Paper detail

Investigation of the Initial State of the Moon-Forming Disk: Bridging SPH Simulations and Hydrostatic Models

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 Moons 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 fast spinning Earth and a small impactor, (c) sub Earths, a collision between two objects with half Earths 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. 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. In these cases, we estimate non-unique disk models by conserving global quantities. We also develop a semi analytic model for the thermal structure of the disk, which requires only two inputs: the average entropy and the surface density of the disk.