Resolving the Super-Earth Paradox

Researchers looking to solve the super-Earth paradox finally have found what very likely is the resolution. Their resolution also has revealed more evidence for the fine-tuning of the solar system to support advanced life.

Super-Earths are planets possessing a mass between 1.2 and 13 times the mass of Earth. For comparison, Uranus and Neptune weigh in at 14.54 and 17.15 Earth masses, respectively. Another term for a super-Earth is a mini-Neptune. The diameters of known super-Earth planets range from about 120 to 220 percent of Earth’s diameter (about 30 to 54 percent of Neptune’s diameter). The featured image shows a comparison of the sizes of super-Earths (middle of the image) relative to Earth (left of the image) and relative to Uranus (lower left) and Neptune (upper right).

So far, astronomers have discovered 3,721 planets orbiting nuclear burning stars.¹ Of these 3,721 planets with known masses, 16.2 percent are in the super-Earth category, making it the second most populous of all planet categories. The most populous category are hot Jupiters at 20.9 percent, which are planets greater or equal to Jupiter’s mass that orbit their host stars closer than Earth orbits the Sun.

The super-Earth paradox is that, according to our best understanding of how planets form, there should not be any super-Earth planets at all. Observed super-Earths are all in the critical mass range—that is, they possess enough mass to accrete gas very efficiently. Nothing should stop them from becoming planets dominated by massive gaseous atmospheres like Jupiter, Saturn, Uranus, and Neptune.

The Kepler spacecraft clearly has proven that super-Earths do exist and that they exist in large numbers. In an effort to resolve the super-Earth paradox, in 2014, UC Berkeley astronomers Eve Lee, Eugene Chiang, and Chris Ormel proposed a metallicity gradient in the proto-planetary disks of planet-forming stars.² That is, they suggested that for proto-planetary disks, the ratio of heavy elements to light elements declines in proportion to the distance from the host star. Therefore, planets forming in close proximity to their host stars will lack the abundance of gas to accrete that exists farther out from the host stars.

There are two problems for this metallicity gradient scenario. One is that most models for the formation of super-Earths have the super-Earth planets forming far from their host stars and subsequently migrating inward toward the host stars. A second problem is that it is very difficult in proto-planetary disk models to get the necessary steep metallicity gradient.

In 2016, Lee and Chiang proposed another way to resolve the super-Earth paradox. They speculated that, while gas giant planets form early, super-Earth planets form late.³ They pointed out that, as proto-planetary disks age, the abundance of gas in the disk falls and that the gas abundance can drop by several orders of magnitude. Therefore, if super-Earth planets form late enough, they will be gas-poor compared to gas giant planets.

The gas abundance in old proto-planetary disks indeed drops precipitously. However, the abundance of dust and rocks in such disks also drops precipitously. Thus, planet formation is much less productive and efficient in older proto-planetary disks. Such low productivity and efficiency are contradicted by the very large population of super-Earth planets.

In an open access paper (yes, you can read the entire paper for free) published in the December 1, 2017 issue of the Astrophysical Journal, astronomer Cong Yu of Sun Yet-Sen University in Guangzhou, China, proposed⁴ a solution to the super-Earth paradox that avoids the problems in the scenarios developed by Lee, Chiang, and Ormel. In Yu’s model, super-Earth planets form as a result of tidally forced turbulent diffusion.

Yu notes that if a planet forms close enough to its host star, tidal interactions between the host star and the planet can periodically perturb the planet. Heating by tidal dissipation can so inhibit gas cooling in primordial super-Earth atmospheres as to dramatically limit the amount of gas that the planet can accrete. Specifically, Yu’s calculations established that “the thermal feedback associated with the externally forced turbulent stirring may greatly alter the accretion history of super-Earths.”⁵ Thus, he demonstrated that “tidally forced turbulent diffusion effectively helps super-Earths evade growing into gas giants.”⁶

Yu’s model also explains planetary systems that possess both super-Earth and gas giant planets. His calculations show that “the condition for turbulence-induced formation of super-Earths is more readily satisfied in the inner disk region but is harder to satisfy in the outer disk region.”⁷ The deductions from Yu’s calculations are consistent with observations. In planetary systems with both super-Earth and gas giant planets, the super-Earths orbit nearby their host stars while the gas giants orbit much farther away.

Yu ends his paper by admitting that not all the details are worked out. How and when the turbulence is initiated during planet formation remains to be modeled in detail. Yu used a simple opacity model for his planet atmospheres. More realistic opacities need to be invoked. Nevertheless, Yu’s model already goes a long way toward resolving the super-Earth paradox.

While the super-Earth paradox apparently is very close to being fully resolved, the solar system paradox remains. Our solar system is like no other known planetary system. It contains none of the most common planets. Neither super-Earths nor hot Jupiters exist in the solar system. Furthermore, the sizes and the orbital locations of the Sun’s four gas giant planets are unique.

As I explain in my book, Improbable Planet,⁸ there are excellent reasons for the unique features of the solar system. All eight of the Sun’s planets must possess exquisitely fine-tuned physical and orbital characteristics for advanced life to be possible on Earth. The reason why the solar system is so different compared to the other 2,792 planetary systems that have been discovered so far, is that apparently, it alone has been fashioned by the Creator of the universe to be a fit home for humans and human civilization.