VELOCITY-DEPENDENT CATASTROPHIC DISRUPTION CRITERIA FOR PLANETESIMALS

The resistance of planetesimals to collisional erosion changes dramatically during planet formation. The transition between accretion and erosion from a collision is defined by the relationship between the mass of the largest remnant (M(lr)) and the normalized specific impact energy (Q/Q(D)*), where Q(D)* are the size-dependent catastrophic disruption criteria (the Q required to disperse half the target mass). Here, we calculate Q(D)* for gravitationally bound aggregates subject to low-velocity collisions (1-300 m s(-1)) and compare the results to previous work at high velocities. We find that Q(D)* varies by orders of magnitude depending on the impact velocity and material properties. We define new variables to describe catastrophic disruption that remove ambiguities (over material density and projectile-to-target mass ratio) that are inherent in the traditional variables (Q and target radius): R(C1) is the spherical radius of the combined projectile and target masses (M(tot)) at a density of 1 g cm(-3), Q(R) is 0.5 mu V(i)(2)/M(tot) (mu is the reduced mass and V(i) is the impact velocity), and Q(RD)* is the Q(R) required to disperse half the combined mass. We derive a universal law for the largest remnant, M(lr)/M(tot) = -0.5(Q(R)/Q(RD)*-1) + 0.5, and velocity-dependent catastrophic disruption criteria for strong and weak planetesimals for use in numerical studies of planet formation. Weak aggregate bodies are easily disrupted due to efficient momentum coupling during low-velocity collisions. Collisional growth of planetesimals requires a dynamically cold environment; alternatively, a noncollisional mechanism is required to form planetesimals large enough to be resistant to collisional disruption (several tens of kilometers).