Potassium Isotope Anomalies from Evaporative Mass Loss in Planetesimals

The terrestrial planets are depleted in moderately volatile elements (e.g., K and Zn) relative to chondritic material. This depletion could be due to incomplete condensation or evaporative loss, either in precursor material or in accreting bodies. Potassium isotopes may distinguish between these different processes as they correlate with body mass, the smaller bodies being isotopically lighter (Tian et al., 2021), implying evaporative loss from the fully-formed bodies. However, the correlation of isotopic fractionation with elemental concentration is weak, and evaporative loss from a body as large as the Earth is challenging. In this work, we investigate how K loss and isotopic fractionation proceed during planetary growth, using a quantitative model of evaporative loss and a N-body accretion model. We consider adiabatic conditions for mass flux and equilibrium at the melt-vapour interface with a temperature-dependent partition coefficient and a constant isotope fractionation factor ?=0.99913. First, we model mass loss as a consequence of heating events (e.g. impacts) by elevating temperatures, and find that mass loss does not occur for bodies exceeding roughly 1023 kg (~1.5 lunar masses). Second, we study the potential for K loss driven by 26Al heating. Contrasting with previous work (Young et al, 2019), we find that temperatures buffer near the solidus with negligible evaporative loss and thus negligible isotopic fractionation, because once liquid-supported convection initiates, cooling rates exceed 26Al heating rates. Additional, rapid heating by e.g. impacts is thus required for significant evaporative loss from planetesimals. In ongoing work, we track potassium loss and isotopic fractionation over the course of N-body simulations of the runway and oligarchic stages of accretion. Preliminary results show a rough inverse correlation between body mass and isotope anomaly, implying that the observed correlation (Tian et al., 2021) could be a result of early evaporative loss followed by accretion, as well as mixing and dilution after overall mass loss ceases.