Magma ocean formation due to giant impacts

Current understanding of the last stages of planetary accretion suggests that mass and energy accumulation are dominated by a few large impacts. An important thermal consequence of such impacts is melting and formation of a large melt pond. If the planet's isostatic adjustment time scale is short compared to the magma pond's cooling time scale, the melt may be extruded onto the surface and form a magma ocean of approximately uniform depth. Although a giant impact striking at 10-15 km s^-1 deposits enough energy to melt the entire planet, the distribution of that energy is important in determining the thermal outcome of the collision. We examine the thermal effects of giant impacts by estimating the melt volume generated by the initial shock wave and corresponding magma ocean depths. Additionally, we examine the effects of the planet's initial temperature on the generated melt volume. The Hugoniot curve plotted in pressure-entropy space is used to determine the shock pressure required to completely melt the material. For room temperature dunite, this pressure is about 150 GPa and the partial melt region is narrow. For dunite initially at the solidus temperature, this pressure is about 115 GPa.

The partial melt region extends throughout the planet. Once the melting pressure is known, an impact melting model based on the second Hugoniot equation, the linear shock-particle velocity relationship, and the empirical particle velocity-distance relationship is used to estimate the radial distance melting occurred from the impact site. Once the distance is found, the melt region's geometry determines the associated melt volume. Partial melt volume is also estimated. The melt fraction that is not excavated during crater formation is estimated and magma ocean depths resulting from both excavated and retained melt are calculated. The model is also used to estimate the fraction of a planet melted by the initial shock wave. Nominal conditions of the Moon-forming giant impact (projectile/planet mass=0.14, impact speed=15 km s^-1) generate melting of 30-65% of the planet depending on its initial temperature. Whole planet melting requires projectile/planet mass ratios of <0.4 for a 15 km s^-1 impact if the planet was near its solidus before the impact. Isostatic relaxation may generate a significant volume of additional melting.