Feb 12 2024

The Exoplanet Radius Gap

Published by under Astronomy
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As of this writing, there are 5,573 confirmed exoplanets in 4,146 planetary systems. That is enough exoplanets, planets around stars other than our own sun, that we can do some statistics to describe what’s out there. One curious pattern that has emerged is a relative gap in the radii of exoplanets between 1.5 and 2.0 Earth radii. What is the significance, if any, of this gap?

First we have to consider if this is an artifact of our detection methods. The most common method astronomers use to detect exoplanets is the transit method – carefully observe a star over time precisely measuring its brightness. If a planet moves in front of the star, the brightness will dip, remain low while the planet transits, and then return to its baseline brightness. This produces a classic light curve that astronomers recognize as a planet orbiting that start in the plane of observation from the Earth. The first time such a dip is observed that is a suspected exoplanet, and if the same dip is seen again that confirms it. This also gives us the orbital period. This method is biased toward exoplanets with short periods, because they are easier to confirm. If an exoplanet has a period of 60 years, that would take 60 years to confirm, so we haven’t confirmed a lot of those.

There is also the wobble method. We can observe the path that a star takes through the sky. If that path wobbles in a regular pattern that is likely due to the gravitational tug from a large planet or other dark companion that is orbiting it. This method favors more massive planets closer to their parent star. Sometimes we can also directly observe exoplanets by blocking out their parent star and seeing the tiny bit of reflected light from the planet. This method favors large planets distant from their parent star. There are also a small number of exoplanets discovered through gravitational microlensing, and effect of general relativity.

None of these methods, however, explain the 1.5 to 2.0 radii gap. It’s also likely not a statistical fluke given the number of exoplanets we have discovered. Therefore it may be telling us something about planetary evolution. But there are lots of variables that determine the size of an exoplanet, so it can be difficult to pin down a single explanation.

One theory has to do the atmospheres if planets. Exoplanets that are small and rocky but larger than Earth are called super-earths. Here is an example of a recent super-earth discovered in the habitable zone of a nearby red star – TOI-715 b. It has a mass of 3.02 earth masses, and a radius 1.55 that of Earth. So it is right on the edge of the gap. I calculated the surface gravity of this planet, which is 1.25 g. It has an orbital period of 19.3 days, which means it is likely tidally locked to its parent star. This planet was discovered by the TESS telescope using the transit method.

Planets like TOI-715 b, at or below the gap, likely are close to their parent stars and have relatively thin atmospheres (something like Earth or less). If the same planet were further out from its parent star, however, with that mass it would likely retain a thick atmosphere. This would increase the apparent radius of the planet using the transit method (which cannot distinguish a rocky world from a thick atmosphere), increasing its size to greater than two Earth radii – vaulting it across the gap. These worlds, above the gap, are called mini-Neptunes or sub-Neptunes. So according to this theory the main factor is distance from the parent star and whether or not the planet can retain a thick atmosphere. When small rocky worlds get big enough and far enough from their parent star, they jump to the sub-Neptune category by retaining a thick atmosphere.

But as I said, there are lots of variables here, such as the mass of the parent star.  A recent paper adds another layer – what about planets that migrate? One theory of planetary formation (mainly through simulations) holds that some planets may migrate either closer to or farther away from their parent stars over time. Also the existence of “hot Jupiters” – large gas planets very close to their parent stars – suggests migration, as such planets likely could not have formed where they are.  It is likely that Neptune and Uranus migrated farther away from the sun after their formation. This is part of a broader theory about the stability of planetary systems. Such systems, almost by definition, are stable. If they weren’t, they would not last for long, which means we would not observe many of them in the universe. Our own solar system has been relatively stable for billions of years.

There are several possible explanations for this remarkable stability. One is that this is how planetary systems evolve. The planets form from a rotating disc of material which means they form roughly circular orbits all going in the same plane and same direction. But it is also possible that early stellar systems develop many more planets than ultimately survive. Those is stable orbits survive long term, while those in not stable orbits either fall into their parent star or get ejected from the system to become rogue planets wandering between the stars. There is therefore a selection for planets in stable orbits. There is also now a third process likely happening, and that is planetary migration. Planets may migrate to more stable orbits over time. Eventually all the planets in a system jockey into position in stable orbits that can last billions of years.

Observing exoplanetary systems is one way to test our theories about how planetary systems form and evolve. The relative gap in planet size is one tiny piece of this puzzle. With migrating planets what the paper says is likely happening is that if you have sub-Neptunes that migrate closer to their parent star, the thick atmosphere will be stripped away leaving behind a smaller rocky world below the gap. But also they hypothesize that a very icy world may migrate closer to their parent star, melting the ice and forming a thick atmosphere, jumping the gap to large planetary size.

What all of these theories of the gap have in common is the presence or absence of a thick atmosphere, which makes sense. There are some exoplanets in the gap, but it’s just much less likely. It’s hard to get a planet right in the gap, because either it’s too light to have a thick atmosphere, or too massive not to have one. The gap can be seen as an unstable region of planetary formation.

The more time that goes by the more data we will have and the better our exoplanet statistics will be. Not only will we have more data, but longer observation periods allow for the confirmation of planets with longer orbital periods, so our data will become progressively more representative. Also, better telescopes will be able to detect smaller worlds in orbits more difficult to observe, so again the data will become more representative of what’s out there.

Finally, I have to add, with greater than 5000 exoplanets and counting, we have still not found an Earth analogue. No exoplanet that is a small rocky world of roughly Earth size and mass in the habitable zone of an orange or yellow star. Until we find one, it’s hard to do statistics, except to say that truly Earth-like planets are relatively rare. But I anxiously await the discovery of the first true Earth twin.

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