March 1, 2024

Simulations Provide Potential Explanation for Mysterious Gap in Super-Earth Size Distribution

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Artist’s depiction of an exoplanet whose surface water ice is increasingly vaporizing and forming an atmosphere as it approaches the planetary system’s central star. This process increases the measured planetary radius compared to the value the planet would have at its place of origin. Credit: Thomas Müller (MPIA)

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Artist’s depiction of an exoplanet whose surface water ice is increasingly vaporizing and forming an atmosphere as it approaches the planetary system’s central star. This process increases the measured planetary radius compared to the value the planet would have in its place of origin. Credit: Thomas Müller (MPIA)

Typically, planets in evolved planetary systems, such as the solar system, follow stable orbits around their central star. However, many indications suggest that some planets may move away from their birthplaces during their early evolution, migrating inwards or outwards.

This planetary migration may also explain an observation that has intrigued researchers for several years: the relatively low number of exoplanets about twice the size of Earth, known as a radius valley or gap. On the other hand, there are many exoplanets smaller and larger than this size.

“Six years ago, a reanalysis of data from the Kepler space telescope revealed a shortage of exoplanets with sizes around two Earth radii,” explains Remo Burn, exoplanet researcher at the Max Planck Institute for Astronomy (MPIA) in Heidelberg. He is the lead author of the paper reporting the findings described in this paper, now published in Nature Astronomy.

Where does lightning valley come from?

“In fact, we – like other research groups – predicted based on our calculations even before this observation that such a gap should exist,” explains co-author Christoph Mordasini, member of the National Center for Research Competence (NCCR). PlanetaS. He heads the Division for Space Research and Planetary Sciences at the University of Bern. This prediction originated during his tenure as a scientist at the MPIA, which has been investigating this field together with the University of Bern for many years.

The most commonly suggested mechanism to explain the emergence of such a radius trough is that planets may lose a part of their original atmosphere due to irradiation from the central star, especially volatile gases such as hydrogen and helium. “However, this explanation neglects the influence of planetary migration,” explains Burn.

It was established about 40 years ago that, under certain conditions, planets can move in and out through planetary systems over time. How effective this migration is and to what extent it influences the development of planetary systems impacts its contribution to the formation of the lightning valley.

Enigmatic Sub-Neptunes

Two different types of exoplanets inhabit the size range around the gap. On the one hand, there are rocky planets, which can be more massive than Earth and are therefore called super-Earths. On the other hand, astronomers are increasingly discovering so-called sub-Neptunes (also mini-Neptunes) in distant planetary systems, which are, on average, slightly larger than super-Earths.

“However, we do not have this class of exoplanets in the solar system”, highlights Burn. “That is why, even today, we are not sure about its structure and composition.”

Still, astronomers largely agree that these planets have significantly more extensive atmospheres than rocky planets. Consequently, understanding how the characteristics of these sub-Neptunes contribute to the radius gap has been uncertain. Could the gap suggest that these two types of worlds form differently?


The number of exoplanets decreases between 1.6 and 2.2, producing a pronounced trough in the distribution. Instead, there are more planets present with sizes around 1.4 and 2.4 Earth radii. The latest simulations, which for the first time take into account the realistic properties of water, indicate that icy planets that migrate into planetary systems form thick atmospheres of water vapor. This makes them appear larger than they would be in their place of origin. These produce the peak at about 2.4 Earth radii. At the same time, smaller rocky planets lose part of their original gas envelope over time, causing their measured radius to decrease and thus contributing to the accumulation at about 1.4 Earth radii. Credit: R. Burn, C. Mordasini/MPIA

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The number of exoplanets decreases between 1.6 and 2.2, producing a pronounced trough in the distribution. Instead, there are more planets present with sizes around 1.4 and 2.4 Earth radii. The latest simulations, which for the first time take into account the realistic properties of water, indicate that icy planets that migrate into planetary systems form thick atmospheres of water vapor. This makes them appear larger than they would be in their place of origin. These produce the peak at about 2.4 Earth radii. At the same time, smaller rocky planets lose part of their original gas envelope over time, causing their measured radius to decrease and thus contributing to the accumulation at about 1.4 Earth radii. Credit: R. Burn, C. Mordasini/MPIA

Wandering ice planets

“Based on simulations that we already published in 2020, the most recent results indicate and confirm that, instead, the evolution of sub-Neptunes after their birth contributes significantly to the observed radius valley”, concludes Julia Venturini, from the University from Geneva. She is a member of the PlanetS collaboration and led the 2020 study.

In the icy regions of their birthplaces, where the planets receive little warming radiation from the star, the sub-Neptunes should indeed have sizes missing from the observed distribution. As these presumably icy planets migrate closer to the star, the ice melts, eventually forming a thick atmosphere of water vapor.

This process results in a change in the planet’s radii to larger values. After all, the observations used to measure planetary radii cannot differentiate whether the determined size is due solely to the solid part of the planet or to an additional dense atmosphere.

At the same time, as already suggested in the previous image, rocky planets “shrink” when they lose their atmosphere. Overall, both mechanisms produce a lack of planets with sizes around two Earth radii.

Physical computer models simulating planetary systems

“The theoretical research of the Bern-Heidelberg group has already significantly advanced our understanding of the formation and composition of planetary systems in the past”, explains MPIA director Thomas Henning. “The present study is therefore the result of many years of joint preparatory work and constant improvements in physical models.”

The latest results come from calculations of physical models that trace planetary formation and subsequent evolution. They cover processes in the disks of gas and dust that surround young stars and that give rise to new planets. These models include the emergence of atmospheres, the mixing of different gases, and radial migration.

“The center of this study was the properties of water at the pressures and temperatures that occur inside planets and in their atmospheres,” explains Burn. Understanding how water behaves over a wide range of pressures and temperatures is crucial for simulations. This knowledge has only been of sufficient quality in recent years. It is this component that allows realistic calculations of the behavior of sub-Neptunes, thus explaining the manifestation of extensive atmospheres in hotter regions.

“It is remarkable how, as in this case, physical properties at molecular levels influence large-scale astronomical processes, such as the formation of planetary atmospheres,” adds Henning.

“If we expand our results to colder regions, where water is liquid, this could suggest the existence of water worlds with deep oceans,” says Mordasini. “These planets could potentially host life and would be relatively simple targets for biomarker searches, thanks to their size.”

More work ahead

However, the current work is just one important milestone. Although the simulated size distribution closely matches the observed one and the radius gap is in the right place, the details still have some inconsistencies. For example, many icy planets end up very close to the central star in calculations. However, researchers do not consider this circumstance a disadvantage, but hope to learn more about planetary migration this way.

Observations with telescopes like the James Webb Space Telescope (JWST) or the under-construction Extremely Large Telescope (ELT) could also help. They would be able to determine the composition of planets depending on their size, thus providing a test for the simulations described here.

The MPIA scientists involved in this study are Remo Burn and Thomas Henning.

Other researchers include Christoph Mordasini (University of Bern, Switzerland [Unibe]), Lokesh Mishra (University of Geneva, Switzerland [Unige]and Unibe), Jonas Haldemann (Unibe), Julia Venturini (Unige) and Alexandre Emsenhuber (Ludwig Maximilian University Munich, Germany, and Unibe).

NASA’s Kepler space telescope searched for planets around other stars between 2009 and 2018 and discovered thousands of new exoplanets during its operation. He used the transit method: when a planet’s orbit is tilted so that the plane is within the telescope’s line of sight, the planets periodically block some of the star’s light during their orbit. This periodic fluctuation in the star’s brightness allows indirect detection of the planet and determination of its radius.

More information:
A radial valley between migrated vapor worlds and evaporated rock cores, Nature Astronomy (2024). DOI: 10.1038/s41550-023-02183-7

Diary information:
Nature Astronomy

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