Simulations of the lunar-forming impact using a new equation of state

Sammanfattning: In this thesis we add a temperature dependence to the newly developed variable polytrope equation of state (Varpoly EOS) from Weppner et al. (2015), making it more universal and more applicable for planetary simulations. In this process we develop a new model for the Gruneisen parameter, which is a parameter that describes how pressure changes with the internal energy. This new model conforms to theoretical infinite pressure values, which other models often fail to do. We also show that this new model fits well with high pressure melting data of hexagonal close packaged iron and to an experimental density model of the Earth (Dziewonski and Anderson, 1981). The giant-impact models are the closest to capturing all the properties of the Earth-Moon system. However most of the models have a problem in recreating the isotopic and FeO deviation that we see between the Earth and the Moon. The similarity in isotopic compositions requires that the disk is composed of the same fraction of proto-Earth material as the Earth; while to explain the FeO deviation we require more material from the impactor in the resulting disk. Karato (2014) suggested that this is a problem with modeling planets with just one homogeneous silicate layer and that the compositional difference between the Earth and the Moon could be explained if Earth had a primordial magma ocean. During the collision the magma would have been asymmetrically heated and ended up enriching the orbiting debris, that eventually coalesced into the Moon. To verify the need of an additional enrichment source, we show from a compositional analysis that FeO/MgO ratio’s are inconsistent with a single homogeneous silicate layer and that additional enrichment of FeO in the disk is required. Using our new EOS we present simulations done on the lunar-forming impact, investigating the effect of a primordial magma ocean. This is investigated using the impact parameters of both the ’canonical’ case (Benz et al., 1989; Canup and Asphaug,2001) in which a Mars-sized impactor hit a non-rotating Earth at an oblate angle and the fast-rotating case (Cuk and Stewart, 2012), in which a half-sized Mars impactor hit a fast spinning Earth head on. We find that the magma ocean results in little to no different in the resulting Moon and we conclude that the ’canonical’ case best captures the dynamical aspect (final masses,spin and angular momentum) of the current Earth-Moon system. We find that the fast-spinning case is unable to form the Moon with our models. We also investigate the effect that an icy Theia would have on the lunar-forming collision, we find that this reduces the probability of a successful Moon forming collision. The simulations are done with the VINE smoothed particle hydrodynamics program (Wetzstein et al., 2009). Aside from this we also perform an analysis on the effect that the different artificial viscosity prescriptions in SPH have on the Moon-forming impacts.