The Bloated Hydrogen Envelope and Tidal Distortions of Sub-Neptune Kepler-36c

In the catalog of extrasolar worlds discovered by the Kepler Space Telescope, few systems challenge our understanding of planetary formation as dramatically as Kepler-36. Located approximately 1,200 light-years from Earth in the constellation Cygnus, this system is home to two planets orbiting in unprecedented proximity. The outer companion, Kepler-36c, is a classic sub-Neptune—a class of planets intermediate in size between Earth and Neptune that has no analogue in our own Solar System. While its inner neighbor, Kepler-36b, is a dense, scorched super-Earth, Kepler-36c is a highly bloated, low-density world wrapped in a massive envelope of primordial hydrogen and helium.

First confirmed in 2012 using transit timing variations, Kepler-36c has become a cornerstone target for astrophysicists studying planetary atmospheres, orbital dynamics, and migration theory. The physical contrast between the two tightly packed planets, which orbit their host star at distances differing by a mere 0.013 astronomical units (AU), provides a natural laboratory for testing how stellar irradiation shapes planetary evolution. Kepler-36c represents the puffier, volatile-rich end of this cosmic pairing, retaining a deep gaseous shroud despite its close proximity to a highly active subgiant star.

The Bloated Hydrogen Envelope and Tidal Distortions of Sub-Neptune Kepler-36c - Section 1 overview

Physical Architecture and Low-Density Profile

Kepler-36c possesses a mass of approximately 8.1 Earth masses ($M_{\oplus}$), yet its radius is expanded to roughly 3.67 Earth radii ($R_{\oplus}$). This disproportionate ratio of mass to volume yields a bulk density of just 0.89 grams per cubic centimeter—less than the density of liquid water and significantly lower than any rocky planet. This physical profile classifies Kepler-36c as a "puffy" sub-Neptune, a transition state between solid terrestrial planets and true gas giants.

To maintain such a low density, Kepler-36c must host a substantial gaseous envelope. Numerical models suggest that hydrogen and helium make up between 5% and 10% of the planet's total mass. While this percentage sounds modest, these light gases occupy the vast majority of the planet's volume, extending thousands of kilometers above any localized solid or liquid core. This thick atmospheric blanket is kept warm by the intense radiation of its host star, Kepler-36, an F-type subgiant that is older, larger, and hotter than our Sun. The equilibrium temperature of Kepler-36c is estimated to be approximately 900 Kelvin, a thermal regime that prevents the atmosphere from contracting and contributes directly to the planet's bloated physical dimensions.

Atmospheric Chemistry and Photoevaporative Loss

The atmosphere of Kepler-36c is dominated by molecular hydrogen ($H_2$) and helium ($He$), with trace abundances of water vapor ($H_2O$), methane ($CH_4$), and carbon monoxide ($CO$). Due to the planet's high equilibrium temperature, photochemistry in the upper atmosphere is highly active. Stellar ultraviolet light breaks down methane molecules, driving the synthesis of heavier hydrocarbons that can condense into high-altitude photochemical hazes. These hazes act as a reflective, semi-translucent blanket, scattering incoming starlight and giving the upper cloud decks a muted, golden-cyan hue.

Because Kepler-36c orbits only 0.128 AU from its host star, it is subjected to a relentless torrent of high-energy X-ray and extreme ultraviolet (EUV) radiation. This high-energy flux heats the hydrogen in the exosphere to temperatures where the thermal velocity of the gas exceeds the planet's escape velocity. This process, known as photoevaporation, drives a continuous hydrodynamic escape of atmospheric gas. Kepler-36c is actively losing mass to space, generating a diffuse, comet-like tail of escaping neutral hydrogen that streams outward along its orbital path. Over billions of years, this process can strip sub-Neptunes of their volatile envelopes entirely, potentially transforming them into rocky super-Earths—a fate that its inner sibling, Kepler-36b, may have already suffered.

The Dynamic Choreography of the Kepler-36 Resonance

The most remarkable aspect of Kepler-36c is its orbital relationship with Kepler-36b. The two planets are locked in a near-perfect 7:6 mean-motion resonance, meaning that for every seven orbits Kepler-36b completes, Kepler-36c completes exactly six. This tight resonance ensures that the planets regularly pass incredibly close to one another. Every 97 Earth days, the two worlds reach conjunction, approaching within just 1.9 million kilometers of each other—less than five times the distance between the Earth and the Moon.

During these close approaches, the gravitational interaction between the two bodies is immense. The mutual gravitational tugs cause massive tidal distortions in Kepler-36c’s bloated envelope, stretching the atmosphere into a subtle triaxial ellipsoid. These interactions also trigger severe orbital variations, causing the transit times of both planets to shift by up to several hours from a regular schedule. The tidal dissipation of energy resulting from these regular gravitational distortions generates significant internal friction, heating the deep interior of Kepler-36c and contributing to the thermal expansion of its atmosphere.

Internal Structure: From Gas to Supercritical Core

Beneath the vast, low-density hydrogen-helium envelope of Kepler-36c lies a high-pressure transition zone. As depth increases, the atmospheric gas is compressed into a supercritical state, where the distinction between gas and liquid disappears. This deep, warm fluid mantle is likely composed of water, ammonia, and methane, often referred to by planetary scientists as an "ionic ocean." At these extreme depths, the pressure is sufficient to strip molecules of their electrons, turning the fluid into a highly conductive medium capable of generating a local magnetic field.

At the center of Kepler-36c lies a solid, rocky core composed of iron-nickel alloys and silicate minerals, estimated to weigh between 4 and 6 Earth masses. This core is roughly comparable in size to the entirety of Kepler-36b, suggesting that the two planets formed from similar rocky building blocks. However, while Kepler-36b lost or never acquired a thick gaseous envelope, Kepler-36c successfully accreted and retained its volatile shroud during the protoplanetary disk phase. The preservation of this core-envelope structure makes Kepler-36c a primary target for testing planetary migration models, demonstrating how two vastly different worlds can coexist on the very edge of orbital stability.

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