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 (Mlr) 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): RC1 is the spherical radius of the combined projectile and target masses (Mtot) at a density of 1 g cm−3, QR is 0.5μV2i/Mtot (μ is the reduced mass and Vi is the impact velocity), and Q*RD is the QR required to disperse half the combined mass. We derive a universal law for the largest remnant, Mlr/Mtot = −0.5(QR/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).