Orbital migration

This is chapter 4 in the Solar System’s story. This chapter shows how planets rarely stay home as they grow — they often migrate far from their birthplace.


Migration of planetary embryos through the disk (“type 1”)

Massive planetary “embryos” — which may grow into the cores of the giant planets (coming in chapter 5) — are several times more massive than Earth. They are massive enough to migrate.

A massive core launches density waves within the gaseous disk (note: I use “core” and “embryo” more or less interchangeably). As you can see, it’s quite pretty:

Hydrodynamical simulation of a 10 Earth-mass planetary embryo embedded in its gaseous disk. The colors correspond to density differences in the gas. Credit: Frederic Masset.

The most obvious density waves are those nice spirally ones. But there are others right near and along the planet’s orbit. Those small changes in color correspond to different amounts of gas, which mean that the gravitational force that the planet feels pulling it forward along its orbit is different than the force felt holding it back. Even a small imbalance makes a difference.

These density waves push on the planets’ orbits. The spiral density waves almost universally try to shrink a planet’s orbit — this is called inward migration. The density changes along a planet’s orbit can go either way: sometimes they push the planet outward (leading to outward migration) and sometimes inward.

[Technical note: density perturbations in the disk “torque” the planets’ orbits, and that is what leads to the orbits growing or shrinking. I discussed torques at length in this post, although in that case torques were from the galactic disk changing the orbits of wide binary stars.]

In most situations, planets migrate inward. Migration of planetary embryos may play a key role in the formation of close-in “super-Earths”, planets between the size of Earth and Neptune on close orbits, which exist around up to half of all stars in the Galaxy (see here). Outward migration may play a role in certain situations (here is one crazy idea) but is probably not the norm.

Migration is faster for higher-mass planets. Below about a Mars-mass (roughly 10% of Earth’s mass), migration is too slow to matter. But a 10 Earth-mass core migrates on a timescale of 10-100 thousand years — since the gas disks last many millions of years, this is really fast.

Migration is not always smooth. If disks are turbulent and have clumps of higher- and lower-density, then there can be a random (“stochastic”) element to migration. This makes planets “jiggle” as they migrate along, depending on how turbulent the disk is.

Migration of giant planets (“type 2”)

Once planets get really massive, they don’t just keep migrating faster and faster. Rather, they transition to a new mode of migration, which is quite a bit slower. (It’s sort of like kids, who can run faster as they age until they become lazy teenagers who don’t get off the couch).

The transition is marked by a planet opening a gap within the disk. This is kind of an “anti-donut” — a ring-shaped region in the disk that is mostly empty (rather than filled with donuty-goodness). It looks like this:

Hydrodynamical simulation of a Jupiter-mass planet that has opened a gap in its gaseous disk. Credit: Frederic Masset.

Once a planet has carved a gap in the disk, it becomes locked to the disk. Instead of migrating through the gas, it migrates along with the gas as the disk itself evolves. Disks evolve slowly, and most of the gas ends up draining onto the star. Likewise, a giant planet that has cleared a gap slowly migrates inward (usually). The planet’s migration will usually keep going until it either reaches the inner edge of the disk or the disk dissipates.

[Technical note: although migration slows down after a planet clears a gap, there can be a phase of very fast migration (called “type 3”) as the planet is clearing the gap. Interestingly, this tends to happen for planets of about Saturn’s mass (foreshadowing of the Grand Tack model).]

Multiple planets migrating in the same disk

Some interesting things can happen when many planets grow and migrate in orbit around the same star. Let me highlight two interesting cases (illustrated with these two images).

In the first case (image on the left), a group of planetary embryos migrate in the same disk. As they approach each other, they don’t collide. Rather, they become trapped in orbital resonances, where the orbits of neighboring planets make simple ratios — for instance, the inner planet might complete 3 orbits for every 2 of the outer planet. In computer simulations we sometimes form chains with ten or twenty planets in a long chain of these resonances. These resonant chains rarely survive after the gas disk dissipates, so they are rare among exoplanet systems. But sometimes they do survive: the longest-known is the Trappist-1 exoplanet system, with all seven planets in a long resonant chain.

The second case (image on the right) is when two giant planet orbit in the same disk. Each planet opens a gap, and sometimes the planets migrate close enough that their gaps merge into one single, wide gap with the planets trapped in an orbital resonance. Once this happens, migration can take an interesting turn — it all depends on which planet is more massive. If the planets are about the same mass, or the outer planet is more massive, then the two planets migrate inward together. If, however, the inner planet is more massive, then the two planets can turn around and migration outward together. This is the central piece of the Grand Tack model, which we will explore in a few chapters.

Other types of migration

There are other, fundamentally different types of migration that are not driven by interactions between growing planets and their star’s gaseous disks. These all take places long after the disk is gone. The two most important are planetesimal-driven migration and tidal migration.

Planetesimal-driven migration is driven by a planet interacting with a ring or a disk of planetesimals. The planet gravitationally scatters planetesimals, and each time it kicks one inward (or outward), the planet is pushed slightly outward (or inward). This can make the planet’s orbit grow (or shrink). Planetesimal-driven migration was likely a key force in the evolution of the outer Solar System (as we will see in a few chapters — see also this thread).

Tidal migration happens when a planet’s orbit brings it very close to a star. Dissipation of orbital energy (usually within the star, but in some cases the planet) can shrink a planet’s orbit. It is especially pronounced when the planet’s orbit becomes very stretched-out but passes close to the star — this can be the result of gravitational forcing from another star or planet.

There are other processes that change planets’ orbits, such as dynamical instabilities. I wouldn’t call those “migration”, though, and will frown pretty hard at anyone who does!

Wrap-up

The TL;DR version of this post: Earth- to Neptune-mass planets migrate through the disk — usually inward, and fast. Giant planets carve gaps in the disk (“anti-donuts”) and migrate slowly, usually inward. Things can get crazy when lots of planets migrate together.


Additional Information

  • The Solar System’s story (with links to all posts in the series)
  • Cover image credit: Tyler D. Rickenbach/Getty Images — A flock of sandhill cranes flying above the Platte River at sunset in Kearney, Nebraska. A shout-out to Ludmila Carone for encouraging me to stick to inspiring images like this one.
  • Richard Nelson and Willy Kley made a series of very nice clear videos explaining the basics of orbital migration — here is the first one (with the soothing British narration of Richard Nelson).
  • Orbital migration according to Wikipedia (pretty nice page, honestly)
  • Anyone hoping to get a permanent job as a scientist often has to undergo their own sort of migration, usually involving temporary positions in different cities or countries. In 2016 I dedicated a paper to the partners of all scientists — especially to Marisa — without whom this migration just wouldn’t be worth it.

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