Rubble Piles & Monoliths
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Transcript of Rubble Piles & Monoliths
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 [email protected] 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