Impact-induced melting of planetary surfaces

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Abstract
The objective of this paper is to determine the thickness of the melt layer relative to the crater diameter for simple and complex craters. A numerical code was employed to calculate the amount of melting and the crater geometry. We used the code results and the scaling formalism of Holsapple and Schmidt (1987) to determine the scaling laws for the relative melt layer thickness. Simple crater dimensions are dominated by impact parameters and the planet’s strength, whereas complex crater dimensions are dominated by planetary gravity, strength, and the impact parameters. The volume of melt is proportional to impact energy for impact velocities and melt enthalpies of interest to planetary science. Crater geometry and dimensions scale with an exponent, μ, which is intermediate between momentum (μ = 1/3) and energy (μ = 2/3) scaling. For simple craters, the melt layer thickness/crater diameter, T/D, for a given planetary surface (constant melt enthalpy and mean impact velocity), is independent of the crater size. For complex craters, T/D, for a given planetary surface (constant melt enthalpy, impact velocity, and gravitational acceleration), increases with the size of the crater. For simple craters, at a fixed size, the relative melt layer thickness, T/D, increases slowly with increasing impact velocity, U, according to ∝ U 0.1), whereas, for complex craters (∝ U 0.22).

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