Support for NASA Lunar Science Institute – Year 2, 15-R8225
Principal Investigators
Robin M. Canup
J. Salmon
C. Visscher
Inclusive Dates: 10/01/11 – 10/01/12
Background — It is generally accepted the Earth's Moon accreted from a disk generated by the impact of a Mars-size object on the protoearth. However, predictions of existing models of the Moon's accumulation from such a disk are problematic because they (1) seem inconsistent with the likely state of disk material, (2) do not allow for compositional equilibration between the disk and the protoearth, which may be necessary, and (3) necessitate a fully molten Moon, potentially at odds with geological and geochemical constraints.
Approach — In Task 1, the project team is developing a more physically realistic model of the Moon's accretion after a giant impact. It was previously thought that the Moon's mantle was anhydrous. Recent water content estimates of lunar volcanic glasses, however, suggest that the Moon's mantle may contain up to several hundred parts-per-million water, comparable to the Earth's bulk water content (Saal et al. 2008). Numerical simulations of the giant impact predict disk temperatures of ˜ 2500 K to 5000 K, and imply tidal disruption of much of the disk material down to meter-sized droplets (Stewart 2000), which would lead to volatile degassing and potential water loss. At present it is not known to what extent a moon formed from an impact-generated disk can retain water. In Task 2, the project team is developing a model for water loss/retention from the protolunar disk.
Accomplishments — To better address the Moon's accretion, a hybrid numerical model was developed consisting of (1) a fluid disk to represent the material within the Roche limit (the distance below which accretion is prevented by tidal forces from the planet), and (2) an N-body code to track solid particles orbiting outside the Roche limit. The Roche-interior disk spreads due to its viscosity, and can deliver material beyond the Roche limit, where it can accrete to form new moonlets. For the disk's viscosity, either an instability-driven viscosity (Ward and Cameron 1978) or a radiation-limited viscosity (Thompson and Stevenson 1988) is used, depending on the disk's properties. Collisions between orbiting particles are treated using the tidal accretion criteria of Canup and Esposito (1995). They also interact with the fluid disk at Lindblad resonances. Finally, the project team included the possibility of bodies scattered toward the planet and crossing the fluid disk to be captured. If such a capture happens, it is assumed that the body is tidally disrupted, and its mass and angular momentum are added to the fluid disk. This results in a three-step accretion process: (1) outer bodies rapidly collide and accrete, until only a few massive bodies remains, then (2) these massive bodies confine the inner disk within the Roche limit due to resonant interactions, and they in turn recede away, and (3) the fluid disk spreads back out to the Roche limit, new moonlets are spawned and collide with outer object to form the final Moon. Contrary to accretion timescales of a few months with prior pure N-body simulations, the slow spreading of the fluid disk leads to accretion timescales of hundreds of years in the SwRI model, which is comparable to the timescales necessary for the disk's composition to equilibrate with that of the Earth. These results have been accepted for publication in the Astrophysical Journal (Salmon and Canup, "Lunar Accretion from a Roche-interior Fluid Disk," 2012).
A modified version of a melt-vapor equilibrium code (MAGMA; Fegley and Cameron 1987) was used to determine the total vapor pressure and chemical speciation in the vapor phase for a number of different potential disk compositions, including bulk silicate Earth-Moon (BSEM), present-day Moon as inferred from lunar samples, and various meteorite classes. The BSEM composition has been adopted as a nominal initial composition and plausibly represents the silicate composition of the Earth-Moon system shortly after the giant impact (e.g., higher initial Na and K contents than in the present-day Moon because of subsequent escape of volatiles). The model results have also been used to calculate oxygen fugacity of the silicate vapor — a key parameter that influences the overall chemical behavior of the disk. Preliminary results suggest a highly oxidizing vapor phase dominated by Na, O, O2, and SiO, which is largely independent of the adopted bulk composition. Assuming equilibrium between melt and vapor phases, the oxygen fugacity can be used to calculate the H2O/H2 in the gas phase, via the equilibrium reaction H2 + 0.5O2 = H2O (cf. Elkins-Tanton & Grove 2011). Results of this calculation are shown in the illustration. The resulting H2O/H2 ratios will be used to estimate the expected escape rates of water vapor from the protolunar disk.
