The thermal evolution of rocky planets on geological timescales (Gyr) depends on the heat input from the long-lived radiogenic elements potassium, thorium, and uranium. Concentrations of the latter two in rocky planet mantles are likely to vary by up to an order of magnitude between different planetary systems because Th and U, like other heavy r-process elements, are produced by rare stellar processes. Here we discuss the effects of these variations on the thermal evolution of an Earth-size planet, using a 1D parameterized convection model. Assuming Th and U abundances consistent with geochemical models of the Bulk Silicate Earth based on chondritic meteorites, we find that Earth had just enough radiogenic heating to maintain a persistent dynamo. According to this model, Earth-like planets of stars with higher abundances of heavy r-process elements, indicated by the relative abundance of europium in their spectra, are likely to have lacked a dynamo for a significant fraction of their lifetimes, with potentially negative consequences for hosting a biosphere. Because the qualitative outcomes of our 1D model are strongly dependent on the treatment of viscosity, further investigations using fully 3D convection models are desirable.
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