Special Collection: Olivine: Rates and styles of planetary cooling on Earth, Moon, Mars, and Vesta, using new models for oxygen fugacity, ferric-ferrous ratios, olivine-liquid Fe-Mg exchange, and mantle potential temperature

Abstract Mantle potential temperatures (Tp) provide insights into mantle circulation and tests of whether Earth is the only planet to exhibit thermally bi-modal volcanism—a distinctive signature of modern plate tectonics. Planets that have a stagnant lid, for example, should exhibit volcanism that is uni-modal with Tp, since mantle plumes would have a monopoly on the genesis of volcanism. But new studies of magmatic ferric-ferrous ratios (XFe2O3liq/XFeOliq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$) (Cottrell and Kelley 2011) and the olivine-liquid Fe-Mg exchange coefficient, KD(Fe-Mg)Ol-liq (or KD) (Matzen et al. 2011) indicate that re-evaluations of Tp are needed. New tests and calibrations are thus presented for oxygen fugacity (fO2), XFe2O3liq/XFeOliq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$, potential temperature (Tp), melt fraction (F), KD, and peridotite enthalpies of fusion (∆Hfus) and heat capacities (CP). The new models for XFe2O3liq/XFeOliq$X_{{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}}^{{\text{liq}}}{\text{/}}X_{{\text{FeO}}}^{{\text{liq}}}$ and fO2 reduce error by 25–30%, and residual error for all models appears random; this last observation supports the common, but mostly untested, assumption that equilibrium is the most probable of states obtained by experiment, and perhaps in nature as well. Aggregate 1s error on Tp is as high as ~±77 °C, and estimates of F, and mantle olivine composition, are the greatest sources of error. Pressure and ∆Hfus account for smaller, but systematic uncertainties (a constant ∆Hfus can under-predict Texcess = Tpplume−Tpambient$T_{\text{p}}^{{\text{plume}}} - T_{\text{p}}^{{\text{ambient}}}$; assumptions of 1 atm can under-predict Tp). However, assumptions about whether parental magmas are incremental, accumulated, or isobaric batch melts induces no additional systematic error. The new models show that maximum Tp estimates on the oldest samples from Earth, Mars, Moon, and Vesta, decrease as planet size decreases. This may be expected since Tp should scale with accretion energy and reflect the Clausius-Clapeyron slope for the melting of silicates and Fe-Ni alloys. This outcome, however, occurs only if shergottites (from Mars) are 4.3 Ga (e.g., Bouvier et al. 2009; Werner et al. 2014), and the highest MgO komatiites from Earth’s Archean era (27–30% MgO; Green et al. 1975) are used to estimate Tp. With these assumptions, Earth and Mars exhibit monotonic cooling, and support for Stevenson’s (2003) idea that smaller planets cool at similar rates (~90–135 °C/Ga), but at lower absolute temperatures. Tp estimates for Mars and Earth are also important in two other ways: Mars exhibits non-linear cooling, with rates as high as 275–550 °C/Ga in its first 0.5 Ga, and Archean volcanism on Earth was thermally bi-modal. Several hundred Archean volcanic compositions are in equilibrium with Fo92–94 olivine, and yield Tp modes at 1940 and 1720 °C, possibly representing plume and ambient mantle, respectively. These estimates compare to modern Tp values of 1560–1670 °C at Mauna Loa (plume) and 1330–1450 °C at MORB (ambient). We conclude that plate tectonics was active in some manner in the Archean, and that assertions of an Archean “thermal catastrophe” are exaggerated. Our new models also show that the modern Hawaiian source, when compared at the same T, has a lower fO2 compared to MORB, which would discount a Hawaiian source rich in recycled pyroxenite.