Whole Planet Cooling and the Radiogenic Heat Source Contents of the Earth and Moon

It is widely believed that the surface heat ftows 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 h~t st~te, but with a wide varlet~ of choices for the parameters characterizing the rheology and convective vtgor. All models are constramed to be consistent with present-day surface heat ftux~s, and many of the terrestrial models are consistent with the mantle viscosities indicated by postglaCial rebound. For the earth the acceptable models give a radiogenic heat production that is only 6585% o~the s~ace heat output, the ~erence being due to secular cooling of the earth (about 50°-l00°C ~r 10 years m the ~pper mantle). It IS argued that the actual heat generation may be substantially less, sm':l' t_he models omit core heat, upward migration of heat sources, possible layering of the mantle, and ~eVIations ~rom steady ~nvection. Geochemical models which are near to chondritic (apart from potas51111:'1 depletion) are marginally consistent with surface heat ftow. In the lunar models, heat generation is typ1cally only 70-80% of the surface heat ftow, 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 differ ence is real and should be incorporated in geochemical modeling of the planets.