward, of course the torques on the inside push outward, but there's so much more mass that you get more of a push in than out and so the planet migrates its way in until, we still don't know exactly where they stop it, around three days, but we think that's the process by which we get hot Jupiters. So if I were to plot the total mass of the disk interior and exterior, this is something like mass, this is something like distance. Not really assuming major access, but distance. And let's say the forming Jupiter is right here. We have mass on the interior and it goes down to zero, where Jupiter has it's mass on the exterior. Goes up here. Now usually, you're used to me drawing this thing that looks kind of like this. This is the mass per unit area. Now this is just the total mass, so the total mass interior is small even if the mass per unit area is bigger. That's why they look different. Now, imagine that Jupiter is minding its own business migrating inward, and then exterior to Jupiter another planet forms. Let's call a Saturn. It does the same thing. It probably forms out here at the ice line like it should and it takes away the gas and takes away the gas and it starts to migrate inward also. There's less mass in through here than outward. Eventually it's going to catch up with Jupiter because there's a lot more mass out here than there is in here. We'll be left in a situation look sort of like this. It tends to stop when it's in a resonance. Tends to stop and when it's in maybe the 2 to 1 resonance or the 3 to 2 resonance when these two things are resonantly interacting. Now I always said that when you get these two things resonantly interacting, they start to shake and everything goes crazy. But you have so much gas around that it stabilizes them. They stay calm with all these gas around and so they're not going crazy. These guys could have migrated quite a bit inward. Let's say they've migrated into 2AU at this point. When Saturn catches up, an interesting thing happens. Jupiter no longer sees a massive junk of gas behind it. There's just this wimpy little Saturn thing and then gas way out there. And so the torque from the inner part of a disk suddenly pushes Jupiter faster this way than the torque from way out here pushes it inward. So Jupiter, although it had been started out out here and had moved in Suddenly turns around and it starts to move back upward. When it turns around and moves back upward it locks Saturn into this resonants, just like the way the type of roller objects did or maybe didn't lock into a resonants with Neptune when they got pushed up, and so Jupiter goes upward, Neptune goes upward with it in resonants. If you think you're really hard you might remember that this could we'll be the start of the nice model, suddenly Jupiter and Saturn are in resonance if the gas would all disappear suddenly then boom start the nice model. So this is all pre-nice model as there's still gas as this things are growing, the consequence of this, the important consequence of this is that this gas disc right here has been truncated down to about. 1 AU. This is what we were looking for. The reason, in this scenario, that Mars is so small is because, indeed, the gas disc was in an annulus at 1 AU because Jupiter came in, all the way into maybe 2 AU. Let's take a look at what a simulation of this really looks like. Here's the actual simulations that show what happens if Jupiter is moving in, Saturn is coming up behind it, small bodies are strewn everywhere in the solar system. And here's something I want you to notice is the time score here. Here's zero and the longest time scale we get to is 600,000 years. Remember that the Nice model is 600 million years until that explosion potentially happens. So this is all, well before the Nice model ever starts, this is when there's still all this gas still in the disc. And the gas in the disc is the thing that makes Jupiter and Saturn move. Okay, so here we start out with a Jupiter, Saturn, Uranus, Neptune and the size of them shows how big they are. Notice they're all a little bit smaller to begin with except for Jupiter. Jupiter is big enough that it makes a gap in it's disk and as soon is it makes a gap its disk starts to move. The other thing that's happening is that into here there are planetesimals and oligarchs. The round circles are oligarchs. The little red things are planetesimals. And the oligarchs are allowed to coagulate together to try to form larger planets. The planetesimals just get scattered as they go in. So Jupiter is moving inward and note what happens. Look, one of these oligarchs has already been scattered. It's crossing Jupiter's orbit. It's not going to last for long. These ones that are closest where Jupiter migrates in get very high eccentricities. You can see through here. But the rest of these oligarchs stay at pretty low eccentricity, and they're the ones that are starting to eventually merge. Jupiter continues its inward migration, but notice that it slows. And at this point, Saturn has gotten big enough that it too makes a gap. In the disk. When that happens it very rapidly moves in until it gets into a resonance. In this case the three to two resonance with Jupiter. And it stops at Jupiter from migrating any further, but that's okay. Jupiter's already done it's damage. It has depleted the disk of material into about here. Well in fact even into about here you can see that these oligarchs or high eccentricity, they won't last for long. Maybe some of them will be scattered out to places like where Mars is now. As soon as Saturn catches up of Jupiter, Jupiter doesn't see a disc behind anymore. They both start to migrate back outward fairly quickly and they stay in this resonance. Jupiter captures Saturn into this resonance just like objects get captured by Neptune and they migrate back outward and Uranus and Neptune that capture into resonance too and they migrate outward in sync. That perhaps about 500,000 thousand years. There's not enough disk material that have to let Jupiter migrate anymore and so they're left with what is the starting condition now of the Nice model which is that we have four giant planets all in residences. All about to now go unstable because the gas suddenly has disappeared. But more importantly let's watch what happen to the other things the small planets, the treasure planets form particularly after Jupiter leaves and leaves them alone. They form something like four treasure planets or small one to big ones and another small one further outside. There's other small one further outside, they can't quiet track exactly which one it was because one of these they got flung outward early on like we talked about for Mars. What else happens? So, let's take a look at these small planetesimals. Inside of Jupiter, they're all colored red. In between the giant planets are light blue outside their color dark blue. What does that mean? Well, we don't really know, but you can imagine these are more rocky, these are more carbon-rich, ice-rich and these really are icy things out in the Kuiper Belt. And the important thing is they mix up. Notice that as Jupiter moves in, it scatters some of these blue carbon-y objects inwards, see these ones in through here, and it scatters some of the red stony things outward, you can see them out through here. And as these objects plow out into what's going to become the Kuiper belt, you can even see some of these things that are potentially Kuiper belt-ish objects in through here. You can see them close into the giant planets. When all the objects have been cleared out by 600,000 years or a 150 million years from the final assembly, you can see what happens. We don't have any small bodies left in any of these unstable regions. And we have something that looks exactly like the asteroid belt. The asteroid belt is inside of this dash line. The objects that were left over are inside this dash line. And more importantly if you remember about the asteroid belt the composition of the asteroid belt was a function of distance from the sun. Closer to the sun of the earth, earth was here mars is here. Closer to the sun its mostly full of s type asteroids. Those stony type asteroids. Further to the sun seems to be mostly full of those sea type, the carbonaceous asteroids. And as you get even further out there's D types and P types which are sort of unknown exactly what they are but certainly more like carbonaceous, carbon dark things. You see as similar process here closer to the sun there's more red, this would be the stony things were formed here further from the Sun there's more of the light blue. It's not clear how many of the really dark blue, if any of them, get lodged in through here. So what does this tell us? This tells us that this process can explain the problem that we were trying to solve. We were trying to solve the problem of the small mass of Mars. We can do it by not invoking any horrendous process. It's just migration of planets that we know works. That we know what happens in other planetary system and it in fact, it songs another sort of philosophical problem. Which was, why did Jupiter not migrate. The answer is, it did migrate. It just migrated in, it migrated out again. The inward is the standard inward and the outward was because of Saturn coming up close to it and then letting it get driven back out again. The model also explains the asteroids and their locations and their compositions, sort of. And certainly where how those conversations are graded. So I'll have to say it's a very successful model. Is it what happened in the solar system? I don't know. It's a difficult one to answer because this is a model that for now nobody has come up with any of th really clever test that are needed. To tell whether this happened or didn't happen. What you would like to be able to do is find something in the solar system that you could observe and say, if this process really happened, then we will observe this. If this process didn't happen, we will observe this. We haven't found it yet, looking with luck, we'll have an answer for you one of these days. And I hate to end this way, like I always do, stay tuned.
