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. The implications of the existence of multiple branches are graphically illustrated by approximating the globally averaged mantle heat flow as a function of the interior potential temperature. For this assumption to be valid, the mantle heat how needs to be able to change rapidly relative to the potential temperature, or, equivalently, lithosphere needs to be a small fraction 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 be multivalued with a separate branch representing each mode of convection. The heat flow evolves along a branch as the potential temperature changes depending on whether the heat flow is greater or less than the global radioactive heat generation. When the end of a branch is reached, the state of the system jumps to another branch, quickly changing the global heat flow. Examples include transitions from a magma ocean to plate tectonics, probably on the Earth and Mars, and conceivably Venus; and the transition from a stagnant-lid planet to a magma ocean on Venus and the eventual return to a stagnant-lid planet.