Scaling and Thermal Evolution of Internally Heated Planets: Yield Stress and Thermal History.

Abstract:

Using coupled 3D mantle convection and planetary tectonics models of bi-stable systems, we show how system behaviors for mobile-lid and stagnant-lid states scale as functions of internal heating rates (Q) and basal Ra (Ra_b). With parameter ranges for temperature- and depth-dependant viscosities: 1e4 – 3e4, Ra_b: 1e5– 3e5, Q: 0 – 100, and yield stress: 1e4 – 2e5, it can be shown the internal temperatures, velocities, heat fluxes, and system behaviors for mobile-lid and stagnant-lid states diverge, for equivalent parameter values, as a function of increasing Q. For the mobile-lid regime, yielding behavior in the upper boundary layer strongly influences the dynamics of the system. Internal temperatures, and consequently temperature-dependant viscosities, vary strongly as a function of yield stress for a given Q. The temperature distribution across the upper and lower mantles are sub-adiabatic for low to moderate yield stress, and adiabatic to super-adiabatic for high yield stresses. Across the parameter range considered, and for fixed yield stress, the Nu across the basal boundary (Nu_b) is positive and only weakly dependant on Q (varies by ~ 9%). Nu_b varies strongly as a function of yield stress (maximum variation of ~84%). Both mobile-lid velocities and lid-thicknesses are yield stress dependant for a given Q and Ra. In contrast to mobile-lids, the stagnant-lid regime is governed by the relative inefficiency of heat transport through the surface boundary layer. Internal temperatures are yield stress independent, and are on average 30% greater. Nu_b has a strong dependence on heating rates and surface boundary layer thicknesses. Within the parameter space considered, the maximum stagnant-lid Nu_b corresponds to the minimum mobile-lid Nu_b (for high yield stress), and decreases with increasing Q. For high Q, super-heated stagnant-lids may develop, with Nu_b< 0, and changes in trends for system behaviors. Planets with high levels of internal heating and/or high yield stresses (e.g. Super-Earths), may favor super-heated stagnant-lids early in their evolution. These regimes indicate reduced heat transport efficiencies (from the nominal stagnant-lid), and as a result, increasing heat flux into the core with increasing Q. Implications for terrestrial and Super-Earth planetary evolution will be discussed.