Asteroid rotation and shape: gravitational aggregate...
Transcript of Asteroid rotation and shape: gravitational aggregate...
![Page 1: Asteroid rotation and shape: gravitational aggregate ...irtfweb.ifa.hawaii.edu/~sjb/CD07/talks/Tanga_slides.pdf · P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION Asteroid](https://reader035.fdocuments.net/reader035/viewer/2022081521/5ba349eb09d3f208588db035/html5/thumbnails/1.jpg)
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Asteroid rotation and shape: gravitational aggregate
simulationsTanga, P. (OCA Nice)
Delbo, M. (OCA Nice, INAF/Torino) Hestroffer, D., (IMCCE Paris)
Richardson, D.C. (Univ. of Maryland)
Alicante 2007
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
The origin of asteroid shapes• Why we care about shape sculpting?
– They are related to collisions!– Generated in post-disruption reaccumulation:
• Connected to the internal structure properties• Connected to the presence/stability of satellites• …
– Growing observational set (photometry, probes, occultation profiles…)
• Shapes can be complex…
…a complex problem, interesting for numerical studies, and requiring simplifications
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Isolated particle cloudInitial velocity, 2 components:
- rigid rotation- random
Widely different situations possible:-fast accretion on single body-slower chaotic accretion
•• How a re-accumulated body gets its shape ?
• Is the result driven by total angular momentum ?
• Can any shape form in a re-accumulation process ? How they compare with equilibrium shapes ?
• Is the angular momentum related to satellite formation ?
Our study: the concept
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Different approaches to reaccumulationpkdgrav N-body code
Michel, Benz, Tanga,Richardson 2001…
merging particles
this study
Rotating cloud: size ~10-20X final body
Restitution: ε ⊥ = 0.8
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
t = 0.17 j t = 0.23 j
t = 0.29 j t = 0.47 j t = 23.25 j
t = 0.01 j
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Description of resulting shapes
• Flattening b/a, c/a
• Rotation
• Angular momentum
we use 4 parameters for the interpretation of the simulations
abc
In terms of ellipsoids
RGMLL
G
3=
Ω=Ω
πρ
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Holsapple, 2001Φ=40°
Pre-built, closely packed ellipsoidal aggregates
1 0.8 0.6 0.4 0.2 0
0.8
0.6
0.4
0.2
0.0
c/a
Ω/(2
Gπρ
)1/2
Richardson Richardson et al.et al. 20052005
Comparison to:Previous investigations, Richardson et al. 2005
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Comparison to: observational dataset
Jacobi
Maclaurin
ab
c
ac
a
source: PDS node, Magnusson database
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Results: shapes
N
1500
500initial cloud elongation
Results: shapes + observations
L
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Results: rotational parameters
compressible polytropic fluid (Lai, Rasio, Shapiro 1993), n~0.7
RGMLL
G
3=
Ω=Ω
πρ
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Even “virtual” experiments deserve careful measurements!
Original ellipsoidal hull:• Including the full volume of the most
external particles
Improved hull:• Including the center of the most
external spheres
correction of measured porosity from 55-50% 34% !corrected values for densities
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
…with appropriate densities
RGMLL
G
3=
Ω=Ω
πρ
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Results of our experiments• Resolution matters (especially when fitting a shape) – but it is not so
critic
• Cloud shapes are relevant in the high-L regimesome memory of initial conditions ( G. Consolmagno)first experiments with complex ejection fields
• Shapes cluster around the fluid equilibrium linesgravity does not create the observed or allowed variety of shapesthis seems consistent to objects w. satellites ( F. Marchis)
• Binary generation: clouds of large L can collapse to binaries
• Ellipsoids are a good approximation of the resulting shapes (but…)
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
The End
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Shapes from lightcurvesEllipsoidal envelope
ProsEasy to implementGood for statisticsWorks for most objects
ConsCould fail on complex shapes
Multi-parametric inversion
Detailed shapesWorks on complex lightcurves
Uncertainty on parametersConvergence problems
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
pkdgravpkdgrav usedused in «in « bouncingbouncing » mode» mode
particlesparticles nevernever stick stick eacheach otherother
P
P ’
v ’⊥ =- ε ⊥ v ⊥
v ’// ~ ε// v//v⊥
v// P
SphericalSpherical particlesparticles
N = 500 - 5000
ε// = 1, ε ⊥ = 0.8
P ’
Hard sphere collisions
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Problems• Obtained results are:
– …well represented by ellipsoids– ... clustered in regions of the parameter space– … not strictly corresponding to “fluid”
equilibrium, but not so far from it– … preferentially ellipsoids, but not only.
• How to explain them?– Memory of initial conditions (cloud shape,
velocity distribution…)?– Is the physical model appropriate?
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P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION