Using a geometrical algorithm to provide N-body initial conditions for the gravitational phase of asteroid family formation

Numerical studies of asteroid family formation use the size-frequency and ejection-speed distributions of the reaccumulated fragments as the main constraints to validate asteroid collision models. However, when shape and spin are also considered, they add new constraints that must be matched simultaneously. While this poses new challenges, it also serves to increase the reliability of numerical models. Coupled with advances in shape and spin determination in ground and space-based observations, numerical simulations are poised to become a crucial tool for understanding asteroid-family-forming events and to infer internal properties of family members. Numerical simulations have typically relied on a two-stage process for modelling these events. First, a hydrocode models the progenitor's fragmentation. In this study, the considered hydrocode is based on smoothed-particle hydrodynamics (SPH) techniques. Secondly, the SPH output is fed to an N-body code to model the reaccumulation or escape of fragments. Here, we explore the upgraded capabilities for the second stage. We use a soft-sphere discrete element method to accurately model the contact forces as fragments reaccumulate. However, SPH simulations typically result in large particle overlaps, some of which have large speeds that drive the time-step requirement to prohibitively low values. We introduce a novel approach for handling the transition between SPH and N-body by using a computational geometry technique called α-shape modelling. This technique will enable future studies to explore the large parameter space of asteroid family formation in order to link observed asteroid family properties with specific collision scenarios and to probe asteroid material and internal properties.