A Globally Shaken and Fractured Asteroid with Brazilian Nut Effect

1. A Globally Shaken and Fractured Asteroid with Brazilian Nut Effect G.Tancredi,S.Bruzzone, S.Roland, S. Favre, A. Maciel Depto. Astronomía, Fac. Ciencias Observatorio Astronómico Los Molinos URUGUAY

2. Gaspra (Galileo - ’91) En color verdadero y color resaltando las variaciones de albedo superficial

3. Eros (NEAR - ’00)

4. Eros (NEAR - ’00)

5. MUSES – C / Hayabusa (eagle)

7. Itokawa

10. Asteroid structures Rubble-piles covered by dust Solid with surface craters Solid with big cracks Agglomerate of boulders

11. “Standard” Model for the formation of Itokawa (Fujiwara et al. 2006)

12. A little bit of impact seismology Richardson et al. (2005)

13. A little bit of dynamics … NEA and Mars crosser Very low inclination (i=1.6°) Yoshikawa (2007)

14. Origin of Itokawa

15. A little bit of dynamics + collisions … Arbitrary units Collision probability Collision probability Computed with a method similar to “Cube” (Liou 2006) but developed independently

16. Projectile Consequences of collisions:after a few equations … Itokawa Based on Richardson et al. (2005), with corrections by R. Gil-Hutton

17. GLOBAL SHAKING Assuming a cumulative size distribution of projectiles with exp. -2.6: There would be 107 global shaking collisions before a catastrophic disruptive one. • Mean time between collisions: • Shaking (~cm projectile) Catastrophic (~10m proj.) • At present: 80 yr 800 Myr • During the Inner MB stage: 1 yr 10 Myr • The non-catastrophic collisions would fracture the asteroid and they would produce a frequent shaking of the entire body.

18. Brazilian Nut effect Kudrolli (2004) Well known phenomenon in the physics of granular media and rock mechanics.

19. Global shaking could produce a Brazilian Nut effect in Itokawa’s entire body. Brazilian nut effect in asteroids It was proposed by Ausphaug et al. (2001) to explain the size-sorting of Eros’ regolith; motions driven by surface gravitational slopes.

20. V ¿How do we calculate the total potential of an irregular body? Total Potential Gravitational Potential Centrifugal Rotacional Potencial Computation: Monte Carlo integration over Gaskell faceted shape model

23. What do we observe? Regions of LOW POTENTIAL – SMALL BOULDERS Regions of HIGH POTENTIAL – LARGE BOULDERS ALETERNATIVE SCENARIO Due to the past collisional evolution, the global shaking induced by impacts is the main reshaping and boulders relocation mechanism in Itokawa. The size distribution should then be correlated with the total potential.

24. Where do we count boulders?

25. The minimum size for detectable boulders was of apox. 5 px ~ 10 cm (in close-up images). Counting boulders (1)

26. Counting boulders (2) Number of boulders counted per image Head Bottom Body highlands # 128 1688 47 482 434 Transition zone Muses Sea Over 5000 boulders were visually counted !!! Thanks Santiago and Sebastián !! # 192 / 2182 7 120

27. Cumulative

28. Cumulative

29. Correlation between potential and size distribution

30. Conclusions • The high frequency of collision regime experienced by Itokawa could induce global shaking associated phenomena, like the Brazilian nut effect. A numerical simulation is needed to study this effect. Thanks to Dr. M. Yoshikawa for introducing us the Hayabusa archive.

31. Numerical methods applied to the study of granular media • Asteroids are modelled as agglomerate of small pieces: rubble-piles • Three methods can be considered: • Smoothed Particle Hydrodynamics (SPH) • Interacting ellipsoids • Granular Physics

32. Smoothed Particle Hydrodynamics(SPH) • Computational method to model a flux of particles. The evolution of each particle is given from the properties of the near by particles. The properties of the particles are smoothed with a characteristic “smoothing length”. • SPH simulation of the formation of asteroids families (Michel et al. 2002)

33. Interacting ellipsoids(Roig et al. 2003) • Rigidi ellipsoids interacting with an artificial repulsive potential and disipative function

34. Granular Physics • Granular materials reveal very different behavior under different circumstances: • Excited (fluidized) granular material often resembles a liquid. It flows through pipes. • In other situations it behaves more like a solid (a heap of sand) • The numerical simulation of the evolution granular materials has been done recently with the Discrete Element Method (DEM). • DEM is a family of numerical methods for computing the motion of a large number of particles like molecules or grains under given physical laws. • Molecular Dynamics (MD), is a particular case of a DEM, when the particles are spherical molecules.

35. Interaction scheme Linear Dashpot Force Normal direction Tangential direction Alternative force models: Viscoelastic Spheres

36. Main Limitations (I)Computer efficiency “Bottle neck” of the method: Computation of the interacting forces for each particle at each timestep. • Simple approach: N(N-1)/2 operations per time step. • But if the particles are equal spheres, each one interact with at most 6. The number of operations should be 3N • Efficient methods to reduce the number of pairs to compute • Verlet Lists Method • Link Cells Algorithm • Lattice algorithm

37. Main Limitations (II)Timestep • The timestep should be: t << duration of collisions (typically 1/10-1/20 of duration of collisions) • Based on the Hertzian elastic contact theory the duration time of contact is   v-1/5 • Typically  ~ 10-5 sec t~10-6 sec !!

38. Some experimentsfrom Computational Granular Dynamics (Pöschel and Schwager 2005)

39. First experiment using DEM in impact process(Wada et al. 2006) Vertical impacts on a target made of a large number of spherical particles under Earth gravity.

40. Our experiments • Code from Computational Granular Dynamics (Pöschel and Schwager 2005) • 2D shaking box with 1800 small spherical particles of radius 4mm and one large particle of 25mm. • Floor and walls of spherical particles of radius 5mm • The elastic and physical parameters of the particles were chosen of typical rocks, and some of them are fixed by simulating a particle bouncing on the floor.

41. Simulating a seism • The floor and the walls are vertically displaced according to a predefined function of the form: • The process is repeated after a fixed number of seconds, depending on the settling time given by the gravity regime. • The simulations typically takes 1 day of CPU time for 100sec in PC 2.4GHz 8Gb RAM.

42. Earth g=9.8 m/s2 Max amp=3cm Moving floor Beating Freq. = 30 Hz Time between seism = 10s

43. Earth g=9.8 m/s2 Max amp=3cm Moving floor Beating Freq. = 30 Hz Time between seism = 10s

44. Eros g=6.1x10-3 m/s2 Max amp=3mm Shaking box Beating Freq. = 14 Hz Time between seism = 30s

45. Eros g=6.1x10-3 m/s2 Max amp=3mm Shaking box Beating Freq. = 14 Hz Time between seism = 30s

46. Itokawa g=9.1x10-5 m/s2 Max amp=0.5mm Shaking box Beating Freq. = 14 Hz Time between seism = 60s

47. Itokawa g=9.1x10-5 m/s2 Max amp=0.5mm Shaking box Beating Freq. = 14 Hz Time between seism = 60s

48. Preliminary conclusions of the DEM experiments • The Brazil nut effect does work in low-gravity regimes Further work is needed to simulate the evolution of a rubble-pile due to frequent impact seismic events.