Network-based representation of rubble-pile asteroids and the corresponding dynamical evolution

Context. Most asteroids are gravitational aggregates - loosely bound assemblies of material held together by inter-particle gravitational forces. Their dynamics and structural stability are challenging to model due to their granular nature, resulting in a complex N-body problem. Aims. With this study, we aim to evaluate whether network theory can effectively represent rubble-pile asteroids and, if so, how such a representation can be constructed. We propose an alternative methodology to investigate the stability and dynamical evolution patterns of rubble piles using network-based metrics. Unlike classical approaches that analyse the evolution of the rubble pile through global physical parameters (e.g. total energy, angular momentum), the proposed method tracks the temporal evolution of the networks that represent the structure of the rubble pile. Methods. We applied graph and network theory to model the dynamics of rubble piles. Based on this representation, we developed a methodology to analyse asteroid stability using network-specific metrics - average degree, global clustering coefficient, percolation, and network entropy - computed at successive time snapshots and establish the suitability of network theory in complex environments such as those represented by rubble piles. Results. We find that the temporal evolution of the percolation threshold and the average degree reliably capture the dynamical evolution of the rubble piles, and in cases of disaggregation, they quantify the severity of fragmentation. Additionally, percolation through quasi-random edge removal, while not very accurate, effectively predicts potential disaggregation pathways and identifies centres of cohesive substructures (communities) within the aggregate. Conclusions. The network-based approaches proved to be potentially useful in the study of granular asteroid dynamics.