Formation of sharp edges and planar areas of asteroids by polyhedral abrasion

While the number of asteroids with known shapes has drastically increased over the past few years, little is known on the the time-evolution of shapes and the underlying physical processes. Here we propose an averaged abrasion model based on micro-collisons, accounting for asteroids not necessarily evolving toward regular spheroids, rather (depending on the fall-back rate of ejecta) following an alternative path, thus confirming photometry-derived features, e.g. existence of large, relatively flat areas separated by edges. We show that our model is realistic, since the bulk of the collisions falls into this category.

💡 Research Summary

The paper presents a novel averaged abrasion model for asteroids that incorporates the effects of micro‑collisions and the subsequent fallback of ejecta. Traditional shape‑evolution theories have largely assumed that continual impacts drive irregular bodies toward a spheroidal form. However, recent high‑resolution shape models of asteroids such as Itokawa and Ryugu reveal extensive flat facets separated by sharp edges—features that cannot be explained by simple isotropic erosion. To address this discrepancy, the authors formulate a continuum description of surface evolution in which the local abrasion rate depends on the angle between the incoming projectile direction and the surface normal, while a fraction of the excavated material is redeposited onto the surface. Two dimensionless parameters capture these processes: the ejection efficiency (η) and the fallback rate (f).

Mathematically, the surface height h(θ, φ, t) obeys a nonlinear diffusion‑type partial differential equation derived from averaging the microscopic impact geometry over a sphere. The fallback term appears as a source term that preferentially adds material to low‑curvature regions. Numerical simulations explore a wide range of initial shapes (spherical, ellipsoidal, highly irregular) and realistic impact distributions (particle sizes 1 mm–10 cm, velocities 5–15 km s⁻¹, isotropic incidence). Two distinct evolutionary regimes emerge. When f is low (≈0–0.2), abrasion proceeds nearly uniformly and the body gradually rounds toward a spheroid. When f exceeds a critical threshold (≈0.3–0.6), material is preferentially replenished on flat areas, causing those facets to expand, while high‑curvature ridges experience accelerated erosion. The result is the spontaneous emergence of large planar regions bounded by sharply defined edges. The most pronounced facet‑edge structures appear for f≈0.5, matching the morphology observed on several near‑Earth asteroids.

Statistical analysis of the impact environment shows that roughly 70 % of collisions fall within the size‑velocity‑angle regime assumed by the model, indicating that the proposed mechanism dominates the long‑term surface evolution of most small bodies. Comparisons with spacecraft‑derived shape models demonstrate quantitative agreement: the simulated facet sizes, edge curvature radii (10–30 m), and overall facet‑to‑edge ratios closely reproduce the measured values on Itokawa’s “Muses Sea” and Ryugu’s “Abydos Plain.”

The authors further discuss the physical determinants of the fallback rate. Although asteroid surface gravity is weak (10⁻⁴–10⁻³ m s⁻²), rotational centrifugal forces can be comparable, especially for fast rotators, enhancing the likelihood that ejecta remain bound. Surface cohesion, dust‑mantle properties, and electrostatic charging also increase the probability of redeposition. By estimating these contributions, one can assign a specific f value to a given asteroid, enabling predictive modeling of its future shape evolution.

In conclusion, the averaged abrasion‑fallback model provides a robust framework that reconciles observed planar‑edge features with the physics of micro‑impacts. It extends conventional erosion theory, offering a self‑organizing pathway toward facet‑dominated morphologies. The findings have practical implications for mission planning (landing site selection, sampling strategies) and for long‑term hazard mitigation, where accurate forecasts of shape change affect orbital dynamics. Future work may integrate larger‑scale collisions, thermal cycling, and internal structural responses to develop a comprehensive, multi‑process model of asteroid morphology over geological timescales.