Nice Model.

Did you make it yourself?

We’ve known for a long time the broad details of how the Solar System formed. The Nebular Hypothesis was first proposed back in the 18th century and has been refined over time with the aid of detailed observations of areas where other star systems are in the process of being born into its current general state. The theory goes that you start with what is called a molecular cloud – a big clump of gas that is mostly hydrogen. At first the matter in this cloud will be very diffuse and spread out, but since it isn’t exactly evenly distributed the cloud will have areas where there is a slightly higher concentration of gas molecules than the average. This is enough to get the gravitational ball rolling: those small concentrations of gas molecules are heavy enough to attract and absorb other gas molecules, which makes them heavier, which lets them attract yet more molecules etc. etc. It’s a runaway process that eventually draws most of the surrounding gas cloud in towards a common centre of mass. While this is happening the Brownian motion of the gas molecules in the cloud will average out so that the cloud starts to rotate in the direction of its net angular momentum1, causing the outer regions of the cloud to flatten into a disc shape. The centre of the cloud collapses to the point where the pressure and temperature are enough to kickstart a nuclear fusion process, creating a star. This leaves a disc-shaped remnant of gases that is rotating around the star in the direction of the original cloud’s rotation, and this is where we eventually get the planets from.

This protoplanetary disc then goes on to form the planets in much the same way as the molecular cloud formed the star. This time the starting point is a dust grain within the disk. This dust grain collides with another dust grain in the disk, and the two stick together. Repeat this process a couple of million times and you now have a clump of matter several hundred metres on a side hurtling around the proto-star. Smash many of these clumps together and eventually a planetesimal will be created; this is a chunk of stuff about 1 km in diameter. The planetesimal stage is the point where the process becomes runaway since planetesimals are large enough to attract one another through their own self-gravity – they collide, merge and the resulting boost in mass means they attract even more planetesimals.

Eventually you end up with a load of planets that have cleared all the matter immediately surrounding their orbits (hence the inclusion of this condition as part of the IAU’s definition of a planet in 2006). Any gas remaining in the protoplanetary disc either falls onto the Sun or else is blown away by the solar wind. So far, so good. But this is where the Nebular Hypothesis runs into a few problems; namely, that the Solar System structure predicted by this model of accretion from a protoplanetary disc does not match what we see in the Solar System today. There should be a lot more planetesimals, the gas giants should be located closer to the Sun than they are today (this goes back to the “hot Jupiters” we often find orbiting other stars), and there should be a fairly dense cloud of leftover material outside the orbit of Neptune. Since none of these things are true, something obviously happened in the four billion years separating the formation of the planets and the present day to account for the difference in what we should see and what we do see.

Current best candidate for that something is the Nice Model. It explains the following:

  • Where all the planetesimals went.
  • Why the gas giants are where they are.
  • Why the Kuiper Belt, Scattered Disc and Oort Cloud are structured the way they are.
  • The Late Heavy Bombardment, an approximately 300 million year-long period just after the formation of the Solar System during which all the inner planets were subjected to a much, much higher rate of asteroid and comet impacts than they are today (as inferred from the very large number of impact craters on the surface of the Moon which date from around this time).

As the Nice Model would have it, none of these things makes sense on its own but when you put them all together you can in fact come up with a model of the evolution of the Solar System that works.

The starting point is the one suggested by the Nebular Hypothesis: all the planets clustered in a narrow 15 AU radius from the Sun, with a very dense disc of icy detritus containing many planetesimals that didn’t quite make it as planets surrounding them from 15 up to about 30 AU. One of the planetesimals gets nudged inwards and approaches the outermost gas giant. The gas giant gives it a gravitational velocity kick by exchanging angular momentum with it; conservation laws dictate that this leads to an equivalent loss of angular momentum – and thus orbital speed – in the gas giant, shifting it to an orbit further away from the Sun.

The planetesimal is tossed from gas giant to gas giant like a gigantic mystery parcel, getting a gravity boost that shifts the orbit of each gas giant outwards. Then it encounters Jupiter, fattest of all the planets. Jupiter has no time for tiny planetesimals and gives it such a smack that the planetesimal is ejected from the Solar System altogether; this moves the orbit of Jupiter inwards rather than outwards. One single planetesimal doing this will have next to no effect on the orbits of the gas giants – they’re sodding huge, after all – but if the process is repeated several thousand times as new planetesimals are leached from the outer debris disk, it will all add up and start to produce a significant effect. Over millions of years the orbits of the outer three gas giants will slowly migrate outwards, while Jupiter migrates inwards. Eventually they get to the point where Jupiter reaches a 1:2 orbital resonance with Saturn, at which point all hell breaks loose.

The greatly-increased gravitational effect of the resonance of the two largest planets in the Solar System throws everything else into chaos. The video above illustrates quite nicely the slow migration and subsequent catastrophic interactions of the planets. Saturn gets shunted out into a wider orbit, which in turn moves Uranus and Neptune outwards3. This sends Neptune careening into that huge, densely populated disc of icy planetesimals that had previously been outside its orbit, scattering them in every direction like ninepins. Many planetesimals are scattered inwards towards the terrestrial planets, turning that region of space into a shooting gallery for the next couple of hundred million years: this is how the Nice Model explains the Late Heavy Bombardment. Others are scattered outwards at all inclinations and eccentricities, explaining the Scattered Disc and the Oort Cloud. Finally, the stuff at the innermost edge of the debris disc – the stuff closest to Neptune – is booted out of the Solar System entirely unless it is fortunate enough to fall into one of the narrow orbital bands defined by stabilising resonances with Neptune, as with Pluto and the rest of the classical Kuiper belt population.

That’s the Nice Model. I think it’s a very convincing piece of work, but it’s worth bearing in mind that the only criteria for the correctness of the Nice Model we have is that it produces something close to what we see today. It’s entirely possible that it happened entirely differently — we’ll never know for sure exactly how without a time machine — and even the Nice Model has several significant question marks hanging over it, such as the inability to explain the two distinct population types found in the Kuiper Belt and the fact that the Late Heavy Bombardment might not have even happened; the evidence for it consists of an extremely limited sampling of a few lunar impact sites and it’s possible that their common origin is just a rather large coincidence.

 As far as meshing with the currently prevailing scientific theories on the history of the Solar System goes, though, the Nice Model is the best we’ve got. Next week: Oort? Kuiper? What hell they? I attempt to explain.

  1. Don’t worry if you don’t understand the specifics of this; you’re in good company. As far as I can make out exerting a unidirectional gravitational force on an object that is already undergoing Brownian motion that has a component lateral to that force will create a torque force on the molecule, which results in the gas molecules in the cloud acquiring a rotational motion about the axis of the cloud’s centre of mass. That makes sense to me, and past there I guess since random Brownian motion of all the gas molecules in the cloud won’t average out exactly to zero (it would be pretty goddamn amazing if it did) the sum of the angular momentum of the cloud will also not be zero. Hence the cloud as a whole rotates one way or the other, and this rotation will get faster as the cloud gets smaller due to conservation of angular momentum (same principle as an ice skater pulling their arms in closer to their torso to spin faster) which causes the cloud to flatten into a disc thanks to centrifugal force2. This could be complete rubbish, but hey – I’m just a poor Solar System scientist. Can’t expect me to know everything.
  1. One of the things they try to drill into you at Physics School is that centrifugal force isn’t a real force. It’s an approximation that only “exists” to make calculations within rotating reference frames (i.e. the surface of the Earth) easier. So whenever somebody wrote down the word “centrifugal” on their work it’d come back with red pen all over it and eventually the practice was stamped out, but I secretly keep the flame alive in my heart.
  1. It’s suspected that Neptune may actually have formed as the seventh planet from the Sun, with Uranus as the outermost planet, and that when Saturn boosted Neptune and Uranus outwards they switched places. The model seems to work just as well either way.


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8 thoughts on “Nice Model.

  1. MD Game Pro says:

    Impressive stuff!!! Mind blowing

  2. Sam says:

    I seriously need to learn more about star and planet formation. I don’t particularly know much about gas dynamics below a parsec (and above atmospheric scales, I guess). It’s becoming increasingly clear that astronomers don’t really know much about why there are certain numbers of stars of different sizes (i.e. what the stellar initial mass function is or why it’s that).

    • Sam says:

      And yes, discs form because the gas has some angular momentum to begin with, so it collapses in the direction it has no rotational support. And sure, it’s not a “real” force, but whatever. Call it the Galilean invariant acceleration if you like. I tend to say that a disc is rotationally supported rather than using centrifugal force, but it’s just terminology.

    • hentzau says:

      The detailed mechanics of how stars work is slightly above my pay grade (I do planet-scale stuff mostly) but I’m constantly amazed that we’ve even managed to work out the things we currently know about stars and star formation. After all it’s not like we can watch it happening in any meaningful sense, or cut open a star to see what’s going on inside. So, you know, there’s a lot of stuff astronomers don’t know, and since they have to figure things out with the scientific equivalent of guy wire and scotch tape it’s likely that understanding the fine detail of star and planet formation will remain beyond us for a good long time to come.

      I think, anyway.

      • Sam says:

        The general way that simulations work is that you throw more physics at a problem until you either a) get the right answer or b) realise that the program you’re using has some fatal flaw, and carry on anyway. Examples include particle hydrodynamics not capturing instabilities properly, Riemann-problem-based grid hydrodynamics inducing weird instabilities in grid-aligned shocks (that or being too dissipative), etc. That and the problem is inherently nonlinear, so it’s not like you can perfectly rebuild a real system like the Milky Way anyway.

        The thing I think school physics doesn’t get across is how messy the real world is. Doing at least one non-linear system would be useful, since people come away with the idea that if you get better computers you can solve any problem, whereas the five-day forecast is actually about as good as we’ll ever get with weather forecasting, weather engineering aside.

        (Incidentally, this is Gap Gen from Sekrit)

  3. slimbuk says:

    hentzau, did you see the Horizon episode on Black holes last night? A post about that, rebuttal or otherwise would be awesome!

    • hentzau says:

      I shall have a look see. If it’s about how black holes are going to kill us all then I may be able to gin something up because that sort of thing really pisses me off.

  4. [...] to eject the other ninety-nine percent. “Whatever happened” is overwhelmingly likely to be the chaotic gravitational interactions, peturbations and resonances of the solar system’s early years. For example, there’s lots of [...]

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