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.     

Dust production from the hypervelocity impact disruption of the Murchison hydrous CM2 meteorite: Implications for the disruption of hydrous asteroids and the production of interplanetary dust

More than half of the C-type asteroids, the dominant type of asteroid in the outer half of the main-belt, show evidence of hydration in their reflectance spectra. In order to understand the collisional evolution of asteroids and the production of interplanetary dust and to model the infrared signature of small particles in the Solar System it is important to characterize the dust production from primary impact disruption events, and compare the disruption of hydrous and anhydrous targets. We performed a hypervelocity impact disruption experiment on an ∼30 g target of the Murchison CM2 hydrated carbonaceous chondrite meteorite, and compared the results with our previous disruption experiments on anhydrous meteorites including Allende, a CV3 carbonaceous chondrite, and nine ordinary chondrites. Murchison is significantly more friable than the ordinary chondrites or Allende. Nonetheless, on a plot of mass of the largest fragment versus specific impact energy, the Murchison disruption plots within the field of the anhydrous meteorites points, suggesting that Murchison is at least as resistant to impact disruption as the anhydrous meteorites, which require about twice the energy for disruption as terrestrial anhydrous basalt targets. We determined the mass-frequency distribution of the debris from the Murchison disruption over a nine order-of-magnitude mass range, from ∼10⁻⁹ g to the mass of the largest fragment produced in the disruption. The cumulative mass-frequency distribution from the Murchison disruption is fit by three power-law segments. For masses >10⁻² g the slope is only slightly steeper than that of the corresponding segment from the disruption of most anhydrous meteorites. Over the range from ∼10⁻⁶ to 10⁻² g the slope is significantly steeper than that for the anhydrous meteorites. For masses <10⁻⁶ g the slopes of both the Murchison and the anhydrous meteorites are almost flat. Thus the Murchison disruption significantly over-produced small fragments (10⁻⁶-10⁻³ g) compared to anhydrous meteorite targets. If the Murchison results are representative of hydrous asteroids, the hydrous asteroids may dominate over anhydrous asteroids in the production of interplanetary dust >100 μm in size, the size of micrometeorites recovered from the polar ices, while both types of asteroids might produce comparable amounts of ∼10 μm interplanetary dust. This would explain the puzzle that polar micrometeorites (>100 μm in size) are similar to hydrous meteorites, while the majority of the ∼10 μm interplanetary dust particles are anhydrous.     

Photometry and spin rate distribution of small-sized main belt asteroids

Photometry results of 32 asteroids are reported from only seven observing nights on only seven fields, consisting of 34.11 cumulative hours of observations. The data were obtained with a wide-field CCD (^40.5′×^27.3′) mounted on a small, 46-cm telescope at the Wise Observatory. The fields are located within ±1.5° from the ecliptic plane and include a region within the main asteroid belt. The observed fields show a projected density of ∼23.7 asteroids per square degree to the limit of our observations. 13 of the lightcurves were successfully analyzed to derive the asteroids' spin periods. These range from 2.37 up to 20.2 h with a median value of 3.7 h. 11 of these objects have diameters in order of two kilometers and less, a size range that until recently has not been photometrically studied. The results obtained during this short observing run emphasize the efficiency of wide-field CCD photometry of asteroids, which is necessary to improve spin statistics and understand spin evolution processes. We added our derived spin periods to data from the literature and compared the spin rate distributions of small main belt asteroids (5>D>0.15 km) with that of bigger asteroids and of similar-sized NEAs. We found that the small MBAs do not show the clear Maxwellian-shaped distribution as large asteroids do; rather they have a spin rate distribution similar to that of NEAs. This implies that non-Maxwellian spin rate distribution is controlled by the asteroids' sizes rather than their locations.     

Lightcurve Analysis of Four New Monolithic Fast-Rotating Asteroids

We present lightcurves and analysis for four new monolithic fast-rotating asteroids: 2000 AG₆, 2000 DO₈, 2000 EB₁₄, and 2000 HB₂₄. Their rotation periods of 4.60, 1.30, 107.47, and 13.05 min place them well below the critical threshold for the rotation rate of strengthless prolate ellipsoids, as we demonstrate. These four objects join the five previously identified fast-rotating asteroids. The sharp segregation in spin rates between these nine objects and asteroids with more typical spin rates is somewhat puzzling. No observed objects larger than about 200 m spin with rates faster than the critical rate for strengthless prolate ellipsoids, while no objects smaller than 200 m have shown spin rates slower than this critical limit. We hypothesize that these small, fast-rotating objects are representative of the building blocks of the “rubble pile” asteroids and are in fact derived from impacts into already existing “rubble piles.”     

Influence of the YORP effect on rotation rates of near‐Earth asteroids

The distribution of near‐Earth asteroid (NEA) rotation rates differs considerably from the similar distribution of Main Belt asteroids (MBAs) by the presence of excesses of fast and slow rotators, which are not observed or not so prominent in the distribution for MBAs. Among possible reasons for the difference, there can be influence of solar radiation on spin rate of small NEAs, the so‐called “YORP effect,” which appears due to reflection, absorption, and IR re‐emission of the sunlight by an irregularly shaped rotating asteroid. It is known that the YORP‐effect action strongly depends on the amount of solar energy obtained by the body (insolation), its size, and albedo. The analysis of observation data has shown that: (1) the mean diameter of NEAs decreases from the middle of the distribution to its ends, that is, the excesses of slow rotators (ω ≤ 2 rev day^?1) and fast rotators (ω ≥ 8 rev day^?1) are composed of smaller NEAs than in the middle of the distribution; (2) NEAs of both excesses are in the orbits where their insolation is about 8–10% larger than that of NEAs in the middle of the distribution; and (3) the objects in both excesses have a little lower albedo on average than that of objects in the middle of the distribution. All these results qualitatively agree well with the YORP‐effect action and may be considered as independent arguments in favor of it.     

The large crater on the small Asteroid (2867) Steins

The maximum size of impact craters on finite bodies marks the largest impact that can occur short of impact induced disruption of the body. Recently attention has started to focus on large craters on small bodies such as asteroids and rocky and icy satellites. Here the large crater on the recently imaged Asteroid (2867) Steins (with crater diameter to mean asteroid radius ratio of 0.79) is shown to follow a limit set by other similar sized bodies with moderate macroporosity (i.e. fractured asteroids). Thus whilst large, the crater size is not novel, nor does it require Steins to possess an extremely large porosity. In one of the components of the binary Asteroid (90) Antiope there is the recently reported presence of an extremely large depression, possibly a crater, with depression diameter to mean asteroid radius ratio of ∼(1.4–1.62). This is consistent with the maximum size of a crater expected from previous observations of very porous rocky bodies (i.e. rubble-pile asteroids). Finally, a relationship between crater diameter (normalised to body radius) is proposed as a function of body porosity which suggests that the doubling of porosity between fractured asteroids and rubble-pile asteroids, nearly doubles the size (D/R value) of the largest crater sustainable on a rocky body.     

The strength of regolith and rubble pile asteroids

We explore the hypothesis that, due to small van der Waals forces between constituent grains, small rubble pile asteroids have a small but nonzero cohesive strength. The nature of this model predicts that the cohesive strength should be constant independent of asteroid size, which creates a scale dependence with relative strength increasing as size decreases. This model counters classical theory that rubble pile asteroids should behave as scale‐independent cohesionless collections of rocks. We explore a simple model for asteroid strength that is based on these weak forces, validate it through granular mechanics simulations and comparisons with properties of lunar regolith, and then explore its implications and ability to explain and predict observed properties of small asteroids in the NEA and Main Belt populations, and in particular of asteroid 2008 TC₃. One conclusion is that the population of rapidly rotating asteroids could consist of both distributions of smaller grains (i.e., rubble piles) and of monolithic boulders.     

Dust Production from the Hypervelocity Impact Disruption of Hydrated Targets

More than half of the C-type asteroids, which are the dominant type of asteroid in the outer half of the main belt, show evidence of hydration in their reflectance spectra. In order to understand the collisional evolution of asteroids, the production of interplanetary dust, and to model the infrared signature of small particles in the Solar System it is important to characterize the dust production from primary impact disruption events, and compare the disruption of hydrous and anhydrous targets. We performed impact disruption experiments of three “greenstone” targets, a hydrothermally metamorphosed basalt, and compared the results of these disruptions to our previous disruption experiments on porous, anhydrous basalt targets and to literature data on the disruption of non-porous, anhydrous basalt targets. The greenstone targets were selected because their major hydrous alteration phase is serpentine, the same hydrous alteration phase found in hydrous CM meteorites, like Murchison. The porous, anhydrous basalt targets were selected because their structure, consisting of millimeter-size olivine phenocrysts in a more porous, anhydrous matrix is similar to the structure of anhydrous chondritic meteorites, which consist of millimeter-size olivine chondrules embedded in a more porous, anhydrous matrix. The disruption measurements indicate the threshold collisional specific energy, Q _D^*, is 570 J/kg for the greenstone, which is lower than the literature values for non-porous basalt targets, and significantly lower than the value of 2500 J/kg that we have measured for porous anhydrous basalt targets. We determined the mass-frequency distribution of the debris from the disruption of the greenstone targets, which ranged in mass from 80 to 280 g, over a nine order-of-magnitude mass range, from ~10⁻⁹ g to the mass of the largest fragment. The cumulative mass-frequency distribution from the greenstone targets is fit by two power–law segments, one for masses >10⁻² g, which is significantly steeper than the corresponding segment from the disruption of similar-sized anhydrous basalt, and one in the range from 10⁻⁹ to 10⁻² g, which is significantly flatter than the corresponding segment from the disruption of similar size anhydrous basalt. These hydrous greenstone targets overproduce small fragments (10⁻⁴ to 10⁰ g) compared to anhydrous basalt targets, but underproduce dust-size grains (10⁻⁹ to 10⁻⁴ g) compared to anhydrous basalt targets.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.     

Are Main-Belt Asteroids a Sufficient Source for the Earth-Approaching Asteroids?

This paper predicts the size distribution of the Earth-approaching asteroids with diameterd= 10 m to 10 km, assuming they originate as the fragments of main-belt asteroids with a cumulative size distribution proportional tod^−2.5and that they have self-similar fragmentation properties. The resulting distribution is dominated by “fast-track” bodies originating from parent asteroids with orbits close to the 3:1 mean-motion resonance with Jupiter. Because the dynamical lifetimes of these Earth approachers are shorter than their collisional lifetimes, their size distribution is nearly proportional tod^−3.0, the production distribution in the main belt. This prediction, however, is at odds with the Spacewatch observations. The observed distribution is relatively flat ford> ∼100 m, and relatively steep ford< ∼100 m, so that the number of Earth approachers withd∼ 10 m to 0.3 km is overestimated. If these populations are predominantly of main-belt origin, then the size distribution in the main belt is not a simple power law. A nonuniform size distribution with wave-like oscillations, possibly caused by a cutoff at small sizes, would lead to Earth approachers with a size distribution in better agreement with the observations. If such wave-like oscillations are realistic, then the main belt is sufficient to supply the observed number of Earth approachers throughout the observed size range.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.     

Asteroidal binary systems: Detection and formation

Recent occultation data and an analysis of some photometric lightcurves have shown the possible existence of asteroidal binary systems.A simple geometrical model taking into account mutual shadowing effects shows some peculiar features of the lightcurve which can be recovered in several previously observed objects; therefore the hypothesis of a relatively high frequency of binary asteroids should be seriously considered.On the other hand, while the rotational period distribution of large asteroids (D>200 km) is sharply peaked at about 5–8 hours, the surprisingly higher dispersion towards longer periods for intermediate size objects (50<D<150 km) could be connected with a larger probability of binary nature within this class.From a theoretical point of view, the collisional fragmentation of asteroids could originate gravitationally bound fragments, with a tidal transfer of rotational into orbital angular momentum, causing a rapid synchronization of the system. This kind of processes could more easily occur for intermediate objects since: (a) for large ones, very massive colliding bodies are needed for fragmentation, that means a very rare event; (b) for smaller asteroids, solid state interactions are stronger than the gravitational ones, so that a breakage probably causes a complete disruption of the gravitational binding. Further collisional events could disintegrate some systems, so that the present frequency of binary asteroids could be lower than that of the objects whose rotational period was increased by such processes.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Spin rates of small moonlets embedded in planetary rings: I. Three-body calculations

We investigate the spin rates of moonlets embedded in planetary rings, subject to collisions with surrounding small particles, using three-body integrations including friction and spins. All successive impacts of the particle with the moonlet are followed, including a possible sliding phase after the initial inelastic rebounds. Two methods for treating impacts, (1) as instantaneous velocity changes and (2) using an impact force model, are applied after Salo (1995, Icarus 117, 287). Conducting a series of integrations with various initial summed spin velocity of the moonlet and the particle, we determine the equilibrium spin rate for which the averaged torque vanishes. This equilibrium spin rate corresponds to the final spin rate of the moonlet if the moonlet is much larger than the surrounding particles; it also corresponds to the mean spin rate for a ring composed of identical particles. We find that the equilibrium spin rate is enhanced by sliding orbits as compared with the spin rate determined by considering only the first impacts of the particles with the moonlet. If the random velocities of incident particles are small enough, the resulting equilibrium spin rate of the moonlet can be larger than the synchronous rotation rate, for r_p∼1, where r_p denotes the sum of radii of the colliding pair normalized by their mutual Hill radius. In this special case aggregates without internal strength may become rotationally unstable. However, the equilibrium spin rate decreases with increasing random velocity, and aggregates are always rotationally stable in the more likely case where the relative velocities are comparable to the mutual escape velocity. We also compare our results with the mean spin rates found in previous N-body simulations, and find a good agreement for optically thin rings; however the spin rates for optically thick rings are significantly larger than those predicted by our three-body calculations.     

Impact evolution of asteroid shapes: 1. random mass redistribution

We explore whether the cumulative effect of small-scale meteoroid bombardment can drive asteroids into nonaxisymmetric shapes comparable to those of known objects (elongated prolate forms, twin-lobed binaries, etc). We simulate impact cratering as an excavation followed by the launch, orbit, and reimpact of ejecta. Orbits are determined by the gravity and rotation of the evolving asteroid, whose shape and spin change as cratering occurs repeatedly. For simplicity we consider an end-member evolution where impactors are all much smaller than the asteroid and where all ejecta remain bound. Given those assumptions, we find that cumulative small impacts on rotating asteroids lead to oblate shapes, irrespective of the chosen value for angle of repose or for initial angular momentum. The more rapidly a body is spinning, the more flattened the outcome, but oblateness prevails. Most actual asteroids, by contrast, appear spherical to prolate. We also evaluate the timescale for reshaping by small impacts and compare it to the timescale for catastrophic disruption. For all but the steepest size distributions of impactors, reshaping from small impacts takes more than an order of magnitude longer than catastrophic disruption. We conclude that small-scale cratering is probably not dominant in shaping asteroids, unless our assumptions are naive. We believe we have ruled out the end-member scenario; future modeling shall include angular momentum evolution from impacts, mass loss in the strength regime, and craters with diameters up to the disruption threshold. The ultimate goal is to find out how asteroids get their shapes and spins and whether tidal encounters in fact play a dominant role.     

Asteroid rotation: I. Tabulation and analysis of rates,pole positions and shapes

Data are presented for the 182 asteroids whose rotational properties are available in the literature. Plots are provided for the asteroid rotational frequency f and lightcurve amplitude Δm versus asteroid size; the latter is determined using standard methods if data are available but otherwise is estimated from asteroid albedos, selected depending on taxonomic type or orbital position. A linear least-squares fit to all the data shows that f increases with decreasing size, confirming McAdoo and Burns' (1973) result; this is demonstrated to be primarily caused by relatively more small non-C than C asteroids in our sample, coupled with a slower mean rotation rate for C asteroids (P ≈ 11 hr) than non-C asteroids (P ≈ 9 hr). In terms of the collisional theory of Harris (1979a), this means that the C's are less dense than the other minor planets. Any slight tendency for smaller asteroids to spin faster, even within a taxonomic type, could be due to selection effects; our data are not extensive enough to determine whether the very smallest (? 10-km diameter) spin especially fast. The minor planets of our survey become more irregular at smaller sizes, disputing the conclusions of Bowell (1977b), Degewij (1977), and Degewij et al. (1978), based on other, perhaps more complete, data; selection effects may account for this disagreement. Shapes do not appear to depend on taxonomic type. The dispersion of asteroid rotation rates from the mean is found to be in excellent agreement with a three-dimensional Maxwellian distribution, such as would be developed in a collisionally evolved system. The rotation axes, therefore, appear to be randomly oriented in space. Rotation pole positions are also tabulated and calculated to likely be constant in space over the extent of past observation. Observers are encouraged to measure the rotational properties of faint objects and asteroids of unusual taxonomic types, and to carry out long-time studies of asteroids which over short periods do not seem to vary.     

Experimental study on the collisional disruption of porous gypsum spheres

Abstract— In order to study the catastrophic disruption of porous bodies such as asteroids and planetesimals, we conducted several impact experiments using porous gypsum spheres (porosity: 50%). We investigated the fragment mass and velocity of disrupted gypsum spheres over a wide range of specific energies from 3 times 10³ J/kg to 5 times 10⁴ J/kg. We compared the largest fragment mass (m₁/M_t) and the antipodal velocity (V_a) of gypsum with those of non‐porous materials such as basalt and ice. The results showed that the impact strength of gypsum was notably higher than that of the non‐porous bodies; however, the fragment velocity of gypsum was slower than that of the non‐porous bodies. This was because the micro‐pores dispersed in the gypsum spheres caused a rapid attenuation of shock pressure in them. From these results, we expect that the collisional disruption of porous bodies could be significantly different from that of non‐porous bodies.     

Collisional evolution of the asteroid belt

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

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

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

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.     

Secular spin dynamics of inner main-belt asteroids

Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids (?40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s₆ spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin.