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

Abstract

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 65-85% 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 potas-51111:' 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. INTRODUCTIONAfter the discovery of radioactivity but before the widespread acceptance of mantle convection and plate tectonics, cooling of the earth was thought to contribute substantially to the geothermal heat fiux. Holmes [1916] attributed one quarter of the heat output to original heat, the rest being radiogenic, and Stichter [1941] stressed the large thermal inertia of the earth and the possibility of a large difference between heat generation and heat output.More recently, the acceptance of the idea that there are plate and mantle convective motions with time scales much less than the age of the earth has led to the view that there is essentially a steady state in which heat production and heat loss through the surface are almost balanced (Tozer, 1965;Turcotte and Oxburgh, 1972]. This assumption has been made in discussions of the thermal state of the moon [Runcorn, 1962] and in attempts to estimate the abundances of uranium, thorium, and potassium in the earth and moon [Langseth et a/., 1976].However, the 'steady state' assumption only implies that heat generated deep within the body can be transported to the surface in a time much smaller than the age of that body; it does not imply equality of heat generation and heat output. This can be demonstrated by the following contradiction. Suppose heat generation and heat output were always equal Since heat generation decreases with time because of the decay of...

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