Collisional growth of debris clusters during the early stage of asteroid system formation

Rotational instability of rubble-pile asteroids can generate debris clouds that represent the earliest stage of asteroid system formation. The collisional evolution of centimeter- to decimeter-sized debris within such environments remains poorly constrained. We investigated the dynamical and collisional evolution of debris cloud clusters numerically generated around a Didymos-like progenitor, focusing on the mesoscopic regime that links particle-scale interactions to macroscopic systems. We performed full-scale simulations of debris evolution using a cross-spatial-scale approach based on the discrete element method (DEM), and extracted the statistical properties of the collisional environment. These results were subsequently used to construct a cluster-scale simulation framework that quantifies cluster growth efficiency and structural evolution, while alleviating the computational constraints of long-timescale simulations. Our simulations reveal that the collisional velocity distribution within the collision-dominated region is well described by a Weibull function and spans a consistent velocity range across radial distances. The growth of clusters is primarily controlled by the relative collision velocity and mass ratio, which define accretion and fragmentation regimes. Clusters grow efficiently from centimeter--decimeter scales to meter-sized aggregates, developing compact and moderately porous structures. No bouncing barrier is observed at the meter scale, and continued growth is enabled through low- to moderate-velocity impacts. Our findings provide quantitative constraints on the collisional growth of debris clusters, and demonstrate that mesoscopic granular interactions play a key role in bridging particle-scale debris and the early formation of asteroid systems. Future missions such as Hera, DESTINY+, and Lucy will offer critical opportunities to test these mechanisms through direct observations of debris clouds and dust ejecta.