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

Mantle potential temperatures ( T p ) 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 T p , since mantle plumes would have a monopoly on the genesis of volcanism. But new studies of magmatic ferric-ferrous ratios ( X liq Fe2O3 / X liq FeO ) (Cottrell and Kelley 2011) and the olivine-liquid Fe-Mg exchange coefficient, K D (Fe-Mg) Ol-liq (or K D ) (Matzen et al. 2011) indicate that re-evaluations of T p are needed. New tests and calibrations are thus presented for oxygen fugacity ( f O 2 ), X liq Fe 2 O 3 / X liq FeO , potential temperature ( T p ), melt fraction ( F ), K D , and peridotite enthalpies of fusion (Δ H fus ) and heat capacities ( C P ). The new models for X liq Fe 2 O 3 / X liq FeO and f O 2 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 1σ error on T p is as high as ~±77 oC, and estimates of F , and mantle olivine composition, are the greatest sources of error. Pressure and Δ H fus account for smaller, but systematic uncertainties (a constant Δ H fus can under-predict T excess = T p plume – T p ambient ; assumptions of 1 atm can under-predict T p ). However, assumptions about whether parental magmas are incremental, accumulated, or isobaric batch melts induces no additional systematic error. The new models show that maximum T p estimates on the oldest samples from Earth, Mars, Moon, and Vesta, decrease as planet size decreases. This may be expected since T p 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 T p . 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 oC/Ga), but at lower absolute temperatures. T p estimates for Mars and Earth are also important in two other ways: Mars exhibits non-linear cooling, with rates as high as 275–550 oC/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 T p modes at 1940 and 1720 oC, possibly representing plume and ambient mantle, respectively. These estimates compare to modern T p values of 1560–1670 oC at Mauna Loa (plume) and 1330–1450 oC 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 f O 2 compared to MORB, which would discount a Hawaiian source rich in recycled pyroxenite.