Asteroidal catastrophic collisions simulated by hypervelocity impact experiments

ICARUS

66, 487-514 (1986)

Asteroidal Catastrophic Collisions Simulated by Hypervelocity Impact Experiments F. CAPACCIONI,*'t P. CERRONI,* M. CORADINI,* M. DI MARTINO,$ P. F A R I N E L L A , § E. FLAMINI, IIG. MARTELLI, *'ll P. PAOLICCHI, a P. N. SMITH, It A. W O O D W A R D , tl AND V. ZAPPALA$ *lstituto di Astrofisica Spaziale, Reparto di Planetologia, Roma, Italy; tSpace Science Group, Department of Physics, The University of Canterbury, Kent, United Kingdom; :~Osservatorio Astronomico di Torino, Pino Torinese, Italy; §Dipartimento di Matematica, Universitdl di Pisa, Pisa, Italy; dlSpace and Plasma Physics Group, University of Sussex, Brighton, United Kingdom; and alstituto di Astronomia, Universitd~ di Pisa, Pisa, Italy Received August 26, 1985; revised February 14, 1986 We report the results of six impact fragmentation experiments carried out with free-falling macroscopic targets of different compositions and shapes, and with projectile velocities close to 9 km/sec, i.e., significantly higher than the sound velocity in the target materials. The data have been examined by deriving the mass and shape distributions of the fragments, by reconstructing two of the shattered targets in order to study the geometry of the fracture surfaces, and by analyzing the properties of the fine-grained high-velocity ejecta. The fragment mass distributions show clearly that the degree of target fragmentation depends strongly on the impact parameter. Apart from the few largest fragments, these distributions are well represented by two power laws with different exponents, connected at a size of about 1 cm. The fragment shapes are generally in good agreement with those observed in previous experiments, and no significant shape vs size dependence has been found down to sizes of the order of 0.1 mm. The fragments tend to become larger and possibly more irregular in shape when they are generated farther from the impact point. The fracture surfaces are oriented roughly along meridians and parallels (with the pole at the impact point) when the target is spherical, but are clustered around the symmetry planes when the target is ellipsoidal. Fine-grained particles, with typical sizes and velocities of 0.01 cm and 1 km/sec, respectively, are ejected at lowelevation angles and in a rather collimated way, starting both from the neighborhood of the impact point and from regions of incipient cracking. Particular attention has been paid to a comparison between these results and the observed properties of the outcomes of asteroidal catastrophic collisions, like the dynamical families and the small inner planet crossing objects. While the collisional theory for the origin of families is fully consistent with the experimental results (with some indication for a significant role of the parent asteroid's self-gravitation), the elongated shapes of several Apollo-Amor objects are much rarer among the laboratory fragments, and thus appear to require a different explanation. © 1986AcademicPress. Inc. 1. INTRODUCTION

The role of catastrophic collisions in the evolution of asteroids and small natural satellites has become increasingly apparent in the last decade. Problems like the origin of the Hirayama dynamical families, of the Apollo-Amor objects and of meteorites, the evolution of the asteroid rotational properties and of the total amount of material present in the belt, the dynamical and geological history of satellite systems have

all been the subject of new investigations which have clearly shown that a deeper understanding of collisional breakup processes is an essential condition for the development of more complete and accurate theoretical models (see, e.g., Farinella et al., 1982a; Zappalb. et al., 1984; Chapman and McKinnon, 1984; Davis et al., 1985). However, the breakup of solid bodies by hypervelocity impacts is at present a poorly understood phenomenon, in the sense that we are not able to predict in a quantitative

487

0019-1035/86 $3.00 Copyright© 1986by AcademicPress, Inc. All fightsof reproductionin any form reserved.

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CAPACCIONI ET AL.

and reliable way the outcome of a collision with well-defined "initial conditions" (mass, shape, rotation, composition, and velocity of the colliding bodies). Collisional models have received so far the most significant empirical input from impact experiments carried out in the laboratory (Gault and Wedekind, 1969; Fujiwara et al., 1977, 1978; Fujiwara and Tsukamoto, 1980, 1981 Lange and Ahrens, 1981; Matsui et al., 1982; Waza and Matsui, 1983; Bianchi et al., 1984; Capaccioni et al., 1984; Takagi et al., 1984). The breakup modalities and the mass, shape, velocity, and spin rate distributions of the fragments have been determined and analyzed. The wide range of mass, shape, and composition of the targets and of the impact velocity have been used to discriminate between general features of the fragmentation process and effects of a particular choice of parameters. For celestial bodies, these are largely unknown, and must be inferred from the observed collisional outcomes. In this paper we describe the results of a set of impact experiments carried out at a velocity of about 9 km/sec, which is more than twice the velocities used in the past in similar experiments. This choice is justified by three reasons: (1) Naturally occurring catastrophic collisions involve velocities ranging from - 5 km/sec for main-belt asteroids to 10-20 km/sec for the satellites of the outer planets. Previous experiments explored only the lower end of this range. (2) For most geologic materials the sound velocity is in the range 3 to 5 km/sec, so that impacts at velocities significantly higher than this could cause peculiar effects and perhaps alter the fragmentation process. (3) We are in possession of an experimental technique which allows projectiles with mass of the order of 1 g to be accelerated routinely up to 10 km/sec or so. 2. E X P E R I M E N T A L P R O C E D U R E

In our experiments, aluminium projectiles of mass of the order of 1 g were accelerated to velocities close to 10 km/sec by

means of a modified shaped charge technique [described in detail by Martelli and Newton (1977)]. The impact velocity was measured to within a few percent by recording successive positions of the flying projectile with the help of a fast framing camera (Martelli et al., 1982). Typical sequences are shown in Figs. la and b. This technique, however, does not allow the mass of the projectile to be predetermined accurately. It can be evaluated only roughly (with an uncertainty of the order of 30%) by means of soft X-ray flash photography of the projectiles just before impact. A composite of computer processed X-ray photographs showing different projectiles in flight is shown in Fig. 2. The values of the projectile mass ranged from 0.3 to 1 g, so that in our experiments the ratio E/Mt of the projectile's kinetic energy to the target mass was in the range 2 to 5 x 10 7 erg/g. As shown in Table I, we have used three representative target shapes (spherical, ellipsoidal, and irregular, the latter being represented by a roughly L-shaped natural basalt block) and two compositions: basalt, in order to test a common rocky material widely used in previous experiments, and high tensile concrete, obtained by mixing fused alumina cement with marble powder in the proportion 1 : 2 by volume. This material is very similar to several natural rocks in cohesive strength (it is stronger than some granites but weaker than many basalts, and falls in the middle of typical meteoritic materials), but has no coarse crystalline structure or hidden fracture planes which could affect its homogeneity and isotropy. The mechanical parameters for a typical basalt and for the concrete used in our experiments are shown in Table II. The targets were placed in a cylindrical chamber of volume about 1 m 3, evacuated to a pressure of --1 Torr, and impacted vertically while free-falling. For the ellipsoidal targets, the impact direction was parallel to the shortest c axis, and the impact point was placed approximately on the plane containing c and the longest a axis. The dis-

HYPERVELOCITY

IMPACTS AND ASTEROIDS

FIG. 1. Typical sequences of fast framing camera pictures. Note that the frames are numbered from right to left as follows: 97531 108642. (a) refers to experiment 6. The projectile in flight, followed by its trail, is clearly visible in frames 1 to 5. (b) refers to experiment 5. The projectile in flight is visible in frame 2.

489

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CAPACCIONI ET AL.

FIG. 2. A composite of computer processed X-ray flash photographs showing the projectile in flight. The linear enlargement is approximately 10 times.

tances (in cm) from the approximate position of impact point to the target "pole", measured on the target surface, are given in Table I for experiments 1 to 5, under the heading "Geometry"; in the table and in what follows, impacts for which this distance was <3 cm are referred to as "central" impacts, the others as "off-center"

impacts. For each experiment, we recovered a number N of fragments having mean diameter D (the diameter of a sphere with the same volume) larger than 10 mm. In the same table MI/Mt and Mz/Mt indicate the ratio of the mass of the first and second largest fragments to the target mass. The next to the last column of the table gives the

TABLE SOME

PARAMETERS

CHARACTERIZING

THE SIX HYPERVELOCITY

AND THEIR

Target Shape

Ellipsoid Ellipsoid Sphere Ellipsoid Ellipsoid Irregular

Composition

Concrete Concrete Concrete Basalt Concrete Basalt

1

Impact features Dimensions

Mt

Velocity

(cm)

[g}

Ikm/sec~

9,940 9.980 10,180 20,850 9.980 17,426

9.7 9.7 8.8 8.8 8.g 8.8

30 x 21 x 30 × 21 x 21 30 × 21 x 30 × 21 x --

15 15 21 15

IMPACT

EXPERIMENTS

OUTCOMES

Geometry

-8, <3, < 3, <3, -4,

Off-center

Central

Central Central Off-center ?, Off-center

Fragments

Mass

Fracture planes, NI

N

MJMt

M,_/Mt

recovery (%~

83 4"~2 1311 644 654 176

0.76 0.11 0.01 0.43 0.20 0.35

0.12 l).08 0.01 0.09 0.03 0.31

98 94 78 96 94 98

46 176

6g 85

HYPERVELOCITY IMPACTS AND ASTEROIDS T A B L E II MECHANICAL PARAMETERS FOR A TYPICAL BASALT AND FOR THE CONCRETE USED IN OUR EXPERIMENTS

Mechanical parameters Vp Vs K E p ~r /x

Concrete

3.56 2.16 1.3 2.27 2.01 0.21 9.38

× x x ×

105 105 l011 l0 II

x 101°

Basalt

6.2 3.3 6.7 9.1 2.8 0.3 3.5

× × × x

10'; 105 10 II 1011

× 10 I1

Note. Vp is the compressional wave velocity, Vs the shear wave velocity, p is the density, K the bulk modulus, /~ the shear modulus, tr the Poisson ratio, and E the Young modulus. The units are cgs throughout the table.

percentages of the target mass recovered after the experiments: this is obtained by adding the mass of the fragments mentioned above to the total mass of the smaller fragments recovered by a series of sieves. These numbers show that with the exception of experiment 3 (the most disruptive event), only a small fraction of the target mass was reduced into very fine dust and eventually lost. A final remark is necessary. This type of experiment carries a heavy penalty; because of the lengthy, time-consuming and expensive experimental procedure, our statistics are not as good as we would wish. Furthermore, following an impact at - 10 km/sec in vacuo, a large cloud of extremely luminous and opaque gas and fine dust develops and expands rapidly. This, with very few exceptions, prevents the observation of the velocity and rotation of the fragments.

3. MASS D I S T R I B U T I O N O F F R A G M E N T S

As shown by the values of N, M~/Mt and M2/Mt listed in Table I, the target fragmentation has been extensive in all the six experiments, involving a large fraction of the

491

original mass. We note significant variations, which appear to be correlated more with the impact geometry (central impacts being more disruptive) than with the target composition and shape, impact velocity or E/Mt ratio. The importance of the impact geometry in determining the degree of fragmentation at lower velocities has already been highlighted (see, e.g., Fujiwara and Tsukamoto, 1980, Fig. 4), but in our experiments it seems even more decisive. A conjectural explanation of this fact is the following: for impact velocities significantly higher than the bulk sound velocity, the pulse of shock waves causing the initial rupture could be strongly anisotropic owing to a Mach cone effect, with a higher intensity along the impact direction. As a consequence, for off-center impacts the fragmentation should involve mainly the part of the target surrounding the impact direction, with relatively small damage to the farthest regions. All the recovered fragments and fine powders were sieved. In experiments 1 and 2, four sieves were used, with mesh sizes 0.063, 0.21, 0.59, and 0.84 mm; fragments larger than - 6 mm were individually weighed and measured. In experiments 3, 4, and 6, nine sieves were used, with mesh sizes 0.088, 0.21, 0.42, 0.59, 0.84, 2, 2.83, 4.76, and 9.52 mm; fragments larger than - 5 mm were individually weighed and measured. Finally, in experiment 5, eleven sieves were used, with mesh sizes 0.19, 0.25, 0.45, 0.57, 0.89, 1.6, 2, 2.5, 5, 7, and 9 mm, fragments larger than 9 mm were individually weighed and measured. In Fig. 3, we show the cumulative mass distributions for the six experiments, i.e., a log-log plot of the fraction of the target m a s s Mt converted into fragments of mean diameter D smaller than the values given (in mm) on the horizontal axis. The values used in the diagram were obtained taking into account both the data from the fragments individually weighed (log D > l) and those from the sieves. The general trend of the distributions is very similar in all the experiments,

492

CAPACCIONI ET AL.

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even if the observed mass fractions of the least (exp. 1) and the most (exp. 3) disrupted targets differ by almost two orders of magnitude. N o clear differentiation appears to be associated with different compositions. The distributions show a distinct change of slope for D = 10 -+ 3 mm, while outside this interval they are well approximated by p o w e r laws. Thus we can represent the distributions in the differential form: d N o~ M-q dM,

pact, following collisions with the walls or the bottom of the vacuum chamber. This "grinding" effect might have flattened the distribution by increasing the number of small fragments at the expense of the larger pieces. H o w e v e r , the fact that concrete and basalt fragments, which have a different strength, behave in a similar way, supports the idea that the main features of the distributions arose from the impact event itself. The values of the exponent q listed in Table

(1) T A B L E 111

where d N is the number of fragments in the mass range (M, M + dM), the exponents q__giving the best fit to the data for " s m a l l " (D < 10 mm) and " l a r g e " (D > 10 mm) fragments being listed in Table III. In the first range we find 1.87 < q < 1.97 and in the second 1.66 < q < 1.81. A word of caution about the observed change of slope is necessary, because we cannot exclude the possibility that the mass distribution has been somewhat affected by further fracturing o f small fragments after the main im-

EXPONENTS OF THE DIFFERENTIAL MASS DISTRIBUTIONS OF FRAGMENTS

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1 2 3 4 5 6

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D>

lOmm

1.87 1.88 1.96 1.97 1.92 1.91

--- 0.01 ± 0.01 -+ 0.01 ± 0.01 -+ 0.01 ± 0.01

1.66 1.69 1.82 1.76 1.76 1.81

~ 0.03 _+ 0.02 _+ 0.01 -+ 0.01 -+ 0.01 _ 0.03

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Ill are generally consistent with those obtained in experiments at lower velocities, and also with those derived for fragments produced by different shattering processes (Hartmann, 1969). On the other hand, a detailed comparison with previous experiments shows some intriguing discrepancies: for instance, Fujiwara et al. (1977), who studied the disruption of cubic basalt targets at 2.6 km/sec, found a clear change of slope (from q = 1.6 to q --= 1.8) for fragment sizes of 1 mm, while we have found no evidence for a similar effect. In Fig. 4, we have replotted the data for the largest fragments (D > 30 mm), in terms of their individual weights. This representation highlights the fact, already noticed by Fujiwara et al. (1977), that in several cases the "regular" power law distributions are no longer valid for the few largest fragments. The discrepancies are in the sense of decreasing q for the least fragmented targets (experiments 6, 1), and of increasing q for the most fragmented ones (experiment 3 and, possibly, 4 and 5). The behavior of the most massive frag-

493

ments is of particular interest if we aim at a comparison of the experimental results with the available data on asteroid families, which are widely believed to represent the outcomes of asteroidal catastrophic collisions: here, the corresponding parent bodies had sizes of the order of 100 km and were hit at velocities of 3 to 7 km/sec. In the families, we are not able to observe the small member asteroids (say, less than several kilometers in size), and the mass distributions can be determined only for the largest objects (see Zappalh et al., 1984). A suitable way to represent the distributions in these cases, taking into account their inherently discrete nature, has been devised by Kres~ik (1977): in a log-log plot of Mi/Mt vs (2j-l), where Mj is the mass of the jth fragment (ordered by mass), ideal power law distributions would be represented by straight lines of slope (1 - q) ~. As we can see in Fig. 5, where we have used this type of diagram for the fragments from our experiments with D -~ 15 mm, after a few (5 to 10) of the largest objects and for M / M t ~10-2, the distributions become nearly straight and have similar slopes, corresponding to values of q in the range 1.5 to 1.8. These values are not necessarily consistent with those derived earlier from the cumulative mass distributions, because there is no power law valid for all sizes, and the cumulative distributions automatically include the small fragments, while the Kresftk diagrams do not. It is interesting to compare Fig. 5 with Fig. 6, adapted from Zappal~ et al. (1984), where the mass distributions of some representative asteroid families are plotted in the same way. The only significant difference is the presence of a few families presenting a drop by a factor larger than 102 just after the largest object, which includes almost all the mass of the family. As discussed by Zappal& et al., this behavior is probably due to self-gravitational reaccumulation of fragments on the largest collisional remnant, since most fragments were ejected at velocities lower than the targers escape velocity. This interpre-

494

CAPACCIONI ET AL.

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tation is supported by our finding that no experimental impact produced this type of outcome, self-gravitational effects being obviously unimportant at such small target sizes. It is also worth noting that among the observed families there is no case with M~/ Mt -~ 10-2, as in experiment 3; this is probably due to an observational selection effect,

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since for a typical size of the parent body the members of this type of family should be quite small. 4. FRAGMENT SHAPES

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HYPERVELOCITY IMPACTS AND ASTEROIDS iments have been determined for different types of breakup events, and compared with the shapes of small Solar System bodies, like small satellites and asteroids (Lange and Ahrens, 1981; Farinella et al., 1982b, 1985; Capaccioni et al., 1984; Catullo et al., 1984). An intriguing feature of the experimental results described in these papers is that, if the fragment shapes are characterized by the two axial ratios b/a and c/a (a ~, b ~ c being the maximum dimensions of the fragments along three orthogonal directions), these quantities are always distributed in a nearly Gaussian way, with peaks at c/a ~- 0.5, b/a ~- 0.7 and standard deviations of about 0.15. This implies an almost total absence of quasi-spherical bodies (with both the ratios approaching unity) and of highly elongated or flattened shapes (with c/a ~ 0.2, b/a ~ 0.3). The only partial exception to this rule has been observed by Lange and Ahrens (1981), who impacted ice targets at velocities lower than 1 km/sec and found a relationship of the shapes both with temperature and with the degree of fragmentation: at 257°K the fragments from barely catastrophic collisions had an "anomalous" elongation, with average values of c/a and b/a of about 0.4 and 0.6, respectively, while at 81°K and for supercatastrophic collisions the behavior was very similar to that found for rocky fragments. All other experiments gave shape distributions in close agreement with each other, suggesting that the fragment shapes are probably controlled more by the quasi random orientation of the fracture surfaces than by the microscopic properties of the material. If this conclusion can be extrapolated to asteroidal sizes, a comparison with the asteroid shapes inferred from lightcurve data leads to interesting conclusions (Capaccioni et al., 1984; Catullo et al., 1984): large asteroids have values of b/a closer to 1, suggesting that the surface layers can sustain limited nonequilibrium structures; for sizes less than -100 km, asteroids look very much like fragments; on the other hand, Apollo-Amor objects are puzzling,

495

since a significant fraction of them (about 1/4) are elongated at a level that is rarely found among fragments, namely, with inferred values of b/a ~ 0.4. With the aim of extending this type of investigation, we have determined the shape distributions of the fragments from our high-velocity experiments, a, b, and c have been defined as the maximum dimension of a fragment (a), the largest dimension of the same fragment in any direction at right angles to a (b), and the maximum dimension in a direction perpendicular to both a and b (c). These parameters have been measured with a slide caliper to an accuracy of 0.05 mm. Figures 7a-f show the distributions in the b/a vs c/a plane for the six impacts. We have indicated in each case the average values of the two axial ratios and the corresponding standard deviations. The general features are the same as described above, with anomalous low values for both ratios in experiment 4 (resembling Lange and Ahrens ice fragments at 257°K) and low values of c/a only in experiment 6. In both cases the distributions are not broader, but rather show a general shift toward the left part of the diagram, together with a narrowing of the depleted region at small values of c/a. Since experiments 4 and 6 were those involving basalt targets, the data provide some indication that a stronger material gives rise to more irregular fragments: but since Fujiwara et al. (1978) also used basalt targets and their fragments had the same shape distribution as we found for concrete targets, the composition cannot be the only important factor. More systematic experiments are probably needed to better understand the peculiarities of the shape distributions. The observed shapes of the ApolloAmor asteroids prompted us to analyze the data in a different way. As discussed by Catullo et al. (1984), the Apollo-Amors have typical diameters of a few kilometers, and could correspond to a low-mass tail (with respect to the parent body) of the fragment distribution, which is not repre-

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HYPERVELOCITY IMPACTS AND ASTEROIDS sented in our sample of measured fragments. In order to investigate the possibility that the average fragment shape depends on size, in Figs. 8a-f, we have plotted running-box diagrams of the axial ratios vs the fragment mean diameter D. The fragments have been ordered by size and grouped in bins including 10 (exp. 1), 60 (exp. 2), 100 (exp. 3), 60 (exp. 4), 60 (exp. 5), and 15 (exp. 6) objects; then, the average axial ratios of each bin are shown as a function of D, the upper and lower lines corresponding to plus or minus one standard deviation. The lines look sometimes smoother at larger sizes, where they connect more spaced points (because there are fewer fragments). Over almost an order of magnitude in size, no significant systematic trend of the axial ratios is apparent, or at least no variation exceeds the l-or level. In just one case (exp. 1) the few largest fragments are clearly less "irregular" than the average, but the same feature is not reproduced for instance in experiment 6, which is also characterized by a comparatively low degree of fragmentation. In experiments 3 and 4 some decrease of c/a can be observed at the smaller measured sizes, but again this trend is not reproduced in the other experiments (moreover, the parameter directly related to lightcurve amplitudes is not c/a but b/a). In order to see what happens over a wider range of fragment sizes, we have collected a sample of 131 fragments from experiment 4 in the size range from 0.1 to 1 ram, and we have imaged them by an electron microscope; a typical microscope image of the fragments is shown in Fig. 9. The axial ratio of the observed images should have been very close to the b/a ratio defined before, though not exactly coincident with it because of the deviations of the line of view with respect to the c axis. The mean fragment size has been redefined as D~ = (ab) I/2, and Fig. 10 shows the new b/a running box diagram of experiment 4 comparing the shapes of fragments over a size range of almost three orders of magnitude. The fact that the aver-

497

age b/a for the sample of microscopic fragments is 0.69 (with a standard deviation of 0.14), that is even larger than for centimeter-sized fragments from the same impact, appears to be quite relevant to the problem of the Apollo-Amor asteroids, because it rules out the possibility that their odd shapes were simply a consequence of their being small-sized fragments from large parent bodies. Instead, some physical explanation is required, related to a peculiar origin or evolution of these objects. 5. G E O M E T R I C A L CHARACTERISTICS OF THE BREAKUP PHENOMENON

The reconstruction of the target is a troublesome task, being a three-dimensional puzzle with an ill-defined number of pieces. It is nevertheless a task which in some cases can be carried out with some degree of success, and the results are of remarkable interest. The analysis of a reassembled target is a suitable tool for the definition of semiempirical models of breakup phenomena, leading to the understanding of correlations between mass distribution, position, shape, initial velocity, and rotation of the fragments. These models are crucial in improving our picture of the collisional evolution of asteroids, since their predictions can be compared fruitfully with the observations of asteroidal sizes, rotation periods, and shapes, as well as with the properties of dynamical families. The reconstruction of the target and the study of the major fracture planes was carried out as described in Bianchi et al. (1984). It should be noted that, although the fracture surfaces generated in a catastrophic fragmentation event are never truly planar, the average slope of each surface is easily identified, curvature and surface roughness affecting it only by a few percent ( ~ 5%). We recall that, in order to study the distribution and orientation in space of the major fracture planes, a cartesian orthogonal system was chosen with the x, y, and z axes coinciding with the principal axes of the ellipsoidal targets. Thus, the

498

CAPACCIONI ET AL.

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FIG. 8 (a-f). Running box diagrams of the b/a and c/a axial ratios vs the logarithm of the fragment mean diameter for experiments 1 to 6. The upper and lower lines give the l-or deviations from the central line. x axis coincides with the major axis a (direction E - W ) , the axis y with the intermediate axis b (direction N - S ) , and the z axis with the minor axis c; i.e., it is parallel to the line o f flight o f the projectile. Only four out o f the six targets were reass e m b l e d - o n e of them (exp. 3) only partially b e c a u s e o f its extreme degree of fragmentation. Furthermore, it should be noted

that near the impact region all targets were so deeply cratered and shattered into dustsized ejecta that any attempt at reconstruction o f the impact region w a s impossible. The best reconstruction was achieved in experiments 2 and 4, and Figs. l l a - f and 1 2 a - f s h o w the reassembled ellipsoids at various aspects, including the approximate position o f the impact point. It can be seen

HYPERVELOCITY IMPACTS AND ASTEROIDS

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FIG. 8--Continued.

that, as already noted by Fujiwara and Asada (1983), the fracture patterns on the target surface vary from experiment to experiment, but show some common general features. The surface map of the fractures consists of a set of radial lines expanding from the approximate position of the impact point, and a set of concentric lines centered about it. The radial lines are usually longer and continuous, while the concentric lines are shorter and broken. The radial pat-

tern of the fracture planes inside the target is particularly evident in Fig. l i e , which shows a side view of target 2 after reassembling. This radial pattern reflects somehow the spherical expansion of the compression pulse from the impact point. We shall now discuss the overall characteristics of the fragmentation process using the surface of the reassembled ellipsoids to correlate the location of the fragments in the target (with respect to the symmetry

500

CAPACCIONI ET AL.

FIG. 9. Electron microscope image of basaltic fragments. The white bar indicating the scale corresponds to 0,1 mm.

axes of the ellipsoid) with their physical properties (mainly size and shape). The analysis of the major fracture planes inside the targets will be described later in this section. The dependence of the size and shape of the fragments on the geometry of the targets and on the impact parameters are not

easily separated: in experiment 2, a triaxial target was hit slightly off center, along its major axis, resulting in an asymmetric fragmentation process, while in experiment 4, the impact occurred very close to the "pole" of a biaxial ellipsoid. Also taking into account the differences in mass and composition (and consequently strength

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FIG. 10. Running box diagram of the b/a ratio vs the logarithm of D~ = (ab) ~/2 for experiment 4. The right part of the figure shows the same diagram for the fragments measured by the electron microscope.

HYPERVELOCITY IMPACTS AND ASTEROIDS

E

w

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FIG. II. The r e a s s e m b l e d ellipsoid of experiment 2, seen at various aspects. The shaded areas

indicate the missing part of the target, while the crossed areas indicate inner surfaces of the ellipsoid. (a) and (b) are side views (plane of the c and a axes) seen from the North and the South directions, respectively, with the arrow showing the approximate position of the impact point. (c) is a top view (plane of a and b), so that the line of flight of the projectile is perpendicular to the plane of this figure. Note that the eastern hemisphere is almost totally missing. (d) shows the antipodal region, namely, the plane of a and b seen from the opposite direction. (e) is a photograph of the missing eastern hemisphere (plane of b and c). (f) shows the same plane, seen from the western side.

and sound velocity) of the targets, and the p o o r s t a t i s t i c s , w e s h a l l l i m i t o u r s e l v e s to the definition of a few general characterist i c s . I n o r d e r t o d o t h i s , w e d e f i n e t w o par a m e t e r s r e l a t e d to t h e s i z e a n d s h a p e o f

each fragment and which can be easily meas u r e d o n t h e s u r f a c e o f t h e r e a s s e m b l e d targets: (a) t h e s i z e S o f a f r a g m e n t , d e f i n e d as t h e s q u a r e r o o t o f its a r e a m e a s u r e d o n t h e t a r -

502

CAPACCIONI ET AL.

b

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w

E

30 cm

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FIG. 12. The reassembled ellipsoid of experiment 4, seen at various aspects. (a) and (b) are side views (plane of the c and a axes) seen from the north and the south directions, respectively, with the arrows showing the approximate position of the impact point. (c) is a top view of the "cratered" region (plane of a and b). (d) shows the same plane, but from the antipodal side. (e) and (f) are the western and eastern hemispheres (plane of b and c), respectively, with the arrows showing the line of flight of the projectile.

HYPERVELOCITY IMPACTS AND ASTEROIDS 13

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get surface (the area was evaluated by approximating the fragment shapes with simple poligonal figures); (b) the irregularity parameter 1, defined as the ratio between the square of the perimeter and the area. The definition of this latter parameter deserves a few further considerations. It clearly contains two kinds of information on the fragment properties: (a) the deviation from a spherical shape (for a circle I attains its minimum value, namely 4rr, while it is larger than that for any other figure and tends to infinity for an infinitely narrow rectangle); (b) the "roughness" of the shape as caused, for instance, by the presence of internal angles larger than 180°. In our simplified analysis we decided to limit the number of parameters, and did not consider other quantities which could have allowed these two effects to be separated [such as, for example, the ellipticity parameter defined

in Leone (1983) as the ratio between the square of the largest segment contained in each figure and its surface]. On the other hand, we have estimated the areas and perimeters by simple poligonal fits, and while this method allows quick and reliable estimates, it tends to cancel the small-scale irregularities, thus decreasing their relative importance on I. Figures 13a and b show S vs d for the two experiments, where d is defined as the distance in space between the impact point and the barycenter of the fragment surface. In both cases the mean value of S increases with d, the effect being more evident for experiment 4 where the largest fragment retains about half of the total mass. It should also be noted that the largest fragment is almost exactly antipodal and does not lie in the core of the target, as frequently found in previous experiments. The increase of S with d means that only for large values of d

504

CAPACCIONI ET AL. 4C "8

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sizeable fragments survive, although small ones are not forbidden there. This fact is probably related to the fact that both the excess of volume energy density and surface effects contribute to the fracturing process. Figures 14a and b show the dependence of I on x, the distance obtained by projecting d onto the (xy) plane perpendicular to the impact direction. In the case of experiment 2 there is a clear correlation between I and x, leading to larger I values for larger x distances. The correlation is not so evident for experiment 4, where the figure shows a quasi-random distribution in the plane I vs x. Three reasons might possibly account for this discrepancy: the different degree of fragmentation, the difference in supersonic propagation of the shock waves in the target material (since the sound velocity in basalt is almost twice that in concrete), and the different geometry of the target and of the impact (as already discussed above). The distribution and orientation in space of the major fracture planes has been analyzed in experiments 1, 2, 3, and 4, and the total number of measured fracture planes in each experiment is given in Table I. As in

Bianchi et al. (1984), a fracture plane is identified by its dip and strike angles. The dip angle is defined as the angle between the fracture and the xy plane, while the strike angle is the angle (measured counterclockwise) between the intersection of the fracture plane with the xy plane, and the N S direction. The histograms of the dip angles in the four experiments are shown in Fig. 15. The most striking feature is the large prevalence of fracture planes nearly parallel to the line of flight of the projectile, as shown by the large percentage of fracture planes having dip angles between 70 and 90° (49, 55, and 59% in exps. 1, 2, and 4, respectively, but only 36% in exp. 3). The fracture planes with dip angles between 70 and 90° contribute to the radial pattern observed on the surface of the targets, while those with dip angles smaller than 60° are the concentric lines centered about the impact point. The lowest inclinations are obviously found in the equatorial region of the target, while those at higher latitudes contribute twice (north and south). This explains the prevalence of intermediate values for the dip angles in the range 0 to 60°, and the apparent bimodality of the distribution in the case of the spheri-

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cal target where, owing to the thorough fragmentation, only the equatorial zone has been reassembled. The distribution of the strike angles is Ikot

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506

CAPACCIONI ET AL.

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FiG. 17. Cross-sectional view of the vacuum chamber showing the relative positions of the target, the four arenas, and the cardinal points in experiments 3 to 6 (in exps. 1 and 2 the two arenas were in positions 2 and 3). The projectile flies perpendicularly into the page, impacting the target along its longest axis in the approximate points specified by the distances given in Table 1. soids, both biaxial and triaxial, the distribution is a s y m m e t r i c along the N - S and E - W directions (which coincide with the s y m m e try axes of the targets). Such an a s y m m e t r y does not a p p e a r in e x p e r i m e n t 3 (the sphere), where the strike angle distribution is r e m a r k a b l y s y m m e t r i c , apart from a " b u m p " in the distribution for strike angles b e t w e e n 100 and 160 °. This last feature can be explained as follows, at least in part. The fracture planes on the sphere lie along meridians and parallels, the orientation of the fracture planes thus reflecting the original position of the fragments defining them on the surface. An apparent a s y m m e t r y is due to a portion of the sphere being m o r e extensively reconstructed, the larger n u m b e r of fracture planes thus identified in that region being responsible for the apparent excess of fracture planes with dip angles between 80 and 120 ° . The s y m m e t r i c distribution of the fracture planes in the case of the sphere confirms the interpretation p r o p o s e d by Bianchi et al. (1984), on the basis of data from

e x p e r i m e n t s 1 and 2: the clustering of fracture planes along the axes of the ellipsoids reflects the a s y m m e t r i c reflection of the shock w a v e s along these axes. This result is not surprising and highlights a t e n d e n c y of the fragmentation process toward a s y m m e t r y , which might be maintained and enhanced in subsequent collisions. It would be interesting to find a relationship b e t w e e n the distribution of fracture planes in the fragmentation process and the elongated shapes typical of fragments f r o m catastrophic collisions. 6. EJECTA In order to investigate the ejection of fine-grained material during the fragmentation process, witness plates (arenas) were placed around the impact area. In the experiments 1 and 2 only two arenas were used. T h e s e were m a d e of four alternating layers of graph paper, aluminium foil, and felt, in this order, each layer being - 5 m m thick. In the e x p e r i m e n t s 3 to 6, four arenas were used. T h e y were made of a lead sheet 4 m m thick and placed as shown in Fig. 17. The arenas had dimension 90 x 31 cm 2 (arenas 1 and 2) and 80 x 23 cm 2 (arenas 3 and 4), and were positioned at a distance from the target center of - 4 0 cm, in a direction such that the normal to the arena surface f o r m e d an angle of 45 ° to the direction N - S . The top of the ellipsoid was at a height (along the vertical) of 65 to 71 cm, measured f r o m the basis of the arenas (see Fig. 18). In what follows, we shall discuss mostly results f r o m tests 3 to 6, as the material chosen for the arenas in tests 1 and 2 did not allow a quantitative analysis of seco n d a r y craters to be made. At a first inspection the surfaces of the witness plates in e x p e r i m e n t s 3 to 6 showed a n u m b e r of holes and irregular indentations; in order to be able to quantify our considerations, in what follows we will only refer to the features exhibiting a typical crater m o r p h o l o g y , i.e., a raised external rim and a roughly hemispherical cavity. A photograph of typical craters found on the are-

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nas is shown in Fig. 19. The distribution of craters on the four arenas from the experiments 3 to 6 is shown in Fig. 20. In view of the geometry of our experiments, the distribution of crater density vs height on the witness plates was not expected to be homogeneous and/or isotropical. In fact, particles ejected from the vicinity of the impact area and traveling in a straight line could not be responsible for any cratering below a height given by the intersection of the plane tangent to the target surface at the impact point and the surface of the plate. If the impact is central this

507

height will be the same for the four arenas; if, on the other hand, the impact parameter is :~ 0, the shadowing effect due to the curved surface of the target will induce an anisotropy in the secondary cratering. The height below which no secondary cratering from particles from the vicinity of the impact point was possible is indicated by the dashed lines in Fig. 20, after both the impact parameter and the original inclination of the target, if any, have been taken into account. It is evident that even geometrically "forbidden" regions of the plates have been cratered; thus, high-velocity particles from regions other than the impact area should be responsible for these craters. Particle ejection from a region roughly antipodal to that of crater formation has indeed been observed a few microseconds after impact in the photographic record of one of our experiments, and a similar ejection has been reported to take place, although not further investigated, by Fujiwara and Tsukamoto (1980). Thus, we will assume that two populations of particles contribute to the overall cratering of the arenas, the first ejected from the vicinity of the impact point during the crater-forming stage, the second from

FIG. 19. Photograph of typical craters formed on the arenas by fine powders ejected during the fragmentation event. The scale indicated by the white bar is 1 cm.

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CAPACCIONI ET AL. H(¢m)

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FiG. 20 (a-d). Distribution of craters vs height on the four arenas, labeled according to the positions indicated in Fig. 17, for experiments 3 to 6. The dashed lines indicate the height below which the arenas were geometrically "in shadow" for particles ejected from the impact region. The dashed area in Fig. 20c indicates a region so densely cratered that individual crater measuring was impossible. regions (not necessarily antipodal) of incipient cracking, prior to the actual formation of the fracture planes. The m o s t striking feature exhibited by craters due to particles from the impact area is their being clustered within a very narrow area ( - 1 5 cm high) around the impact height ( - 7 0 cm), corresponding to a rather collimated b e a m of impacting particles ejected within a cone of opening angle ~ 2 0 °. This is particularly evident in arena 1 from e x p e r i m e n t 5: here particles were geometrically allowed to impact both beneath and a b o v e the o b s e r v e d densely cratered area (from 65 to 80 c m in elevation), but no craters h a v e b e e n found outside this region. The analysis of the arenas used in experiments 1 and 2 yielded similar results. In these e x p e r i m e n t s no morphological analysis of the i m p a c t - p r o d u c e d features was possible; the n u m b e r of impacts on each arena, defined as the n u m b e r of perfora-

tions in the foil, is shown as a function of height in Fig. 21 for the two arenas used in e x p e r i m e n t 2. It can be seen that the particles carrying the largest m o m e n t u m , i.e., the particles penetrating through two or more layers, are ejected in a region centered at the impact height and approximately 20 cm wide. This result seems to confirm the findings from h y p e r v e l o c i t y impact experiments on semi-infinite targets, where the fastest components of the ejecta are ejected at low elevation (<30 °) during the c o m p r e s s i o n stage (see, e.g., Gault and Heitowit, 1963; Gault et al., 1963). On the other hand, our results seem to indicate a higher degree of collimation and ejection at still lower angles. This could be an effect of the curvature of the target surface which, as suggested by Cintala et al. (1978), would cause the velocity vectors of the shock-accelerated particles to intersect the surface at increasingly

HYPERVELOCITY IMPACTS AND ASTEROIDS

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FIG. 21. Histogram showing the distribution of craters vs height for the two arenas used in experiment 2, which were placed in the positions indicated by 2 and 3 in Fig. 17. The dashed line shows the approximate elevation of the impact, and the numbers indicate how many particles penetrated through the first layer of the arena in the specified height ranges. The dashed and crossed areas for arena 2 indicate the presence of particles penetrating through two or three layers, respectively. On the same arena, " S A T " indicates a region so densily cratered to be considered in saturation.

larger angles, resulting in radial velocity components and ejection of material at low angles. It is interesting to note that the different inclination between the line of flight of the projectile and the tangent to the target surface at the impact point does not seem to affect the ejection process. In fact, experiment 4 is a 90 ° impact while experiment 5 is an " o b l i q u e " impact, the impact parameter of about 4 cm corresponding to an angle to the tangent to the surface of - 6 0 ° . This again confirms the results obtained by Gault et al. (1978) for oblique impacts into semiinfinite targets, where no dependence on the impact angle was found for the ejection modalities, as long as the impact angle varied between 90 and 60 ° . The ejection of particles from the fracture-forming zones does not seem confined to any particular region, as shown by arena 3 in experiment 5, which is uniformly cratered at all elevations. The number of ejected particles seems to exhibit a direct correlation with the degree of fragmentation (expressed by the ratios M1/Mt and M2/ Mt given in Table I), the number of craters in experiment 5 (Mi/Mt = 0.2, Mz/Mt = 0.03) being much larger than in experiment 6 (Ml/Mt = 0.35, Mz/Mt = 0.31),

where almost no craters have been found in the region " f o r b i d d e n " to particles from the impact area. This result is not surprising. In fact, although the modalities of ejection are not well understood, one would expect the n u m b e r of high-velocity particles ejected from the fracture-forming regions to be directly related to the number of fracture planes, i.e., to the degree of fragmentation of the target. The results from experiment 3 do not fit into this pattern. Although this target is the most highly fragmented (MJMt = 0.01, M2/ Mt = 0.01), almost no crack-generated ejection has been recorded in this case, and indeed the overall number of observed craters is very low. This could be explained by recalling that no focusing of the shock waves was induced in this target by its shape; on the other hand, we must note that we have reason to believe that the strength of this target was much lower than the strength of the other concrete targets, slower ejecta being associated with lower strength material. The diameters of the craters have been measured by means of microscopic observation for experiments 3 to 6, and their distribution on the arenas and the distribution with respect to the elevation within each

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FIG. 22 (a-d). Distribution of crater diameters in experiments 3 to 6.

arena have been derived. It should be noted that the crater size distribution is limited in the smallest size ranges by the resolution of the microscope (0.25 mm). The most striking feature emerging from an inspection of these distributions is the existence of a preferential crater diameter, independent of the origin of the impacting dust: similar populations of particles seem therefore to be ejected from the impact area and from the crack-forming region. Thus, in order to increase the statistical sample, the data at all elevations on each arena and the data from all the arenas in each experiment have been put together and a single crater diameter distribution has been derived for each experiment. The results, shown in Figs. 22a to d, are Gaussian distributions centered about mean values of the crater diameters

ranging between 5.5 x 10 2 and 6.5 x 10 2 cm.

An idea of the ejection velocities occurred in our experiments can be derived from these results in conjunction with results from calibration tests carried out for our lead arenas at the 2-MeV electrostatic accelerator facilities at the University of Kent, United Kingdom. Fifteen tests were carried out on lead samples impacted by Fe particles with radius of - 1 /~m, travelling at velocities ranging between ! .5 and 4 km/ sec; the diameters of the resulting craters were measured at the SEM facility of the Department of Geology of the University of Rome, and crater diameter distributions were derived. A relation between the impact kinetic energy (in ergs) and the mean value for crater diameter (in cm) of the form

HYPERVELOCITY IMPACTS AND ASTEROIDS loll Dtt -LIIC

-&M

-~1.4

-o'.7

-o~*

- ~.s k~E K

FIG. 23. Mean crater diameter (D~r in cm) vs impact kinetic energy (E~, in ergs) distribution for the calibration tests in lead samples. The best fit line to the data is also shown.

log Dcr = A + k logEk (see Gault, 1973) was used, the values of the constants A and k being found to be k = 0.395 and log A = -3.115, with a correlation coefficient of 0.9. The experimental data on which this calibration law is based are shown in Fig. 23. It should be noted that only 8 out of the 15 tests performed were used, the remaining 7 samples not being sufficiently cratered

511

to yield statistically significant mean crater diameters. A picture of a typical cratered sample is shown in Fig. 24. Using this calibration law, and supposing the ratio Dcr/d between the crater diameter and the diameter of the impacting particle to range between 1 and 10 (see, e.g., Schneider, 1979), we found the velocities of the ejected particles to range between 150 m/sec and 5.5 km/sec, velocities of the order of 1 km/sec being most probable. This confirms results from previous experiments both on finite and on semi-infinite targets. In fact, Fujiwara et al. (1977) report the observation of the ejection of very fast dust during the early stages of the fragmentation process, although no quantitative estimate of the ejection velocity was made. On the other hand, the fast component of the ejecta from hypervelocity impact cratering experiments are known to travel at velocities of a few kilometers per second (Gault and Heitowit, 1963).

FIG. 24. Electron microscope photograph of craters formed on lead samples in the calibration tests. The scale indicated by the white bar is 10/xm.

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It is interesting to speculate whether these results can be used to shed some light on the problem of high-velocity fragment ejection during asteroidal collisions, a problem crucial to the understanding of the structure and evolution of these bodies as well as to the origin of meteorites. Some caution must be used in extrapolating the results on fast ejection from the impact area during laboratory cratering experiments to asteroidal situations, since the ejection modalities are probably dominated more by the local excess of specific energy than by scale-dependent processes. On the other hand, the mechanism of ejection from the fracture-forming regions is not well documented or understood, although it seems to be quite typical of catastrophic destruction events. We are planning experiments which will allow us to overcome the observational difficulties created by the luminous and opaque gas cloud, which has so far made impossible the direct study of the ejection mechanism during catastrophic fragmentation events.

ments. The very elongated shapes inferred from the lightcurves of several ApolloAmor objects appear to require a different explanation, since they are very rare both among laboratory fragments and among main-belt asteroids. (c) The fragments tend to become larger and possibly more irregular in shape when they are generated farther from the impact point. The fracture surfaces are oriented roughly along meridians and parallels (with the pole at the impact point) when the target is spherical, but are asymmetrically distributed, namely, clustered around the symmetry planes, when the target is ellipsoidal. These features should be reproduced by theoretical models of the breakup process. (d) Fine-grained particles, with typical sizes and velocities of 0.01 cm and 1 km/ sec, respectively, are ejected at low-elevation angles and in a rather collimated way, starting both from the neighborhood of the impact point and from regions of incipient cracking. It is tempting to speculate that the asteroidal counterparts of these ejecta 7. CONCLUSIONS might give rise to at least some types of The most interesting findings from our meteorites. experiments can be summarized as follows: We have not derived and studied other (a) The fragment mass distributions show parameters and quantities which have been clearly the importance of the impact geom- only marginally investigated at lower imetry, possibly enhanced by some focusing pact velocities, like the ejection velocity of the impact-generated shock waves, in and the spin rate distribution of fragments, determining the degree of target fragmenta- and their correlation with the mass, shape, tion. Apart from the few largest fragments, and original position in the target. As we the mass distributions are well represented stated before, we are planning to work in by two power laws with different expo- this direction by further refining the experinents, connected at a size of about 1 cm. mental procedure. Systematic experimental These distributions fit well those observed studies of these subjects will be an essential for asteroid families, apart from some cases input both for obtaining reliable theoretical where the parent asteroid's gravity has models of the fragmentation process and probably caused a partial reaccumulation of for a direct comparison with the properties fragments. of small Solar System bodies. (b) The fragment shapes are generally in good agreement with those observed in preACKNOWLEDGMENTS vious experiments and with the shapes of The experiments described in this paper were carmain-belt asteroids less than 100 km across. ried out at the proving ground of the firm "Difesa e No significant shape vs size dependence Spazio" in Colleferro, Italy, in collaborationwith Dr. has been found down to 0.1 mm-sized frag- F. Scoretti and Mr. A. Dell'Orco, who provided in-

HYPERVELOCITY IMPACTS A N D ASTEROIDS valuable help in the preparation and the execution of the experiments. We are particularly indebted to Mr. B. Blackmann of the University of Sussex for his help in building and maintaining most of the mechanical instrumentation used in our tests. The authors are also indebted to Dr. J. A. M. McDonnell and Dr. R. Flavill of the University of Kent, United Kingdom, who allowed the calibration tests of our arenas to be carried out at the Electrostatic Accelerator Facility at their University, and provided help and assistance during the tests. Finally, we thank the reviewers T. J. Ahrens and A. Fujiwara for their helpful suggestions and comments.

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