Resolution dependence of disruptive collisions between planetesimals in the gravity regime

Collisions are a fundamental process in planet formation. If colliding objects simply merge, a planetary object can grow. However, if the collision is disruptive, planetary growth is prevented. Therefore, the impact conditions under which collisions are destructive are important in understanding planet formation. So far, the critical specific impact energy for a disruptive collision Q_D^* has been investigated for various types of collisions between objects ranging in scale from centimeters to thousands of kilometers. Although the values of Q_D^* have been calculated numerically while taking into consideration various physical properties such as self-gravity, material strength, and porosity, the dependence of Q_D^* on numerical resolution has not been sufficiently investigated. In this paper, using the smoothed particle hydrodynamics (SPH) method, we performed numerical simulations of collisions between planetesimals at various numerical resolutions (from 5×10⁴ to 5×10⁶ SPH particles) and investigated the resulting variation in Q_D^*. The value of Q_D^* is shown to decrease as the number of SPH particles increases, and the difference between the Q_D^* values for the lowest and highest investigated resolutions is approximately a factor of two. Although the results for 5×10⁶ SPH particles do not fully converge, higher-resolution simulations near the impact site show that the value of Q_D^* for the case with 5×10⁶ SPH particles is close to the expected converged value. Although Q_D^* depends on impact parameters and material parameters, our results indicate that at least 5×10⁶ SPH particles are required for numerical simulations in disruptive collisions to obtain the value of Q_D^* within 20% error.