Fig. 5: Rare earth element (REE) temperature systematics.

Temperatures inverted from plagioclase-glass REE distributions (Eqs. 16–19) are plotted against the log of the oxygen fugacity log(fO₂) recovered from Eqs. 7–19 in (a), molar Fe³⁺/(Fe²⁺+ Fe³⁺) in glass calculated using the model of Kress and Carmichael⁴⁷ in (b), plagioclase An# (100 × Ca/(Ca + Na + K), in moles) in (c), and deviation from the fayalite-magnetite-quartz buffer (Δ FMQ) at 0.4 GPa³⁴ in (d). Circles in the background of (c) are plagioclase-saturated experiments with oceanic basalt and basaltic andesite liquids downloaded from the LEPR database⁷⁷. Error bars for the temperatures are estimated from the uncertainty in the slope in the temperature inversions (Supplementary Figs. S5-S7); error bars for fO₂s are estimated 1σ uncertainties recovered from Monte Carlo simulations (see Methods and Supplementary Figs. S10–S12 for details).