Why are sub-Neptunes so abundant?

So many exoplanets have been discovered that the distributions of their observable properties are statistically rich enough to plot and ponder. Among the most striking of distributions is that of planetary radius (measured in Earth radius R_⊕). Planets whose radii are between 2.7 R_⊕ and 3.0 R_⊕ are almost 10 times more abundant than planets whose radii are between 3.3 R_⊕ and 3.7 R_⊕.

The radius cliff, as the drop in frequency is known, falls within range of radii characteristic of sub-Neptunes. (Neptune, shown here, has a radius of 3.9 R_⊕.) It is challenging to explain. Planets form when dust grains agglomerate into pebbles, pebbles agglomerate into rocks, and rocks agglomerate into planetary cores. Whether a core becomes a rocky planet, a gas giant, an ice giant, or other type of planet depends on the distance from the host star, the local density of gas, and other factors. Those factors are expected to vary smoothly from system to system—too smoothly to yield a radius cliff.

Edwin Kite of the University of Chicago and his collaborators have proposed a novel explanation for the radius cliff, and it has to do with the solubility of hydrogen gas in the hot, molten rock that makes up the surface of a young planetary core.

Cores stop growing when they run out of local rocks and pebbles to accrete. The ultimate size of a sub-Neptune, Neptune, or super-Neptune is determined by how much local gas—mostly hydrogen—it can accrete. In principle, the accretion could continue so long as gas is available. Indeed, as the planet becomes heavier, its gravity increases, as does its ability to accrete even more gas. Such runaway accretion is how gas giants form.

But Kite and his colleagues realized that runaway accretion could be stopped, at least around 3 R_⊕. As the atmospheric pressure at the planet’s surface increases, hydrogen no longer behaves like an ideal gas. It becomes less compressible. At that point, hydrogen is readily absorbed by molten rock. If the layer is thick enough and hot enough, the molten rock will keep sequestering hydrogen. The planet’s radius will stop growing until either the local supply of gas is exhausted or the sequestration is saturated, at which time runaway accretion ensues.

Embodying that process in a detailed physical model is difficult. Some of the important ingredients, such as the solubility of hydrogen in liquid rock at 4000 K, are unknown. Nevertheless, with a plausible set of assumptions, Kite and his colleagues demonstrated that their model could account for the location of the radius cliff and its steepness. In particular, a core that accretes less than 1% of its weight in hydrogen will lose its atmosphere and become a super-Earth. One that accretes a few percent of hydrogen becomes a sub-Neptune. And cores that accrete as much as 20% also become sub-Neptunes, hence their abundance. (E. S. Kite et al., Astrophys. J. Lett. 887, L33, 2019 ; E. S. Kite et al., Astrophys. J., in press, https://arxiv.org/abs/2001.09269 .)