Thermal convection of compressible fluid in the mantle of super-Earths

To understand how adiabatic compression influences mantle convection in super-Earths, we carried out linear stability analysis and non-linear numerical simulation of thermal convection for constant viscosity infinite Prandtl number fluid with both constant and pressure-dependent thermal expansivity. The mantle is basally heated and internal heating is not considered. In the case of constant thermal expansivity, thermal convection is totally inhibited in super-Earths of more than about 5 times the Earth's mass owing to the strong effect of adiabatic compression, when the surface temperature is sufficiently high. Pressure-dependence of thermal expansivity is crucial for the onset of convection in massive super-Earths. Even when the thermal expansivity depends on pressure, our numerical simulation shows that the effect of adiabatic compression reduces the efficiency of convective heat transport by up to about 60%, depending on the planetary mass and the surface temperature. The reduction in the efficiency of convective heat transport makes cooling of the mantle more difficult in massive super-Earths, especially when the surface temperature is high. The surface temperature of a planet may affect its thermal history not only through its effects on the mechanical properties of convecting mantle materials, but also through its influence on adiabatic compression of convecting materials.