Terrestrial planet evolution in the stagnant-lid regime: Size effects and the formation of self-destabilizing crust

The ongoing discovery of terrestrial exoplanets accentuates the importance of studying planetary evolution for a wide range of initial conditions. We perform thermal evolution simulations for generic terrestrial planets with masses ranging from that of Mars to 10M _⊕ in the stagnant-lid regime, the most natural mode of convection with strongly temperature-dependent viscosity. Given considerable uncertainty surrounding the dependency of mantle rheology on pressure, we choose to focus on the end-member case of pressure-independent potential viscosity, where viscosity does not change with depth along an adiabatic temperature gradient. We employ principal component analysis and linear regression to capture the first-order systematics of possible evolutionary scenarios from a large number of simulation runs. With increased planetary mass, crustal thickness and the degree of mantle processing are both predicted to decrease, and such size effects can also be derived with simple scaling analyses. The likelihood of plate tectonics is quantified using a mantle rheology that takes into account both ductile and brittle deformation mechanisms. Confirming earlier scaling analyses, the effects of lithosphere hydration dominate the effects of planetary mass. The possibility of basalt-eclogite phase transition in the planetary crust is found to increase with planetary mass, and we suggest that massive terrestrial planets may escape the stagnant-lid regime through the formation of a self-destabilizing dense eclogite layer.