Collisional Disruption of Gravity Dominated Bodies: New Data and Scaling

Abstract:

We present data from a suite of 169 hydrocode simulations of collisions between planetary bodies with radii from 100 to 1000 km. The data is used to derive a simple scaling law for the threshold for catastrophic disruption, defined as a collision that leads to half the total colliding mass escaping the system post impact. For a target radius $100\le{R_T}\le{1000}\,\mathrm{km}$ and a mass $M_T$ and a projectile radius $r_p\le{R_T}$ and mass $m_p$ we find that a head-on impact with velocity magnitude $v$ is catastrophic if the kinetic energy of the system in the center of mass frame, $K=0.5{M_T}{m_p}/(M_T + m_p)\,v^2$, exceeds $K^*_\mathrm{RD}=(3.3 \pm 0.6)\,U_R$ where $U_R = (3/5)G{M_T}^2/R_T + (3/5)G{m_p}^2/{r_p} + G{M_T}{m_p}/(M_T + m_p)$ is the gravitational binding energy of the system at the moment of impact; $G$ is the gravitational constant. Oblique impacts are catastrophic when the fraction of kinetic energy contained in the volume of the projectile intersecting the target at impact exceeds $\sim\!{1.9}\,K^*_\mathrm{RD}$ for $30^\circ$ impacts and $\sim\!{3.5}\,K^*_\mathrm{RD}$ for $45^\circ$ impacts. We compare predictions made with this scaling to those made with existing scaling laws in the literature extrapolated from numerical studies on smaller targets. We find significant divergence between predictions where in general our data suggest a lower threshold for disruption except for highly oblique impacts with $r_p\ll{R_T}$. This result has implications for the efficiency of collisional grinding in the asteroid belt (Morbidelli, A., Bottke, W.~F., Nesvorny,~D., \& Levison, H.~F., 2009, Icarus, 204, 558–573), Kuiper belt (Greenstreet, S., Gladman, B., \& McKinnon, W.~B., 2015, Icarus, 258, 267–288), and early solar system accretion (Chambers, J.~E., 2013, Icarus, 224, 43–56).