Catastrophic Impacts on Gravity Dominated Asteroids

Abstract

We use the smoothed particle hydrodynamics method to simulate catastrophic collisions on silicate bodies whose impact response is dominated by gravity rather than material strength. Encounter speeds of 3, 5, and 7 km sec−1, impact angles of 15°, 45°, and 75°, and target diameters of 10 to 1000 km are investigated. The projectile and target materials are modelled using the Tillotson equation of state for granite. Our model treats gravity rigorously, but neglects strength and fracture effects. We calculate the initial hydrodynamic phase of each event; after the impact shock wave crosses the target, particle motions are nearly ballistic and can be treated analytically. Material that does not escape may reaccrete ∼1 hr to ∼1 yr after the impact. The partitioning of impact energy into heat and motion of projectile and target material favors kinetic energy at higher speeds and larger projectile:target diameter ratios, but does not depend on the absolute size scale of the event. After the impact, most of the kinetic energy is carried by a small amount of fast ejecta. Particle velocity distributions are not sensitive to size scale and have complex, evolving shapes that are poorly represented by simple approximations. The catastrophic threshold (impact energy per unit target mass required to permanently eject 50% of the target against gravity) ranges from 8 × 103J kg−1at 10 km diameter to 1.5 × 106J kg−1at 1000 km, varying as target diameter to the 1.13 ± 0.01 power. Extrapolating these results suggests that gravity dominance extends to stony bodies as small 250 ± 150 m in diameter, smaller than previously believed. This result implies that asteroids as small as a few hundred meters across may be “rubble piles.” Nearly catastrophic impacts can exhume target core material and catapult surface rocks to the antipodes (“scrambling” the target), but selective removal of the outer layers is inefficient. Most material strongly heated in these impacts escapes, limiting globally averaged heating from a single collision to ≤50°C for asteroids ≤1000 km in diameter.