A radiogenic heating evolution model for cosmochemically Earth-like exoplanets

Discoveries of rocky worlds around other stars have inspired diverse geophysical models of their plausible structures and tectonic regimes. Severe limitations of observable properties require many inexact assumptions about key geophysical characteristics of these planets. We present the output of an analytical galactic chemical evolution (GCE) model that quantitatively constrains one of those key properties: radiogenic heating. Earth's radiogenic heat generation has evolved since its formation, and the same will apply to exoplanets. We have fit simulations of the chemical evolution of the interstellar medium in the solar annulus to the chemistry of our Solar System at the time of its formation and then applied the carbonaceous chondrite/Earth's mantle ratio to determine the chemical composition of what we term "cosmochemically Earth-like" exoplanets. Through this approach, predictions of exoplanet radiogenic heat productions as a function of age have been derived. The results show that the later a planet forms in galactic history, the less radiogenic heat it begins with; however, due to radioactive decay, today, old planets have lower heat outputs per unit mass than newly formed worlds. The long half-life of 232Th allows it to continue providing a small amount of heat in even the most ancient planets, while 40K dominates heating in young worlds. Through constraining the age-dependent heat production in exoplanets, we can infer that younger, hotter rocky planets are more likely to be geologically active and therefore able to sustain the crustal recycling (e.g. plate tectonics) that may be a requirement for long-term biosphere habitability. In the search for Earth-like planets, the focus should be made on stars within a billion years or so of the Sun's age