The fossilized size distribution of the main asteroid belt

Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9-4.5 Ga. These results suggest the main belt's wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter D?120 km asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near D∼100-120 km are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of D<1000 km bodies) was 150-250 times larger than it is today, in agreement with recent dynamical simulations.     

Can planetesimals left over from terrestrial planet formation produce the lunar Late Heavy Bombardment?

The lunar Late Heavy Bombardment (LHB) defines a time between ∼3.8 to possibly 4.1 Gy ago when the Nectarian and early-Imbrium basins on the Moon with reasonably well-constrained ages were formed. Some have argued that these basins were produced by a terminal cataclysm that caused a spike in the inner Solar System impactor flux during this interval. Others have suggested the basins were formed by the tail end of a monotonically decreasing impactor population originally produced by planet formation processes in the inner Solar System. Here we investigate whether this so-called declining bombardment scenario of the LHB is consistent with constraints provided by planet formation models as well as the inferred ages of Nectaris, Serenitatis, Imbrium, and Orientale. We did this by modeling the collisional and dynamical evolution of the post-planet formation population (PPP) for a range of starting PPP masses. Using a Monte Carlo code, we computed the probability that the aforementioned basins were created at various times after the Moon-forming event approximately 4.54 Ga. Our results indicate that the likelihood that the declining bombardment scenario produced Nectaris, Serenitatis, Imbrium, and Orientale (or even just Imbrium and Orientale) at any of their predicted ages is extremely low and can be ruled out at the 3σ confidence level, regardless of the PPP's starting mass. The reason is that collisional and dynamical evolution quickly depletes the PPP, leaving behind a paucity of large projectiles capable of producing the Moon's youngest basins between 3.8-4.1 Gy ago. If collisions are excluded from our model, we find that the PPP produces numerous South Pole-Aitken-like basins during the pre-Nectarian period. This is inconsistent with our understanding of lunar topography. Accordingly, our results lead us to conclude that the terminal cataclysm scenario is the only existing LHB paradigm at present that is both viable from a dynamical modeling perspective and consistent with existing constraints.     

The primordial excitation and clearing of the asteroid belt—Revisited

We have performed new simulations of two different scenarios for the excitation and depletion of the primordial asteroid belt, assuming Jupiter and Saturn on initially circular orbits as predicted by the Nice Model of the evolution of the outer Solar System [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. First, we study the effects of sweeping secular resonances driven by the depletion of the solar nebula. We find that these sweeping secular resonances are incapable of giving sufficient dynamical excitation to the asteroids for nebula depletion timescales consistent with estimates for solar-type stars, and in addition cannot cause significant mass depletion in the asteroid belt or produce the observed radial mixing of different asteroid taxonomic types. Second, we study the effects of planetary embryos embedded in the primordial asteroid belt. These embedded planetary embryos, combined with the action of jovian and saturnian resonances, can lead to dynamical excitation and radial mixing comparable to the current asteroid belt. The mass depletion driven by embedded planetary embryos alone, even in the case of an eccentric Jupiter and Saturn, is roughly 10-20× less than necessary to explain the current mass of the main belt, and thus a secondary depletion event, such as that which occurs naturally in the Nice Model, is required. We discuss the implications of our new simulations for the dynamical and collisional evolution of the main belt.     

Size-frequency distributions of fragments from SPH/N-body simulations of asteroid impacts: Comparison with observed asteroid families

We investigate the morphology of size-frequency distributions (SFDs) resulting from impacts into 100-km-diameter parent asteroids, represented by a suite of 161 SPH/N-body simulations conducted to study asteroid satellite formation [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]. The spherical basalt projectiles range in diameter from 10 to 46 km (in equally spaced mass increments in logarithmic space, covering six discrete sizes), impact speeds range from 2.5 to 7 km/s (generally in 1 km/s increments), and impact angles range from 15° to 75° (nearly head-on to very oblique) in 15° increments. These modeled SFD morphologies match very well the observed SFDs of many known asteroid families. We use these modeled SFDs to scale to targets both larger and smaller than 100 km in order to gain insights into the circumstances of the impacts that formed these families. Some discrepancies occur for families with parent bodies smaller than a few tens of kilometers in diameter (e.g., 832 Karin), however, so due caution should be used in applying our results to such small families. We find that ∼20 observed main-belt asteroid families are produced by the catastrophic disruption of D>100 km parent bodies. Using these data as constraints, collisional modeling work [Bottke Jr., W.F., Durda, D.D., Nesvorný, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H.F., 2005b. Icarus 179, 63-94] suggests that the threshold specific energy, , needed to eject 50% of the target body's mass is very close to that predicted by Benz and Asphaug [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20].     

The shape distribution of asteroid families: Evidence for evolution driven by small impacts

A statistical analysis of brightness variability of asteroids reveals how their shapes evolve from elongated to rough spheroidal forms, presumably driven by impact-related phenomena. Based on the Sloan Digital Sky Survey Moving Object Catalog, we determined the shape distribution of 11,735 asteroids, with special emphasis on eight prominent asteroid families. In young families, asteroids have a wide range of shape elongations, implying fragmentation-formation. In older families we see an increasing number of rough spheroids, in agreement with the predictions of an impact-driven evolution. Old families also contain a group of moderately elongated members, which we suggest correspond to higher-density, more impact-resistant cores of former fragmented asteroids that have undergone slow shape erosion. A few percent of asteroids have very elongated shapes, and can either be young fragments or tidally reshaped bodies. Our results confirm that the majority of asteroids are gravitationally bound “rubble piles.”     

Yarkovsky depletion and asteroid collisional evolution

The orbital parameters of small asteroids change with time, as a consequence of the so-called Yarkovsky effect. This leads to a steady removal of objects from the Main Belt, which takes place when the objects reach one of the major resonant regions in the orbital elements space. The process may influence the evolution of the inventory and size distribution of Main Belt asteroids, but it has not been taken into account by classical models of the collisional evolution of the asteroid population. In this paper we discuss the role of the Yarkovsky effect in producing the current observed size distribution. We show that adding Yarkovsky effect to purely collisional mechanisms may increase the removal of objects at sizes around 1 km by a factor of about 2 with respect to a purely collisional scenario. Moreover, waves in the size distribution may also be produced. However, taking also into account current uncertainties in the efficiency of purely collisional mechanisms, the role of the Yarkovsky effect seems not dominant, and cannot be unambiguously determined.     

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

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

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

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

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.     

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.     

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.     

Interacting ellipsoids: a minimal model for the dynamics of rubble-pile bodies

A simple mechanical model is formulated to study the dynamics of rubble-pile asteroids, formed by the gravitational re-accumulation of fragments after the collisional breakup of a parent body. In this model, a rubble-pile consists of N interacting fragments represented by rigid ellipsoids, and the equations of motion explicitly incorporate the minimal degrees of freedom necessary to describe the attitude and rotational state of each fragment. In spite of its simplicity, our numerical examples indicate that the overall behavior of our model is in line with several known properties of collisional events, like the energy and angular momentum partition during high velocity impacts. Therefore, it may be considered as a well defined minimal model.     

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.     

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.     

Numerical simulations of impacts involving porous bodies: II. Comparison with laboratory experiments

In this paper, we compare the outcome of high-velocity impact experiments on porous targets, composed of pumice, with the results of simulations by a 3D SPH hydrocode in which a porosity model has been implemented. The different populations of small bodies of our Solar System are believed to be composed, at least partially, of objects with a high degree of porosity. To describe the fragmentation of such porous objects, a different model is needed than that used for non-porous bodies. In the case of porous bodies, the impact process is not only driven by the presence of cracks which propagate when a stress threshold is reached, it is also influenced by the crushing of pores and compaction. Such processes can greatly affect the whole body's response to an impact. Therefore, another physical model is necessary to improve our understanding of the collisional process involving porous bodies. Such a model has been developed recently and introduced successfully in a 3D SPH hydrocode [Jutzi, M., Benz, W., Michel, P., 2008. Icarus 198, 242-255]. Basic tests have been performed which already showed that it is implemented in a consistent way and that theoretical solutions are well reproduced. However, its full validation requires that it is also capable of reproducing the results of real laboratory impact experiments. Here we present simulations of laboratory experiments on pumice targets for which several of the main material properties have been measured. We show that using the measured material properties and keeping the remaining free parameters fixed, our numerical model is able to reproduce the outcome of these experiments carried out under different impact conditions. This first complete validation of our model, which will be tested for other porous materials in the future, allows us to start addressing problems at larger scale related to small bodies of our Solar System, such as collisions in the Kuiper Belt or the formation of a family by the disruption of a porous parent body in the main asteroid belt.     

The Asteroid Veritas: An intruder in a family named after it?

The Veritas family is located in the outer main belt and is named after its apparent largest constituent, Asteroid (490) Veritas. The family age has been estimated by two independent studies to be quite young, around 8 Myr. Therefore, current properties of the family may retain signatures of the catastrophic disruption event that formed the family. In this paper, we report on our investigation of the formation of the Veritas family via numerical simulations of catastrophic disruption of a 140-km-diameter parent body, which was considered to be made of either porous or non-porous material, and a projectile impacting at 3 or 5 km/s with an impact angle of 0° or 45°. Not one of these simulations was able to produce satisfactorily the estimated size distribution of real family members. Based on previous studies devoted to either the dynamics or the spectral properties of the Veritas family, which already treated (490) Veritas as a special object that may be disconnected from the family, we simulated the formation of a family consisting of all members except that asteroid. For that case, the parent body was smaller (112 km in diameter), and we found a remarkable match between the simulation outcome, using a porous parent body, and the real family. Both the size distribution and the velocity dispersion of the real reduced family are very well reproduced. On the other hand, the disruption of a non-porous parent body does not reproduce the observed properties very well. This is consistent with the spectral C-type of family members, which suggests that the parent body was porous and shows the importance of modeling the effect of this porosity in the fragmentation process, even if the largest members are produced by gravitational reaccumulation during the subsequent gravitational phase. As a result of our investigations, we conclude that it is very likely that the Asteroid (490) Veritas and probably several other small members do not belong to the family as originally defined, and that the definition of this family should be revised. Further investigations will be performed to better constrain the definitions and properties of other asteroid families of different types, using the appropriate model of fragmentation. The identification of very young families in turn will continue to serve as a tool to check the validity of numerical models.     

Experimental study on the impact fragmentation of core-mantle bodies: Implications for collisional disruption of rocky planetesimals with sintered core covered with porous mantle

Impact experiments of inhomogeneous targets such as layered bodies consisting of a dense core and porous mantle were conducted to clarify the effect of the layered structure on impact strength. The layered structure of small bodies could be the result of the thermal evolution of planetesimals in the solar nebula. So, the impact disruption of thermally evolved bodies with core-mantle structure is important for the origin of small bodies such as asteroids. We investigated the impact strength of rocky-layered bodies with porous mantle-sintered cores, which could be formed at an initial stage of thermal evolution. Spherical targets composed of soda-lime glass or quartz core and porous gypsum mantle were prepared as an analog of small bodies with a core-mantle structure, and the internal structure was changed. A nylon projectile was impacted at the impact velocity from 1 to 5 km/s. The impact strength of the core-mantle targets decreases with the increase of the core/target mass ratio (RCM) in the specific energy range from 1×¹⁰³ to 4×¹⁰⁴ J/kg. We observed two distinct destruction modes characterized by the damage to the core: one shows a damaged core and fractured mantle, and the other shows an intact core and broken mantle. The former mode was usually observed with increasing RCM, and the boundary condition of the core destruction () was experimentally found to be , where is the specific energy required to disrupt a glass core. From this empirical equation, it might be possible to discuss the destruction conditions of a thermally evolved body with a porous mantle-sintered core structure. We speculate that the impact strength of the body could be significantly reduced with the progress of internal evolution at the initial stage of thermal evolution.     

Impact cratering and break up of the small bodies of the Solar System

We consider the largest impact craters observed on small satellites and asteroids and the impact disruption of such bodies. Observational data are considered from 21 impact-like structures on 13 satellites and 8 asteroids (target body radii in the range 0.7-265 km). If the radius of the target body is R and the diameter of the largest crater observed on this body D, the ratio D/R is then the main observational parameter of interest. This is found on the observed bodies and compared to data obtained in the laboratory. Taking the largest observed value for D/R as a proxy for the ratio Dc/R (where Dc is the diameter of the largest crater that can be formed on a body without shattering it) it was found that for the observed icy satellites Dc,icy≈1.2R and for the asteroids and the rocky satellites Dc,rocky≈1.6R. In laboratory experiments with ice targets at impactor speeds of 1 to 3 km s⁻¹ we obtained Dc,icy≈1.64R.     

Models of the collisional damping scenario for ice-giant planets and Kuiper belt formation

Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895-911] have recently proposed that the observed structure of the Kuiper belt could be the result of a dynamical instability of a system of ∼5 primordial ice-giant planets in the outer Solar System. According to this scenario, before the instability occurred, these giants were growing in a highly collisionally damped environment according to the arguments in Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497-507; Annu. Rev. Astron. Astrophys. 42, 549-601]. Here we test this hypothesis with a series of numerical simulations using a new code designed to incorporate the dynamical effects of collisions. We find that we cannot reproduce the observed Solar System. In particular, Goldreich et al. [Goldreich, P., Lithwick, Y., Sari, R., 2004. Astrophys. J. 614, 497-507; Annu. Rev. Astron. Astrophys. 42, 549-601] and Chiang et al. [Chiang, E., Lithwick, Y., Murray-Clay, R., Buie, M., Grundy, W., Holman, M., 2007. In: Protostars and Planets V, pp. 895-911] argue that during the instability, all but two of the ice giants would be ejected from the Solar System by Jupiter and Saturn, leaving Uranus and Neptune behind. We find that ejections are actually rare and that instead the systems spread outward. This always leads to a configuration with too many planets that are too far from the Sun. Thus, we conclude that both Goldreich et al.'s scheme for the formation of Uranus and Neptune and Chiang et al.'s Kuiper belt formation scenario are not viable in their current forms.