  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.
