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