  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. 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. We implement a parameterized model of mantle convection to
determine the thermal evolution of rocky exoplanets with graphite layer
thicknesses up to 1000 km. We find that, due to the high thermal conductivity
of graphite, conduction is the dominant heat transport mechanism in a graphite
layer for the 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 in order to
produce similar thermal evolution.

Earth and Planetary Astrophysics