First, the amount of internal heat production in the mantle is determined by the concentration of radioactive isotopes, such as 238U and 232Th, and geochemical estimates on the composition of the primitive mantle ( 8, 9), after correcting for continental crust, suggest that internal heat production in the convecting mantle accounts for only ~10 to 30% of convective heat loss ( 10, 11). However, despite its prevailing popularity, the actual efficacy of self-regulated mantle convection is debatable, at least for the case of Earth, which is undoubtedly the best understood terrestrial planet.
Whether a planet had a hot or cold start, its subsequent evolution would quickly adjust its internal temperature so that the vigor of mantle convection is adequate for the amount of heat provided by radioactive decay. One important corollary of self-regulation is that the thermal evolution of a planet becomes virtually insensitive to its initial condition. An approximate version of self-regulating mantle convection has since been regarded as the standard theory for the thermal evolution of Earth and other terrestrial planets ( 5– 7). ( 3), but their theoretical modeling of Earth’s thermal evolution, along with a similar study by Davies ( 4), still indicated that the surface heat flux should follow closely with the temporal variation of internal heat generation. The validity of “exact” thermal equilibrium was later questioned by Schubert et al. Tozer ( 2) was the first to quantify the thermal adjustment time scale using temperature-dependent viscosity, and his estimate of ~200 million years to achieve self-regulation was deemed sufficiently short. The thermal adjustment time scale becomes shorter as the sensitivity of heat flux to temperature change increases, and the sensitivity can be quite high if one considers the temperature dependency of mantle viscosity.
Because radiogenic heat production decreases steadily with time, the convecting mantle must be able to adjust its internal temperature sufficiently quickly. Conversely, if heat flux is lower than heat production, the planet heats up to enhance the vigor of convection until the balance is achieved between surface heat loss and internal heat production. If the surface heat flux of a planet is higher than its internal heat production, the planet cools down, lowering the vigor of convection and thus heat flux. The possibility of self-regulating mantle convection arises from the following negative feedback, which was originally suggested to H.
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