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.

岩石行星在地质时标上的热演化（吉尔）取决于长期存在的放射性元素钾，th和铀的热量输入。后两者在岩石行星地幔中的浓度可能会在不同行星系统之间变化一个数量级，因为Th和U像其他沉重的r-过程元素，是由罕见的恒星过程产生的。在这里，我们使用一维参数化对流模型讨论这些变化对地球大小的行星的热演化的影响。假设Th和U的丰度与基于粒状陨石的大硅酸盐地球化学模型相符，我们发现地球仅具有足够的放射源加热来维持持续的发电机。根据这个模型，像地球一样的恒星具有更高的重r光谱中spectra的相对丰度表明该过程元素在其生命的相当大部分时间内都缺乏发电机，这对承载生物圈可能产生负面影响。由于我们的一维模型的定性结果在很大程度上取决于粘度的处理，因此需要使用完全3D对流模型进行进一步研究。