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.     

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.     

Asteroid rotation rates: II. A theory for the collisional evolution of rotation rates

A model for the evolution of the mean rotation rate of asteroids arising from mutual collisions yields reasonable agreement with observed rotation rates. The mean rotation rate of large asteroids for which gravitational binding energy exceeds material strength should be constant with respect to size. Since collisional erosion of small asteroids is more rapid than collisional spin-up, the onset of increased mean rotation rate occurs at a considerably smaller radius than the size at which material strength begins to dominate gravitational binding energy. For strong igneous rock, increased rotation rates are not expected among bodies larger than a few kilometers. If there is a real trend toward more rapid rotation among asteroids of ≈1?km radius (Degewij and Gehrels, (1976). Bull. Amer. Astron. Soc.8, 459), then a substantial population of strong asteroids in that size range is implied by this model. The slower mean rotation rate of C-type asteroids than other types (paper I) implies a ratio of densities of ≈2:3 between those types, in the context of this model.     

Fugitives from the Vesta family

Spectroscopic observations of Asteroid (4) Vesta and numerous members of the Vesta family located in the inner asteroid belt have determined that these objects have reflectance properties of basaltic material. A plausible hypothesis is that the surface of Vesta was punctured by large impacts in the past which dispersed fragments of its basaltic crust into space and produced one of the most prominent asteroid families ever created in the belt. Until recently, Vesta was the only known object in the asteroid belt which underwent differentiation and survived to the present epoch. Since 2000, many new small basaltic asteroids have been discovered in the inner and outer parts of the asteroid belt, possibly representing fragments from distinct differentiated bodies. These discoveries may help us to better understand the number and nature of objects in the inner Solar System that underwent geological differentiation. To investigate these issues we performed extensive numerical simulations whose aim was to reproduce, as precisely as possible, the dynamical evolution of Vesta's ejected fragments over timescales comparable to the family's age. Specifically, we numerically integrated the orbital evolution of 6600 test bodies with orbits that started within the Vesta family and dynamically evolved over 2 Gy. Our model included gravitational perturbation of all planets (except Mercury) and the Yarkovsky effect. The results show that a relatively large fraction of the original Vesta family members may have evolved out of the family borders defined by clustering algorithms and are now dispersed over the inner asteroid belt. We compared the orbital distribution of our model fragments with the orbital locations of known basaltic asteroids in various parts of the inner main belt to find that: (i) Most basaltic asteroids with semimajor axis located outside the Vesta family's borders in the inner main belt, including (809) Lundia and (956) Elisa, are most likely fugitives from the Vesta family that have evolved to their current orbits via various identified dynamical pathways. Our results also suggest that the Vesta family is at least ∼1 Gy old. (ii) Interestingly, orbits of many basaltic asteroids with , like those of (4796) Lewis and (5379) Abehiroshi, are displaced from the Vesta family to low inclinations and are not obtained in our simulations with sufficient efficiency. We propose that: (i) these small basaltic asteroids may be fragments of differentiated bodies other than (4) Vesta; or (ii) they were liberated from the Vesta's surface before (or during) the Late Heavy Bombardment epoch ∼3.8 Gy ago and their orbital inclinations separated from that of Vesta when secular resonances swept through the region.     

Collisional evolution of the asteroid belt

A new synthesis of asteroid collisional evolution is motivated by the question of whether most asteroids larger than ∼1 km size are strengthless gravitational aggregates (rubble piles). NEAR found Eros not to be a rubble pile, but a shattered collisional fragment, with a through-going fracture system, and an average of about 20 m regolith cover. Of four asteroids visited by spacecraft, none appears likely to be a rubble pile, except perhaps Mathilde. Nevertheless, current understanding of asteroid collisions and size-dependent strength, and the observed distribution of rotation rates versus size, have led to a theoretical consensus that many or most asteroids larger than 1 km should be rubble piles. Is Eros, the best-observed asteroid, highly unusual because it is not a rubble pile? Is Mathilde, if it is a rubble pile, like most asteroids? What would be expected for the small asteroid Itokawa, the MUSES-C sample return target? An asteroid size distribution is synthesized from the Minor Planet Center listing and results of the Sloan Digital Sky Survey, an Infrared Space Observatory survey, the Small Main-belt Asteroid Spectroscopic Survey and the Infrared Astronomical Satellite survey. A new picture emerges of asteroid collisional evolution, in which the well-known Dohnanyi result, that the size distribution tends toward a self-similar form with a 2.5-index power law, is overturned because of scale-dependent collision physics. Survival of a basaltic crust on Vesta can be accommodated, together with formation of many exposed metal cores. The lifetimes against destruction are estimated as 3 Gyr at the size of Eros, 10 Gyr at ten times that size, and 40 Gyr at the size of Vesta. Eros as a shattered collisional fragment is not highly unusual. The new picture reveals the new possibility of a transition size in the collisional state, where asteroids below 5 km size would be primarily collisional breakup fragments whereas much larger asteroids are mostly eroded or shattered survivors of collisions. In this case, well-defined families would be found in asteroids larger than about 5 km size, but for smaller asteroids, families may no longer be readily separated from a background population. Moreover, the measured boulder size distribution on Eros is re-interpreted as a sample of impactor size distributions in the asteroid belt. The regolith on Eros may result largely from the last giant impact, and the same may be true of Itokawa, in which case about a meter of regolith would be expected there. Even a small asteroid like Itokawa may be a shattered object with regolith cover.     

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.     

Steady-state size distributions for collisional populations:: analytical solution with size-dependent strength

The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws—one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.     

Modelling the outcomes of high-velocity impacts between small solar system bodies

We present a self-consistent numerical algorithm aimed at predicting the outcomes of high-velocity impacts between asteroids (or other small bodies of the solar system), based on a set of model input parameters which can be estimated from the available experimental evidence, and including the possible gravitational reaccumulation of ejected fragments whose velocity is less than a suitably defined escape velocity. All the fragment mass distributions are modelled by truncated power laws, and a possible correlation between fragment ejection velocity and mass is taken into account in different ways, including a probabilistic one. We analyze in particular the effectiveness of the gravitational reaccumulation process in terms of different choices of the collisional parameters and the assumed relationship between fragment speed and mass. Both the transition size beyond which solid targets are likely to reaccumulate a large fraction of the fragment mass and the collision energy needed to disperse most of the fragments are sensitive functions of the assumed fragment velocity versus mass relationship. We also give some examples of how our algorithm can be applied to study the origin and collisional history of small solar system bodies, including the asteroid 951 Gaspra (recently imaged by the Galileo probe) and the asteroid families.     

Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation

This paper builds on preliminary work in which numerical simulations of the collisional disruption of large asteroids (represented by the Eunomia and Koronis family parent bodies) were performed and which accounted not only for the fragmentation of the solid body through crack propagation, but also for the mutual gravitational interaction of the resulting fragments. It was found that the parent body is first completely shattered at the end of the fragmentation phase, and then subsequent gravitational reaccumulations lead to the formation of an entire family of large and small objects with dynamical properties similar to those of the parent body. In this work, we present new and improved numerical simulations in detail. As before, we use the same numerical procedure, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational reaccumulation phase. However, this reaccumulation phase is now treated more realistically by using a merging criterion based on energy and angular momentum and by allowing dissipation to occur during fragment collisions. We also extend our previous studies to the as yet unexplored intermediate impact energy regime (represented by the Flora family formation) for which the largest fragment's mass is about half that of the parent body. Finally, we examine the robustness of the results by changing various assumptions, the numerical resolution, and different numerical parameters. We find that in the lowest impact energy regime the more realistic physical approach of reaccumulation leads to results that are statistically identical to those obtained with our previous simplistic approach. Some quantitative changes arise only as the impact energy increases such that higher relative velocities are reached during fragment collisions, but they do not modify the global outcome qualitatively. As a consequence, these new simulations confirm previous main results and still lead to the conclusion that: (1) all large family members must be made of gravitationally reaccumulated fragments; (2) the original fragment size distribution and their orbital dispersion are respectively steeper and smaller than currently observed for the real families, supporting recent studies on subsequent evolution and diffusion of family members; and (3) the formation of satellites around family members is a frequent and natural outcome of collisional processes.     

A Search for the Collisional Parent Bodies of Large NEAs

A search for the most likely parent bodies of multi-km near-Earth asteroids (NEAs) is attempted, in the framework of a scenario based on a few simple assumptions. (1) Multi-km NEAs are produced by collisional fragmentation of single parent bodies. (2) The fragments are injected into either the 3/1 mean-motion resonance with Jupiter or the ν₆ secular resonance, or they achieve Mars-crossing orbits. (3) The collisional events responsible for the production of multi-km NEAs do not produce observable dynamical families. We show that a limited number of potential parent bodies of multi-km NEAs compatible with the above assumptions do exist in the asteroid Main Belt. It is not clear whether these objects can likely explain the current inventory of known NEAs having sizes around 1-2 km. Our results seem to indicate that the assumed scenario is not completely adequate to justify the number of observed NEAs larger than 2 km. This preliminary analysis must be complemented by a more precise analysis of the rates of occurrence of NEA-feeding events. If present results are confirmed, the conclusion that the origin of multi-km NEAs must be explained by different models, based on long-term dynamical diffusion produced by the interplay of collisional, gravitational, and nongravitational mechanisms in the Main Belt, plus a possible cometary contribution, will be strengthened.     

Asteroids and meteorites: Parent bodies and delivered samples

Meteorites may be pieces of main-belt asteroids, derived by cratering collisions. The physical strength of an asteroid critically affects the quantity of ejecta that can be placed in orbits (probably resonant) that evolve to cross the Earth's. Asteroid strengths very widely due to initial composition and size (e.g., weak carbonaceous material or strong rock), subsequent geophysical evolution (e.g., formation of a strong iron core), and subsequent collisional evolution (e.g., conversion of a strong rocky body into a weak rubble pile). The meteorite yield on Earth further depends on meteorite strength, which affects longevity in space and survival through the atmosphere. We show that meteorites may be derived mainly by cratering rather than by disruptive fragmentation and from large main-belt asteroids rather than from small, Earth-approaching bodies. The model combines a wide variety of evidence from various disciplines to yield results consistent with meteorite statistics. However, no claim is made for uniqueness of this model, and many elements still admit considerable uncertainty.     

Meteoroids, Meteors, and the Near-Earth Object Impact Hazard

In considering the modern-day hazard from infalling near-Earth asteroids and comets, the focus has shifted toward the smallest, most frequent impacts that can do damage on the ground, like the 1908 Tunguska aerial burst. There is considerable uncertainty about the potential for damage by objects in the range 20 to 100 m diameter. Since smaller, less dangerous, meter-sized meteoroids are part of a continuum of small interplanetary bodies, derived by a collisional cascade and Yarkovsky spin-up, research on such phenomena by meteor scientists can shed light on a vital question that will soon have great practical relevance as new telescopic searches for near-Earth asteroids come on line: what is the threshold size between harmless high-altitude airbursts and impacts that can cause lethal damage on the ground?     

Catastrophic fragmentation and formation of families: Preliminary results from a new numerical model

Preliminary results of an improved version of the semiempirical model for catastrophic break up processes developed by Paolicchi et al., (1989) are presented. Among the several changes with respect to the old version, the most important seem to be related to the new treatment of gravitational effects, including self-compression and reaccumulation of fragments. In particular, the new model is able to analyze processes involving both cm-sized objects, like those studied by means of laboratory experiments, as well as much larger bodies, for which self-gravitational effects are dominant; moreover, in this latter case the model seems in principle adequate to describe with the same physics very different phenomena, like the formation of plausible asteroid families and the creation of single, rapidly spinning, objects. This fact, if confirmed by refined analyses, may be of high importance for our general understanding of asteroid collisional evolution.     

Numerical simulations of granular dynamics II: Particle dynamics in a shaken granular material

Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties.We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration.We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments.     

Scaling forces to asteroid surfaces: The role of cohesion

The scaling of physical forces to the extremely low ambient gravitational acceleration regimes found on the surfaces of small asteroids is performed. Resulting from this, it is found that van der Waals cohesive forces between regolith grains on asteroid surfaces should be a dominant force and compete with particle weights and be greater, in general, than electrostatic and solar radiation pressure forces. Based on this scaling, we interpret previous experiments performed on cohesive powders in the terrestrial environment as being relevant for the understanding of processes on asteroid surfaces. The implications of these terrestrial experiments for interpreting observations of asteroid surfaces and macro-porosity are considered, and yield interpretations that differ from previously assumed processes for these environments. Based on this understanding, we propose a new model for the end state of small, rapidly rotating asteroids which allows them to be comprised of relatively fine regolith grains held together by van der Waals cohesive forces.     

The distribution of basaltic asteroids in the Main Belt

We present the observational results of a survey designed to target and detect asteroids whose photometric colors are similar to those of Vesta family members and thus may be considered as candidates for having a basaltic composition. Fifty basaltic candidates were selected with orbital elements that lie outside of the Vesta dynamical family. Optical and near-infrared spectra were used to assign a taxonomic type to 11 of the 50 candidates. Ten of these were spectroscopically confirmed as V-type asteroids, suggesting that most of the candidates are basaltic and can be used to constrain the distribution of basaltic material in the Main Belt. Using our catalog of V-type candidates and the success rate of the survey, we calculate unbiased size-frequency and semi-major axis distributions of V-type asteroids. These distributions, in addition to an estimate for the total mass of basaltic material, suggest that Vesta was the predominant contributor to the basaltic asteroid inventory of the Main Belt, however scattered planetesimals from the inner Solar System (a<2.0 AU) and other partially/fully differentiated bodies likely contributed to this inventory. In particular, we infer the presence of basaltic fragments in the vicinity of Asteroid 15 Eunomia, which may be derived from a differentiated parent body in the middle Main Belt (2.5<a<2.8). We find no asteroidal evidence for a large number of previously undiscovered basaltic asteroids, which agrees with previous theories suggesting that basaltic fragments from the ∼100 differentiated parent bodies represented in meteorite collections have been “battered to bits” [Burbine, T.H., Meibom, A., Binzel, R.P., 1996. Meteorit. Planet. Sci. 31, 607-620].     

The collisional and dynamical evolution of the main-belt and NEA size distributions

The size distribution of main belt of asteroids is determined primarily by collisional processes. Large asteroids break up and form smaller asteroids in a collisional cascade, with the outcome controlled by the strength-size relationship for asteroids. In addition to collisional processes, the non-collisional removal of asteroids from the main belt (and their insertion into the near-Earth asteroid (NEA) population) is critical, and involves several effects: strong resonances increase the orbital eccentricity of asteroids and cause them to enter the inner planet region; chaotic diffusion by numerous weak resonances causes a slow leak of asteroids into the Mars- and Earth-crossing populations; and the Yarkovsky effect, a radiation force on asteroids, is the primary process that drives asteroids into these resonant escape routes. Yarkovsky drift is size-dependent and can modify the main-belt size distribution. The NEA size distribution is primarily determined by its source, the main-belt population, and by the size-dependent processes that deliver bodies from the main belt. All of these effects are simulated in a numerical collisional evolution model that incorporates removal by non-collisional processes. We test our model against a wide range of observational constraints, such as the observed main-belt and NEA size distributions, the number of asteroid families, the preserved basaltic crust of Vesta and its large south-pole impact basin, the cosmic ray exposure ages of meteorites, and the cratering records on asteroids. We find a strength-size relationship for main-belt asteroids and non-collisional removal rates from the main belt such that our model fits these constraints as best as possible within the parameter space we explore. Our results are consistent with other independent estimates of strength and removal rates.     

Collisional history of asteroids: Evidence from Vesta and the Hirayama families

Collisional evolution studies of asteroids indicate that the initial asteroid population at the time mean collisional velocities were pumped up to ～5 km/sec was only modestly larger than it is today; i.e., the asteroid belt was already depleted relative to the mean surface density elsewhere in the planetary region. Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run, subject to three constraints: they must (a) evolve to the present observed asteroid size distribution, (b) preserve Vesta's basaltic crust, and (c) produce at least the observed number of major Hirayama families. A “runaway growth” initial asteroid population distribution is found to best satisfy these constraints. A new model is presented for calculating the fragmental size distribution for the disruption of large, gravitationally bound bodies in which the material strength is increased by hydrostatic self-compression. This model predicts that large asteroid behave as intrinsically strong bodies, even if they have had a history of being collisionally fractured. This model, when applied to the breakup of the Themis and Eos family parent bodies, gives size distributions in reasonably good agreement with those observed.     

Fundamentally distinct outcomes of asteroid collisional evolution and catastrophic disruption

The outcomes of asteroid collisional evolution are presently unclear: are most asteroids larger than 1 km size gravitational aggregates reaccreted from fragments of a parent body that was collisionally disrupted, while much smaller asteroids are collisional shards that were never completely disrupted? The 16 km mean diameter S-type asteroid 433 Eros, visited by the NEAR mission, has surface geology consistent with being a fractured shard. A ubiquitous fabric of linear structural features is found on the surface of Eros and probably indicates a globally consolidated structure beneath its regolith cover. Despite the differences in absolute scale and in lighting conditions for NEAR and Hayabusa, similar features should have been found on 25143 Itokawa if present. This much smaller, 320 m diameter S-asteroid was visited by the Hayabusa spacecraft. Comparative analyses of Itokawa and Eros geology reveal fundamental differences, and interpretation of Eros geology is illuminated by comparison with Itokawa. Itokawa lacks a global lineament fabric, and its blocks, craters, and regolith may be inconsistent with formation and evolution as a fractured shard, unlike Eros. An object as small as Itokawa can form as a rubble pile, while much larger Eros formed as a fractured shard. Itokawa is not a scaled-down Eros, but formed by catastrophic disruption and reaccumulation.