  As the number of detected rocky extrasolar planets increases, the question of
whether their surfaces could be habitable is becoming more pertinent. On Earth,
the long-term carbonate silicate cycle is able to regulate surface temperatures
over timescales larger than one million years. Elevated temperatures enhance
weathering, removing CO$_2$ from the atmosphere, which is subducted into the
mantle. At mid-ocean ridges, CO$_2$ is supplied to the atmosphere from the
interior. The carbon degassing flux is controlled by the melting depth beneath
mid-ocean ridges and the spreading rate, influenced by the pressure- and
temperature-dependent mantle viscosity. The influences of temperature and
pressure on mantle degassing become increasingly important for more massive
planets. Here, we couple a thermal evolution model of Earth-like planets of
different masses with a model of the long-term carbon cycle and assess their
surface temperature evolution. We find that the spreading rate at 4.5 Gyr
increases with planetary mass up to 3 $M_\oplus$, since the
temperature-dependence of viscosity dominates over its pressure-dependency. For
higher mass planets, pressure-dependence dominates and the plates slow down. In
addition, the effective melting depth at 4.5 Gyr as a function of planetary
mass has its maximum at 3 $M_\oplus$. Altogether, at 4.5 Gyr, the degassing
rate and therefore surface temperature have their maximum at 3 $M_\oplus$. This
work emphasizes that both age and mass should be considered when predicting the
habitability of exoplanets. Despite these effects, the long-term carbon cycle
remains an effective mechanism that regulates the surface temperature of
massive Earth-like planets.
