Evolution of the mode of convection within terrestrial planets

Magma oceans, plate tectonics, and stagnant-lid convection have transferred heat out of the terrestrial planets at various times in their histories. T he implications of the existence of multiple branches are graphically illus trated by approximating the globally averaged mantle heat flow as a functio n of the interior potential temperature. For this assumption to be valid, t he mantle heat how needs to be able to change rapidly relative to the poten tial temperature, or, equivalently, lithosphere needs to be a small fractio n of the mass planet. This criterion is satisfied by the Earth, Venus, and Mars, but not the Moon. At a given potential temperature the function may b e multivalued with a separate branch representing each mode of convection. The heat flow evolves along a branch as the potential temperature changes d epending on whether the heat flow is greater or less than the global radioa ctive heat generation. When the end of a branch is reached, the state of th e system jumps to another branch, quickly changing the global heat flow. Ex amples include transitions from a magma ocean to plate tectonics, probably on the Earth and Mars, and conceivably Venus; and the transition from a sta gnant-lid planet to a magma ocean on Venus and the eventual return to a sta gnant-lid planet.