Derek C. Richardson (U Maryland)Derek C. Richardson (U Maryland)

Rubble Piles & MonolithsRubble Piles & Monoliths

CD-VI CannesCD-VI Cannes

PreshatteredPreshattered RubbleRubble

This online version does not include the movies.

Please e-mail dcr@astro.umd.edu if you want them.

CollaboratorsCollaborators

E. AsphaugE. Asphaug

UCSCUCSC

W. BenzW. Benz

U BernU Bern

W. F. Bottke Jr.W. F. Bottke Jr.

SwRISwRI

D. D. DurdaD. D. Durda

SwRISwRI

B. L. EnkeB. L. Enke

SwRISwRI

Z. M. LeinhardtZ. M. Leinhardt

U MarylandU Maryland

H. J. MeloshH. J. Melosh

LPLLPL

P. MichelP. Michel

Obs. Cote d’AzurObs. Cote d’Azur

T. QuinnT. Quinn

U WashingtonU Washington

D. J. ScheeresD. J. Scheeres

U MichiganU Michigan

J. StadelJ. Stadel

U ZurichU Zurich

P. TangaP. Tanga

Obs. Cote d’AzurObs. Cote d’Azur

K. J. WalshK. J. Walsh

U MarylandU Maryland

OverviewOverview

Gravitational AggregatesGravitational Aggregates– What are they? Do they exist?What are they? Do they exist?

Numerical SimulationsNumerical Simulations– How do they work?How do they work?

Gravitational Reaccumulation (Rubble Piles)Gravitational Reaccumulation (Rubble Piles)– Families & Binaries, Collisions & Tidal DisruptionFamilies & Binaries, Collisions & Tidal Disruption

Pushing the Envelope (Monoliths!)Pushing the Envelope (Monoliths!)– More realism without sacrificing too much speed.More realism without sacrificing too much speed.

Cf. Richardson et al. 2003: Asteroids III

ClassificationsClassifications

Stress response may be predicted by plotting tensile Stress response may be predicted by plotting tensile strength (resistance to stretching) strength (resistance to stretching) vsvs. porosity.. porosity.

Other parameters: Mass fraction of largest component, etc.Other parameters: Mass fraction of largest component, etc.

Richardson Richardson et alet al. 2003. 2003

Gravitational AggregatesGravitational Aggregates

Evidence includes:Evidence includes:1.1. Breakups: Breakups: CatenaeCatenae, Doublets, & , Doublets, & BinariesBinaries

2.2. Underdensity: Underdensity: Giant CratersGiant Craters & Grooves & Grooves

3.3. Dynamics: Asteroid Dynamics: Asteroid SpinsSpins & Unusual Shapes & Unusual Shapes

Tidal BreakupsTidal BreakupsRequire low tensile strength.Require low tensile strength.

Comet breakups like D/SL9 Comet breakups like D/SL9 can make crater chains.can make crater chains.

Asteroid breakups may explain a Asteroid breakups may explain a few catenae seen on the Moon.few catenae seen on the Moon.

Davy Chain, ~47 kmDavy Chain, ~47 km

Low DensitiesLow Densities

Many asteroids appear underdense, Many asteroids appear underdense, particularly C-class asteroids.particularly C-class asteroids.

Large craters and low density of Large craters and low density of Mathilde imply high porosity.Mathilde imply high porosity.

~59 km ~59 km NEARNEAR

Asteroid SpinsAsteroid SpinsMost large (> 150 m) asteroids spin slower Most large (> 150 m) asteroids spin slower

than the rubble breakup limit.than the rubble breakup limit.Pravec & Harris 2000Pravec & Harris 2000

3.0 g/cc

Latest EvidenceLatest EvidenceGalileo flyby of Amalthea revealed bulk Galileo flyby of Amalthea revealed bulk

density of just 1 g/cc for this 270 km moon.density of just 1 g/cc for this 270 km moon.

Leading

Trailing

Morphological EvolutionMorphological Evolution Collisions are the Collisions are the

dominant geologic dominant geologic process affecting process affecting large main-belt large main-belt asteroids.asteroids.

Expect collisionally Expect collisionally evolved population evolved population in gravity regime to in gravity regime to consist of shattered consist of shattered and/or and/or reaccumulated reaccumulated bodies.bodies.

Asphaug Asphaug et al.et al. 2003 2003

strength|gravity

Aggregates Resist DisruptionAggregates Resist DisruptionOnce shattered, impact energy is more Once shattered, impact energy is more

readily absorbed at impact site.readily absorbed at impact site.Asphaug et al. 1998

Dam

aged

Coh

eren

t

Earliest bodies may have started as loose Earliest bodies may have started as loose aggregates, growing by pairwise accretion aggregates, growing by pairwise accretion until large enough to melt.until large enough to melt.

PlanetesimalsPlanetesimals

Leinhardt Leinhardt et alet al. 2000. 2000

Numerical SimulationsNumerical 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.

Numerical MethodNumerical 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.

Gravitational ReaccumulationGravitational Reaccumulation

Pkdgrav has been used to simulate:

Asteroid families (Michel et al.)

Asteroid satellites (Durda et al.)

NEA BinariesNEA 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.

Simulations of Tidal DisruptionSimulations of Tidal Disruption

Earth

vv

qq 32 Simulations32 Simulations

1.2 < q < 2.0 R1.2 < q < 2.0 R

3.0 < v < 18 km/s3.0 < v < 18 km/s

RRRocheRoche = 3.47 R = 3.47 R

2 km

4 km

6 h

= 2.0 g/cc

Cf. Richardson & Scheeres 2003Cf. Richardson & Scheeres 2003

Sample ResultSample Resultq = 1.6, v = 6q = 1.6, v = 6

11 = 0.38, = 0.38, 22 = 0.19 = 0.19

< a > = 6.4 km, < e> = 0.33< a > = 6.4 km, < e> = 0.33

< P< P11 > = 4.7 h, < P > = 4.7 h, < P22 > = 7.1 h > = 7.1 h

SL9 Binaries?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)

Pushing the EnvelopePushing 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.

New StrategyNew 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.

Gravity TorquesGravity 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

Collision TorquesCollision 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.

Sample Movie (no collisions)Sample Movie (no collisions)

Extended IntegrationExtended Integrationq = 1.6, v = 6q = 1.6, v = 6

Sample Movie (sticking only)Sample Movie (sticking only)

SummarySummaryMany (most?) small bodies in the Solar Many (most?) small bodies in the Solar

System may be gravitational aggregates.System may be gravitational aggregates.Asteroid families and clusters can be Asteroid families and clusters can be

explained by gravitational reaccumulation explained by gravitational reaccumulation of debris after a high-speed impact.of debris after a high-speed impact.

Collisions and tidal disruption play a key Collisions and tidal disruption play a key role in forming asteroid binaries.role in forming asteroid binaries.

Future WorkFuture Work

Add bouncing to rigid body treatment to Add bouncing to rigid body treatment to enable compaction (next week!).enable compaction (next week!).

Trace evolution of individual particles from Trace evolution of individual particles from breakup to reaccumulation.breakup to reaccumulation.

Study binary formation via YORP spinup.Study binary formation via YORP spinup.Consider application to slow and tumbling Consider application to slow and tumbling

rotators.rotators.

THE ENDTHE END