The origin of the Moon and the single-impact hypothesis III

Abstract

In previous papers in this series the smoothed particle hydrodynamics method (SPH) has been used to explore the conditions in which a major planetary collision may have been responsible for the formation of the Moon. In Paper II (W. Benz, W.L. Slattery, and A.G.W. Cameron 1987, Icarus 71, 30–45) it was found that the optimum conditions were obtained when the mass ratio of the impactor to the protoearth was 0.136. In the present paper we investigate the importance of the equation of state by running this optimum case several times and varying the equation of state and other related parameters. The two equations of state compared are the Tillotson (used in the previous papers) and the CHART D/CSQ ANEOS. Because of differences in these equations of state, including the fact that different types of rocks were used in association with each, it was not possible to prepare initial planetary models that were comparable in every respect, so several different simulations were necessary in which different planetary parameters were matched between the equations of state. We also used a new version of the SPH code. The results reaffirmed the previous principal conclusions: the collisions produced a disk of rocky material in orbit, with most of the material derived from the impacting object. These results indicate that the equation of state is not a critical factor in determining the amount of material thrown into orbit. This confirms the conclusions of Paper II that gravitational torques, and not pressure gradients, inject the orbiting mass. However, the way this mass is distributed in orbit is affected by the equation of state and the choice of rock material, the Tillotson equation for granite giving a slightly larger mean orbital radius for the particles left in orbit than the ANEOS dunite for the same impact parameter. We also find, compared to Paper II, that in all subsequent cases the new SPH code leads to a slightly less extended prelunar accretion disk. We think this is due to the new shape adopted for the kernel. A few additional calculations were made to test the effects of increasing the impact parameter on the calculations, other parameters remaining unchanged. The motivation for this was that solar tides will have reduced the Earth-Moon angular momentum somewhat over the course of time. An increment of 6% in the angular momentum of the collision increases the amount of iron-free material in orbit and its mean orbital radius, but more than that leaves increasing amounts of iron in orbit (the iron has a small mean orbital radius). The debris from the destroyed impacting object tends to form a straight rotating bar which is very effective in transferring angular momentum. If the material near the end of the bar extends well beyond the Roche lobe, it may become unstable against gravitational clumping.