1. Derek C. Richardson (U Maryland) Rubble Piles & Monoliths CD-VI Cannes PreshatteredRubble This online version does not include the movies. Please e-mail dcr@astro.umd.edu if you want them.dcr@astro.umd.edu

2. Collaborators E. Asphaug UCSC W. Benz U Bern W. F. Bottke Jr. SwRI D. D. Durda SwRI B. L. Enke SwRI Z. M. Leinhardt U Maryland H. J. Melosh LPL P. Michel Obs. Cote d’Azur T. Quinn U Washington D. J. Scheeres U Michigan J. Stadel U Zurich P. Tanga Obs. Cote d’Azur K. J. Walsh U Maryland

3. Overview Gravitational Aggregates Gravitational Aggregates – What are they? Do they exist? Numerical Simulations Numerical Simulations – How do they work? Gravitational Reaccumulation (Rubble Piles) Gravitational Reaccumulation (Rubble Piles) – Families & Binaries, Collisions & Tidal Disruption Pushing the Envelope (Monoliths!) Pushing the Envelope (Monoliths!) – More realism without sacrificing too much speed. Cf. Richardson et al. 2003: Asteroids III

4. Classifications Stress response may be predicted by plotting tensile strength (resistance to stretching) vs. porosity. Other parameters: Mass fraction of largest component, etc. Richardson et al. 2003

5. Gravitational Aggregates Evidence includes: Evidence includes: 1. Breakups: Catenae, Doublets, & Binaries 2. Underdensity: Giant Craters & Grooves 3. Dynamics: Asteroid Spins & Unusual Shapes

6. Tidal Breakups Require low tensile strength. Require low tensile strength. Comet breakups like D/SL9 can make crater chains. Asteroid breakups may explain a few catenae seen on the Moon. Davy Chain, ~47 km

7. Low Densities Many asteroids appear underdense, particularly C-class asteroids. Many asteroids appear underdense, particularly C-class asteroids. Large craters and low density of Mathilde imply high porosity.  ~59 km  NEAR

8. Asteroid Spins Most large (> 150 m) asteroids spin slower than the rubble breakup limit. Most large (> 150 m) asteroids spin slower than the rubble breakup limit. Pravec & Harris 2000  3.0 g/cc

9. Latest Evidence Galileo flyby of Amalthea revealed bulk density of just 1 g/cc for this 270 km moon. Galileo flyby of Amalthea revealed bulk density of just 1 g/cc for this 270 km moon. Leading Trailing

10. Morphological Evolution Collisions are the dominant geologic process affecting large main-belt asteroids. Collisions are the dominant geologic process affecting large main-belt asteroids. Expect collisionally evolved population in gravity regime to consist of shattered and/or reaccumulated bodies. Expect collisionally evolved population in gravity regime to consist of shattered and/or reaccumulated bodies. Asphaug et al. 2003  strength|gravity 

11. Aggregates Resist Disruption Once shattered, impact energy is more readily absorbed at impact site. Once shattered, impact energy is more readily absorbed at impact site. Asphaug et al. 1998 Damaged Coherent

12. Earliest bodies may have started as loose aggregates, growing by pairwise accretion until large enough to melt. Earliest bodies may have started as loose aggregates, growing by pairwise accretion until large enough to melt. Planetesimals Leinhardt et al. 2000

13. Numerical Simulations Gravitational aggregate dynamics can be explored with fast N-body code: pkdgrav. – Model bodies as rubble piles: collections of indestructible spherical particles. – Particle motions evolve via collisions and gravity. – Collisions may be dissipative and may alter particle spins via surface friction. – Gravity may include external perturbations.

14. Numerical Method Use hierarchical treecode and highly parallelized algorithms to improve speed. Solve Newton’s laws using leapfrog integrator (multistepping optional). – Timestep small fraction of dynamical time. Predict collisions during drift interval and resolve using restitution model. Repeat for many dynamical times.

15. Gravitational Reaccumulation Pkdgrav has been used to simulate: Asteroid families (Michel et al.) Asteroid satellites (Durda et al.)

16. NEA Binaries High frequency of occurrence, fast rotating primaries, and terrestrial doublet crater population suggest tidal disruption may be an important mechanism for forming NEA binaries.

17. Simulations of Tidal Disruption Earth v q 32 Simulations 1.2 < q < 2.0 R  3.0 < v < 18 km/s R Roche = 3.47 R  2 km 4 km 6 h  = 2.0 g/cc Cf. Richardson & Scheeres 2003

18. Sample Result q = 1.6, v = 6  1 = 0.38,  2 = 0.19 = 6.4 km, = 0.33 = 6.4 km, = 0.33 = 4.7 h, = 7.1 h = 4.7 h, = 7.1 h

19. SL9 Binaries? Recent work by Walsh to better constrain SL9 progenitor parameters shows binary formation is natural outcome… May explain late splitting? (unstable dynamical system)

20. Pushing the Envelope Current large-scale simulations by Michel & Durda oversimplify reaccumulation process by assuming perfect merging. – Reduces cost of particle collision computation in rubble piles. – BUT: spins, shapes, and gravity fields of reaccumulated bodies unrealistic.

21. New Strategy Reduce computation cost by freezing the rubble pile particles into coherent (rigid) aggregates, i.e. (porous) monoliths! – Requires diagonalization of inertia tensors and computation of gravitational & collisional torques, but still much cheaper! – Also need speed-dependent sticking/breaking criteria  new model parameters to be tuned.

22. Gravity Torques Compute gravity torques using treecode (fast): only need aggregate centers of mass. Evolve spin vectors via Euler equations during drift interval: I 1 (dω 1 /dt) – ω 2 ω 3 (I 2 – I 3 ) = N 1 I 2 (dω 2 /dt) – ω 3 ω 1 (I 3 – I 1 ) = N 2 I 3 (dω 3 /dt) – ω 1 ω 2 (I 1 – I 2 ) = N 3

23. Collision Torques Collisions now oblique (non-central), requiring more sophisticated approach. Case of point-contact, instantaneous impacts with no surface friction has been solved: see Richardson 1995 for equations. – Straightforward to compute since constituent particles still just spheres.

24. Sample Movie (no collisions)

25. Extended Integration q = 1.6, v = 6

26. Sample Movie (sticking only)

27. Summary Many (most?) small bodies in the Solar System may be gravitational aggregates. Many (most?) small bodies in the Solar System may be gravitational aggregates. Asteroid families and clusters can be explained by gravitational reaccumulation of debris after a high-speed impact. Asteroid families and clusters can be explained by gravitational reaccumulation of debris after a high-speed impact. Collisions and tidal disruption play a key role in forming asteroid binaries. Collisions and tidal disruption play a key role in forming asteroid binaries.

28. Future Work Add bouncing to rigid body treatment to enable compaction (next week!). Add bouncing to rigid body treatment to enable compaction (next week!). Trace evolution of individual particles from breakup to reaccumulation. Trace evolution of individual particles from breakup to reaccumulation. Study binary formation via YORP spinup. Study binary formation via YORP spinup. Consider application to slow and tumbling rotators. Consider application to slow and tumbling rotators.

29. THE END