A climate induced transition in the tectonic style of a terrestrial planet

We explore the possibility that an increase in the surface temperature of a terrestrial planet due to an enhanced concentration of atmospheric greenhouse gasses and/or increased solar luminosity could initiate a transition from an active-lid mode of mantle convection (e.g., plate tectonics) to an episodic or stagnant-lid mode (i.e., single plate planet). A scaling theory is developed to estimate the required temperature change as a function of the temperature dependence of mantle viscosity and the yield stress of the lithosphere. The theory relies on the assumptions that convective stresses scale with mantle viscosity and that a planet will adjust to surface temperature changes so as to maintain a surface heat flow that balances internal heat production. The theory is tested against a suite of numerical simulations of mantle convection. The comparisons are favorable. The combined theory and numerics suggest that if the yield stress for the earthsʹ lithosphere is 30–35 MPa, then a surface temperature change of 60–120° could shut down an active-lid mode of convection assuming present day conditions. Lower values are predicted for higher yield stresses and for earlier times in the earth geologic evolution.