COLLISIONS BETWEEN GRAVITY-DOMINATED BODIES. I. OUTCOME REGIMES AND SCALING LAWS

Abstract

Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. Collision outcomes are described in terms of the impact conditions and the catastrophic disruption criteria, Q * RD —the specific energy required to disperse half the total colliding mass. All planet formation and collisional evolution studies have assumed that catastrophic disruption follows pure energy scaling; however, we find that catastrophic disruption follows nearly pure momentum scaling. As a result, Q * RD is strongly dependent on the impact velocity and projectile-to-target mass ratio in addition to the total mass and impact angle. To account for the impact angle, we derive the interacting mass fraction of the projectile; the outcome of a collision is dependent on the kinetic energy of the interacting mass rather than the kinetic energy of the total mass. We also introduce a new material parameter, c *, that defines the catastrophic disruption criteria between equal-mass bodies in units of the specific gravitational binding energy. For a diverse range of planetesimal compositions and internal structures, c * has a value of 5 ± 2; whereas for strengthless planets, we find c * = 1.9 ± 0.3. We refer to the catastrophic disruption criteria for equal-mass bodies as the principal disruption curve, which is used as the reference value in the calculation of Q * RD for any collision scenario. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution.