PLANETPLANET

This is chapter 6 in the Solar System’s story. This is an action-packed, epic chapter in which a lot of pieces of the puzzle are put together in different ways. (It’s my favorite part.)

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Reproducing the inner Solar System

The over-arching goal of planet formation models is to match what we see. What exactly does that mean for the Solar System?

Our computer simulations cannot hope to match the exact position of every asteroid, or nail down the size and mass of the planets to within a few grams. We just don’t have enough computing power (or patience). Nonetheless, we want to match the overall characteristics of our system. This animation shows how I break it down for the inner Solar System (interior to Jupiter):

The goal is to match the overall distribution of the planets: the number of planets, their orbits, masses and compositions (and water on Earth). We also want to reproduce the asteroid belt — to explain why it contains so little (less than 1/1000th of an Earth-mass), why the asteroids’ orbits are stretched-out (“eccentric”), and why the inner belt contains dry asteroids and the outer belt mostly hydrated ones.

It’s similar to understanding history on a population-level. We want to figure out the key events that dominated the formation process, and (for now) we must face to the fact that we cannot hope to understand every little thing that happened along the way.

The sequence of events

As we’ll see below, there is no universally agreed-upon story for the formation of the rocky planets. Nonetheless, a few pieces are generally accepted:

• Planetesimals and planetary embryos started to form very quickly in the Sun’s planet-forming disk.
• The gas giants were fully-formed within a few million years of the start of planet formation, when the gas disk dissipated (preventing later formation of gaseous planets).
• Earth’s growth was not complete until 50 to 100 million years later. The last big event in Earth’s growth is thought to have been the Moon-forming impact (coming in chapter 7).
• Mars’ growth was faster than Earth’s, and was complete within 5-10 million years.

The most important thing to realize is that, despite being hundreds of times more massive, the gas giants were fully-grown before Earth. With their titanic gravity, the giant planets may have played an important role in shaping Earth’s final assembly.

The Classical Model and the small Mars problem

The foundational model of rocky planet formation is the so-called “classical model”. It was developed by George Wetherill, and has been studied in depth by many researchers (including myself). The main assumption of the classical model is that the growth of the giant planets can be considered separately from the growth of the rocky planets. Time zero in simulations is the time when the gas disk dissipated, and collisions between the rocky bodies are all that matters.

Below is a simple, cartoon-style animation of the classical model. If you prefer the real thing, here is a simulation I ran for my PhD thesis (that took 15 months to run back in 2004/5).

The classical model systematically messes up Mars. It does a decent job of matching Earth and Venus, but planets that form in Mars’ orbital vicinity are almost always about the same mass as Earth. This is a big contrast with the real Mars, which is only about 1/10th the mass of Earth (or, to be annoyingly precise, 10.7% of Earth’s mass). This is the “small Mars problem”, and I’ve dedicated a significant chunk of my career to trying to solve it. (You could argue that I’ve been too successful and now have many solutions and don’t know which one is right.)

The small Mars problem exists because, within a disk of planetesimals or planetary embryos, neighboring planets tend to form with similar masses (or sizes). The fact that Mars is so much smaller than Earth means that either some process removed mass from Mars’ feeding zone (but not Earth’s), or that mass was never there to begin with. This is how each of the successful models solves the small Mars problem.

The classical model has another big shortcoming: the asteroid belt. The belt starts off with 1-2 Earth masses in planetesimals, and must be depleted by a factor of a thousand or more to match the present-day Solar System. In actual simulations, a few Mars-mass objects are usually stranded in the belt (which are not there, and never were — otherwise we would see their imprint in the orbits of the surviving asteroids).

Successful models

As of the writing of this blog (June 2022), there are five models that can match the inner Solar System:

1. The Low-mass Asteroid belt model
2. Pebble accretion model
3. Convergent migration model
4. The Grand Tack scenario
5. Early Instability model

I’ve ordered them by when the key action happens in the sequence of planet formation. Let’s go through them one at a time. I’ll explain how each scenario works and what its potential Achilles heel may be — in other words, the small piece that could make each model crumble.

1. The Low-mass Asteroid belt model

This model is almost too simple. What if Mars is smaller than Earth simply because there were a lot fewer planetesimals close to Mars than to Earth? To make this work, all four rocky planets could simply have formed from a ring of planetesimals that started off between roughly the orbits of Venus and Earth.

Why would this ever happen? We saw in chapter 2 that planetesimals form from concentrations of drifting pebbles. Images of planet-forming disks around other stars show that pebble-sized dust is often concentrated in narrow rings. So maybe the streaming instability operates to form planetesimals within these rings but not in between. It could look like this:

In the last few years, several new models have come out predicting that planetesimals should indeed form in narrow rings, not in broad disks. The Solar System could have formed from three rings of planetesimals — an inner ring with a few Earth masses in rocky planetesimals to grow the rocky planets, a second with 50-100 Earth masses to grow the giant planets’ cores, and an outer ring of icy planetesimals to form the comets and Kuiper belt.

What would it look like if the rocky planets did form from a ring of planetesimals? Earth and Venus grow big within the ring. Mars was scattered out of the ring and its growth was stunted. The same happened to Mercury on the inner side of the ring. It looks something like this:

This model can do a remarkably good job of matching the terrestrial planets’ masses, including Mars. It’s an elegant, simple solution — if planetesimals really do form in rings.

[Side note: two of the other models — the Grand Tack and convergent migration — end up producing rings of planetesimals or planetary embryos as a way to solve the small Mars problem.]

You might wonder, if the asteroid belt was born empty, wouldn’t that conflict with the fact that asteroids exist today? Well, remember that the asteroid belt only contains very little mass (less than 1/1000th of an Earth mass). Given how wide it is, planetesimals are easily captured into the asteroid belt as the planets formed. The asteroids likely originated across the Solar System — among the rocky planets, in the giant planet region, and even farther out:

All together, the Low-mass Asteroid belt model can match the inner Solar System quite nicely. They assumption it makes is that planetesimals form in rings — at least in the case of the terrestrial planets. That is its potential Achilles heel, and severing groups are working to test it right now.

2. Pebble accretion

This model is a newcomer to the game, but is provocative and worth thinking about. It proposes that the terrestrial planets grew by pebble accretion instead of planetesimal accretion. Shocking!

Pebble accretion can grow planetary embryos very efficiently (see chapter 3) and can explain the rapid formation of the giant planets’ cores. But no one took pebble accretion seriously as a mechanism for forming the terrestrial planets until very recently. This is largely a legacy of the whole Moultin-Chamberlin “planetesimal hypothesis” from 1905, which basically led to the classical model that I described above.

The most complete pebble-driven model for terrestrial planet formation includes two main ingredients and one big assumption. The ingredients are pebble accretion (no surprise there) and orbital migration. The assumption is that planetesimals only formed at a certain location in the inner Solar System, although there were multiple generations.

Let’s follow this train of thought. Each generation of planetesimals formed a little past Mars’ orbit. The most massive planetesimals ate other planetesimals and then started to grab on to drifting pebbles. As they grew into more massive planetary embryos, they started to migrate inward. The next generation of planetesimals again formed an embryo capable of eating pebbles, following in the footsteps of the previous one. So, the most massive planetary embryos should be the farthest from the site of planetesimal formation.

This doesn’t quite work unless we add one more ingredient, because Earth is more massive than Venus, yet Venus is closer to the Sun and presumably would have grown earlier and migrated farther. However, we think that Earth underwent a late giant impact after the gas disk dissipated, which led to the formation of the Moon. The pebble accretion model works if there was no “Earth” at this stage but rather two half-Earths that would later collide to form the Earth. Also, Mercury must have formed in a different way, maybe from iron-rich pebbles that only existed much closer to the Sun.

Put together, here is what the model looks like:

This model can explain the overall distribution of the terrestrial planets using a whole new toolkit — that’s not too shabby. There are some open questions, like how well it can match the asteroid belt and whether it fits with data from meteorites (for example, this paper argues strongly against pebble accretion). But I think this model is too young and exciting to throw it out prematurely. The potential Achilles heel of this model is whether planetesimals should really just form in a given location, as well as confronting it with meteorite measurements, and both are areas of vigorous study right now.

3. Convergent migration

Another new model proposes that the terrestrial planets were shaped by pebble accretion and a different flavor of orbital migration.

As we saw in chapter 4, migration is generally directed inward toward the Sun. But not always; in some places migration can be outward. If there are zones of outward- and inward migration in the same disk, there can be regions toward which planetary embryos migrate. These are called convergence zones.

This new model proposes that within the Sun’s gaseous disk, there was a convergence zone located right around Earth’s orbit. As planetary embryos grew, the most massive migrated into the center of the convergence zone, where they could grow further. The small ones stayed on the fringes. This migration ends up creating a sort of ring of planetary embryos that is broadly similar to the ring of planetesimals in the Low-mass Asteroid belt model. This explains why the big terrestrial planets — Earth and Venus — are located close together, whereas Mercury and Mars are beyond the apparent edges of the ring.

Here is a simple explanation of the convergent migration model:

This model can also match the orbits and masses of the rocky planets, although it remains to be seen whether it can explain the asteroid belt. The potential Achilles heel is simply the zone of convergent migration — do such zones really exist, and in the right place for this to work?

4. The Grand Tack

The Grand Tack is the original “crazy idea” in this game, proposed back in 2011. I described the Grand Tack in one of the earliest posts on this blog.

In the Grand Tack model, Jupiter’s migration cleared out the asteroid belt and Mars’ feeding zone. It happens in two parts. First Jupiter migrated inward on its own. Then Saturn migrated inward and caught up to Jupiter. Then the two planets “tacked” and migrated back outward.

Jupiter could not have migrated too close to the Sun because it would have prevented the formation of the rocky planets. To match the rocky planets, Jupiter’s turnaround point must have been at about 1.5 or 2 astronomical units, just a little past Mars’ current orbit. Jupiter’s inward migration squished the disk of planetary embryos and planetesimals into a narrow ring, and then it migrated back outward and let the terrestrial planets grow in a way that was very similar to the Low-mass Asteroid belt model.

This animation illustrates the main idea:

The Grand Tack has been extensively studied over the past decade and it is robust. It can nicely match the terrestrial planets’ masses and orbits as well as those of the asteroids. But it does have a potential Achilles heel: the outward migration mechanism itself. It has been shown in a number of studies that Jupiter and Saturn should indeed migrate outward but only if certain conditions are met. The key condition is that the Jupiter-to-Saturn mass ratio must be between about 2 and 4. Today, that ratio is about 3.3 so you might naively think it’s fine. But while the gas giants were embedded in the gaseous disk, they were simultaneously migrating and growing. Would their mass ratio have remained within the bounds for long-range outward migration as both planets were growing? This is another active area of study (using hydrodynamical simulations) so hopefully we’ll have an answer soon-ish.

5. The Early Instability model

The Early Instability model connects the dots between the outer and inner Solar System. Its central ingredient is the dynamical instability that is thought to have taken place among the giant planets (first introduced as the “Nice model”).

The instability is important enough to get its own chapter in the Solar System’s story (coming in a couple days). For now, let me give you the quick version. The instability was originally proposed as a delayed event, but recent re-analysis suggests that it happened early in Solar System history. Exactly how early is a key question — in a new paper we proposed that it was triggered by the dispersal of the gaseous disk.

The giant planet instability is thought to have looked something like this (with time zero being when the instability was triggered):

Before the instability, the giant planets are thought to have been in a chain of orbital resonances (as discussed in chapter 5). Outside of their orbits was a ring or disk of icy planetesimals containing 10-30 Earth masses. During the instability, the giant planets scattered off of each other, and one ice giant was likely ejected into interstellar space (leaving behind the two we know and love). The giant planets’ orbits spread out, and the outer planetesimal disk was almost entirely scattered away, except for a small fraction that survives in the Kuiper belt and scattered disk.

What we care about is the effect of the giant planet instability on the growing terrestrial planets. The short answer: it was significant, especially for the parts that are closer to Jupiter. The asteroid belt was strongly depleted, and so was Mars’ feeding zone. But Earth and Venus were only modestly affected. It looked something like this:

The Early Instability model works remarkably well (see here for a slightly more detailed write-up). It does a great job of matching the terrestrial planets and asteroid belt. All it uses to accomplish this is an event that we are already convinced must have taken place, the giant planet instability. And the Early Instability model reproduces the inner Solar System best when it matches the outer Solar System best. It’s a win-win, and a compelling model.

Of course, like all of the models it has a potential Achilles heel: when did the giant planet instability actually take place? Chapter 7 will focus on the instability, so there is a lot more to come. As I mentioned, our new paper argues that it must have been very early. But that is not the final word; I am waiting on some cosmochemical evidence (maybe from meteorites) that strongly corroborates this model. Nonetheless, I’m pretty jazzed about this one.

How do we choose between models?

I’ve laid out five different possible solutions to one problem. How do we evaluate them, to figure out which is most likely to have shaped our Solar System?

I see this as a two-step process. First, does the model work? And second, how can we disprove it?

Each of the models works when certain assumptions are made. The first step in evaluating models is to test those assumptions using studies of the key points of each model — for example, by evaluating when and where planetesimals form using astronomical observations and models, or by testing orbital migration. The second step is confronting each model with some kind of ground truth. For instance, the Early Instability model would be thrown out if we get new meteorite data showing that the instability did not happen early. Likewise, each model must be confronted with the latest measurements; for instance, are the planets produced by each model consistent with the meteorite dichotomy (and Earth’s chemical makeup)?

For now, we really are in a choose-your-own-adventure situation for terrestrial planet formation. From one point of view this as frustrating, because we don’t know what really happened. From another point of view it’s exciting because we are in the midst of an explosion of new ideas, and on the path to figuring out what forces shaped our Solar System.

Wrap-up

The TL;DR version of this post: Terrestrial planet formation models are in a wild-west phase, with five competing models that use different processes — including pebble accretion, migration (of embryos and gas giants), and the giant planet instability — to match the inner Solar System.

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Additional Resources

• The Solar System’s story (with links to all posts)
• Asteroids: the poem (just because).
• Where did Earth’s water come from?
• Key scientific papers for each model: the Low-mass Asteroid belt (1, 2, 3), the pebble accretion model, convergent migration, the Grand Tack, and the Early Instability.
• MOJO video 13: why is Mars smaller than Earth? (A lot like this post, but without the pebble-driven models)