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Modeling Magma Ocean Exoplanets

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cooled black lava is crossed by bright cracks showing hotter lava below. gas billows from multiple bright areas.
Earth's mantle is mostly solid today, but the rocky layer can melt into magma and be pushed up to the surface in the form of lava. Mount Nyiragongo in the Democratic Republic of Congo is the site of Earth's largest lava lake, shown here. [Nina R]

Say you’ve measured an exoplanet’s mass and radius. How do you know if this distant planet is a waterlogged ocean world or a desiccated desert? Astronomers turn to increasingly sophisticated models of planetary interiors to answer this question.

A Case of Planetary Magmatism

a cutaway model of Earth's interior, with the layers labeled. from the outside to the inside: crust, upper mantle, mantle, outer core, inner core

A diagram of Earth’s interior. Earth’s mantle is mostly solid, but it can melt into magma and be extruded onto the surface as lava through volcanoes. [NASA (Adapted from Goddard Media Studios)]

To figure out how much water an exoplanet harbors, astronomers use models to convert observed properties like the planet’s mass and radius into estimates of its composition, including how much water it contains. It’s equally important to understand where an exoplanet keeps its water: in its atmosphere, on its surface, or sequestered deep in its interior. A new article explores the possibility that water-rich planets might hide their water deep in their interiors, dissolved in an ocean of magma.

If an exoplanet orbits close to its parent star or has a thick atmosphere that traps heat, its mantle — the layer between the core and the surface — might be magma rather than solid rock. When water dissolves into this molten material, it seeps into the planet’s interior and reduces the supply of surface water. In today’s article, Caroline Dorn (University of Zurich, Switzerland) and Tim Lichtenberg (University of Oxford, UK) explore the effects of global magma oceans on the observed and inferred properties of exoplanets.

Modeling Molten Mantles

Dorn and Lichtenberg tested the effects of different planetary interiors by modeling exoplanets with iron cores, silicate-rich mantles, and an outer layer of pure water in the form of ice, liquid, or steam. The team solved fluid mechanics equations to determine the equilibrium states of planets with three different interior structures:

cartoon of the three planetary interior models

Schematic of the three models used in this work. [Dorn & Lichtenberg 2021]

  • A: mantle is dry, rocky, and solid throughout
  • B: mantle contains melted regions that do not sequester water (dry melt–solid interior)
  • C: mantle contains melted regions that do sequester water (wet melt–solid interior).

The authors found that a planet’s interior structure has a discernible effect on its size. For planets of the same mass, those with wet melt–solid interiors can be as much as 16% smaller than those with dry melt–solid interiors or rocky interiors. This can be explained on the molecular level: water molecules nestled snugly between silicate molecules in the mantle increase a planet’s radius less than freewheeling water molecules in the atmosphere or on the surface.

How Much Water?

inferred water mass fraction as a function of planetary radius, mass, and interior model

Inferred water mass fraction for a range of planet masses for each of the authors’ three models for the planets’ interiors. [Dorn & Lichtenberg 2021]

Dorn and Lichtenberg also tested how our estimates of a planet’s water content depend on the choice of interior model. They found that the inferred amount of water can vary by up to an order of magnitude based on the choice of model, with wet melt–solid planets resulting in more water-rich estimates than dry melt–solid planets or rocky planets. Their results underscore the important difference between a planet’s bulk water content and its surface water content, a distinction that future models and observations may help to illuminate.

Additionally, these results raise interesting questions about a planet’s supply of water over long timescales; with water safely contained beneath the planet’s surface rather than settled on its surface or suspended in its atmosphere, it may be less likely to be lost to space.

Citation

“Hidden Water in Magma Ocean Exoplanets,” Caroline Dorn and Tim Lichtenberg 2021 ApJL 922 L4. doi:10.3847/2041-8213/ac33af