Eileen V. Ryan, Donald R. Davis, and Ian Giblin

Planetary Science Institute

620 North Sixth Avenue

Tucson, Arizona 85705

Submitted to: ICARUS

11 September 1998

22 Pages

16 Figures

Eileen V. Ryan

Visiting Assistant Professor of Physics

Department of Physical Sciences

New Mexico Highlands University

Las Vegas, New Mexico 87701

Phone: (505) 454-3148

FAX: (505) 454-3103

Email: eryan@cs.nmhu.edu

Running Title:

In September - October 1997, we completed 20 low-velocity airgun shots at the Ames Vertical Gun Range (AVGR) into porous (30 - 45%) and homogeneous ice spheres using aluminum, fractured-ice, and solid ice projectiles. Our goal was to obtain experimental data on the fragmentation of Edgeworth-Kuiper Belt object (EKO) simulants to better understand collisional processes in that region. We found that the very porous ice targets behaved just as strongly as solid ice in collision. Energy is apparently well dissipated by the void spaces within the target, such that these fragile, porous ice structures are strong under impact conditions. Therefore, it would appear that if EKOs are porous, they are not necessarily collisionally weak.

Also, our data have revealed a caveat regarding impact strengths derived using strong projectiles (e.g., aluminum, steel, etc.). The shots we performed in this study provide fundamental information on how porous ice targets fragment when hit by projectiles of differing strengths-- ranging from very strong to very weak, fractured ice projectiles. We observed that if the target and projectile had the same material strength, we could expect a particular fragmentation outcome for the target body. However, if the projectile was stronger than the target, more of the impacting energy was coupled into target breakup, causing increased fragmentation for that body at the same impact energy. In effect, the target responded as if it had a lower-than-normal impact strength. If the projectile was much weaker than the target, more energy was instead coupled into it during the collision, and th same target material appeared much less damaged, or stronger at a particular collisional energy. We attribute this behavior to the depth of penetration of the projectile. A weak object will deposit its collisional energy at a shallower target depth than a stronger projectile, resulting in less efficient energy coupling, and less overall fragmentation. Based on this, if we assume that there has not been significant heating or differentiation in the Edgeworth-Kuiper (E-K) Belt, the most applicable impact strength for the low-velocity E-K belt collisions is likely to be that derived from similar target/projectile materials impacting each other. The laboratory data from this analysis indicate that a value for impact strength ³ 5x10⁵ erg/cm³ is appropriate for porous ice targets impacted with solid/porous ice projectiles.

Understanding the processes that shaped our solar system is one of the goals of planetary science. The origin and evolution of the small body populations, particularly main-belt asteroids and Edgeworth-Kuiper (E-K) transneptunian objects (EKOs) contain clues regarding these processes. As in the asteroid belt, collisions have been shown to be a major factor in the E-K belt (Stern 1995, 1996; Farinella and Davis 1996, Davis and Farinella 1997). Recently, Stern and Colwell (1997) have suggested that collisions may have ground down >90% of the mass of the primordial E-K belt, and this mass was subsequently removed by radiation forces, similar to the mechanism proposed for the asteroid zone. Also, Farinella and Davis (1996) argued that most E-K objects smaller than about 50 km in diameter are collisionally derived fragments rather than primordial objects from the formative era of the solar system. Further, studies by Stern (1996) and Davis and Farinella (1997) suggest that in the current collisional environment of the E-K belt (impact speeds of hundreds of m/s), it is difficult to disrupt bodies hundreds of kilometers in diameter. Escape velocities for these large bodies are too high for a significant fraction of their fragments to avoid reaccumulation. Present interpretations regarding the effect of collisions on E-K objects assume that these bodies fragment similar to the way that asteroids break up in response to energetic high-speed collisions.

This paper reports on a preliminary series of laboratory impact experiments that test this assumpttion, providing basic data o how simulated EKOs fragment in an impact event. An additional experiment run planned for September/October, 1998, will extend this database, filling in the gaps in our record and allowing us to test a new target-type end member, a finely crushed "snowball" model.

To gain a better understanding of what factors influence collisional outcome for icy bodies, we conducted a series of impact experiments from September - October 1997 using the Ames Vertical Gun Range (AVGR, Figure 1). Data were obtained for 20 low-velocity (ranging from 73 m/s to 308 m/s) airgun shots, using porous (30 - 45%) and homogeneous ice spheres and aluminum, fractured-ice, and solid ice projectiles (see Table 1).

Targets and projectiles for this experiment run were prepared in a cold room (kept at 5 F) near the impact chamber. Attempts to additionally cool the ice using liquid nitrogen induced cracks and fissures into the body's structure, and were abandoned. Prior to impact, targets are suspended in a large (~6 ft x 6 ft x 6 ft) vacuum chamber (Figure 2), which is evacuated to a pressure of about 3-13 mbars pressure. The range in evacuation pressure is driven by the need to reduce the time spent by the target at room temperature-- essential to preventing significant melting. Targets were shot at room temperature shortly (within 10 minutes) after being removed from their refrigerated environment. The impact chamber floors and walls are padded to protect against secondary fragmentation of the ejecta material. Three high-speed (~500 frames per second) Milliken cameras are positioned at viewing windows at the side and top of the chamber, perpendicular to the plane of the incoming projectile (Figure 3). A NAC high-framing rate (up to 1000 frames per second) video camera was also used, so that impact shots could be quickly evaluated and faulty shots eliminated from the data analysis. Further, the video camera was our only means of measuring projectile velocities by resolving the incoming projectile's motion on the videotape.

The floor of the impact chamber is lined with a removable plastic tarp to facilitate rapid fragment collection and transfer to a cold room facility. All fragments with a mass greater than 0.5 g were collected and weighed to determine a fragment mass (or equivalently, size) distribution for each of the shots. However, smaller fragments melted almost immediately, and could not be retrieved. The percentage of the target mass recovered and measured for each shot was generally from 80 - 98%. In addition to the size distribution, a mass-velocity distribution for the ejecta will also be determined by measuring fragment speeds from the filmed records of the experiments. This will be the subject of a follow-up paper.

A fundamental question, of course, is what is the real structure of EKOs? Since no one knows as yet, we assumed, like many others, that EKOs are likely to be water-ice/silicate mixtures with a rather porous structure. In the past, a number of impact experiments have been carried out using solid ice targets (e.g., Lange and Ahrens 1981, Cintala et al. 1985, Kawakami et al. 1983) with primarily non-ice projectiles. Therefore, the main focus of our analysis was to, first, incorporate the use of porous targets in experiments, and second, to use ice projectiles as impactors. For this study only ice was used as a target material, but future experiment runs will include some silicate constituent in the target matrix.

In order to compare our results to those of previous workers, we used solid, homogeneous targets as well as the porous bodies. However, three types of target sttructure designs were used for this analysis to construct the porous targets. The first was a pellet-ice target (Figure 4) design, formed from plug-shaped ice disks, having a fairly even particle-size distribution. Figure 5 plots the cumulative mass distribution of the constituent pellets, along side the resulting fragment mass distribution from experiment No. 971020, when the pellet target was hit with an aluminum projectile at 304 m/s. We will discuss the fragment mass distributions in more detail below, but it is clear from Figure 4 that the initial size distribution for the constituent particles in the target has some influence on the post-impact fragment mass distribution. The inflection point for the impact-derived fragment masses occurs just at the turn over point in the initial particle distribution.

The second porous target structure we termed "chipped ice" (Figure 6), since we molded standard water-ice chips into a roughly spherical-shaped target body. The constituent particles for this target type were less regularly formed than the pellet particles, and although still relatively similar in size and shape, had a somewhat wider spread in initial particle masses. Figure 7 shows the initial size distribution for the constituent particles as well as impact experiment No. 971019. Again, the influence of the initial distribution is seen in the resultant fragment mass distribution: the inflection (or turn-over) points in the cumulative distributions occur at the same mass for both distributions.

Our last porous target type was designed to give the constituent particles a form that mimicked the experimental mass distribution's character: a power-law dependence. This was accomplished by randomly crushing the chipped-ice particles so that small masses were far more numerous than large ones. We called this target type "crushed" ice (Figure 8), it will be most closely related to a future end-member target design, the previously mentioned "snowball" target, which will be constructed from even more highly comminuted ice chips. Porosity for the three target types ranged from 30 - 45%.

Again, for comparison to earlier impact experiments using ice targets, we used aluminum projectiles. However, a more realistic collisional set-up should involve icy bodies impacting icy bodies, so we endeavored to shoot ice projectiles with the AVGR airgun. A major experimental problem was keeping the solid ice projectiles (which are weak) intact after launch. In initial experiments, as shown clearly on our film and video records, the projectile broke up in the gun barrel and delivered a spray of fragments to the target. By changing several factors, specifically, ensuring that the projectile was entirely seated within the launch sabot to reduce shear stresses, we finally got the ice projectiles to remain competent until impact. Fortunately, the projectile spray shots could be used to test another variation in collisional condition: the response of our porous targets to a fractured (and presumably much weaker) ice projectile.

Rock targets exhibit several different modes of fragmentation depending on the impact speed of the projectile (Fujiwara et al. 1977, Matsui et al. 1982, Takagi et al. 1984). In the high velocity regime, the outer layer of the target is spalled off, leaving a large central core (core shattering). As the specific energy is increased, the outer-layer fragments become smaller and the core fragment is rubblized. In low-velocity impacts, cone-type shattering is commonly observed, where cone-shaped fragments oriented with the point of the cone aimed towards the impact site are produced. The reason for the different failure modes is not completely clear, but seems to be related to the dimension of the stress pulse in the target, as well as target material and shape (Fujiwara 1986). The width of the stress pulse is determined by the projectile diameter, such that at a fixed collisional energy, low velocity impacts (larger projectiles) have wider stress pulses associated with them than higher velocity (smaller projectiles) impacts.

None of these fragmentation modes had been previously observed for homogeneous, icy targets. Instead, the ice targets were reported to simply break into a few large pieces (Fujiwara et al. 1989). Several of our shots (No.'s 971011, 971012, and 971025) with homogeneous ice spheres clearly displayed cone-type fragmentation (see Figure 9 for shot 971025). Even several of the porous targets seemed to suggest cone-shaped fragments (e.g., 971008, 971021, see Figures 10 and 11).

A frame sequence from film of the impact event for shot No. 971025 is shown in Figure 12, where you can see the cone-shaped fragments form as the energy travels through the body from the impact point.

The degree of disruption a target suffers as a result of a head-on collision is measured by the parameter f_l, the mass ratio of the largest fragment to that of the original target. Impacts at low specific energies (Q) produce only local damage around the impact site (cratering). The excavated volume increases with increasing specific energy and large fragments are broken off around the impact site (giant cratering events). Further increases in collisional energy lead to barely catastrophic disruption f_l = 0.5), where the target hemisphere on which the impact point is centered is fragmented into several large pieces (shape being dependent on impact velocity as described above) along with accompanying smaller fragments. Further collisional energy generates additional comminution of the target with f_l becoming even smaller. The position of the largest fragment post-impact is usually directly opposite to the point of impact, hence, the term ``antipodal'' fragment is often used.

Impact strength is generally defined (see Fujiwara et al. 1977, Takagi et al. 1984, Davis and Ryan 1990, and Ryan et. al. 1991) as the total kinetic energy density (specific energy Q multiplied by the target density) needed for barely catastrophic fragmentation (f_l = 0.5). To obtain a value for impact strength, a series of shots are performed using a particular target/projectile combination, and the collisional energy is varied to produce outcomes ranging from barely cratered to completely shattered. On the average, at least 5 shots are needed to characterize the fragmentation outcome for each pairing of target/projectile types.

The largest fragment mass (normalized to the initial target mass) is shown as a function of the total collisional specific energy Q in Figure 13 for the ice targets of various structures targets using different projectile types. Also shown in Figure 13 are the database of collisional results for ice, rock (adapted from Fujiwara et al. 1989), and cooled metal target materials used in impact experiments. In general, our results indicated that the fragmentation outcomes did not appear to strongly depend on any particular porous target structure. Further, the impact strength we determined for the solid ice targets is comparable to that determined by previous workers using solid ice targets (Lange and Ahrens 1981, Cintala et al. 1985, Kawakami et al. 1983). The data in Figure 11 also show that the porous ice target results follow the same trend as the impact outcomes for solid ice targets. Energy is apparently well dissipated by the void spaces within the target, such that these fragile, porous ice structures are strong in collision. Ryan et al. (1991) also found this to be true for porous, preshattered rock targets. Thus, one of the more interesting results of this study is that even though the very porous ice targets should have a static material strength well below that for solid ice, in collision, they behave just as strongly as solid ice. So it would appear that if EKOs are porous, they are not necessarily collisionally weak.

Additional inspection of the data suggests that there is systematically more collisional damage to the icy targets at the same specific energy as the projectile type varies from aluminum to solid ice to fractured ice. Thus, the main factor affecting outcome appears to be projectile type. Whether a target is solid or porous ice, if it is hit with an aluminum projectile, its impact strength (Q multiplied by the target density) is about 1x10⁵ erg/cm³. If the solid or porous ice target is hit with a solid ice projectile, its impact strength increases to about 5x10⁵ erg/cm³. When a porous target is hit with fractured ice (we do not yet have data for solid ice) its impact strength approaches that determined for rock, ~2x10⁶ erg/cm³.

These results confirm work done previously on collisional energy partitioning between target and projeectile at low velocities. Ryan and Davis (1991) observe that if the target and projectile have the same material strength, the incoming energy is partitioned equally between them. However, if the projectile is stronger than the target, closer to 80-90% of the impacting energy goes into target breakup. We observed that if the target and projectile had the same material strength, we could expect a particular fragmentation outcome for the target body. However, if the projectile was stronger than the target, more of the impacting energy was coupled into target breakup, causing increased fragmentation for that body at the same impact energy. In effect, the target responded as if it had a lower-than-normal impact strength. If the projectile was much weaker than the target, more energy was instead coupled into it during the collision, and the same target material appeared much less damaged, or stronger at a particular collisional energy. We attribute this behavior to the depth of penetration of the projectile. A weak object will deposit its collisional energy at a shallower target depth than a stronger projectile, resulting in less efficient energy coupling, and less overall fragmentation. Based on this, if we assume that there has not been significant heating or differentiation in the Edgeworth-Kuiper (E-K) Belt, the most applicable impact strength for the low-velocity E-K belt collisions is likely to be that derived from similar target/projectile materials impacting each other. The laboratory data from this analysis indicate that a value for impact strength >5x10⁵ erg/cm³ is appropriate for porous ice targets impacted with solid/porous ice projectiles.

The size (or mass) distribution of the target fragments is important for interpreting the collisional process. Collisions generate fragments that are increasingly numerous at smaller sizes. Early workers used a cumulative mass power law distribution with a single exponent to characterize the fragmental distribution over the entire size range (Hartmann 1969, Gault and Wedekind 1969). The cumulative distribution had the form:

where N is the cumulative number of particles having mass > m, C is a constant, m is the fragment mass, and b is the exponent of the cumulative mass distribution. Recent studies have found that, in general, a two-or three-slope power law gives a better fit to fragmentation data, with a steeper slope at large sizes, and a somewhat shallower slope at small sizes (e.g., Fujiwara et al. 1977, Takagi et al. 1984, Davis and Ryan 1990).

The fragment mass distribution data from the impact disruption of our ice targets confirms that indeed a 2-slope power law behavior is still the most appropriate characterization, even for porous targets. Figure 14 shows that far from simply breaking up into their constituent particles, the porous bodies still show the classic power-law trend so common for homogeneous, rocky objects. In general, the mass distribution slope is steeper for the large-mass fragments, and then a much shallower leveling off occurs at the small-mass end. Further, as collisional energy is increased, f_l decreases. The more catastrophic the outcome (i.e., more collisional energy and smaller f_l), the steeper the slope for the large-mass end, resulting in fewer large fragments. For a visual depiction of the fragmentation outcome for the barely catastrophic shot (971021) shown in this figure, see Figure 11.

We can use these fragmentation results (which span the entire mass range) to check our previous conclusions regarding how target/projectile material strength combinations affect collisional outcome. Using only f_l, we noted that the degree of damage a target suffers is strongly linked to the strength of the impactor, and hence to the projectile depth of penetration when collisional energy is deposited. Even at a fixed specific energy, a variation in projectile strength can produce a different level of damage in the target. In Figure 14, target/projectile material combinations are fixed, with a similar projectile material impacting a similar target material. We see that the fragmentation trends are directly related to the collisional energy: f_l gets smaller when energy is increased, and the steepness of the mass distribution slope increases with increasing f_{l .} However, Figure 15 groups together impact shots using like target/projectile materials as well as different material combinations. Examining solid ice target shots 971011 and 971025, which have nearly the same specific energy (3 - 5 x10⁵), we see that when the target is hit with a solid ice projectile, the outcome is barely catastrophic, but when the projectile is much stronger aluminum, the outcome is nearly super catastrophic. Further, the mass distributions display very dissimilar slopes. The mass distribution for experiment No. 971011 is more closely related to shot No. 971023, which is also a strong/weak target/projectile pairing, even though the collisional specific energy of that shot is more than 6 times larger. The same can be said for the two impact shots shown in Figure 14 having similar material target/projectile combinations. The mass distributions for shots 971010 and 971025 have the same general trend, even though different target types are involved, and even though the specific energies differ by a factor of 12.

Finally, Figure 16 depicts mass distribution results for like target/projectile materials and different target/projectile materials, but all shots have about the same collisional specific energy. Results show no similarities to one another, again confirming that fragmentation outcome is not simply governed by the energy of impact, but is more complexly related to the material properties of the bodies involved.

Therefore, the most applicable impact strength for the low-velocity E-K belt collisions is likely to be that derived for similar target/projectile materials impacting each other, a value ³ 5x10⁵ erg/cm³.

Stern, S.A. 1995, Astron. J. 110, 856-868.

Stern, S.A. 1996, Astron. Astrophys. 310, 999-1009.

Farinella, P., and D.R. Davis 1996, Science 273, 938-941.

Davis, D.R., and P. Farinella 1997, Icarus 125, 50-60.

Stern, S.A., and J. Colwell 1997, Astron. J. 114, 841-849.

Lange, A., and T. Ahrens 1981, LPSC XII 1667-1668.

Cintala et al. 1985, LPSC XVI 129-130.

Kawakami et al. 1983, JGR 88, 5806-5814.

Ryan et al. 1991, Icarus 94, 283-298.

Ryan, E., and D.R. Davis 1994, LPSC XV, 1175-1176.

Fujiwara et al. 1989, In Asteroids II, 240-265.

Figure 1. The NASA-Ames Vertical Gun Range at Moffett Field, California.

Figure 2. Porous target suspended in the AVGR vacuum chamber.

Figure 3. Camera set-up (font view) for recording the impact experiments.

Figure 4. Finished pellet target and constituent particles.

Figure 5. Cumulative mass distribution for the constituent pellets used in impact shot No. 971020, as well as the fragment mass distribution that resulted from the impact event.

Figure 6. Finished chipped ice target prior to impact.

Figure 7. Cumulative mass distribution for the constituent ice chips used in impact shot No. 971019, as well as the fragment mass distribution that resulted from the impact event.

Figure 8. Finished crushed ice target prior to impact.

Figure 9. Fragmentation outcome for the solid ice target used in impact shot 971025, showing distinct cone-type fragmentation.

Figure 10. Fragmentation outcome for the porous ice target used in impact shot 971008, suggesting cone-type fragmentation.

Figure 11. Fragmentation outcome for the porous ice target used in impact shot 971021, suggesting cone-type fragmentation.

Figure 12. Series of impact frames for shot 971025 (solid ice target) confirming cone-shaped fragment formation. Each frame is 0.02 seconds apart.

Figure 13. Results on the mass of the largest fragment (f_l) vs. collisional specific energy (Q) from a database of collisional outcomes for ice, rock (adapted from Fujiwara et al. 1989), and cooled metal, as well as new results on porous ice fragmentation.

Figure 14. Cumulative mass distributions for fixed target/projectile material combinations, with a similar projectile material impacting a similar target material.

Figure 15. Cumulative mass distributions for impact shots using like target/projectile materials as well as different material combinations.

Figure 16. Cumulative mass distributions for like target/projectile materials and different target/projectile materials, but all at about the same collisional specific energy.

Tables

(Figure 1)

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16