Impact Cratering on Small Bodies a well-posed problem? Erik Asphaug Earth Sciences Department, UCSC Chapman et al. 2001 Gaspra Galileo SSI Oct 29, 1991 Craters or Facets? Benz and Asphaug 1994,95: rock fracture model is resolution independent and simulates the available laboratory data (Nakamura and Fujiwara 1991; Rubin and Ahrens 1993; Housen and Holsapple 1999) Just so you know catastrophic disruption is far easier to model than cratering. High strain rates can typically be assumed; outcome is typically well defined; simple EOS can often be adequate. Keith: The Siren of CPU Power Housen and Holsapple (1999); simulated in SPH by Bruesch and Asphaug (2002) Large Rocks are More Easily Disrupted Q*DQ*D Q * D R -3/m (Farinella et al. 1982; Fujiwara 1980) Q * D is the specific energy (erg/g) required to catastrophically disrupt a target (fragmentation and dispersal of 50% of the original mass) Benz and Asphaug 1994,95: rock fracture model is resolution independent and simulates the available laboratory data (Nakamura and Fujiwara 1991; Rubin and Ahrens 1993; Housen and Holsapple 1999) Just so you know catastrophic disruption is far easier to model than cratering. High strain rates can typically be assumed; outcome is typically well defined; simple EOS can often be adequate. Keith: The Siren of CPU Power ordinary chondrite meteorite saddle of Himeros on Eros Structural Clues from Meteorites? Meteorites are highly selected! 6489 Golevka 200 km across What about shapes? Shapes by Scott Hudson, Steve Ostro, et al. One is a rock, one is clearly something else Hints from Asteroid Spins Pravec et al Barrier at crit Do asteroids larger than 150 m lack cohesion ? Conversely, are smaller asteroids monolithic? crit 2 = 4/3 G required strength is small, ~R 2 2 Comet LINEAR 1999 S4 Size distribution of the fragments follow a size distribution ~1.56, similar to the comet distribution as a whole and to the size distribution of asteroids (Weissman et al. 2003) If fragments are formed in disruptions where are the small comets? Comet Shoemaker-Levy 9 and the Catenae of Ganymede and Callisto From Asphaug, Schenk and Zahnle (in prep) Can learn target geology from their observed response to impacts 1996: The advent of realistic shape models for code simulations Can begin to seek detailed agreement between modeling and experiments - asteroids as experiments - crater diameter - crater distal rupture - ejecta and block distribution Thomas et al., Science D Eros SPH model with Shoemaker Regio repaired Asteroids as Experiments Castalia Ostro et al shape model Asphaug and Scheeres 1999 And pure forward modeling: can predict outcomes of collisions if we know the target geology! Phobos and Stickney Crater Asphaug and Melosh (1993) concluded that Stickney formed in the gravity regime, and that shattering is much easier to achieve than dispersal. t=12min (Note: radial fractures modeled in 3D SPH) Homogeneous Porous We also found that an incoherent or porous Phobos would not have antipodal fractures, as anticipated from laboratory experiments (e.g. Love, Brownlee and Hrz 1991) Asphaug and Benz 1994; Asphaug et al. 1996 White = Fractured Can we reproduce tectonic features associated with specific impacts? Ida Asteroid Ida Conclusions (from Asphaug et al. Icarus 1996) Ida propagates impact stresses coherently. It may be shattered, but it is not a rubble pile. Gravity regime starts at ~1 km diameter for craters forming on Ida More General Analysis: Cratering or Disruption Outcome Depends on Asteroid Structure Impact modeling of two asteroids, of identical shape and mass, hit by identical smaller asteroid. Mass loss and v differ by more than a factor of 2. Left: monolith Right: rubble-pile Bottom: xy, yz slices Color: fracture damage Momentum and Energy Deposition Vary Widely 5 km/s 16m diameter rock impacting from top into equal-mass targets rubble pile monolith For contact binary asteroids, the shock is confined to the impacted lobe Just as geology is affected strongly by impacts so impacts are affected strongly by geology! Why is this shape so common? space spuds 3D Model: Gravity-regime ejection Werner (1994) polygon gravitation Local angle of repose maintained Analyze time evolution of rotation and shape Do asteroids evolve, through shape instability, into peanuts? Gradual Shape Evolution of Asteroids? So far, the process appears to make muffins rather than peanuts Koycansky and Asphaug (in press) Eros: One might say an aeolian landscape Closest Image of Eros How would sand behave on a 1 km asteroid? Sand exhibits the ability to sustain ~ 33 slopes. There is also some cohesion, which for dry sand in 1G is minimal.. Lets assume a 1 km asteroid, g = G, and ask how cohesive, relative to gravity, is sand? (dgrain 300 m) If cohesion 1/d grain we expect scale-equivalent behavior in 1G by nano-powders m diameter. These are bizarre substances. For reference, Xerox toner particles have diameter 12.7 m, so the desired behavior of sand on a 1 km asteroid would be >10 3 times more cohesive. To get behavior like Xerox toner, youd need grain sizes one meter diameter! Add to that UV ionization at 1AU without an atmosphere (Lee et al. 1996; Sickafoose et al. 2000) Consider a simple assumption: Cohesion contact area / volume (grain size) -1 Small bead coated with particles of Xerox toner Surveyor image of the western lunar horizon shortly after sunset. The white arrow is pointing at a layer of dust levitated ~ 1 meter above the surface. (LASP) Granular segregation Blocks littering the surface of Eros. NEAR image Choo et al., Phys. Rev. Lett., 79 (1997) Upon repeated shaking or other periodic disturbance, granular media can undergo sorting by size, density, or elastic properties. How do we know that the creations of worlds are not determined by falling grains of sand? - Victor Hugo, Les Miserables salt and sand rotating inside of a clear lucite cylinder become self-segregated Largest blocks are 2 to 3 m Descent Image Feb Ponds imaged from low-altitude flyover Explosion Cratering Experiments Mechanics of asteroid and comet surfaces Spectroscopy beneath the surface materials A relatively fail-safe way to poke and prod geologic structures Seismology By filming these events, can create simulation chambers back home for constructing more ambitious landers, hoppers, rovers and excavators Asteroid Surface Probe designed by Ball Aerospace for the Deep Interior spacecraft proposal Is Eros competent? Or is it fragmental? NLR Science Team (L. Prockter) Faults and Joints on Eros a well-defined base or thickness of regolith may not exist on this object. - Robinson et al., The geology of 433 Eros (MAPS 2002) Equations of fault and joint mechanics traction across a fault normal stress across a fault Mohr-Coulomb hydrostatic stress center of Mohr circle + projected deviatoric stress Slopes on Eros NLR Team Eros is not mountainous: Only 2% is steeper than 40 Only 5% is steeper than 33 Angle of Repose Glass beads ~20 o Average for common uncon- solidated materials ~33 o Steepest stable angle for highl angular, poorly sorted rocks (talus) ~40 o -50 o Water-rich soils up to 90 o Zuber et al. (2000); Asphaug et al. (2002) NEAR Image Hypothesis Check: 700m diameter crater Four ~100m diameter rocks Original impactor mass: 210 13 g Impact speed: use v orbit ~1000cm/s Pi-group scaling: assume dry sand D crater ~ 300m Assume constant deceleration 1000cm/s=(2ax) x~10000cm a=-50cm/s 2 Stress = 210 13 g 50cm/s 2 / (1000cm) 2 = 10 8 dyn/cm 2 This is about the expected strength of competent rocks Low-Velocity Impacts Merline et al (Asteroids III): About 15% of all asteroids have satellites! Known from doublet crater statistics (Stansberry and Melosh 1990 Do they form by impact? These things tend to come in pairs -- Woody Allen 1999 KW4 (Ostro et al radar) Galileo Image Gradient Image Dactyl Satellite of Ida Mathilde An Asteroid that Shouldnt Exist? Mathilde is more than 30% crater void The rest of Mathilde is ~50% pore space No evidence for structural damage from impacts (!) No evidence for ejecta emplacement, either: The gravity regime wont work And a very puzzlingly slow rotation (17.4 days) Second image mosaic of Mathilde, at NEARs closest approach: Perfect targeting, but of what? Strength regime does not apply to Mathilde but gravity regime does not apply either! (no ejecta blankets) Asphaug and Thomas 2000 Compaction Cratering to the Rescue? Housen and Holsapple, Nature, 1999 Primitive asteroids begin as porous crushable material Mascons will form at the craters Angular momentum of impactors will be conserved At the early stage existence of dense solar nebula gas keeps relative velocity of the solid bodies lower. This results in low impact velocity and weak impact process. But highly porous material also has a quite low acoustic velocity and low impact velocity yields high Mach state and resultant compaction is induced. - Kurita et al. LPSC 1999 Cumulative Angular Momentum after Seven Giant Impacts on Mathilde Present Angular Momentum of Mathilde = 1.510 20 Probability = 1.5% E E E E E E E E E E+20 Angular Momentum (kg m 2 /s) Percent with Lower Angular Momentum Inelastic Collisions: A Random Walk in 3-Space Spin Axis Mass of Planet Spin Period This is a familiar problem to accretion theorists: Under inelastic accretion, planets start to spin themselves to pieces! Angular Momentum Agnor, Canup and Levison (1999) Nearly all crater ejecta is accelerated to escape velocity The impact deposits less angular momentum to the asteroid No mascons are anticipated at the craters Stalled Shock Cratering Asphaug et al. 2002 So, are rubble piles the natural end state of asteroids? Survival of the Weakest? Initial bombardment, if non-catastrophic, will produce a rubble pile Low crushing strength and rapid shock attenuation allow rubble piles to withstand further bombardment Scientific American 2000 Conclusions : 1) Asteroids and meteorites as benchmarks for impact models 2) SPH with explicit Weibull fracture is a good framework for understanding radial fracture (+ gravity, + Mohr-coulomb) 3) Vesta, the V-type asteroids, and the HED meteorites