Early asymmetric growth of planetary stagnant lids

Convection within planetary bodies is often modelled using a temperature-dependent rheology which, when cooled from the surface, naturally leads to the formation of a so-called stagnant lid at the cold outer surface. However, for sufficiently large planets the phase diagram describing the partially molten system may depend significantly on pressure in addition to temperature, leading to significant variations in solid fraction. The aggregate rheology may therefore exhibit significant dependence on both the temperature and pressure, and hence may exhibit marked dependence on depth in addition to the dependence on the thermal structure due to convection. Here, we consider the growth and stability of a planetary stagnant lid. We first characterise the effect of a pressure-and temperature-dependent rheology on the evolution of a symmetric, planetary stagnant lid. This analysis further suggests that the pressure dependence of the rheology may lead to an instability of the growing stagnant lid which, importantly, may lead to asymmetric lid growth. We find that the most unstable mode is at the longest wavelengths, and discuss the implications for stagnant-lid convection and the growth of asymmetric surfaces of planetary bodies. In particular, we discuss the possibility that this instability has implications for the formation of the crustal dichotomy found on the Moon.