Abstract
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.
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