Fragment ejection velocities and the collisional evolution of asteroids

We have applied the algorithm developed by Petit and Farinella (Celest. Mech. 57, 1–28, 1993) to model the outcomes of impacts between asteroids of different sizes, to show that a crucial feature of these models is the assumed relationship between velocity and mass of fragments ejected after a shattering impact. Not only how the mean velocity depends upon mass is important to determine the extent of fragment reaccumulation, but also the distribution of velocities about the mean values. The available experimental evidence on this issue is still sparse, and does not constrain the collisional models well enough to allow us to make reliable predictions on the outcomes of impacts between bodies of size much larger than the laboratory targets. As a consequence, when the collisional outcome models are used as an input for simulations of the asteroid collisional history since the origin of the solar system, the results show a strong sensitivity to the assumed velocity vs mass relationship. This sensitivity is stronger in the diameter range (a few tens to a few hundreds of km) where the self-gravitational reaccumulation of fragments is most effective, but may also extend to much smaller sizes.     

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.     

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.     

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.     

Fragment properties at the catastrophic disruption threshold: The effect of the parent body’s internal structure

Numerical simulations of asteroid breakups, including both the fragmentation of the parent body and the gravitational interactions between the fragments, have allowed us to reproduce successfully the main properties of asteroid families formed in different regimes of impact energy, starting from a non-porous parent body. In this paper, using the same approach, we concentrate on a single regime of impact energy, the so-called catastrophic threshold usually designated by , which results in the escape of half of the target’s mass. Thanks to our recent implementation of a model of fragmentation of porous materials, we can characterize for both porous and non-porous targets with a wide range of diameters. We can then analyze the potential influence of porosity on the value of , and by computing the gravitational phase of the collision in the gravity regime, we can characterize the collisional outcome in terms of the fragment size and ejection speed distributions, which are the main outcome properties used by collisional models to study the evolutions of the different populations of small bodies. We also check the dependency of on the impact speed of the projectile.In the strength regime, which corresponds to target sizes below a few hundreds of meters, we find that porous targets are more difficult to disrupt than non-porous ones. In the gravity regime, the outcome is controlled purely by gravity and porosity in the case of porous targets. In the case of non-porous targets, the outcome also depends on strength. Indeed, decreasing the strength of non-porous targets make them easier to disrupt in this regime, while increasing the strength of porous targets has much less influence on the value of . Therefore, one cannot say that non-porous targets are systematically easier or more difficult to disrupt than porous ones, as the outcome highly depends on the assumed strength values. In the gravity regime, we also confirm that the process of gravitational reaccumulation is at the origin of the largest remnant’s mass in both cases. We then propose some power-law relationships between and both target’s size and impact speed that can be used in collisional evolution models. The resulting fragment size distributions can also be reasonably fitted by a power-law whose exponent ranges between −2.2 and −2.7 for all target diameters in both cases and independently on the impact velocity (at least in the small range investigated between 3 and 5 km/s). Then, although ejection velocities in the gravity regime tend to be higher from porous targets, they remain on the same order as the ones from non-porous targets.     

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.     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of ≈ 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times ≈ 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.     

The out of ecliptic distribution of interplanetary dust and its relation to other bodies in the solar system

We discuss the out-of-ecliptic component of the interplanetary dust cloud and its relation to the other small bodies in the solar system. The determination of the mass loss of comets, so far is quite uncertain and doesn't allow a finite study of the mass input to the dust cloud. However it is shown, that the dust particles in the inner solar system, i.e. within the earth orbit are most probable produced from a collisional evolution of larger, meteoroid, fragments of cometary origin. A further component of interstellar dust is especially important in the outer solar system and perhaps for the collisional evolution of the small bodies.     

Sweeping of the Jovian resonances and the evolution of the asteroids

During the formation of the solar system the variation of the gravitational field produced by removal of a nebula with its moderately massive accretion disk led to sweeping of the Jovian commensurability resonances through the asteroid zone. This process produced increased eccentricities and random velocities of the early planetesimals which resulted in collisional comminution rather than accretion. The existence of the asteroids, their low mass density, and their high relative velocities are interpreted as due to disruption of the accretion processes of the terrestrial planets by the influence of Jupiter.     

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.     

Catastrophic disruption of pre-shattered parent bodies

In this paper, we analyze the effect of the internal structure of a parent body on its fragment properties following its disruption in different impact energy regimes. To simulate an asteroid breakup, we use the same numerical procedure as in our previous studies, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational re-accumulation phase. To explore the importance of the internal structure in determining the collisional outcome, we consider two different parent body models: (1) a purely monolithic one and (2) a pre-shattered one which consists of several fragments separated by damaged zones and small voids. We present here simulations spanning two different impact energy regimes—barely disruptive and highly catastrophic—corresponding to the formation of the Eunomia and Koronis families, respectively. As we already found for the intermediate energy regime represented by the Karin family, pre-shattered parent bodies always lead to outcome properties in better agreement with those of real families. In particular, the fragment size distribution obtained by disrupting a monolithic body always contains a large gap between the largest fragment and the next largest ones, whereas it is much more continuous in the case of a pre-shattered parent body. In the latter case, the ejection speeds of large fragments are also higher and a smaller impact energy is generally required to achieve a similar degree of disruption. Hence, unless the internal structure of bodies involved in a collision is known, predicting accurately the outcome is impossible. Interestingly, disrupting a pre-shattered parent body to reproduce the Koronis family yields a fragment size distribution characterized by four almost identical largest objects, as observed in the real family. This peculiar outcome has been found before in laboratory experiments but is obtained for the first time following gravitational re-accumulation. Finally, we show that material belonging to the largest fragments of a family originates from well-defined regions inside the parent body (the extent and location of which are dependent upon internal structure), despite the many gravitational interactions that occur during the re-accumulation process. Hence fragment formation does not proceed stochastically but results directly from the velocity field imparted during the impact.     

Computer simulation of the formation of asteroid belt structure

The system of two gravitational centers with variable separation between components one of which (the primary) loses its mass onto another (the secondary) is investigated under condition of total mass and angular momentum conservation. When the primary/secondary mass ratio becomes about that of Jupiter/Sun the small bodies ejected with the gaseous matter through the inner Lagrange point from the Roche lobe of the primary form a ring similar to the asteroid belt of the solar system. The formation of ring structure is calculated by numerical integration of Newtonian equations of N-body problem in orbital plane of the gravitational centers. The results are compared with the planar subsystem of the asteroid belt. The presence of the main gaps in the distribution of their mean motions at 2/1, 3/1, 5/2 and some other commensurabilities with the primary mean motion is found. More fine details of the belt structure are obtained, e.g. the gap asymmetry and a qualitative agreement with the eccentricity distribution. Within the scope of the same model the external part of the ring is investigated all the pairwise interactions being included. The clustering of bodies near 3/2 commensurability isolated from the main belt by the wide gap centered at 5/3 commensurability is obtained. It is supposed that the ring structure and the interplanetary spacing law for the terrestrial planets are due to the same mechanism.     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.     

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations.

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.     

Collisional origin of the asteroid families: Mass and velocity distributions

The origin of asteroid families in terms of collisional breakup is analyzed using the data by Williams (1979, in Asteroids (T. Gehrels, Ed.), pp. 1040–1063, Univ. of Arizona Press, Tucson). The distributions of mass and relative velocity of the minor family members with respect to the largest body are derived. These ditributions are then compared with the outcomes of catastrophic impacts, predicted from theoretical arguments and observed from laboratory experiments. The general features of the mass distributions can be interpreted in terms of collisional disruption of a parent body followed by self-gravitational reaccumulation on the largest remnant; no decisive evidence for multiple reaccumulations is found. The typical ejection velocities of the family members are of the same order as those of laboratory fragments; since the definition of families is based on purely dynamical arguments, this results gives direct observational support to the collisional formation hypothesis. The transition between collisional outcomes dominated by solid-state forces and by self-gravitatation, expected to occur at diameters D ～ 100 km on the basis of rotational studies and of theoretical estimates, is clearly confirmed by the present analysis. A “morphological” classification into three broad classes (asymmetric, dispersed, and intermediate) is introduced; it is based on the distribution of mass vs relative velocity, taking also into account the parent body's (and the largest remnant's) escape velocity. Finally some results are outlined which apparently do not fit the theoretical predictions: (1) the degree of fragmentation in real families is generally lower than that observed for experimental targets and (2) when the relative velocities are computed, including also proper eccentricity and inclination differences, values higher by about a factor 4 than those derived from semiaxes differences only are found. Further studies are proposed, including more observations, better proper elements computation and classification methods, and new investigations on the physics of hypervelocity impacts.     

Experimental study on collisional disruption of highly porous icy bodies

Knowing the collisional process among small porous icy bodies in the outer solar system is a key to understanding the formation of EKBOs and the evolution of icy planetesimals. Impact experiments of sintered porous ice spheres with 40%, 50%, 60% and 70% porosity were conducted by using three types of projectiles at the impact velocity from 2.4 to 489 m/s, and we studied the effects of porosity on the collisional processes. Projectile sticking occurred at the impact velocity higher than 44 m/s for 60% porosity targets and higher than 13 m/s for 70% porosity targets. The antipodal velocity of the porous ice target increased with the increase of energy density, Q, and it increased slightly with the increase of porosity, although it was exceptionally high in cases when the projectile penetrated the target. The shattering strength of porous ice targets was found to decrease from 100 to 31 J/kg with the increase of porosity from 40% to 70%. The cumulative fragment mass distribution was found to depend on the energy density and the target porosity, and the slopes of the distribution in the small fragment region were almost flat for more porous targets. We reanalyzed the cumulative fragment mass distribution and first obtained the empirical equation showing the fragment mass distribution of porous ice targets as a function of the energy density and the porosity.     

Dynamics of the Hungaria asteroids

To try to understand the dynamical and collisional evolution of the Hungaria asteroids we have built a large catalog of accurate synthetic proper elements. Using the distribution of the Hungaria, in the spaces of proper elements and of proper frequencies, we can study the dynamical boundaries and the internal structure of the Hungaria region, both within a purely gravitational model and also showing the signature of the non-gravitational effects. We find a complex interaction between secular resonances, mean motion resonances, chaotic behavior and Yarkovsky-driven drift in semimajor axis. We also find a rare occurrence of large scale instabilities, leading to escape from the region. This allows to explain the complex shape of a grouping which we suggest is a collisional family, including most Hungaria but by no means all; we provide an explicit list of non-members of the family. There are finer structures, of which the most significant is a set of very close asteroid couples, with extremely similar proper elements. Some of these could have had, in a comparatively recent past, very close approaches with low relative velocity. We argue that the Hungaria, because of the favorable observing conditions, may soon become the best known sub-group of the asteroid population.     

Dynamical evolution of cometary asteroids

We present results from long-term numerical integrations of hypothetical Jupiter-family comets (JFCs) over time-scales in excess of the estimated cometary active lifetime. During inactive periods these bodies could be considered as 'cometary' near-Earth objects (NEOs) or 'cometary asteroids'. The contribution of cometary asteroids to the NEO population has important implications not only for understanding the origin of inner Solar system bodies but also for a correct assessment of the impact hazard presented to the Earth by small bodies throughout the Solar system. We investigate the transfer probabilities on to 'decoupled' subJovian orbits by both gravitational and non-gravitational mechanisms, and estimate the overall inactive cometary contribution to the NEO population. Considering gravitational mechanisms alone, more than 90 per cent of decoupled NEOs are likely to have their origin in the main asteroid belt. When non-gravitational forces are included, in a simple model, the rate of production of decoupled NEOs from JFC orbits becomes comparable to the estimated injection rate of fragments from the main belt. The Jupiter-family (non-decoupled) cometary asteroid population is estimated to be of the order of a few hundred to a few thousand bodies, depending on the assumed cometary active lifetime and the adopted source region.