An indirect way of showing that asteroids are rubble piles is to link their behavior in certain situations to phenomena which cannot be easily explained by other means (e.g., the formation of large asteroid craters). To this end, I present a list of unusual objects and strange crater formations observed in the inner solar system that have defied conventional explanations for some time:
(a) Disrupted comet Shoemaker-Levy-9 (SL9) was pulled into more than 20 similar-sized fragments during its penultimate encounter with Jupiter in 1992 when it passed within 1.6 Jovian radii of the planet's center (Asphaug and Benz 1996). How did this disruption occur, and why did it create a train of equal-sized fragments much like a ``string of pearls''?
(b) Catena-type crater chains, defined as a regularly spaced row of three or more impact craters with similar sizes and apparently identical ages, have been discovered on the outer Galilean satellites and on our own Moon (Schenk et al. 1996). Their morphology, setting, and orientation make it improbable that they were formed by falling ejecta from a much larger impact. If true, how do catena-type crater chains form?
(c) Doublet craters, created by the nearly simultaneous impact of objects of comparable size, have been found on all the terrestrial planets. Approximately 10% (3 of 28) of terrestrial impact craters larger than 20 km in diameter have companion craters nearby with the same formation age (Bottke and Melosh 1996a,b). A comparable fraction exists on Venus (Cook et al. 1998), while a somewhat smaller fraction has been found on Mars (Melosh et al. 1996). Proposed formation mechanisms, such as tidal disruption during a rubble pile's final approach to a planet and/or break-up due to atmospheric friction, are insufficient to produce significant separation between the fragments. Thus, doublet craters can only be formed by the impact of binary asteroids (Bottke and Melosh 1996a,b). Why do so many near-Earth asteroids have satellites?
(d) Delay-Doppler radar images of Earth-crossing asteroid 1620 Geographos show it to be the most elongated object yet found in the solar system (e.g., its aspect ratio is 2.76) (Ostro et al. 1995; 1996). Its rotation period is so fast (P = 5.27 h) that loose material is scarcely bound near the ends of the body, while cusps on either end of the body make it look something like a pinwheel when viewed from various aspect angles. How did this asteroid get such an unusual shape?
The connection between (a)-(d) is that all these features can be produced, directly or indirectly, by the tidal disruption of rubble pile asteroids or comets. That is, when these bodies encounter a planet on a close slow trajectory, they are often reshaped or pulled apart by that planet's gravitational forces. Before showing model results supporting this hypothesis, however, I briefly digress to explain why tidal disruption requires asteroids and comets to be rubble piles.
Roche showed in 1847 that a self-gravitating synchronously-rotating liquid satellite circling a spherical planet has no stable equilibrium figure inside a critical distance. To obtain this distance, Roche balanced the liquid satellite's self-gravity against the differential gravitational and centrifugal forces on each end of the satellite. His result, now called the Roche limit, showed that a strengthless body will only disrupt near a planet if it orbits very close to that planet (e.g., a liquid satellite with a density of 2 g cm must orbit within 3.4 Earth radii of Earth's center to undergo disruption). Objects making brief encounters with planets need to pass closer than the Roche limit to break apart. Thus, it is easy to show that if comets and asteroids possess any kind of realistic tensile strength, tidal disruption is virtually impossible.
Using an N-body code, it is possible to model the tidal disruption of km-sized rubble piles by the Earth and other planets (Bottke et al. 1997; Bottke et al. 1998a; Richardson et al. 1998). In the simulations I show here, asteroids are modeled as aggregates of 247 identical spherical particles held together by self-gravity. Interparticle collisions and friction between the bodies are both treated rigorously. The model asteroid's bulk density is 2 g cm , while its shape is reminiscent of 4769 Castalia. It was tested over a range of spin periods, spin axis orientations, and hyperbolic trajectories with Earth.
Several classes of outcomes for these encounters were found, depending on the choice of starting conditions (Fig. 5):
The most severe is ``S'', a ``Shoemaker-Levy-9-type'' catastrophic disruption forming a line of clumps of roughly equal size with the largest fragment containing less than 50% of the progenitor's original mass. This disruption class readily explains Shoemaker-Levy-9 as well as the catena-type crater chains, which form when S-class fragment trains impact a moon of the perturbing planet before escaping to interplanetary space. In all cases tested, S-class events produced fragment trains with orientations, sizes, and spacings consistent with observed catenae.
Less severe, and incapable of making crater chains, is ``B'', break-up with mass shedding of clumps (three or more particles) and single particles, with 50% to 90% of the progenitor's mass in the largest fragment. In many cases, the shed fragments go into orbit around the progenitor, producing binary asteroids. If these binaries were to hit a planet at a later time, they would produce two distinct craters. Bottke and Melosh (1996a,b) and Richardson et al.\ (1998) have shown that tidal disruption can create enough binaries to explain the population of doublet craters seen on the terrestrial planets.
Milder still is ``M'', mass shedding of clumps or particles, with the progenitor retaining more than 90% of its mass. In this disruption class, tidal forces frequently reshape the rubble pile while spinning it up. Probable endstates have been found which mimic all the characteristics of 1620 Geographos (Solem and Hills 1996; Bottke et al. 1998b).
Since we can reproduce (a)-(d) using rubble piles, we can infer that these types of bodies must be common throughout the solar system.
Figure 5: The three main tidal disruption outcome classes. Time proceeds from top to bottom in each column. Frame (1) shows the start of each run and frame (5) the end. Frames (2)-(4) were selected to illustrate distinctive points in the evolution of each class, and so are not spaced evenly in time. Some frames undergo scale changes to show ejected clumps and particles. S-class (leftmost column), B-class (middle column), and M-class (rightmost column) tidal disruptions are defined in the text. (Figure from Richardson et al.\ 1998).