[Paper Review] The role of material strength in collisions -- Comparing solid body and hydrodynamic physics for simulating collisions of planetesimals with icy shells

Thomas I. Maindl, R. Dvořák+2 more|arXiv (Cornell University)|Dec 30, 2013

Astro and Planetary Science1 references3 citations

TL;DR

This study compares solid body (elasto-plastic) and hydrodynamic models in smoothed particle hydrodynamics (SPH) simulations of Ceres-mass planetesimals colliding with icy shells, demonstrating that material strength significantly increases fragmentation and water loss—especially in low-to-mid energy collisions—while enabling detectable water transfer between bodies, challenging assumptions of perfect merging in early planetary system models.

ABSTRACT

Context. We investigate the effects of including material strength in multi-material planetesimal collisions. Aims. The differences between strengthless material models and including the full elasto-plastic model for solid bodies with brittle failure and fragmentation when treating collisions of asteroid-sized bodies as they occur frequently in early planetary systems are demonstrated. Methods. We study impacts of bodies of Ceres-mass with a solid rock impactor and a target with 30 weight-% water content as surface ice.} The initial impact velocities and impact parameters are varied between the escape velocity $v_\mathrm{esc}$ to about 6 $v_\mathrm{esc}$ and from head-on collisions to close fly-bys, respectively. We simulate the collisions using our own SPH code utilizing both strengthless material and the full elasto-plastic material model including brittle failure. Results. One of the most prominent differences is the higher degree of fragmentation and shattered debris clouds in the solid model. In most collision scenarios however, the final outcomes are very similar and differ primarily by the about one order of magnitude higher degree of fragmentation in the solid case. Also, the survivors tend to be of less mass in the solid case which also predicts a higher water loss than the strengthless hydro model. This may be an effect of the relatively low-energy impacts that cannot destroy the solid material instantly. As opposed to giant impacts we also observe an indication that some water ice gets transferred between the bodies.

Motivation & Objective

• To assess the impact of material strength on collision outcomes in planetesimal systems, particularly for Ceres-mass bodies with icy surfaces.
• To challenge the common assumption of strengthless hydrodynamic models in early planetary system simulations, which may oversimplify material transfer and fragmentation.
• To investigate whether solid body physics, including brittle failure and elasto-plastic behavior, alters outcomes like debris distribution, mass loss, and water transfer compared to hydrodynamic models.
• To identify conditions—particularly low-to-mid energy impacts and near-central collisions—where solid body modeling is essential for accurate collision outcome prediction.
• To evaluate the feasibility and necessity of using computationally expensive solid models in large-scale n-body simulations of early planetary systems.

Proposed method

• Uses a custom SPH code implementing both strengthless hydrodynamic and full elasto-plastic material models with brittle failure (based on Libersky & Petschek, 1991; Benz & Asphaug, 1994, 1995).
• Simulates collisions between a Ceres-mass target (30 wt% water ice surface) and a solid rock impactor at velocities from 1 to 6 times escape velocity.
• Varying impact parameters from head-on to close fly-bys to explore a wide range of collision geometries and energies.
• Tracks material evolution, including mass loss, fragment formation, and water content redistribution across survivors and debris clouds.
• Performs simulations over 2000 minutes post-collision to assess final system states and long-term stability of fragments.
• Uses GPU-accelerated SPH for performance, achieving ~50× speedup over CPU-based implementations, enabling large-scale parameter space exploration.

Experimental results

Research questions

• RQ1 How does including material strength affect the degree of fragmentation and debris cloud dispersion in planetesimal collisions compared to strengthless hydrodynamic models?
• RQ2 To what extent does the solid model predict higher water loss from icy planetesimals than the hydrodynamic model, especially in low-energy collisions?
• RQ3 Can material strength enable detectable water (ice) transfer between colliding Ceres-sized bodies, particularly in hit-and-run or partial accretion regimes?
• RQ4 Are there specific collision regimes—such as low-energy or near-central impacts—where the solid model produces significantly different outcomes than the hydro model?
• RQ5 What is the computational cost-benefit trade-off of using solid body models in large-scale n-body simulations of early planetary systems?

Key findings

• The solid model produces approximately one order of magnitude more fragments and more extensive, dust-like debris clouds than the hydrodynamic model.
• Survivors in the solid model are less massive on average due to enhanced fragmentation and material loss.
• Water loss is consistently higher in the solid model, with the difference being most pronounced in low-to-mid energy collisions.
• The simulations show clear evidence of water ice transfer between bodies, particularly in hit-and-run and partial accretion scenarios, a feature not captured by hydrodynamic models.
• Low-energy and near-central collisions exhibit the most significant differences between solid and hydro models, indicating these regimes require solid body physics for accurate simulation.
• The results suggest that solid body models are necessary for realistic modeling of water delivery and asteroid family formation in early planetary systems, especially when material transfer and fragmentation are key concerns.