Sizing Up Methane Planets

Exoplanets, especially those with ~5 to 50 times the mass of Earth, span a huge range of compositions. A study by Helled et al. (2015) from Tel-Aviv University investigates the mass-radius (M-R) relation for a class of planets known as methane (CH4) planets. Ideally, the M-R curve for a planet of a given composition tends to be smooth, whereby the planet’s radius gradually increases with mass. However, phase changes in the bulk composition of the planet as its mass increases can lead to discontinuities in the M-R curve.

Figure 1: Artist’s impression of an exoplanet.

For a pure methane planet, a phase change involving the dissociation of methane can cause the planet’s radius to increase abruptly. It happens when the planet is massive enough and the high pressure in the interior of the planet causes methane to dissociate into its constituents - hydrogen and carbon. The carbon remains in the planet’s core and the hydrogen, being lighter, diffuses to the outer envelope of the planet. This leads to a differentiated planet consisting of a carbon (diamond) core, a methane envelope and a thick hydrogen atmosphere. With such an interior structure, the planet’s radius is significantly larger than one without dissociation. This shows up as a discontinuity in the M-R curve where the radius increases abruptly beyond a certain mass (Figure 2).

The pressure where methane begins to dissociate is known as the methane dissociation pressure. Assuming a methane dissociation pressure of 170 GPa, a pure methane planet needs to have more than ~8 times the Earth’s mass to support methane dissociation. For a higher methane dissociation pressure of 300 GPa, a planet will need more than ~15 times the Earth’s mass for methane dissociation to occur. In reality, a planet is unlikely to consist only of pure methane.

For a methane planet with a silicate (SiO2) core, its M-R curve will be different compared to a pure methane planet. The higher the silicate mass fraction of the planet, the smaller is the increase in the planet’s radius due to methane dissociation. This is because the silicate core sits in the high pressure region inside the planet where methane dissociation tends to take place. A large silicate core means a smaller volume of methane participates in dissociation, resulting in a smaller change in the planet’s radius from methane dissociation.

Nonetheless, a large silicate core, comprising 30 to 50 percent of the planet’s mass, allows methane dissociation to occur at a smaller planetary mass than in the case where no silicate core is present (i.e. pure methane planet) because a large silicate core allows the planet’s interior to have a higher pressure. However, if the silicate core is very large, say 80 percent of the planet’s mass, methane will exist only as an outer envelope around the planet where the pressure is low. As a result, for a planet with a very large silicate core, methane dissociation will require a larger planetary mass than in the case where no silicate core is present.

Figure 2: M-R relation for pure methane planets with isotherms of 50 K (solid), 500 K (dotted), 1,000 K (dashed) and 1,500 K (dashed-dotted), and assuming a dissociation pressure of 170 GPa (left panel) and 300 GPa (right panel). Helled et al. (2015).

Figure 3: M-R relation for methane planets with different mass fractions of a silicate core for a temperature of 500 K, and assuming a dissociation pressure of 170 GPa (left panel) and 300 GPa (right panel). Helled et al. (2015).

Reference:
Helled et al. (2015), “Methane Planets and their Mass-Radius Relation”, arXiv:1505.00139 [astro-ph.EP]