The energetics and convective vigor of mixed-mode heating: Velocity scalings and implications for the tectonics of exoplanets
Matthew B. Weller and Adrian Lenardic

Abstract The discovery of large terrestrial (~1 Earth mass (Me) to<10Me) extrasolar planets has prompted
a debate as to the likelihood of plate tectonics on these planets. Canonical models assume classic basal
heating scaling relationships remain valid for mixed heating systems with an appropriate internal temperature
shift. Those scalings predict a rapid increase of convective velocities (Vrms) with increasing Rayleigh numbers
(Ra) and non-dimensional heating rates (Q). To test this we conduct a sweep of 3-D numerical parameter space
for mixed heating convection in isoviscous spherical shells. Our results show that while Vrms increases with
increasing thermal Ra, it does so at a slower rate than predicted by bottom heated scaling relationships.
Further, the Vrms decreases asymptotically with increasing Q. These results show that independent of specific
rheologic assumptions (e.g., viscosity formulations, water effects, and lithosphere yielding), the differing
energetics of mixed and basally heated systems can explain the discrepancy between different modeling
groups. High-temperature, or young, planets with a large contribution from internal heating will operate in
different scaling regimes compared to cooler-temperature, or older, planets that may have a larger relative
contribution from basal heating. Thus, differences in predictions as to the likelihood of plate tectonics on
exoplanets may well result from different models being more appropriate to different times in the thermal
evolution of a terrestrial planet (as opposed to different rheologic assumptions as has often been assumed).

Weller, M. B., and A. Lenardic (2016), The energetics and convective vigor of mixed-mode heating: Velocity scalings
and implications for the tectonics of exoplanets, Geophys. Res. Lett., 43, doi:10.1002/2016GL069927.