Formation and accretion history of terrestrial planets from runaway growth through to late time: implications for orbital eccentricity

Remnant planetesimals might have played an important role in reducing the orbital eccentricities of the terrestrial planets after their formation via giant impacts. However, the population and the size distribution of remnant planetesimals during and after the giant impact stage are unknown, because simulations of planetary accretion in the runaway growth and giant impact stages have been conducted independently. Here we report results of direct N-body simulations of the formation of terrestrial planets beginning with a compact planetesimal disk. The initial planetesimal disk has a total mass and angular momentum as observed for the terrestrial planets, and we vary the width (0.3 and 0.5AU) and the number of planetesimals (1000-5000). This initial configuration generally gives rise to three final planets of similar size, and sometimes a fourth small planet forms near the location of Mars. Since a sufficient number of planetesimals remains, even after the giant impact phase, the final orbital eccentricities are as small as those of the Earth and Venus.Comment: 36 pages, 9 figures, 1 table, Accepted in Ap

Melting of carbonated pelites at 8-13GPa: generating K-rich carbonatites for mantle metasomatism

The melting behaviour of three carbonated pelites containing 0-1wt% water was studied at 8 and 13GPa, 900-1,850°C to define conditions of melting, melt compositions and melting reactions. At 8GPa, the fluid-absent and dry carbonated pelite solidi locate at 950 and 1,075°C, respectively; >100°C lower than in carbonated basalts and 150-300°C lower than the mantle adiabat. From 8 to 13GPa, the fluid-present and dry solidi temperatures then increase to 1,150 and 1,325°C for the 1.1wt% H2O and the dry composition, respectively. The melting behaviour in the 1.1wt% H2O composition changes from fluid-absent at 8GPa to fluid-present at 13GPa with the pressure breakdown of phengite and the absence of other hydrous minerals. Melting reactions are controlled by carbonates, and the potassium and hydrous phases present in the subsolidus. The first melts, which composition has been determined by reverse sandwich experiments, are potassium-rich Ca-Fe-Mg-carbonatites, with extreme K2O/Na2O wt ratios of up to 42 at 8GPa. Na is compatible in clinopyroxene with $$D_{\text{Na}}^{{{\text{cpx}}/{\text{carbonatite}}}} = 10{-}18$$ at the solidus at 8GPa. The melt K2O/Na2O slightly decreases with increasing temperature and degree of melting but strongly decreases from 8 to 13GPa when K-hollandite extends its stability field to 200°C above the solidus. The compositional array of the sediment-derived carbonatites is congruent with alkali- and CO2-rich melt or fluid inclusions found in diamonds. The fluid-absent melting of carbonated pelites at 8GPa contrasts that at ≤5GPa where silicate melts form at lower temperatures than carbonatites. Comparison of our melting temperatures with typical subduction and mantle geotherms shows that melting of carbonated pelites to 400-km depth is only feasible for extremely hot subduction. Nevertheless, melting may occur when subduction slows down or stops and thermal relaxation sets in. Our experiments show that CO2-metasomatism originating from subducted crust is intimately linked with K-metasomatism at depth of >200km. As long as the mantle remains adiabatic, low-viscosity carbonatites will rise into the mantle and percolate upwards. In cold subcontinental lithospheric mantle keels, the potassic Ca-Fe-Mg-carbonatites may freeze when reacting with the surrounding mantle leading to potassium-, carbonate/diamond- and incompatible element enriched metasomatized zones, which are most likely at the origin of ultrapotassic magmas such as group II kimberlite

Solid solution behaviour of CaSiO3 and MgSiO3 perovskites

Using density functional simulations within the generalized gradient approximation and projector-augmented wave method together with thermodynamic modelling, the reciprocal solubilities of MgSiO3 and CaSiO3 perovskites were calculated for pressures and temperatures of the Earth's lower mantle from 25 to 100GPa and 0 to 6,000K, respectively. The solubility of Ca in MgSiO3 at conditions along a mantle adiabat is found to be less than 0.02 atoms per formula unit. The solubility of Mg in CaSiO3 is even lower, and most important, the extent of solid solution decreases with pressure. To dissolve CaSiO3 perovskite completely in MgSiO3 perovskite, a solubility of 7.8 or 2.3mol% would be necessary for a fertile pyrolytic or depleted harzburgitic mantle, respectively. Thus, for any reasonable geotherm, two separate perovskites will be present in fertile mantle, suggesting that Ca-perovskite will be residual to low degree melting throughout the entire mantle. At the solidus, CaSiO3 perovskite might completely dissolve in MgSiO3 perovskite only in a depleted mantle with <1.25 wt% CaO. These implications may be modified if Ca solubility in MgSiO3 is increased by other major mantle constituents such as Fe and A

The Melting of Carbonated Pelites from 70 to 700 km Depth

Phase assemblages, melting relations and melt compositions of a dry carbonated pelite (DG2) and a carbonated pelite with 1·1 wt % H2O (AM) have been experimentally investigated at 5·5-23·5 GPa and 1070-1550°C. The subsolidus mineralogies to 16 GPa contain garnet, clinopyroxene, coesite or stishovite, kyanite or corundum, phengite or potassium feldspar (≤8 GPa with and without H2O, respectively), and then K-hollandite, a Ti phase and ferroan dolomite/Mg-calcite or aragonite + ferroan magnesite at higher pressures. The breakdown of clinopyroxene at >16 GPa causes Na-rich Ca-carbonate containing up to 11 wt % Na2O to replace aragonite and leads to the formation of an Na-rich CO2 fluid. Further pressure increase leads to typical Transition Zone minerals such as the CAS phase and one or two perovskites, which completely substitute garnet at the highest investigated pressure (23·5 GPa). Melting at 5·5-23·5 GPa yields alkali-rich magnesio-dolomitic (DG2) to ferro-dolomitic (AM) carbonate melts at temperatures 200-350°C below the mantle geotherm, lower than for any other studied natural composition. Melting reactions are controlled by carbonates and alkali-hosting phases: to 16 GPa clinopyroxene remains residual, Na is compatible and the magnesio- to ferro-dolomitic carbonate melts have extremely high K2O/Na2O ratios. K2O/Na2O weight ratios decrease from 26-41 at 8 GPa to 1·2 at 16 GPa when K-hollandite expands its stability field with increasing pressure. At >16 GPa, Na is repartitioned between several phases, and again becomes incompatible as at <3 GPa, leading to Na-rich carbonate melts with K2O/Na2O ratios 1. This leaves the pressure interval of c. 4-15 GPa for ultrapotassic metasomatism. Comparison of the solidus with typical subducting slab-surface temperatures yields two distinct depths of probable carbonated pelite melting: at 6-9 GPa where the solidus has a negative Clapeyron slope between the intersection of the silicate and carbonate melting reactions at ∼5 GPa, and the phengite or potassium feldspar stability limit at ∼9 GPa. The second opportunity is related to possible slab deflection along the 660 km discontinuity, leading to thermal relaxation and partial melting of the fertile carbonated pelites, thus recycling sedimentary CO2, alkalis and other lithophile and strongly incompatible elements back into the mantl

A single ion as a shot noise limited magnetic field gradient probe

It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of \Delta B/B_0 ~ 5*10^{-7} over a test distance of 140 \micro m, which can be extended to the mm range, still with sub \micro m resolution. A fast experimental sequence is presented, facilitating its use as a magnetic field gradient calibration routine, and it is demonstrated that the main limitation is the quantum shot noise.Comment: 5 pages, 3 figure