Measuring the Collisional Evolution of Debris Clusters in an Asteroid System

TL;DR

This study investigates how debris clouds formed by rotational shedding around a Didymos-like asteroid can seed secondary formation. By coupling full-scale debris-cloud simulations with cluster-scale DEM experiments, the authors quantify growth pathways from cm-dm particles to metre-scale clusters, revealing that low-geopotential regions trap material and drive collisions that follow a Weibull distribution with $\lambda=0.0642$ and $k=1.8349$, enabling accretion and compact internal structures ($\Delta I \approx 0.8$, $\phi \approx 0.52$). Meter-scale clusters can overcome the bouncing barrier, undergoing four collision regimes (stick, plastic merge, damage-enhanced growth, fragmentation) with a critical fragmentation velocity around $0.085$ m s$^{-1}$. The results support rotational-instability shedding plus collisional accretion as a robust pathway to secondary formation and offer testable predictions for upcoming missions like Hera, DESTINY+, and Lucy.

Abstract

Context. Rotational instability of rubble-pile asteroids can trigger mass shedding, forming transient debris clouds that may provide the initial conditions for secondary formation in binary systems. Aims. We investigate the dynamical and collisional evolution of a debris cloud numerically generated around a Didymos-like progenitor, as a representative case for the early formation of Dimorphos. The analysis focuses on the growth and structural properties of clusters composed of centimetre- to decimetre-scale particles. Methods. We perform full-scale simulations of debris evolution around a near-critically rotating asteroid using a cross-spatial-scale approach combined with the discrete element method (DEM). To overcome computational timescale limitations, an equivalent cluster-scale simulation framework is introduced to capture the essential collisional growth processes efficiently. These simulations quantify the efficiency of cluster growth and the structural evoution within the debris cloud. Results. Our simulations reveal that particles shed from a rotationally unstable asteroid exhibit a consistent migration pattern toward low-geopotential regions, which governs the mass distribution and dynamical structure of the debris cloud. The collisional velocity are well described by a Weibull distribution (lambda = 0.0642, k = 1.8349), where low-velocity impacts favor accretion. These collisions enable clusters to grow from centimeter-decimeter scales to meter-sized bodies, developing compact, moderately porous structures (Delta I \approx 0.8, phi \approx 0.52). Collisions between meter-sized clusters do not exhibit a bouncing barrier: low-velocity impacts yield Dinkinesh-like shapes, while moderate velocities promote plastic merging and continued growth.

Figures (10)

• Figure 1: (a) Spatial mass density of the accumulated debris cloud at the end of 2.3-day continuous shedding and ballistic stage, shown in the body-fixed equatorial plane. The black regions depict regions with no detected debris particles. Colored areas mark zones where debris particles are present, and the color scale denotes the local mass density. All regions with mass density exceeding 0.5 are saturated and shown in red.(b) Contour lines of the geopotential around Didymos projected onto the equatorial plane. Different colors indicate distinct geopotential values (unit: $\mathrm{J/kg}$). Values outside the color bar range are shown in the same colors as the respective maximum and minimum values.
• Figure 2: (a) Azimuthal sectors selected within the debris cloud. Blue regions indicate $10$° wide azimuthal sectors uniformly sampled at orbital radius $r=[360 ~ \mathrm{m},\,660 ~ \mathrm{m}]$. White dots denote simulated particles, while black areas correspond to regions without particles. (b) Distribution of the relative collision velocity $v_\mathrm{col}$ extracted from the debris cloud. The red curve shows the fitted Weibull probability density function with a scale parameter $\lambda = 0.0642$ and a shape parameter $k = 1.8349$. (c) Collision counts recorded within the azimuthal sectors.
• Figure 3: (a) Evolution of the largest cluster size identified at each step in the full-scale simulation, expressed by the number of constituent particles. Red crosses indicate the growth cases used in Sect. \ref{['sec:level3-3.2.2']}, whose structures are shown in Fig. \ref{['figthrowclu']}(a) and (f). (b-g) Representative clusters sampled during the evolution. Panels (e-f) show supplemented clusters generated using the procedure described in Sec. \ref{['sec:level3-2.2.2']}, with red particles indicating the added components.
• Figure 4: Flow chart of the sequential particle-cluster collision algorithm.
• Figure 5: Mass evolution of the debris cloud during the full-scale DEM simulation. (a) Mass evolution of the simulated particles classified into three parts: particles remaining in orbit around the progenitor (blue), accreted onto the progenitor (red), and escaped from the system (green). (b) Mass evolution of unbound particles (dashed line) and clustered particles (dotted line), which together constitute the orbital component. (c) Temporal evolution of the radial mass distribution within the debris cloud. Colors correspond to different simulation times as indicated in the legend.