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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,
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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.
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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.
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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.