These same impact simulations also suggest that the large craters imaged on asteroids like Gaspra, Ida, Mathilde, and Mars's satellite Phobos could only have been produced if the bodies were rubble piles. Big craters, like the 11 km Stickney crater on 22 km Phobos or the adjacent and undisturbed 19-33 km craters on 53 km Mathilde (Fig. 3), form in the ``gravity-scaling'' regime, where the growth and ultimate size of a crater is controlled by the target's gravity (Love and Ahrens 1996). Craters formed in the gravity regime require a weak or fragmented target much like a rubble pile, which damps the propagation of impact-generated shock waves and thereby limits the effects of an impact to a localized region. (Asphaug et al. 1998). If the projectiles which produced these craters had instead formed in the ``strength'', regime, where crater size is governed by the target body's tensile strength, they would have disrupted the target. Rubble piles, therefore, are even harder to disrupt or pulverize than solid objects.
To give us some insight on the above discussion, I use the following thought experiment. Suppose I took a rifle and shot a bullet into a rock and a sandpile. When the bullet hits the rock, the impact energy is well-coupled throughout the rock's interior, breaking it up and sending the pieces away at high velocity. When the bullet hits a sandpile, however, the impact energy has difficulty moving between sand grain boundaries. The result is that most of the impact energy is released near the impact site, creating a crater but otherwise leaving the sandpile undisturbed. Thus, a strong rock is actually weaker against a high velocity projectile than a strengthless sandpile.
To demonstrate this effect more quantitatively, I show another numerical simulation similar to the one discussed in Sec. II.B, except this time the Castalia-like solid asteroid is effectively a contact-binary with a band of pre-damaged material between the components (Asphaug et al. 1998). Fig. 4 shows the damage caused by the 16 m projectile striking the end of the target body. Note that while the impact energy imparted by the projectile has significantly damaged the right lobe of the asteroid, the pre-damaged material has acted like an impedance barrier to damp the energy and reflect the shock away from the left lobe. Thus, while the right lobe is highly fragmented, the left lobe remains undamaged. The implication is that rubble piles help prevent catastrophic disruption events while protecting intact interior fragments from damage. Thus, the size distribution of fragments inside various rubble pile asteroids may be very different from one another.
Figure 3: Image of 253 Mathilde, a 66 by 48 by 46 km C-type asteroid. Five craters between 19 and 33 km across have been located on the illuminated portions of the asteroid (roughly half of the total area of Mathilde). They were probably formed by the impact of 1-3 km asteroids. Little evidence for large-scale fracturing or disturbed regions adjacent to the craters can be seen. Rim crests and other basic shapes appear to be unaffected by subsequent impacts. The volume and mass derived from images and NEAR spacecraft tracking imply a bulk density of 1.3 g cm , about half that of CM chondrites. (Figure from Veverka et al. 1997).
Figure 4: A contact-binary shortly after being hit by an 16 m projectile striking at 5 km/s on one end. The band about the waist is pre-damaged, underdense (1.7 g cm ) material which presents an impedance barrier for the shock, thereby reflecting its energy back into the impacted lobe. While damage to the right lobe is almost total, very little damage occurs in the left lobe. (Figure from Asphaug et al. 1998).