A scaling relationship for impact-induced melt volume

During the late stages of planetary accretion, protoplanets experience a number of giant impacts and extensive mantle melting. The impactor's core sinks through the molten part of the target mantle (magma ocean) and experiences metal-silicate partitioning (e.g., Stevenson, 1990). For understanding the chemical evolution of the planetary mantle and core, we need to determine the impact-induced melt volume because the partitioning strongly depends on the ranges of the pressures and temperatures within the magma ocean. Previous studies have investigated the effects of small impacts (i.e. impact cratering) on melt volume, but those for giant impacts are not well understood yet. Here, we perform giant impact simulations to derive a scaling law for melt volume as a function of impact velocity, impact angle, and impactor-to-target mass ratio. We use two different numerical codes, namely smoothed particle hydrodynamics we developed (SPH, a particle method) and the code iSALE (a grid-based method) to compare their outcomes. Our simulations show that these two codes generally agree as long as the same equation of state is used. We also find that some of the previous studies developed for small impacts (e.g., Abramov et al., 2012) overestimate giant impact melt volume by orders of magnitudes partly because these models do not consider self-gravity of the impacting bodies. Therefore, these models may not be extrapolated to large impacts. Our simulations also show that melt volume can be scaled by the total mass of the system. In this presentation, we further discuss geochemical implications for giant impacts on planets, including Earth and Mars.