Subsolidus convective cooling histories of terrestrial planets

The subsolidus convective cooling histories of terrestrial planets evolving from hot initial states are investigated quantitatively. A simple analytic model simulating average heat flux from a vigorously convecting mantle and incorporating a mantle viscosity proportional to mantle temperature and a lithosphere which thickens as the planet cools is employed. Heat flux from the convecting mantle is calculated on the basis of a power law relation between Nusselt number and Rayleigh number. The temperature distribution in the lithosphere is assumed to be linear throughout the cooling history of the planet. Cooling histories have been determined for the earth, Mars, Mercury and the moon and the mantle temperature decreases, mantle viscosity increases and decreases of heat flux to the surface and to the base of the lithosphere and of Nusselt and Rayleigh numbers are illustrated for each planet. It is found that primordial heat can contribute substantially to the present surface heat flux of a planet.