PLANETPLANET

This is chapter 7 in the Solar System’s story. We will explore a seismic shift in the giant planets’ orbits, whose consequences were felt across the Solar System: the giant planet dynamical instability.

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The outer Solar System wasn’t always this way.

A huge breakthrough in planetary science came from understanding that the giant planets were probably not born on their present-day orbits. Rather, they shifted after their formation because of two main processes: planetesimal-driven migration and dynamical instability.

Planetesimal-driven migration

The present-day Solar System beyond Neptune is really quite sparse. If you add up the mass in the entire Kuiper belt and scattered disk — including Pluto, Eris, Gonggong and more — it only amounts to about a Mars-mass (about 10% of an Earth-mass). Of course, this doesn’t count Planet Nine, which — if it indeed exists on a wide, stretched-out orbit — is five to ten Earth-masses.

The ice giants are each about 15 Earth-masses, so interactions between the planets and the Kuiper belt don’t have any significant effect on the ice giants’ orbits. But there are hints that the early Kuiper belt contained a lot more mass. For instance, it’s hard to explain the growth of the biggest objects out there (like Pluto) without a much more massive disk of planetesimals to bash into.

What if there really had been a massive disk of planetesimals out beyond the ice giants’ orbits? What would have been the effect on the giant planets?

Back in 1984, Fernandez and Ip showed that an outer planetesimal disk would have caused the planets to migrate. Neptune is the first planet to interact with outer disk planetesimals. Neptune can scatter them in any direction depending on the exact trajectory of a planetesimal through its gravitational field. Planetesimals that are scattered outward come back again, because it takes a whole series of scattering events to eject a planetesimal into interstellar space. But planetesimals scattered inward often don’t return, because they cross Uranus’ orbit and start being scattered by Uranus. So Neptune scatters a lot more planetesimals inward than outward. The back-reaction of this scattering (via Newton’s 3rd law) pushes Neptune outward, causing Neptune’s orbit to grow — outward migration. The same process is repeated for Uranus and Saturn: both preferentially scatter planetesimals inward and migrate outward. This is reversed for Jupiter. With its massive gravity and no closer-in giant planets, Jupiter tends to scatter planetesimals outward and eject them. This makes Jupiter migrate inward.

All together, planetesimal-driven migration causes the planets’ orbits spread out, with Saturn and the ice giants migrating outward and Jupiter migrating inward.

There is evidence within the orbital structure of the Kuiper belt that the giant planets actually did migrate outward. The most dramatic example is Pluto, which is locked in a 2:3 orbital resonance with Neptune such that Pluto completes two orbits for every three of Neptune. In 1993, Renu Malhotra showed how Neptune’s outward migration would have captured Pluto in its resonant orbit, and that result still stands today.

Dynamical instability

The second ingredient in the early evolution of the giant planets — dynamical instability — was inspired by observations of exoplanets. After the first hot Jupiter was (unambiguously) discovered in 1992, it was found in the mid-1990s that the orbits of giant exoplanets were rarely nice and circular. Rather, they were commonly found on stretched-out, “eccentric” orbits.

Dynamical instabilities naturally explain giant exoplanets’ eccentricities via the “planet-planet scattering” model. We think that planets do indeed form on near-circular orbits, but they rarely form alone. When one gas giant forms around a star, it usually has one or two (or many) companion gas giants, and they tend to migrate close to each other (likely into chains of orbital resonances). After the dispersal of the gaseous disk, the planets gravitationally jostle each other and gently stretch out each others’ orbits, sometimes to the point that two planets’ orbits cross. The planets undergo close gravitational encounters and scatter, exchanging orbital energy. The outcome is that one planet is usually ejected into interstellar space (to roam the galaxy as a free-floating planet). The surviving planets have eccentric orbits, essentially scars of this violent dynamical instability.

The “Nice model”

The model that put together dynamical instability and planetesimal-driven migration into a coherent picture was the Nice model, first introduced in 2005 (pronounced “niece”, like the city in France).

The Nice model assumes that the giant planets formed on a more compact orbital configuration than the present-day one, likely in a chain of orbital resonances. There was an outer planetesimal disk containing a total of 20-30 Earth masses. There was likely an extra ice giant, making 5 total giant planets at the start. The reason for this is that one ice giant is almost always ejected, and the model needs to explain that four giant planets survived.

The evolution of the Nice model is shown in the animation below. When the instability is triggered the extra ice giant is ejected into interstellar space after a series of scattering events with Jupiter. Uranus and Neptune interact with the planetesimal disk and trigger a phase of planetesimal-driven migration. The ice giants migrate outward, with Neptune reaching close to the outer edge of the planetesimal disk, which is almost entirely ejected by Jupiter (with a fraction of planetesimals being implanted into the Oort cloud). The giant planets spread out and reach their current orbits.

The Nice model has been remarkably successful in reproducing several hard-to-explain aspects of the Solar System:

• The giant planets’ orbits, including their orbital radii, eccentricities and inclinations.
• The orbits of Jupiter’s Trojan asteroids (which represent planetesimals from the outer planetesimal disk that were captured during the instability).
• The irregular satellites of the giant planets (also captured during the instability)
• The orbital structure of the Kuiper belt and scattered disk (shaped by the giant planets during the instability).

The fact that the model can explain all of these different characteristics of the Solar System is why the planetary science community has adopted the Nice model as the paradigm for the early evolution of the outer Solar System. However, as we will see, there are still some issues to work out.

The Late Heavy Bombardment (“terminal lunar cataclysm”)

The Nice model was originally designed to reproduce the late heavy bombardment (or, more precisely, the “terminal lunar cataclysm”), a perceived spike in the rate of impacts on the Moon about 500-600 million years after the start of planet formation.

The concept of the late heavy bombardment came from analyses of craters on the Moon, especially the giant impact basins. It’s sometimes possible to tell the relative ages of craters: if one crater in on top of another, then the one on top was produced by a more recent impact than the one underneath. But it’s impossible to get absolute ages of craters without more information, specifically from rocks. The Apollo and Luna missions brought rocks back to Earth from different sites on the Moon. Chemical analyses of Moon rocks measured their ages with radioactive dating techniques. Combined with information about the craters where the rocks were collected, analyses calculated the rate of impact bombardment on the Moon throughout its lifetime (the “impact flux”, in technical terms).

While there was never a complete consensus, several early analyses inferred the presence of a delayed spike in the Moon’s impact flux. This spike, or cataclysm, corresponded to the time of the giant planet instability in the original Nice model.

In recent years, evidence for the terminal cataclysm model has disappeared. New analyses have shown that the rocks brought back from the Moon suffer from sampling bias. The giant collisions that produced the youngest impact basins on the moon — especially Imbrium — threw rocks across the surface of the Moon and contaminated the samples collected elsewhere. The spike in impact rates was really just a single big impact.

Rather than a terminal cataclysm, it is now thought that the impact rate on the Moon declined smoothly. There was indeed a big late impact that produced Imbrium, but that was simply the tail end of the large impacts on the Moon.

Nice model challenges and uncertainties

As we saw above, the Nice model has been remarkably successful in matching the Solar System. However, a couple of key questions need to be resolved. Let’s jump into them.

First, given that the terminal lunar cataclysm model is gone, when did the instability actually take place? Analyses of different parts of the Solar System — including highly-siderophile elements, the existence of a binary Trojan asteroid, and impact reset ages of meteorites — all agree that the instability must have happened early. To be more precise, the instability could not have taken place later than 100 million years after the start of Solar System formation.

Second, what is the effect of the giant planet instability on the terrestrial planets? Simulations show that the terrestrial planets are universally disrupted by the giant planet instability, assuming that the rocky planets were already fully-formed. Gravitational kicks from the giant planets perturb the terrestrial planets’ orbits, causing Earth to collide with Venus, or Mars to collide with Earth, or Mercury to fall into the Sun. It does not end up looking like the present-day Solar System.

What if the giant planet instability happened very early, shortly after the dissipation of the Sun’s gaseous disk? This could provide an elegant solution to both of these problems. A very early instability would be consistent with all of the measured constraints (including the impact flux on the Moon). And rather than destroy the terrestrial planets, the giant planet instability could have instead played a role in shaping their orbital distribution (the Early Instability model discussed in chapter 6).

The instability trigger

What triggered the giant planets’ orbits to go unstable? This is important because the instability trigger is naturally linked with the timing. To date there have been a few suggested instability triggers but none that is compelling. Most fall into the category of a roll of the dice — if the Solar System was “lucky” (and rolled two sixes) then things would turn out right and the giant planets would have gone unstable. We can’t disprove such a scenario but it is not very robust or satisfying.

Time for a new idea. In a recent paper we showed that the dispersal of the Sun’s planet-forming disk may have triggered the giant planet instability. Let’s take rewind the clock to the late in the lifetime of the Sun’s gaseous disk. As we discussed in chapter 1, planet-forming disks are thought to disperse from the inside-out, driven by high-energy radiation from the central star. It looks like this:

Clearly, disks do not dissipate smoothly at all orbital distances at the same time. The inner parts of the disk disappear first, creating an inner hole. That hole expands until the disk is gone. Consider a planet migrating out in the blue part of the disk as the disk itself is evaporating. The inner edge of the disk sweeps past the planet’s orbit — what happens next?

The animation below shows what happens to an ice giant-mass planet as it migrates in close to its star. The inner edge of the disk expands in time, and this expansion pushes the planet along with it, causing outward migration. This is called the “rebound” effect.

Let’s put the pieces together in the context of the early Solar System. The giant planets formed and migrated into a chain of orbital resonances. Then the disk started to disperse from the inside-out. The outward-sweeping inner edge of the disk played a central role.

Because Jupiter had opened a wide gap in the disk, it was barely affected as the inner edge swept by. But as the edge approached Saturn, it pushed Saturn outward toward the ice giants. Given that the ice giants were still trying to migrate inward, the planets’ orbits were squished together until they were too compressed to remain stable (“squished” is indeed the technical term). This triggered dynamical instability. The ice giants scattered off of each other, and one ice giant was ejected by Jupiter. the giant planets’ orbits spread out and they eventually reached their current configuration.

We ran thousands of simulations to show that the rebound effect is a very reliable instability trigger. Below is an animation of an actual simulation from our paper:

The giant planet instability in this new model proceeds in a similar way to the Nice model. The model can match the giant planets’ orbits, and I think it should be able to reproduce Jupiter’s Trojan asteroids, the irregular satellites and Kuiper belt (that work is in progress).

The main difference compared with the Nice model is the instability trigger. Since the gas disk’s dispersal is the trigger, this pinpoints the timing of the instability. We know from astronomical observations that most planet-forming disks around other stars last for a few million years before they disperse. The formation times of meteorites that we think formed in the Sun’s gaseous disk span a similar range of 3-4 million years. In the context of this new model, the giant planet instability therefore took place a few million years after the start of planet formation. This is consistent with all of the available constraints, both astronomical and cosmochemical, and sets the stage for terrestrial planet formation via the Early Instability model.

Another change with the new model is that, since the gas disk provides some outward migration, the outer planetesimal disk could have been lower in mass, with perhaps 5-10 Earth masses rather than the 20-30 envisioned by the Nice model.

This makes me wonder how we should name evolving models. Should the name “Nice model” just expand to include our new, gas-driven instability trigger? Or should we use a different name like “Rebound model”, to separate it? The Nice model really pushed things forward, yet some researchers consider it to be obsolete since the instability did not happen late, as the Nice model original envisioned. This is something to ponder.

To conclude, it’s interesting to note the near-universal importance of dynamical instability. To explain their stretched-out orbits, at least three-quarters (and up to 95%) of all systems of giant exoplanets must be the survivors of planet-planet scattering-type instabilities. Likewise, to explain the distribution of close-in super-Earths, 98-99% of those systems must have undergone dynamical instability, but due to their low masses these ended in collisions rather than ejections. And even the Solar System’s relatively well-behaved giant planets (Jupiter and Saturn’s orbital eccentricities are only about 5%) underwent a dynamical instability.

Clearly, nature likes to shake things up!

Wrap-up

The TL;DR version of this post: The giant planets underwent a dynamical instability that shook up the entire Solar System and likely ejected an extra ice giant. The instability happened early, perhaps triggered by the dispersal of the gaseous planet-forming disk.

Additional Resources

• The Solar System’s story (with links to all posts)
• Were it not for cosmic good fortune, we wouldn’t be here (Nautilus article about the rebound-driven instability in the context of exoplanets)
• Asteroids: the poem (just because)
• Websites of Beibei Liu and Seth Jacobson, my collaborators on the new instability model
• When good Jupiters go bad — how giant dynamical instabilities can destroy rocky planets, illustrated by a mustachioed Jupiter: