Thermal evolution of rocky exoplanets with a graphite outer shell

Context. The presence of rocky exoplanets with a large refractory carbon inventory is predicted by chemical evolution models of protoplanetary disks of stars with photospheric C/O > 0.65, and by models studying the radial transport of refractory carbon. High-pressure high-temperature laboratory experiments show that most of the carbon in these exoplanets differentiates into a graphite outer shell. Aims. Our aim is to evaluate the effects of a graphite outer shell on the thermal evolution of rocky exoplanets containing a metallic core and a silicate mantle. Methods. We implemented a parameterized model of mantle convection to determine the thermal evolution of rocky exoplanets with graphite layer thicknesses up to 1000 km. Results. We find that because of the high thermal conductivity of graphite, conduction is the dominant heat transport mechanism in a graphite layer for long-term evolution (>200 Myr). The conductive graphite shell essentially behaves like a stagnant lid with a fixed thickness. Models of Kepler-37b (Mercury-size) and a Mars-sized exoplanet show that a planet with a graphite lid cools faster than a planet with a silicate lid, and a planet without a stagnant lid cools the fastest. A graphite lid needs to be approximately ten times thicker than a corresponding silicate lid to produce similar thermal evolution.