The chaotic teenage Solar System

At a Solar System party, in a room full of planets, the asteroid belt is full of angst. And it should be. It’s out of place. It’s wearing a clown outfit but it’s not a costume party.

What makes the asteroid belt so different? Well, for one, it’s not just one object like each individual planet. It’s a whole bunch of bodies, more than a million that are stadium-sized or larger. But that is not what makes the asteroids strange.

InnerSolarSystem-en.png

Positions of the asteroid belt between the orbits of Mars and Jupiter. Source: Wikipedia.

Think of the Solar System like a pancake. The planets follow nearly circular paths around the Sun. And as they orbit the Sun, the planets stay in the same plane, within the pancake. Their orbits never veer more than a couple of degrees off course.

The asteroids have weird orbits. Most of them follow stretched-out ellipses around the Sun instead of circles. And they don’t stay within the pancake! It’s like an asteroidal donut plopped right in the middle of the planetary pancake. Here is what it looks like:

Today’s question is, why are the asteroids’ orbits so different than the planets?

Is it just gravity? If the asteroids started on nice, pancake-like orbits, could the planets have gravitationally twisted the asteroids’ orbits into a donut?

The answer is no. Decades of research in celestial mechanics have shown that the planets cannot have created the donut. It’s not that the planets’ gravity is too weak. After all, Jupiter is more than 300 times more massive than Earth, making it about a million times more than the whole asteroid belt. Plus, it’s got a kick-ass sidekick in Saturn, which is 95 times more massive than Earth.

The problem is that Jupiter and Saturn can only exert their influence in specific spots, not across the whole asteroid belt. The gas giants can only really change asteroids’ orbits in special places called resonances. Resonances are where small kicks add up. An asteroid in a resonance can have its orbit change shape: the orbit will become stretched out and often puff up, from the pancake to the donut.

There are holes in the asteroid belt at the strongest resonances, called the Kirkwood gaps. These holes exist because these resonances are so strong those orbits are not stable. Over billions of years Jupiter dug a hole out of the asteroid belt at each of those spots. This kind of resonance happens when the time it takes an asteroid to circle the Sun has a simple relationship with how long it takes Jupiter. For instance, the gap at 5:2 is where an asteroid makes exactly 5 loops of the Sun for every 2 loops of Jupiter.kirkwood_gaps.png

The number of asteroids across the belt. Each vertical line represents a different resonance with Jupiter’s orbit. Jupiter’s gravity has carved gaps in the asteroid distribution at those resonances. From Wikipedia.

Imagine Jupiter and its sidekick Saturn (the Ringed Wonder) as crime fighters. They have sources within the crime world, but only in specific places. A snitch in one crime family, a drug dealer who owes them, a pickpocket. These are like the orbital resonances. They are the specific connections where our crime fighters can shake things up. But there are vast areas of the crime world where our heroes have no access (gambling, prostitution, corruption, you name it). How can we explain that the entire crime world — the entire asteroid belt — is shaken up?

In a new study we propose a solution to this long-standing problem. We think the answer is chaos.  When they were younger, Jupiter and Saturn’s orbits may have been chaotic. This doesn’t mean that their orbits were unstable or not pancake-shaped. What it means is that their exact orbital configuration jumped around unpredictably. And when planets are chaotic, resonances move. Instead of staying in one spot the resonances jump from one spot to the next, depending on the exact orbits of the gas giants at that time. Instead of only kicking the orbits of asteroids in a few spots, and kicking them to death until they open gaps, the gas giants change asteroids’ orbits across the whole belt.

It’s like our crime fighters on a rampage. Instead of sticking to their normal pattern and their normal sources, Jupiter and sidekick plow through the entire crime world. They knock down doors and threaten bad guys. They abandon their “good guy” tactics and beat some of them up. The net result: all of the crime bosses are worried and the crime world is shaken up in its entirety.

But wait! Jupiter and Saturn are not in a chaotic state right now.[1] This story must have taken place earlier in the Solar System’s history. The Sun and planets are 4.5 billion years old. We think that the giant planets only reached their final positions after a hard-to-pin-down delay of perhaps 100-500 million years. The chaotic phase must have happened very early on, after the planets had formed but before they had reached maturity. Let’s call it the adolescent Solar System. The unpredictable, teenage Solar System.

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Created using publicly-available images from pixabay.com and nasa.gov.

This fits nicely into our superhero story. It is during the teenage years that superheroes (and pretty much all humans) are at their most volatile. When they are most likely to try to take out the big crime boss singlehandedly. To throw a tantrum when things don’t go their way. And the asteroid belt may simply be an artifact of this kind of short chaotic phase.

We used computer simulations to show that Jupiter and Saturn’s early orbits had many paths to chaos. It is entirely plausible that the gas giants’ orbits had a chaotic phase in the adolescent Solar System. That phase would have shaken up the asteroids’ orbits but not the other planets’ because the asteroids are closest to the gas giants and the smallest and most vulnerable.

Punchline: A phase of orbital chaos in Jupiter and Saturn’s early orbits can explain the asteroids’ strange orbits (why the asteroid belt is a donut, not a pancake).

The chaotic Teenage Solar System. Boom!


Questions, comments, words of wisdom? 

 

For the gory details, you can download the scientific paper here.  The lead author is Andre Izidoro, formerly a postdoc in Bordeaux, France, and now a researcher in Guarantigueta, Brazil.

[1] Technically, we don’t actually know whether Jupiter and Saturn’s present-day orbits are chaotic (see here). There are both chaotic and regular (non-chaotic) solutions within the roughly meter-sized error bars in the planets’ positions. However, this is not important for the purposes of our gas giant crime fighters. What matters is past chaos.

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17 thoughts on “The chaotic teenage Solar System

  1. Intriguingly the plots in Fig. 4 cut off at 1.8 AU. Now I’m wondering if this might affect the formation of the Earth and Mars, or if the chaos might leave them with more eccentric orbits.

  2. Would this chaos erase the asteroid families that formed before the LHB by spreading out their inclinations and eccentricities?

    • Yes, any asteroid families clustered in eccentricity and inclination would be spread out by chaotic evolution. But they wouldn’t be spread in semimajor axis. In any case, the giant planet instability (Nice model) that is thought to have occurred later would likely smear out any primordial families, if an ice giant was even very briefly scattered interior to Jupiter (Brasil et al 2016).

      • Thanks, when I looked at that earlier in the year (actually squinted at the figures since its pay-walled) I thought that they used cases 2 and 3 (not 1 and 3) so I had doubts about it working.

  3. “In simulations in which Jupiter’s eccentricity remained much larger than its current value of ~0.05 for longer than 100 Myr, parts of the belt were emptied.”

    This sound like the chaos orbits could be a problem if the Grand Tack occurred with Jupiter and Saturn in a 2:1 resonance.

    • Too much chaos can entirely clear out parts of the belt. This only happened occasionally in the simulations — it depended on both the orbital eccentricity of Jup and Sat as well as their exact chaotic evolution. With J and S in 2:1 resonance embedded in the gaseous disk there are a range of possible eccentricities (Pierens et al 2014).

      There are many ways for the chaos model to work. Too much is not good but that only happens when things are pushed strongly in one direction.

  4. Would the eccentricity distribution for asteroids with inclinations above 20 degrees, with most of the large asteroids with e > 0.1 inside 3 AU as I would expect if they got there during the Grand Tack, a problem for this model? Or are these still thought to be part of a collision family?

    • I don’t completely understand the question. Are you asking about high-inc asteroids and whether they can be generated by chaos? The answer is yes to that one. High-ecc asteorids inside 3 AU are not a problem either.

      • I once plotted eccentricity vs. semimajor axis for just the asteroids with inclination above 20 degrees. Their eccentricity distribution was different than for those below 20 degrees with most having eccentricities above 0.1, at least for those inside 3 AU. I read somewhere this was due to them being part of a collisional family although IIRC this was before the Grand Tack was published.

    • Ah, the old “sweeping secular resonances” idea! Well, it’s interesting to see it coming back. I haven’t seen an actual paper on those results — and they are from 2011 — so I’m pretty skeptical. Still, an interesting idea.

  5. Pingback: Chaos! | The MOJO Project

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