Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids. II. Effects of initial rotation and spin-down through disruptive collisions

Expanding on our previous N-body simulation of impacts between initially non-rotating rubble-pile objects [Takeda, T., Ohtsuki, K., 2007. Icarus 189, 256-273], we examine effects of initial rotation of targets on mass dispersal and change of spin rates. Numerical results show that the collisional energy needed to disrupt a rubble-pile object is not sensitive to initial rotation of the target, in most of the parameter range studied in our simulations. We find that initial rotation of targets is slowed down through disruptive impacts for a wide range of parameters. The spin-down is caused by escape of high-velocity ejecta and asymmetric re-accumulation of fragments. When these effects are significant, rotation is slowed down even when the angular momentum added by an impactor is in the same direction as the initial rotation of the target. Spin-down is most efficient when the impact occurs in the equatorial plane of the target, because in this case most of the ejected fragments originate from the equatorial region of the target and a significant amount of angular momentum can be easily removed. In the case of impacts from directions inclined relative to the target's equatorial plane, spin-down still occurs with reduced degree, unless impacts occur onto the pole region from the vertical direction. Our results suggest that such spin-down through disruptive impacts may have played an important role in spin evolution of asteroids through collisions in the gravity-dominated regime.     

N-Body Simulations of Late Stage Planetary Formation with a Simple Fragmentation Model

We present results of two-dimensional gravitationalN-body simulations of the late stage of planetary formation. This stage is characterized by the direct accretion of hundreds of lunar-sized planetesimals into planetary bodies. Our simulation code is based on the Hermite Individual Timestep integration algorithm, and gravitational interactions among all bodies are included throughout the simulations. We compare our simulation with earlier works that do not include all interactions, and we find very good agreement. A previously published collisional fragmentation model is included in our simulation to study the effects of the production of fragments on the subsequent evolution of the larger planetary bodies. It is found that for realistic two-body collisions that, according to this model, both bodies will suffer fragmentation, and that the outcome of the collision will be a relatively large core containing most of the mass and a few small fragments. We present the results of simulations that include this simple fragmentation model. They indicate that the presence of small fragments have only a small effect on the growth or orbital evolution of the large planet-sized bodies.     

Express delivery of fossil meteorites from the inner asteroid belt to Sweden

Our understanding of planet formation depends in fundamental ways on what we learn by analyzing the composition, mineralogy, and petrology of meteorites. Yet, it is difficult to deduce the compositional and thermal gradients that existed in the solar nebula from the meteoritic record because, in most cases, we do not know where meteorites with different chemical and isotopic signatures originated. Here we developed a model that tracks the orbits of meteoroid-sized objects as they evolve from the ν₆ secular resonance to Earth-crossing orbits. We apply this model to determining the number of meteorites accreted on the Earth immediately after a collisional disruption of a D∼200-km-diameter inner-main-belt asteroid in the Flora family region. We show that this event could produce fossil chondrite meteorites found in an ≈470 Myr old marine limestone quarry in southern Sweden, the L-chondrite meteorites with shock ages ≈470 Myr falling on the Earth today, as well as asteroid-sized fragments in the Flora family. To explain the measured short cosmic-ray exposure ages of fossil meteorites our model requires that the meteoroid-sized fragments were launched at speeds >500 m s⁻¹ and/or the collisional lifetimes of these objects were much shorter immediately after the breakup event than they are today.     

Fragmentation model dependence of collision cascades

Mass depletion of bodies through successive collisional disruptions (i.e., collision cascade) is one of the most important processes in the studies of the asteroids belt, the Edgeworth-Kuiper belt, debris disks, and planetary formation. The collisional disruption is divided into two types, i.e., catastrophic disruption and cratering. Although some studies of the collision cascades neglected the effect of cratering, it is unclear which type of disruption makes a dominant contribution to the collision cascades. In the present study, we construct a simple outcome model describing both catastrophic disruption and cratering, which has some parameters characterizing the total ejecta mass, the mass of the largest fragment, and the power-law exponent of the size distribution of fragments. Using this simple outcome model with parameters, we examine the model dependence of the mass depletion time in collision cascades for neglect of coalescence of colliding bodies due to high collisional velocities. We find the cratering collisions are much more effective in collision cascades than collisions with catastrophic disruption in a wide region of the model parameters. It is also found that the mass depletion time in collision cascades is mainly governed by the total ejecta mass and almost insensitive to the mass of the largest fragment and the power-law exponent of fragments for a realistic parameter region. The total ejecta mass is usually determined by the ratio of the impact energy divided by the target mass (i.e. Q-value) to its threshold value for catastrophic disruption, as well as in our simple model. We derive a mass depletion time in collision cascades, which is determined by of the high-mass end of collision cascades. The mass depletion time derived with our model would be applicable to debris disks and planetary formation.     

Planetary growth with collisional fragmentation and gas drag

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 10⁷ years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.     

General model of depolarization and transfer of polarization of singly ionized atoms by collisions with hydrogen atoms

Simulations of the generation of the atomic polarization is necessary for interpreting the second solar spectrum. For this purpose, it is important to rigorously determine the effects of the isotropic collisions with neutral hydrogen on the atomic polarization of the neutral atoms, ionized atoms and molecules. Our aim is to treat in generality the problem of depolarizing isotropic collisions between singly ionized atoms and neutral hydrogen in its ground state. Using our numerical code, we computed the collisional depolarization rates of the p-levels of ions for large number of values of the effective principal quantum number n^* and the Unsöld energy E_p. Then, genetic programming has been utilized to fit the available depolarization rates. As a result, strongly non-linear relationships between the collisional depolarization rates, n^* and E_p are obtained, and are shown to reproduce the original data with accuracy clearly better than 10%. These relationships allow quick calculations of the depolarizing collisional rates of any simple ion which is very useful for the solar physics community. In addition, the depolarization rates associated to the complex ions and to the hyperfine levels can be easily derived from our results. In this work we have shown that by using powerful numerical approach and our collisional method, general model giving the depolarization of the ions can be obtained to be exploited for solar applications.     

A comparison between rubble-pile and monolithic targets in impact simulations: Application to asteroid satellites and family size distributions

Collisions are a fundamental process in the creation of asteroid families and in satellite formation. For this reason, understanding the outcome of impacts is fundamental to the accurate modeling of the formation and evolution of such systems. Smoothed-Particle Hydrodynamics/N-body codes have become the techniques of choice to study large-scale impact outcomes, including both the fragmentation of the parent body and the gravitational interactions between fragments. It is now possible to apply this technique to targets with either monolithic or rubble-pile internal structures. In this paper we apply these numerical techniques to rubble-pile targets, extending previous investigations by Durda et al. (Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M. [2004]. Icarus 170, 243–257; Durda, D.D., Bottke, W.F., Nesvorný, D., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C. [2007]. Icarus 186, 498–516). The goals are to study asteroid–satellite formation and the morphology of the size–frequency distributions (SFDs) from 175 impact simulations covering a range of collision speeds, impact angles, and impactor sizes. Our results show that low-energy impacts into rubble-pile and monolithic targets produce different features in the resulting SFDs and that these are potentially diagnostic of the initial conditions for the impact and the internal structure of the parent bodies of asteroid families. In contrast, super-catastrophic events (i.e., high-energy impacts with large specific impact energy) result in SFDs that are similar to each other. We also find that rubble-pile targets are less efficient in producing satellites than their monolithic counterparts. However, some features, such as the secondary-to-primary diameter ratio and the relative separation of components in binary systems, are similar for these two different internal structures of parent bodies.     

The asteroids as outcomes of catastrophic collisions

The role of catastrophic collisions in the evolution of the asteroids is discussed in detail, employing extrapolations of experimental results on the outcomrs of high-velocity impacts. We determine the range of the probable largest collision for target asteroids of different sizes during the solar system's lifetime, and we conclude that all the asteroids have undergone collisional events capable of overcoming the material's solid-state cohesion. Such events do not lead inescapably to complete disruption of the targets, because (i) for a previously unfractured target, experiments show that fragments of significant size can survive breakup, depending on the energy and geometry of the collision; (ii) self-gravitation can easily cause a reaccumulation of fragments for targets exceeding a critical size, which seems to be of the order of 100 km. In the intermediate diameter range 100?D ?300 km, where formation of gravitationally bound “rubble piles” is frequent, the transfer of angular momentum can be large enough to produce objects with triaxial equilibrium shapes (Jacobi ellipsoids) or to cause fission into binary systems. In the same size range, low-velocity escape of collisional fragments can also occur, leading to the formation of dynamical families. Asteroids smaller than ～100 km are mostly multigeneration fragments, while for $\text{D?300}\text{km}$ the collisional process produces nearly spheroidal objects covered by megaregoliths; whether their rotation is “primordial” or collisionally generated depends critically on the past flux of colliders. The complex and size-dependent phenomenology predicted by the theory compares satisfactorily with the observational evidence, as derived both by a classification of asteroids in terms of their size, spin rate, and lightcurve amplitude, and by a comparison between the rotational properties of family and nonfamily asteroids. The fundamental result of this investigation is that almost all asteroids are outcomes of catastrophic collisions, and that these events cause either complete fragmentation of the target bodies or, at least, drastic readjustments of their internal structure, shape, and spin rate.     

Deciphering the origin of the regular satellites of gaseous giants - Iapetus: The Rosetta ice-moon

Ever since their discovery the regular satellites of Jupiter and Saturn have held out the promise of providing an independent set of observations with which to test theories of planet formation. Yet elucidating their origins has proven elusive. Here we show that Iapetus can serve to discriminate between satellite formation models. Its accretion history can be understood in terms of a two-component gaseous subnebula, with a relatively dense inner region, and an extended tail out to the location of the irregular satellites, as in the SEMM model of Mosqueira and Estrada (2003a,b) (Mosqueira, I., Estrada, P.R. [2003a]. Icarus 163, 198-231; Mosqueira, I., Estrada, P.R. [2003b]. Icarus 163, 232-255). Following giant planet formation, planetesimals in the feeding zone of Jupiter and Saturn become dynamically excited, and undergo a collisional cascade. Ablation and capture of planetesimal fragments crossing the gaseous circumplanetary disks delivers enough collisional rubble to account for the mass budgets of the regular satellites of Jupiter and Saturn. This process can result in rock/ice fractionation as long as the make up of the population of disk crossers is non-homogeneous, thus offering a natural explanation for the marked compositional differences between outer solar nebula objects and those that accreted in the subnebulae of the giant planets. For a given size, icy objects are easier to capture and to ablate, likely resulting in an overall enrichment of ice in the subnebula. Furthermore, capture and ablation of rocky fragments become inefficient far from the planet for two reasons: the gas surface density of the subnebula is taken to drop outside the centrifugal radius, and the velocity of interlopers decreases with distance from the planet. Thus, rocky objects crossing the outer disks of Jupiter and Saturn never reach a temperature high enough to ablate either due to melting or vaporization, and capture is also greatly diminished there. In contrast, icy objects crossing the outer disks of each planet ablate due to the melting and vaporization of water-ice. Consequently, our model leads to an enhancement of the ice content of Iapetus, and to a lesser degree those of Titan, Callisto and Ganymede, and accounts for the (non-stochastic) compositions of these large, low-porosity outer regular satellites of Jupiter and Saturn. For this to work, the primordial population of planetesimals in the Jupiter-Saturn region must be partially differentiated, so that the ensuing collisional cascade produces an icy population of ?1 m size fragments to be ablated during subnebula crossing. We argue this is likely because the first generation of solar nebula ∼10 km planetesimals in the Jupiter-Saturn region incorporated significant quantities of ²⁶Al. This is the first study successfully to provide a direct connection between nebula planetesimals and subnebulae mixtures with quantifiable and observable consequences for the bulk properties of the regular satellites of Jupiter and Saturn, and the only explanation presently available for Iapetus’ low density and ice-rich composition.     

Collisional processes among interplanetary dust grains: An unlikely origin for the β meteoroids

The question of the collisional production of the β meteoroids is reexamined incorporating recent experimental results (A. Fugiwara, G. Kamimoto, A. Tsukamoto, 1977, Icarus31, 277–288). The collisional model yields a flux of fragments supported by the conservation of mass flux which does not account by far for the observed flux of submicron grains. Particles larger than about 100 μm will be destroyed by collisions inside 1 AU, well before they can get near the Sun. The existence of two independent populations of interplanetary dust grains as proposed by L. B. Le Sergeant and Ph. L. Lamy (1978, Nature266, 822–824; 1980, Icarus43, 350–372) appears reinforced. It is proposed that the bulk of submicron grains does not necessarily travel in hyperbolic orbits and that β meteoroids may be a phenomenon—possibly transitory—of limited importance.     

Evolution of a Keplerian disk of colliding and fragmenting particles: a kinetic model with application to the Edgeworth-Kuiper belt

We present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass-semimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass-semimajor axis-eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass-semimajor axis-eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic “core” of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth-Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB's age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune.     

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.     

High-resolution model of Asteroid 4179 Toutatis

A model of the shape of Toutatis based on “high-resolution” radar images obtained in 1992 and 1996 consists of 39,996 triangular facets of roughly equal area, defined by the locations of 20,000 vertices. These define the average spatial resolution of the model as approximately 34 m, significantly finer than Hudson and Ostro’s (1995, Science 270, 84-86) model (1600 vertices, resolution 84 m). The high-resolution model reveals complex linear features as well as circular crater-like structures down to the resolution limit. There is a dichotomy between the gravitational slope distributions on the asteroid’s two lobes. The noncraterlike features may be the manifestation of complex interior configurations involving monolithic fragments with various sizes and shapes, presumably due to collisions in various energy regimes. However, it may be impossible to decipher the interior structure and responsible collisional history of Toutatis and other small objects without extended, intensive, direct examination.     

Accretion among preplanetary bodies: The many faces of runaway growth

When preplanetary bodies reach proportions of ∼1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. The numerical model is novel as it attempts to preserve the individual particle nature of the bodies (like N-body codes); yet it is statistical in nature since it must incorporate the very large number of planetesimals. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R₀. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We associate the initial runaway growth phase with increasing GF-factors for the largest body. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high-mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two-component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. We identify the peak of GF with the transition between the runaway growth and oligarchy accretion stages. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius, especially at the outer disk. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion, which could lead to a very fast growth.     

Mass dispersal and angular momentum transfer during collisions between rubble-pile asteroids

We perform N-body simulations of impacts between initially non-rotating rubble-pile asteroids, and investigate mass dispersal and angular momentum transfer during such collisions. We find that the fraction of the dispersed mass (Mdisp) is approximately proportional to , where Qimp is the impact kinetic energy; the power index α is about unity when the impactor is much smaller than the target, and 0.5?α<1 for impacts with a larger impactor. Mdisp is found to be smaller for more dissipative impacts with small values of the restitution coefficient of the constituent particles. We also find that the efficiency of transfer of orbital angular momentum to the rotation of the largest remnant depends on the degree of disruption. In the case of disruptive oblique impacts where the mass of the largest remnant is about half of the target mass, most of the orbital angular momentum is carried away by the escaping fragments and the efficiency becomes very low (<0.05), while the largest remnant acquires a significant amount of spin angular momentum in moderately disruptive impacts. These results suggest that collisions likely played an important role in rotational evolution of small asteroids, in addition to the recoil force of thermal re-radiation.     

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.     

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 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.     

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.