Investigation of the initial state of the Moon-forming disk: Bridging SPH simulations and hydrostatic models

Abstract

According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto-Earth and a Mars-sized impactor. The initial structure of the disk significantly affects the Moon-forming process, including the Moon's mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon-forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here, we show the extent to which the properties of the disk can be inferred from Smoothed Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and mass distributions of the SPH outputs as approximately conserved quantities, we compute the two-dimensional disk structure. We investigate four different models: (a) standard, the canonical giant impact model, (b) fast-spinning Earth, a collision between a fastspinning Earth and a small impactor, (c) sub-Earths, a collision between two objects with half Earth's mass, and (d) intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH calculations show that the initial disk has approximately uniform entropy. This is because the materials of different angular momenta are shocked to similar extents. The disks of the fast-spinning Earth and sub-Earths cases are hotter and more vaporized (∼ 80-90% vapor) than the standard case (∼20%). The intermediate case falls between these values. In the highly vaporized cases, our procedure fails to establish a unique surface density profile of the disk because the disk is unstable according to the Rayleigh criterion (the need for a monotonically increasing specific angular momentum with radius). In these cases, we estimate non-unique disk models by conserving global quantities (mass and total angular momentum). We also develop a semi-analytic model for the thermal structure of the disk, including the radial temperature structure and the vapor mass fraction. The model requires only two inputs: the average entropy and the surface density of the disk.

Water in the Moon's interior: Truth and consequences

“…than a bulk silicate Earth composition. Furthermore, we consider it likely that any ejected atmosphere will be pushed out to large distances from the Earth, ahead of the expanding proto-lunar disk as the molten ejecta from the giant impact expands in an attempt to reach hydrostatic equilibrium (Thompson and Stevenson, 1988;Pahlevan and Stevenson, 2007;Nakajima and Stevenson, 2014a).…”

“…Importantly, the rain-out of silicate droplets will lead to formation of a magma disk in a planar geometry around the midplane, while the vapor phase of the disk is predicted to expand in a nearly spherical geometry enveloping both the Earth and the disk (Genda and Abe, 2003b;Pahlevan and Stevenson, 2007;Nakajima and Stevenson, 2014a). At the edges of the disk when silicate begins to condense, the vapor phase is expected to contain roughly equal molar proportions of O 2 , Na and Zn (Visscher and Fegley, 2013) and equal molar amounts of F and H 2 , assuming BSE proportions of volatile elements.…”

“…Consider the full magma disk itself; consisting of 2 lunar masses, spread out to a distance of 5 Earth radii, it will have an average condensed (vapor-free) thickness of only 160 km; at high silicate vapor mass fractions associated with very energetic giant impacts, the magma disk may be only tens of kilometers thick (Nakajima and Stevenson, 2014a). Under such conditions, the atmospheric escape problem reduces to that of a gas envelope surrounding the Earth (Zahnle et al, 1988;Genda and Abe, 2003b), and at the outer regions of the disk beyond the Roche radius where proto-Moons can coalesce, the vapor pressure could be sufficiently low as to result in the condensation of very little of the gas cloud surrounding the Earth.…”

Magmatic volatiles (H, C, N, F, S, Cl) in the lunar mantle, crust, and regolith: Abundances, distributions, processes, and reservoirs

“…However, there remains uncertainty over the mechanisms for retaining hydrogen in a vapor-silicate disk, including the role and effects of hydrodynamic escape on volatiles such as H (Pahlevan and Stevenson 2007). Recent modeling studies seem to indicate limited hydrodynamic escape of H 2 /H 2 O in oxidized vapor-silicate disk as long as the vapor phase is dominated by silicate Nakajima and Stevenson 2014;Visscher and Fegley 2013). However, the limited timescales of the proto-lunar disk (hundreds of years) likely prohibits the accretion of sufficient H 2 O-rich materials to explain estimates for the H 2 O content of the bulk silicate Moon .…”

Coordinated Hard Sphere Mixture (CHaSM): A simplified model for oxide and silicate melts at mantle pressures and temperatures

“…Giant impact simulations indicate that events like the moon-forming impact efficiently deliver heat to great depths, supporting the possibility of a deep potentially whole-mantle magma ocean early in Earth's history (Nakajima and Stevenson, 2014). The evolution of this planetary-scale magma ocean as it cools and crystallizes is dominated by the poorly understood behavior of silicates at extreme pressures and temperatures.…”