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 QD∗ has been investigated for various types of collisions between objects ranging in scale from centimeters to thousands of kilometers. Although the values of QD∗ have been calculated numerically while taking into consideration various physical properties such as self-gravity, material strength, and porosity, the dependence of QD∗ 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 QD∗. The value of QD∗ is shown to decrease as the number of SPH particles increases, and the difference between the QD∗ 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 QD∗ for the case with 5 × 106 SPH particles is close to the expected converged value. Although QD∗ 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 QD∗ within 20% error.