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Abstract It is generally accepted that the Moon accreted from the disk formed by an impact between the proto-Earth and impactor, but its details are highly debated. Some models suggest that a Mars-sized impactor formed a silicate melt-rich (vapor-poor) disk around Earth, whereas other models suggest that a highly energetic impact produced a silicate vapor-rich disk. Such a vapor-rich disk, however, may not be suitable for the Moon formation, because moonlets, building blocks of the Moon, of 100 m–100 km in radius may experience strong gas drag and fall onto Earth on a short timescale, failing to grow further. This problem may be avoided if large moonlets (≫100 km) form very quickly by streaming instability, which is a process to concentrate particles enough to cause gravitational collapse and rapid formation of planetesimals or moonlets. Here, we investigate the effect of the streaming instability in the Moon-forming disk for the first time and find that this instability can quickly form ∼100 km-sized moonlets. However, these moonlets are not large enough to avoid strong drag, and they still fall onto Earth quickly. This suggests that the vapor-rich disks may not form the large Moon, and therefore the models that produce vapor-poor disks are supported. This result is applicable to general impact-induced moon-forming disks, supporting the previous suggestion that small planets (<1.6R_⊕) are good candidates to host large moons because their impact-induced disks would likely be vapor-poor. We find a limited role of streaming instability in satellite formation in an impact-induced disk, whereas it plays a key role during planet formation. 

Abstract The amount of vapor in the impact-generated protolunar disk carries implications for the dynamics, devolatilization, and moderately volatile element isotope fractionation during lunar formation. The equation of state (EoS) used in simulations of the giant impact is required to calculate the vapor mass fraction (VMF) of the modeled protolunar disk. Recently, a new version of M-ANEOS (Stewart M-ANEOS) was released with an improved treatment of heat capacity and expanded experimental Hugoniot. Here, we compare this new M-ANEOS version with a previous version (N-SPH M-ANEOS) and assess the resulting differences in smoothed particle hydrodynamics (SPH) simulations. We find that Stewart M-ANEOS results in cooler disks with smaller values of VMF and in differences in disk mass that are dependent on the initial impact angle. We also assess the implications of the minimum “cutoff” density (ρ_c), similar to a maximum smoothing length, that is set as a fast-computing alternative to an iteratively calculated smoothing length. We find that the low particle resolution of the disk typically results in >40% of disk particles falling toρ_c, influencing the dynamical evolution and VMF of the disk. Our results show that the choice of EoS,ρ_c, and particle resolution can cause the VMF and disk mass to vary by tens of percent. Moreover, small values ofρ_cproduce disks that are prone to numerical instability and artificial shocks. We recommend that future giant impact SPH studies review smoothing methods and ensure the thermodynamic stability of the disk over simulated time. 

Key Points The shock physics code iSALE is successfully benchmarked against subsonic water impact experiments A scaling law is proposed for the crater depth as a function of the Mach and Froude numbers which are varied as independent parameters In the limit of high Mach numbers, our scaling suggests that the maximum crater depth is controlled by the sound velocity and gravity, but not by the impact speed