Impact-induced energy partitioning, melting, and vaporization on terrestrial planets

Hypervelocity flows produced by impact of iron and gabbroic anorthosite objects onto a half-space of gabbroic anorthosite at speeds of 5-45 km/ sec are considered in detail in terms of the following processes, or regimes: penetration, cavitation, and excavation. The flows are computed using Eulerian finite-difference methods which take into account the major phase changes and thermodynamic properties of silicates and iron at high pressure, and rheological properties at the stress levels at which dynamic yielding occurs. For iron (Fe) and gabbroic anorthosite (An) impactors most of the kinetic energy of the meteoroid is converted into internal energy residing in the planetary surf ace material. The fraction of meteoroid kinetic energy transformed into internal energy ranges from 0.70 at 5 km/sec to 0.85 at 30 km/sec for an An → An impact, and 0.74-0.91 at these same speeds for an Fe → An impact. At low velocities (for both cases) much of the internal energy (approximately 0.5 at 5 km/sec) is produced by the plastic work resulting from a finite yield strength of the rock whereas the balance of the internal energy results largely from shock heating. The relative fraction of the impact energy residing in the kinetic energy of the planetary surface ranges from 0.1 to 0.07 for the An → An impacts and 0.09-0.07 for the Fe → An impacts. Most of this energy resides in the ejecta. Our results imply that the energy consumed by plastic work in strong rocks is available for conversion to kinetic energy in weak rocks and thus can increase the amount of ejecta for impact into weak rocks and unconsolidated regoliths. The degree of melting and vaporization produced by impact was calculated by constructing the isentropes, passing through the energy and volume states at 1 atm pressure, that correspond to incipient and complete melting and vaporization. The amount of melt for an An → An impact ranged from approximately 1.5 times the meteoroid volume at 7.5 km/sec to 102 times the meteoroid volume at 45 km/sec; for an Fe → An impact the volume ranged from approximately 5 times the meteoroid volume at 7.5 km/sec to over 250 times the meteoroid volume at 45 km/sec. The use of a similarity variable (which is related to the physical properties of both the projectile and target) allows the relative volumes of melt and the condensed volumes of vaporized materials to be plotted on a single curve. For high impact velocities the relative masses of melted and vaporized material are found to be proportional to impactor kinetic energy and the mass of impact melt exceeds the mass of vaporized material by a factor of 6. From the observed dependence of crater diameter, D, on impact energy and planetary surface gravity we infer the volume of melt relative to the volume of the crater would increase with crater diameter at least as rapidly as D^(0.55). This predicted relative increase in melting with crater diameter is observed in terrestrial and inferred to occur in lunar craters. The results also predict that the amount of melt for a given crater diameter is greater for planets that have higher values of surface gravity. This implies that more melt will be observed in large terrestrial craters than similar-sized lunar craters.