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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.

We evaluate a numerical model on the thermal evolution of terrestrial planets to estimate life-time of planetary intrinsic magnetic field for various mass planets. In this model, we take into account the pressure-dependency of density profile of the planet by using Birch-Murnaghun equation of state, and simulate thermal evolution of the planet by means of mixing length theory. According to our numerical results, the planetary mass must be between 0.1 and 1.4 Earth mass to sustain the intrinsic magnetic field for 4.5Gyr. If existence of intrinsic magnetic field were a key factor to make the planet habitable, the mass range above indicates that super-Earths would not be habitable.