Catastrophic disruption of asteroids and family formation: a review of numerical simulations including both fragmentation and gravitational reaccumulations

In the last few years, thanks to the development of sophisticated numerical codes, a major breakthrough has been achieved in our understanding of the processes involved in small body collisions. In this review, we summarize the most recent results provided by numerical simulations, accounting for both the fragmentation of an asteroid and the gravitational interactions of the generated fragments. These studies have greatly improved our knowledge of the mechanisms that are at the origin of some observed features in the asteroid belt. In particular, the simulations have demonstrated that, for bodies larger than several kilometers, the collisional process not only involves the fragmentation of the asteroid but also the gravitational interactions between the ejected fragments. This latter mechanism can lead to the formation of large aggregates by gravitational reaccumulation of smaller fragments, and helps explain the presence of large members within asteroid families. Numerical simulations of the complete process have thus reproduced successfully for the first time the main properties of asteroid families, each formed by the disruption of a large parent body, and provided information on the possible internal structure of the parent bodies. A large amount of work remains necessary, however, to understand in deeper detail the physical process as a function of material properties and internal structures that are relevant to asteroids, and to determine in a more quantitative way the outcome properties such as fragment shapes and rotational states.     

Asteroid rotation and shapes from numerical simulations of gravitational re-accumulation

We present simulations of the gravitational collapse of a mono-disperse set of spherical particles for studying shape and spin properties of re-accumulated members of asteroid families. Previous numerical studies have shown that these “gravitational aggregates” exhibit properties similar to granular continuum models described by Mohr-Coulomb theory. A large variety of shapes is thus possible, in principle consistent with the observed population of asteroid shapes.However, it remains to be verified that the re-accumulation following a catastrophic disruption is capable of naturally producing those shapes. Conversely, we find that fluid equilibrium shapes (flattened two-axis spheroids, in particular) are preferentially created by re-accumulation. This is rather unexpected, since the dynamical system used could allow for other stable configurations. Jacobi three-axial ellipsoids can also be created, but this seems to be a less common outcome.The results obtained so far seem to underline the importance of other non-disruptive shaping factors during the lifetime of rubble-pile asteroids.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

The shape distribution of boulders on Asteroid 25143 Itokawa: Comparison with fragments from impact experiments

Laboratory impact experiments have found that the shape of fragments over a broad size range is distributed around the mean value of the axial ratio 2:√2:1, which is independent of a wide range of experimental conditions. We report the shape statistics of boulders with size of 0.1-30 m on the surface of Asteroid 25143 Itokawa based on high-resolution images obtained by the Hayabusa spacecraft in order to investigate whether their shape distribution is similar to the distribution obtained for fragments (smaller than 0.1 m) in laboratory impact experiments. We also investigated the shapes of boulders with size of 0.1-150 m on Asteroid 433 Eros using a few arbitrary selected images by the NEAR spacecraft, in order to compare those with the shapes on Asteroid Itokawa. In addition, the shapes of small- and fast-rotating asteroids (diameter <200 m and rotation period <1 h), which are natural fragments from past impact events among asteroids, were inferred from archived light curve data taken by ground-based telescopes. The results show that the shape distributions of laboratory fragments are similar to those of the boulders on Eros and of the small- and fast-rotating asteroids, but are different from those on Itokawa. However, we propose that the apparent difference between the boulders of Itokawa and the laboratory fragments is due to the migration of boulders. Therefore, we suggest that the shape distributions of the boulders ranging from 0.1 to 150 m in size and the small- and fast-rotating asteroids are similar to those obtained for the fragments generated in laboratory impact experiments.     

The formation of asteroid satellites in large impacts: results from numerical simulations

We present results of 161 numerical simulations of impacts into 100-km diameter asteroids, examining debris trajectories to search for the formation of bound satellite systems. Our simulations utilize a 3-dimensional smooth-particle hydrodynamics (SPH) code to model the impact between the colliding asteroids. The outcomes of the SPH models are handed off as the initial conditions for N-body simulations, which follow the trajectories of the ejecta fragments to search for the formation of satellite systems. Our results show that catastrophic and large-scale cratering collisions create numerous fragments whose trajectories can be changed by particle-particle interactions and by the reaccretion of material onto the remaining target body. Some impact debris can enter into orbit around the remaining target body, which is a gravitationally reaccreted rubble pile, to form a SMAshed Target Satellite (SMATS). Numerous smaller fragments escaping the largest remnant may have similar trajectories such that many become bound to one another, forming Escaping Ejecta Binaries (EEBs). Our simulations so far seem to be able to produce satellite systems qualitatively similar to observed systems in the main asteroid belt. We find that impacts of 34-km diameter projectiles striking at 3 km s⁻¹ at impact angles of ∼30° appear to be particularly efficient at producing relatively large satellites around the largest remnant as well as large numbers of modest-size binaries among their escaping ejecta.     

Orbital evolution of the Gefion and Adeona asteroid families: close encounters with massive asteroids and the Yarkovsky effect

Asteroid families are groupings of minor planets identified by clustering in their proper orbital elements; these objects have spectral signatures consistent with an origin in the break-up of a common parent body. From the current values of proper semimajor axes a of family members one might hope to estimate the ejection velocities with which the fragments left the putative break-up event (assuming that the pieces were ejected isotropically). However, the ejection velocities so inferred are consistently higher than N-body and hydro-code simulations, as well as laboratory experiments, suggest. To explain this discrepancy between today’s orbital distribution of asteroid family members and their supposed launch velocities, we study whether asteroid family members might have been ejected from the collision at low speeds and then slowly drifted to their current positions, via one or more dynamical processes. Studies show that the proper a of asteroid family members can be altered by two mechanisms: (i) close encounters with massive asteroids, and (ii) the Yarkovsky non-gravitational effect. Because the Yarkovsky effect for kilometer-sized bodies decreases with asteroid diameter D, it is unlikely to have appreciably moved large asteroids (say those with D > 15 km) over the typical family age (1-2 Gyr).For this reason, we numerically studied the mobility of family members produced by close encounters with main-belt, non-family asteroids that were thought massive enough to significantly change their orbits over long timescales. Our goal was to learn the degree to which perturbations might modify the proper a values of all family members, including those too large to be influenced by the Yarkovsky effect. Our initial simulations demonstrated immediately that very few asteroids were massive enough to significantly alter relative orbits among family members. Thus, to maximize gravitational perturbations in our 500-Myr integrations, we investigated the effect of close encounters on two families, Gefion and Adeona, that have high encounter probabilities with 1 Ceres, by far the largest asteroid in the main belt. Our results show that members of these families spreads in a of less than 5% since their formation. Thus gravitational interactions cannot account for the large inferred escape velocities.The effect of close encounters with massive asteroids is, however, not entirely negligible. For about 10% of the simulated bodies, close encounters increased the “inferred” ejection velocities from sub-100 m/s to values greater than 100 m/s, beyond what hydro-code and N-body simulations suggest are the maximum possible initial ejection velocity for members of Adeona and Gefion with D > 15 km. Thus this mechanism of mobility may be responsible for the unusually high inferred ejection speeds of a few of the largest members of these two families.To understand the orbital evolution of the entire family, including smaller members, we also performed simulations to account for the drift of smaller asteroids caused by the Yarkovsky effect. Our two sets of simulations suggest that the two families we investigated are relatively young compared to larger families like Koronis and Themis, which have estimated ages of about 2 Byr. The Adeona and Gefion families seems to be no more than 600 and 850 Myr old, respectively.     

Electrostatic dust transport on Eros: 3-D simulations of pond formation

NEAR-Shoemaker spacecraft images of the surface of the near-Earth Asteroid 433 Eros reveal that more than 200 craters on Eros are partially filled with smooth deposits, termed ponds [Veverka, J., and 32 colleagues, 2001a. Science 292, 484-488]. These ponds appear smooth even at a high resolution of 1.2 cm/pixel and spectral analysis suggests that they may be made up of particles ?50 μm in size [Robinson, M.S., Thomas, P.C., Veverka, J., Murchie, S., Carcish, B., 2001. Nature 413, 396-400; Riner, M.A., Eckart, J.M., Gigilio, J.G., Robinson, M.S., 2006. Lunar Planet. Sci. XXXVII. Abstract 2291]. Coupled with the concentration of ponds at low latitudes, the possible small particle size suggests that these deposits might be related to electrostatic transport of dust near the local terminator [Robinson, M.S., Thomas, P.C., Veverka, J., Murchie, S., Carcish, B., 2001. Nature 413, 396-400]. The work presented here incorporates the precise lighting geometry within a crater at a specified latitude into two models for electrostatic transport of dust grains in order to explore dust deposition and pond formation via this mechanism, particularly as a function of latitude. We find that micrometer-sized dust particles are preferentially transported into craters at latitudes where solar illumination angles are often low. In addition we find that if particles are electrostatically lifted off the surface they are preferentially transported into topographic depressions independent of whether the particles undergo stable levitation. The primary limiting factor for our model is uncertainty concerning the dust launching mechanism. Despite that, and though it does not match the observed north-south asymmetry in pond distribution, our model demonstrates potential for good general agreement between future predictions of pond formation via electrostatic transport of dust and observations of pond locations on the surface of Eros.     

Visible spectroscopic and photometric survey of L5 Trojans: investigation of dynamical families

In this paper we present results obtained in the framework of a visible spectroscopic and photometric survey of Trojan asteroids. We concentrated on bodies orbiting at the L5 Lagrangian point of Jupiter that are also members of dynamical families. Spectroscopy is a crucial tool that allows us to characterize the mineralogical composition of families and their parent bodies, gives evidence of ongoing space weathering, and confirms family membership. We have observed 18 objects belonging to the Aneas, Astyanax, Sarpedon, and Phereclos families as defined by Beaugé and Roig (2001, Icarus 53, 391). In addition, we have determined the spectroscopic properties of 8 background Jupiter Trojans. The observed spectra are reddish with a dominance of D-type asteroids. As expected, the spectra of the non-family members are more heterogeneous compared to the spectra of family members, with the exception of the members of the Aneas family. We also confirm the lack of absorption features in the visible region, as already reported by other authors.     

Asteroid families: Recent results and present scenario

After several decades of frustrating results showing a generally poor agreement among different asteroid family classifications, recent studies based on high accuracy proper elements, as well as on objective statistical methods of cluster analysis have largely improved the situation. Now, a number of asteroid families have been recognized on the basis of different methods of cluster analysis, using asteroid proper elements data sets computed by means of different theories. For these reasons, they should be considered of very high reliability. Moreover, spectroscopic observations confirm in some cases these results, indicating surface compositions of the family members in agreement with a geochemically plausible parent body. However, in particular zones of the belt, like the Flora region, further efforts should be performed in order to establish the real consistence of the resulting clusterings of objects. In addition, the size distribution and the taxonomic types of some well established families seem to indicate particular features of the family sample when compared with the field objects. We recall that asteroid families, in the framework of asteroid collisional evolution, are of the highest importance for understanding the mechanisms of injection of fragments into the Earth-crossing zone through mean-motion and secular resonances and, as a consequence, for evaluating the impact rate on Earth of asteroidal objects.     

Mineralogical characterization of some basaltic asteroids in the neighborhood of (4) Vesta: first results

We present reflectance spectra of 19 V-type asteroids obtained at the 3.6 m Telescopio Nazionale Galileo covering 0.8 to 2.5 μm. For 8 of these asteroids we obtained also visible spectra in the same observational run. The range from 0.8 to 2.5 μm, encompassing the 1 and 2 μm pyroxene features, allows a precise mineralogical characterization of these asteroids. The obtained data suggests the possible coexistence of distinct mineralogical groups among the V-type asteroids, either probing different layers of (4) Vesta or coming from different bodies. No clear correlation was found between mineralogies and the objects being, or not, member of the Vesta dynamical family.     

Olivine or impact melt: Nature of the “Orange” material on Vesta from Dawn

NASA’s Dawn mission observed a great variety of colored terrains on asteroid (4) Vesta during its survey with the Framing Camera (FC). Here we present a detailed study of the orange material on Vesta, which was first observed in color ratio images obtained by the FC and presents a red spectral slope. The orange material deposits can be classified into three types: (a) diffuse ejecta deposited by recent medium-size impact craters (such as Oppia), (b) lobate patches with well-defined edges (nicknamed “pumpkin patches”), and (c) ejecta rays from fresh-looking impact craters. The location of the orange diffuse ejecta from Oppia corresponds to the olivine spot nicknamed “Leslie feature” first identified by Gaffey (Gaffey, M.J. [1997]. Icarus 127, 130–157) from ground-based spectral observations. The distribution of the orange material in the FC mosaic is concentrated on the equatorial region and almost exclusively outside the Rheasilvia basin. Our in-depth analysis of the composition of this material uses complementary observations from FC, the visible and infrared spectrometer (VIR), and the Gamma Ray and Neutron Detector (GRaND). Several possible options for the composition of the orange material are investigated including, cumulate eucrite layer exposed during impact, metal delivered by impactor, olivine–orthopyroxene mixture and impact melt. Based on our analysis, the orange material on Vesta is unlikely to be metal or olivine (originally proposed by Gaffey (Gaffey, M.J. [1997]. Icarus 127, 130–157)). Analysis of the elemental composition of Oppia ejecta blanket with GRaND suggests that its orange material has ∼25% cumulate eucrite component in a howarditic mixture, whereas two other craters with orange material in their ejecta, Octavia and Arruntia, show no sign of cumulate eucrites. Morphology and topography of the orange material in Oppia and Octavia ejecta and orange patches suggests an impact melt origin. A majority of the orange patches appear to be related to the formation of the Rheasilvia basin. Combining the interpretations from the topography, geomorphology, color and spectral parameters, and elemental abundances, the most probable analog for the orange material on Vesta is impact melt.     

The origin of Vesta’s crust: Insights from spectroscopy of the Vestoids

High quality VNIR spectra of 15 Vestoids, small asteroids that are believed to originate from Vesta, were collected and compared to laboratory spectra and compositional data for selected HED meteorites. A combination of spectral parameters such as band centers, and factors derived from Modified Gaussian Model fits (band centers, band strengths, calculation of the low to high-Ca pyroxene ratio) were used to establish if each Vestoid appeared most like eucrite or diogenite material, or a mixture of the two (howardite). This resulted in the identification of the first asteroid with a ferroan diogenite composition, 2511 Patterson. This asteroid can be used to constrain the size of diogenite magma chambers within the crust of Vesta. The Vestoids indicate that both large-scale homogeneous units (>5 km) and smaller-scale heterogeneity (<1 km) exist on the surface of Vesta, as both monomineralogic (eucrite or diogenite material alone) and mixed (both eucrite and diogenite) spectra are observed. The small-scale of the variation observed within the Vestoid population is predicted by the partial melting model, which has multiple intrusions penetrating into the crust of Vesta. It is much more difficult to reconcile the observations here with the magma ocean model, which would predict much more homogeneous layers on a large-scale both at the surface and with depth.     

Global survey of color variations on 433 Eros: Implications for regolith processes and asteroid environments

High-resolution imaging acquired with the Near Earth Asteroid Rendezvous Shoemaker (NEAR Shoemaker) spacecraft is used to elucidate the spectral properties and spatial distribution of color units on Asteroid 433 Eros. Previous workers mapped four distinct types of color units on the surface (bright streaks, dark soils, ponded materials, average regolith). These units exhibit albedo and color boundaries but there is no evidence to indicate they represent distinct rock types. Rather the units are thought to show evidence of complex regolith transport and sorting processes. Here we report the results of a comprehensive study of all viable color MultiSpectral Imager (MSI) data to identify and characterize the distribution and nature of color units across the whole asteroid. Due to a spacecraft upset that resulted in contamination of the MSI optics, color images are affected with a scattered light problem that hampers interpretation of subtle color contrasts, even after a rigorous remediation. To constrain interpretations of the MSI color data we characterize this residual scattered light and demonstrate how complete correction would affect derived color ratios. Results of our comprehensive study are consistent with previous mapping—confirming that bright streaks, average regolith and dark soils fall on a mixing line, consistent with space weathering effects. We find that the ponded deposits do not fall on this putative mixing line. The color and reflectance of the ponded deposits are consistent with some combination of compositional, grain size and maturity variations from the average regolith. Additionally we show that spectral separation of the four units on ratio plots would only increase with full removal of residual scattered light, especially for features that are small in terms of pixels. Global analysis of the Eros color units illustrates complex regolith processes and grain sorting that may hold clues to understanding space weathering processes and the link between asteroids and meteorites.     

A fast method for finding bound systems in numerical simulations: Results from the formation of asteroid binaries

We present a new code (companion) that identifies bound systems of particles in O(NlogN) time. Simple binaries consisting of pairs of mutually bound particles and complex hierarchies consisting of collections of mutually bound particles are identifiable with this code. In comparison, brute force binary search methods scale as O(N²) while full hierarchy searches can be as expensive as O(N³), making analysis highly inefficient for multiple data sets with N?¹⁰³. A simple test case is provided to illustrate the method. Timing tests demonstrating O(NlogN) scaling with the new code on real data are presented. We apply our method to data from asteroid satellite simulations [Durda et al., 2004. Icarus 167, 382-396; Erratum: Icarus 170, 242; reprinted article: Icarus 170, 243-257] and note interesting multi-particle configurations. The code is available at http://www.astro.umd.edu/zoe/companion/ and is distributed under the terms and conditions of the GNU Public License.     

Visible spectroscopic and photometric survey of Jupiter Trojans: Final results on dynamical families

We present the results of a visible spectroscopic and photometric survey of Jupiter Trojans belonging to different dynamical families. The survey was carried out at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory (La Silla, Chile) in April 2003, May 2004 and January 2005. We obtained data on 47 objects, 23 belonging to the L5 swarm and 24 to the L4 one. These data together with those already published by Fornasier et al. [Fornasier, S., Dotto, E., Marzari, F., Barucci, M.A., Boehnhardt, H., Hainaut, O., de Bergh, C., 2004a. Icarus 172, 221-232] and Dotto et al. [Dotto, E., Fornasier, S., Barucci, M.A., Licandro, J., Boehnhardt, H., Hainaut, O., Marzari, F., de Bergh, C., De Luise, F., 2006. Icarus 183, 420-434], acquired since November 2002, constitute a total sample of visible spectra for 80 objects. The survey allows us to investigate six families (Aneas, Anchises, Misenus, Phereclos, Sarpedon, Panthoos) in the L5 cloud and four L4 families (Eurybates, Menelaus, 1986 WD and 1986 TS6). The sample that we measured is dominated by D-type asteroids, with the exception of the Eurybates family in the L4 swarm, where there is a dominance of C- and P-type asteroids. All the spectra that we obtained are featureless with the exception of some Eurybates members, where a drop-off of the reflectance is detected shortward of 5200 Å. Similar features are seen in main belt C-type asteroids and commonly attributed to the intervalence charge transfer transition in oxidized iron. Our sample comprises fainter and smaller Trojans as compared to the literature's data and allows us to investigate the properties of objects with estimated diameter smaller than 40-50 km. The analysis of the spectral slopes and colors versus the estimated diameters shows that the blue and red objects have indistinguishable size distribution, so any relationship between size and spectral slopes has been found. To fully investigate the Trojans population, we include in our analysis 62 spectra of Trojans available in literature, resulting in a total sample of 142 objects. Although the mean spectral behavior of L4 and L5 Trojans is indistinguishable within the uncertainties, we find that the L4 population is more heterogeneous and that it has a higher abundance of bluish objects as compared to the L5 swarm. Finally, we perform a statistical investigation of the Trojans's spectra property distributions as a function of their orbital and physical parameters, and in comparison with other classes of minor bodies in the outer Solar System. Trojans at lower inclination appear significantly bluer than those at higher inclination, but this effect is strongly driven by the Eurybates family. The mean colors of the Trojans are similar to those of short period comets and neutral Centaurs, but their color distributions are different.     

Dust production from the hypervelocity impact disruption of the Murchison hydrous CM2 meteorite: Implications for the disruption of hydrous asteroids and the production of interplanetary dust

More than half of the C-type asteroids, the dominant type of asteroid in the outer half of the main-belt, show evidence of hydration in their reflectance spectra. In order to understand the collisional evolution of asteroids and the production of interplanetary dust and to model the infrared signature of small particles in the Solar System it is important to characterize the dust production from primary impact disruption events, and compare the disruption of hydrous and anhydrous targets. We performed a hypervelocity impact disruption experiment on an ∼30 g target of the Murchison CM2 hydrated carbonaceous chondrite meteorite, and compared the results with our previous disruption experiments on anhydrous meteorites including Allende, a CV3 carbonaceous chondrite, and nine ordinary chondrites. Murchison is significantly more friable than the ordinary chondrites or Allende. Nonetheless, on a plot of mass of the largest fragment versus specific impact energy, the Murchison disruption plots within the field of the anhydrous meteorites points, suggesting that Murchison is at least as resistant to impact disruption as the anhydrous meteorites, which require about twice the energy for disruption as terrestrial anhydrous basalt targets. We determined the mass-frequency distribution of the debris from the Murchison disruption over a nine order-of-magnitude mass range, from ∼10⁻⁹ g to the mass of the largest fragment produced in the disruption. The cumulative mass-frequency distribution from the Murchison disruption is fit by three power-law segments. For masses >10⁻² g the slope is only slightly steeper than that of the corresponding segment from the disruption of most anhydrous meteorites. Over the range from ∼10⁻⁶ to 10⁻² g the slope is significantly steeper than that for the anhydrous meteorites. For masses <10⁻⁶ g the slopes of both the Murchison and the anhydrous meteorites are almost flat. Thus the Murchison disruption significantly over-produced small fragments (10⁻⁶-10⁻³ g) compared to anhydrous meteorite targets. If the Murchison results are representative of hydrous asteroids, the hydrous asteroids may dominate over anhydrous asteroids in the production of interplanetary dust >100 μm in size, the size of micrometeorites recovered from the polar ices, while both types of asteroids might produce comparable amounts of ∼10 μm interplanetary dust. This would explain the puzzle that polar micrometeorites (>100 μm in size) are similar to hydrous meteorites, while the majority of the ∼10 μm interplanetary dust particles are anhydrous.     

The surface composition of Ceres: Discovery of carbonates and iron-rich clays

We present observational evidence that carbonates and iron-rich clays are present on the surface of Ceres. These components are also present in CI chondrites and provide a means of explaining the unusual spectrum of this object as well as providing potential insight into its evolution.     

Compaction and fragmentation of porous gypsum targets from low-velocity impacts

We performed low-velocity impact experiments of gypsum spheres with porosity ranging from 0 to 61% and diameter ranging from 25 to 83 mm. The impact velocity was from 0.2 to 22 m/s. The target was an iron plate. The outcome of gypsum spheres with porosity 31-61% was different from those of non-porous ice [Higa M., Arakawa, M., Maeno, N., 1996. Planet. Space Sci. 44, 917-925; Higa M., Arakawa, M., Maeno, N., 1998. Icarus 133, 310-320] and non-porous gypsum. In between the intact and fragmentation modes, the outcome of the non-porous ice and gypsum was crack growth at the impact point. However, the outcome of the porous gypsum was compaction. We found that the restitution coefficients of the porous gypsum spheres were all in a similar range, in spite of the difference of the porosity and size at impact velocities up to about 10 m/s where they begin to be fragmented in pieces. Moreover, there is not a large difference between the restitution coefficient of porous and non-porous gypsum. These results collectively indicate that restitution coefficient of gypsum spheres of cm-size is not strongly dependent upon the porosity and compaction process.     

Catastrophic disruptions and cratering of solar system bodies: a review and new results

Collisions of bodies of the solar system have played an important role in their evolution and current observable state, but the mechanics and outcomes of those collisions are not well understood. This contribution discusses the mechanics and outcomes of those impacts, melding the existing theory, recent experiments and observations into a new and revised scaling theory, for both catastrophic disruptions and for the largest basins remaining for impacts below that threshold. New evidence is obtained by an analysis of those largest solar system basins and craters, and from some recent experiments on disruptions. The paper will present certain problems with the quantitative estimates of former approaches (Holsapple and Housen, Memorie della Societa Astronomica Italiana57, 65–85, 1986; Housen and Holsapple, Icarus84, 226–253, 1990), discuss remaining areas of uncertainty, and will give updated estimates for these important phenomena.     

Catastrophic fragmentation as a stochastic process: sizes and shapes of fragments

It is rather difficult to understand theoretically and to analyse the experimental data concerning the mass and shape distributions of fragments created by catastrophic collisions. The fragmentation process is discussed as being a purely stochastical phenomenon; the size and shape distributions obtained in this way are compared with the results of laboratory experiments. The results are presented of some computer simulations of random volume fragmentation processes; they are a 3-D generalization of the numerical experiments described in Grady and Kipp (J. Appl. Phys. 58(3), 1210–1222, 1985). The features of the size distribution are discussed, comparing it with the expectations of the Mott-Linfoot and Grady-Kipp theories. In the literature the shape of fragments is defined in terms of the ratios B/A and C/A, where A, B, C are defined as the sizes of a fragment along three orthogonal axes. The definition of the shape of a fragment cannot be considered unique, since it is not obvious in which order to define the three axes when the fragments are not ellipsoidal. A few possible methods are introduced explicity, and the resulting differences are discussed. In this light, the shape results (the mean values and the distribution of the axial ratios) obtained in recent laboratory experiments are rediscussed and critically reviewed. For what concerns the stochastical modelling, the results of various simulations, corresponding to different assumptions regarding fragmentation properties are presented. It is shown that the main features of the shape distributions from laboratory experiments cannot be satisfactorily reproduced. Comparison of the results with the outcomes of the semiempirical fragmentation model by Paolicchi et al. (Icarus 121, 126–157, 1996), as well as with some results coming out from hydrodynamical simulations, shows how only a “global” and physical model, not a purely statistical one (neither global nor “local”), can afford to reproduce the observed data.