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/QD), where Q ∗ D are the size-dependent catastrophic disruption criteria (the Q required to disperse half the target mass). Here, we calculate QD 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 QD 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-totarget 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 0.5μV 2 i /Mtot (μ is the reduced mass and Vi is the impact velocity), and QRD is the QR required to disperse half the combined mass. We derive a universal law for the largest remnant, Mlr/Mtot = −0.5(QR/QRD − 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).