Asteroid rotation and shape: gravitational aggregate...
Transcript of Asteroid rotation and shape: gravitational aggregate...
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
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
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
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
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
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
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
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
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
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
Results: shapes
N
1500
500initial cloud elongation
Results: shapes + observations
L
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
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
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
…with appropriate densities
RGMLL
G
3=
Ω=Ω
πρ
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…)
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
The End
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION
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
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
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?
P. Tanga June 28, 2007 VII WORKSHOP ON CATASTROPHIC DISRUPTION