Whole planet cooling and the radiogenic heat source contents of the Earth and Moon

It is widely believed that the surface heat flows of the earth and moon provide good measures of the total amounts of radioactives in these bodies. Simple thermal evolution models, based on subsolidus whole mantle convection, indicate that this may not be the case. These models have been constructed assuming an initially hot state, but with a wide variety of choices for the parameters characterizing the rheology and convective vigor. All models are constrained to be consistent with present‐day surface heat fluxes, and many of the terrestrial models are consistent with the mantle viscosities indicated by post‐glacial rebound. For the earth the acceptable models give a radiogenic heat production that is only 65–85% of the surface heat output, the difference being due to secular cooling of the earth (about 50°–100°C per 10 9 years in the upper mantle). It is argued that the actual heat generation may be substantially less, since the models omit core heat, upward migration of heat sources, possible layering of the mantle, and deviations from steady convection. Geochemical models which are near to chondritic (apart from potassium depletion) are marginally consistent with surface heat flow. In the lunar models, heat generation is typically only 70–80% of the surface heat flow, even with allowance for the strong near‐surface enhancement of radioactives. Despite the simplicity of the models the persistence of a significant difference between heat generation and heat output for a wide range of parameter choices indicates that this difference is real and should be incorporated in geochemical modeling of the planets.