Rubble Piles & Monoliths

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

2. Collaborators

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

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

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

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

8. Asteroid Spins • 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. Leading Trailing

10. Morphological Evolution Asphaug et al. 2003 • 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.  strength|gravity 

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

12. Planetesimals • Earliest bodies may have started as loose aggregates, growing by pairwise accretion until large enough to melt. 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. q 2 km Earth 4 km 6 h  = 2.0 g/cc v Simulations of Tidal Disruption 32 Simulations 1.2 < q < 2.0 R 3.0 < v < 18 km/s RRoche = 3.47 R Cf. Richardson & Scheeres 2003

18. < a > = 6.4 km, < e> = 0.33 < P1 > = 4.7 h, < P2 > = 7.1 h Sample Result q = 1.6, v = 6 1 = 0.38, 2 = 0.19

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: I1(dω1/dt)– ω2ω3(I2 – I3) = N1 I2(dω2/dt)– ω3ω1(I3 – I1) = N2 I3(dω3/dt)– ω1ω2(I1 – I2) = N3

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. • 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.

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

29. THE END