Super-Earths: breaking the (resonant) chains!

Super-Earths.  They’re so hot right now.  Super-Earths.

They are the most abundant type of planet (that we know of) in the Galaxy.  About half of all Sun-like stars have one. Many stars have a bunch: up to seven have been found orbiting a single star. The Kepler space telescope has opened the Super-Earth floodgates.

Yet Super-Earths are a mystery. How did they get there? And if they are so common, why don’t we have any in the Solar System?

In this post I will describe a new model we’ve built for the origin of super-Earths.  I’ll also explain how the Solar System might fit into this picture.

The setting: a pristine disk of gas and dust orbiting a baby star.  This is where planets form, and they form fast.  These planet nurseries only last a few million years before the gas evaporates. (A few million years may seem like a long time, but remember that the Galaxy is 13 billion years old, so this is very short from that point of view.)

Artist’s view of a planet-forming disk around a young star.  Credit: ESO/L. Calçada

Our idea is a simple three-step process:

  1. Large (Mars- to Earth-sized) bodies grow out where it is cold enough that ice is a building block (past the snow line).  These planetary embryos are massive enough to launch waves in the disk. The waves push back on the embryos’ orbits and push the embryos slowly toward the star. This is orbital migration.
  2. Embryos don’t migrate all the way onto the star because the disk has an inner edge that stops them.  The first embryo reaches the inner edge. Later embryos migrate inward toward the first one but they don’t just collide.  Instead, they are trapped in orbital resonances. The orbits of neighboring embryos have a special setup, where they re-align every so often. Resonances are measured by the ratio of the orbital periods of neighbors. For example, the 2:1 resonance means that for every 2 orbits of the inner planet, the outer one completes 1 orbit.  The embryos end up in a resonant chain, where each pair of neighbors is in resonance.
  3. The gas disk — which was holding the embryos’ hands while they sat in a resonant chain — evaporates. With no gas, the resonant chain of embryos goes unstable about 90-95% of the time. There is a phase of giant collisions (similar to the late phases of growth of our own rocky planets).  The survivors are the super-Earths we see, along with the 5-10% of lucky systems in stable resonant chains.


Our computer simulations of this process match the actual super-Earths. Simulations always make resonant chains.  And when we combine 90-95% of unstable resonant chains with 5-10% stable ones, we match the properties of the super-Earths found by Kepler.

A small fraction of super-Earths in resonant chains do exist. These are some of the very prettiest planetary systems out there. For example, the recently-discovered TRAPPIST-1 system (poem here) is a 7-planet resonant chain!

Artist’s view of the TRAPPIST-1 system, with the resonances between neighboring planets added by hand. Credit: NASA/R. Hurt/T. Pyle

Each pair of neighboring planets is in resonance. The 7 planets are in a giant resonant chain that periodically re-aligns.  Every 2 orbits of the outermost planet (planet h), planets b, c, d, e, f, and g complete exactly 24, 15, 9, 6, 4, and 3 orbits, respectively, and all seven planets re-align. You can even make music with the orbits of the system (see here).

This elegant setup would not occur by chance.  Orbital migration is the only way we know of to create such well-behaved systems.

Just like children, all systems of super-Earths are beautiful and perfect (resonant chains) when they are born.  Unfortunately, once the calming influence of the gas disk is gone (like teachers and parents losing hold), most go unstable. And just like super-Earth systems, at 90-95% of society is made up of people who have survived instability.  (And you don’t want to hang around with the 5-10% of stable people anyway.)

There is an added bonus.  We might be able to explain why the Solar System is different.

Remember those planetary embryos?  What if, before it migrated too far, the first embryo grew big enough to capture gas from the disk and become a gas giant like Jupiter?  Then the story changes.  A gas giant carves a gap in the disk and blocks the inward migration of the other embryos.


The gas giant holds back the migrating invaders, and protects the inner Solar System.  The ice giants Uranus and Neptune, as well as Saturn’s core, may represent “failed super-Earths”, embryos that were trying to migrate in close to the Sun but were blocked by Jupiter.   (My more detailed post about this idea here).

According to this story, Jupiter’s growth is what caused our Solar System’s evolution to branch away from that of super-Earth systems. What makes our Solar System unusual or special. This is testable, because the idea predicts an anti-correlation between Jupiter-like planets and super-Earth systems.  Right now it’s hard to say, but within a few years we should have an answer.

A quick recap in image form:


You are welcome to read the gory details in the scientific paper (downloadable version here).


PS – A lot of astronomers dislike the term “super-Earth” because we have no idea how similar to Earth these planets are. There are good reasons to think that they are generally not like Earth. Unfortunately, “super-Earth” has caught on. Also, there is no alternative that I find satisfactory (at the moment).  So, I’ve run with super-Earth.  Sorry if I upset you!


21 thoughts on “Super-Earths: breaking the (resonant) chains!

  1. Is the stability of the Trappist-1 system related to the particular resonance chains it follows?

    For example, the first four are 8:5:3:2, so b is 4:1 with e, instead of a series of 3:2’s where that wouldn’t work.

    And similar combinations farther out that produce 2:1, 3:1, 5:1, and 6:1 resonances between planets separated by multiple planets.

    1. The stability depends sensitively on the resonances and planet masses. The exact details of what type of resonant chain is stable and which is not is not that well known (see Matsumoto et al 2012). I’m sure there will be a lot more study of the stability of resonant chains in the coming years.

  2. How would this incorporate the Grand Tack, though?
    If such a gap in the protoplanetary disk impeded any inward-migration
    of the outer plants, what would then cause Jupiter
    to lose orbital momentum and move inwards?

    Good read, though!
    Only a wider range of discovered planetary system may prove or disprove this
    in the future.

    1. HI Aiden — in the Grand Tack Jupiter migrates inward, then Jupiter and Saturn migrate outward. If Jupiter was holding back the inward migration of, for example, Saturn’s core, it would not have much of an effect on Jupiter’s migration. Jupiter would still go inward. Then Jupiter and Saturn would migrate outward together once Saturn was large enough to start opening a gap to drive the 2-planet outward migration.

  3. Can this late-collision process account the recently discovered uniformity in radius, masses, and spacings of Kepler planets? It seems in situ formation would just naturally explain this feature.

    1. Yes, the migration model matches the “peas in a pod” nature of super-Earths quite well. It is important to realize that the “in-situ” formation model popularized by Chiang & Laughlin (2013) is not self-consistent and cannot be the right answer. There are other good models that don’t require as much migration, but the in-situ model just doesn’t add up.

      1. That’s so interesting. Are migrated planets inevitably water-rich (something like 10%-70%), since they usually formed beyond snowline and migrated inward? Is there a mechanism that can explain some rocky super-Earths we’ve discovered lately, like LHS 1140b, because it obviously violates in-situ formation while holds very little amount of volatile. Thanks a lot for answering my question.

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