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.     

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.     

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.     

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.     

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].     

Impact cratering on porous asteroids

The increasing evidence that many or even most asteroids are rubble piles underscores the need to understand how porous structures respond to impact. Experiments are reported in which craters are formed in porous, crushable, silicate materials by impacts at 2 km/s. Target porosity ranged from 34 to 96%. The experiments were performed at elevated acceleration on a centrifuge to provide similarity conditions that reproduce the physics of the formation of asteroid craters as large as several tens of kilometers in diameter.Crater and ejecta blanket formation in these highly porous materials is found to be markedly different from that observed in typical dry soils of low or moderate porosity. In highly porous materials, the compaction of the target material introduces a new cratering mechanism. The ejection velocities are substantially lower than those for impacts in less porous materials. The experiments imply that, while small craters on porous asteroids should produce ejecta blankets in the usual fashion, large craters form without ejecta blankets. In large impacts, most of the ejected material never escapes the crater. However, a significant crater bowl remains because of the volume created by permanent compaction of the target material. Over time, multiple cratering events can significantly increase the global density of an asteroid.     

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

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

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.     

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.     

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.     

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.     

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.”     

Spin rates of fast-rotating asteroids and fragments in impact disruption

We present a new experimental result of fragment spin-rate in impact disruption, using a thin glass plate. A cylindrical projectile impacts on a side (edge) of the plate. Dispersed fragments are observed using a high-speed camera and the spin rates of fragments are measured. We find that the measured fragment spin-rate decreases with increasing size. Assuming that the rotational energy of fragments is supplied from the residual stress, the spin rate ω decreases with increasing fragment size r as ω∼r−1, which explains the above experimental results. This size-dependence is similar to that of the observed spin rates of small fast-rotating asteroids. Our results suggest that spin rates of fragments of small asteroids immediately after disruption may have a similar size-dependence, and can provide constraints on the subsequent spin-state evolution of small asteroids due to thermal torques.     

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.     

Combined effect of YORP and collisions on the rotation rate of small Main Belt asteroids

The rotation rate distribution of small Main Belt asteroids is dominated by YORP and collisions. These mechanism act differently depending on the size of the bodies and give rise to non-linear effects when they both operate. Using a Monte Carlo method we model the formation of a steady state population of small asteroids under the influence of both mechanisms and the rotation rate distribution is compared to the observed one as derived from Pravec et al. (Pravec, P. et al. [2008]. Icarus 197, 497-504). A better match to observations is obtained with respect to the case in which only YORP is considered. In particular, an excess of slow rotators is produced in the model with both collisions and YORP because bodies driven to slow rotation by YORP have a random walk-like evolution of the spin induced by repeated collisions with small projectiles. This is a dynamical evolution different from tumbling and it lasts until a large impact takes the body to a faster rotation rate. According to our model, the rotational fission of small asteroids is a very frequent event and might explain objects like P/2010 A2 and its associated tail of millimeter-sized dust particles. The mass loss during fission of small asteroids might significantly influence the overall collisional evolution of the belt. Fission can in fact be considered as an additional erosion mechanism, besides cratering and fragmentation, acting only at small diameters.     

Craters on asteroids: Reconciling diverse impact records with a common impacting population

O'Brien and Greenberg [O'Brien, D.P., Greenberg, R., 2005. Icarus 178, 179-212] developed a self-consistent numerical model of the collisional and dynamical evolution of the main-belt and NEA populations that was tested against a diverse range of observational and theoretical constraints. In this paper, we use those results to update the asteroid cratering model of Greenberg et al. [Greenberg, R., Nolan, M.C., Bottke, W.F., Kolvoord, R.A., Veverka, J., 1994. Icarus 107, 84-97; Greenberg, R., Bottke, W.F., Nolan, M., Geissler, P., Petit, J., Durda, D.D., Asphaug, E., Head, J., 1996. Icarus 120, 106-118], and show that the main-belt asteroid population from the O'Brien and Greenberg collisional/dynamical evolution modeling is consistent with the crater records on Gaspra, Ida, Mathilde, and Eros, the four asteroids that have been observed by spacecraft.     

Linking the collisional history of the main asteroid belt to its dynamical excitation and depletion

The main belt is believed to have originally contained an Earth mass or more of material, enough to allow the asteroids to accrete on relatively short timescales. The present-day main belt, however, only contains ∼5×¹⁰⁻⁴ Earth masses. Numerical simulations suggest that this mass loss can be explained by the dynamical depletion of main belt material via gravitational perturbations from planetary embryos and a newly-formed Jupiter. To explore this scenario, we combined dynamical results from Petit et al. [Petit, J. Morbidelli, A., Chambers, J., 2001. The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347] with a collisional evolution code capable of tracking how the main belt undergoes comminution and dynamical depletion over 4.6 Gyr [Bottke, W.F., Durda, D., Nesvorny, D., Jedicke, R., Morbidelli, A., Vokrouhlický, D., Levison, H., 2005. The fossilized size distribution of the main asteroid belt. Icarus 175, 111-140]. Our results were constrained by the main belt's size-frequency distribution, the number of asteroid families produced by disruption events from diameter D>100 km parent bodies over the last 3-4 Gyr, the presence of a single large impact crater on Vesta's intact basaltic crust, and the relatively constant lunar and terrestrial impactor flux over the last 3 Gyr. We used our model to set limits on the initial size of the main belt as well as Jupiter's formation time. We find the most likely formation time for Jupiter was 3.3±2.6 Myr after the onset of fragmentation in the main belt. These results are consistent with the estimated mean disk lifetime of 3 Myr predicted by Haisch et al. [Haisch, K.E., Lada, E.A., Lada, C.J., 2001. Disk frequencies and lifetimes in young clusters. Astrophys. J. 553, L153-L156]. The post-accretion main belt population, in the form of diameter D?1000 km planetesimals, was likely to have been 160±40 times the current main belt's mass. This corresponds to 0.06-0.1 Earth masses, only a small fraction of the total mass thought to have existed in the main belt zone during planet formation. The remaining mass was most likely taken up by planetary embryos formed in the same region. Our results suggest that numerous D>200 km planetesimals disrupted early in Solar System history, but only a small fraction of their fragments survived the dynamical depletion event described above. We believe this may explain the limited presence of iron-rich M-type, olivine-rich A-type, and non-Vesta V-type asteroids in the main belt today. The collisional lifetimes determined for main belt asteroids agree with the cosmic ray exposure ages of stony meteorites and are consistent with the limited collisional evolution detected among large Koronis family members. Using the same model, we investigated the near-Earth object (NEO) population. We show the shape of the NEO size distribution is a reflection of the main belt population, with main belt asteroids driven to resonances by Yarkovsky thermal forces. We used our model of the NEO population over the last 3 Gyr, which is consistent with the current population determined by telescopic and satellite data, to explore whether the majority of small craters (D<0.1-1 km) formed on Mercury, the Moon, and Mars were produced by primary impacts or by secondary impacts generated by ejecta from large craters. Our results suggest that most small craters formed on these worlds were a by-product of secondary rather than primary impacts.