Chemical and mineralogical size segregation in the impact disruption of inhomogeneous, anhydrous meteorites

We performed impact disruption experiments on pieces from eight different anhydrous chondritic meteorites—four weathered ordinary chondrite finds from North Africa (NWA791, NWA620, NWA869 and MOR001), three almost unweathered ordinary chondrite falls (Mbale, Gao, and Saratov), and an almost unweathered carbonaceous chondrite fall (Allende). In each case the impactor was a small (1/8 or 1/4 in) aluminum sphere fired at the meteorite target at , comparable to the mean collision speed in the main-belt. Some of the ∼5 to debris from each disruption was collected in aerogel capture cells, and the captured particles were analyzed by in situ synchrotron-based X-ray fluorescence. For each meteorite, many of the smallest particles ( up to in size, depending on the meteorite) exhibit very high Ni/Fe ratios compared to the Ni/Fe ratios measured in the larger particles , a composition consistent with the smallest debris being dominated by matrix material while the larger debris is dominated by fragments from olivine chondrules. These results may explain why the interplanetary dust particles (IDPs) collected from the Earth's stratosphere are C-rich and volatile-rich compared to the presumed solar nebula composition. The IDPs may simply sample the matrix of an inhomogeneous parent body, structurally and mineralogically similar to the chondritic meteorites, which are inhomogeneous assemblages of compact, strong, C- and volatile-poor chondrules that are distributed in a more porous, C- and volatile-rich matrix. In addition, these results may explain why the micrometeorites, which are to millimeters in size, recovered from the polar ices are Ni- and S-poor compared to chondritic meteorites, since these polar micrometeorites may preferentially sample fragments from the Ni- and S-poor olivine chondrules. These results indicate that the average composition of the IDPs may be biased towards the composition of the matrix of the parent body while the average composition of the polar micrometeorites may be more heavily weighted towards the composition of the chondrules and clasts. Thus, neither the IDPs nor the polar micrometeorites may sample the bulk composition of their respective parent bodies.We determined the threshold collisional specific energy for these chondritic meteorites to be 1419 J/kg, about twice the value for terrestrial basalt. Comparison of the mass of the largest fragment produced in the disruption of an sample of the porous ordinary chondrite Saratov with the largest fragment produced in the disruption of an sample of the compact ordinary chondrite MOR001 when each was struck by an impactor having approximately the same kinetic energy confirms that it requires significantly more energy to disrupt a porous target than a non-porous target.These results may also have important implications for the design of spacecraft missions intended to sample the composition and mineralogy of the chondritic asteroids and other inhomogeneous bodies. A Stardust-like spacecraft intended to sample asteroids by collecting only the small debris from a man-made impact onto the asteroid may collect particles that over-sample the matrix of the target and do not provide a representative sample of the bulk composition. The impact collection technique to be employed by the Japanese HAYABUSA (formerly MUSES-C) spacecraft to sample the asteroid Itokawa may result in similar mineral segregation.     

Impact crater formed on sintered snow surface simulating porous icy bodies

To improve the scaling parameter controlling the impact crater formation in the strength regime, we conducted impact experiments on sintered snow targets with the dynamic strength continuously changed from 20 to 200 kPa, and the largest crater size formed on small icy satellites was considered by using the revised scaling parameter. Ice and snow projectiles were impacted on a snow surface with 36% porosity at an impact velocity from 31 m s⁻¹ to 150 m s⁻¹. The snow target was sintered at the temperature from −5 °C to −18 °C, and the snow dynamic strength was changed with the sintering duration at each temperature. We found that the mass ejected from the crater normalized by the projectile mass, π_V, was related to the ratio of the dynamic strength to the impact pressure, , as follows: , where the impact pressure was indicated by P = ρ_tC_0tv_i/2 with the target density of ρ_t, when the impact velocity, v_i, was much smaller than the bulk sound velocity C_0t (typically 1.8 km s⁻¹ in our targets). The ratio of the largest crater diameter to the diameter of the target body, d_max/D, was estimated by calculating the crater diameter at the impact condition for catastrophic disruption and then compared to the observed d_max/D of jovian and saturnian small satellites, in order to discuss the formation condition of these large d_max/D in the strength regime.     

A process to make massive ice in the martian regolith using long-term diffusion and thermal cracking

This paper describes a “simple standard” model of water transport through regolith that includes diffusive migration and phase changes driven by damped seasonal temperature waves. A hitherto unused first-order process is then added, that can produce ice densities much greater than those allowed by the initial dry porosity. Voids are produced in cooling icy regolith when tensile stresses exceed the cracking threshold . These stresses build up through an interaction of thermal contraction and elastic-plastic response. When the cracks open up after tensile failure there is purely thermal void enhancement and subsequent reduction as the regolith warms again. When the cracks are open the porosity is increased and they partially fill with ice crystals. Thus the void reduction on warming cannot go back to the original zero point and the bulk density of ice is increased with each temperature cycle. The cracking and thermal adjustment happen at scales of meters to millimeters. The large cracks can occur in pure ice and/or homogeneous icy material and the smaller cracks are produced by rock cobbles, pebbles, and grains having a much smaller coefficient of thermal expansion than ice. Thus a hierarchy of cracks and voids forms each temperature cycle and augments the ice content. The process can take the upper few meters of a pore-saturated icy soil from 28% by mass ice content to 70% in 10 Ma. This mechanism and the seasonal temperature cycle can plausibly produce massive ice deposits in the upper few meters of Mars' high-latitude regolith by diffusion and also keep the massive-ice regolith effectively porous to water vapor transport. The obliquity cycle can produce tensile stresses nearing 2 MPa down to depth so even deeper cracking could be happening.     

Low-speed impacts between rubble piles modeled as collections of polyhedra, 2

We present the results of additional calculations involving the collisions of km-scale rubble piles. In new work, we used the Open Dynamics Engine (ODE), an open-source library for the simulation of rigid-body dynamics that incorporates a sophisticated collision-detection and resolution routine. We found that using ODE resulted in a speed-up of approximately a factor of 30 compared with previous code. In this paper we report on the results of almost 1200 separate runs, the bulk of which were carried out with 1000-2000 elements. We carried out calculations with three different combinations of the coefficients of friction η and (normal) restitution ?: low (η=0,?=0.8), medium (η=0,?=0.5), and high (η=0.5,?=0.5) dissipation.For target objects of ∼1 km in radius, we found reduced critical disruption energy values in head-on collisions from 2 to 100 J kg⁻¹ depending on dissipation and impactor/target mass ratio. Monodisperse objects disrupted somewhat more easily than power-law objects in general. For oblique collisions of equal-mass objects, mildly off-center collisions (b/b₀=0.5) seemed to be as efficient or possibly more efficient at collisional disruption as head-on collisions. More oblique collisions were less efficient and the most oblique collisions we tried (b/b₀=0.866) required up to ∼200 J kg⁻¹ for high-dissipation power-law objects. For calculations with smaller numbers of elements (total impactor or 200 elements) we found that collisions were more efficient for smaller numbers of more massive elements, with values as low as for low-dissipation cases. We also analyzed our results in terms of the relations proposed by Stewart and Leinhardt [Stewart, S.T., Leinhardt, Z.M., 2009. Astrophys. J. 691, L133-L137] where where Q_R is the impact kinetic energy per unit total mass m_i+m_T. Although there is a significant amount of scatter, our results generally bear out the suggested relation.     

Comparison between the findings of Deep Impact and our experimental results on large samples of gas-laden amorphous ice

The findings of Deep Impact on the structure and composition of Tempel-1 are compared with our experimental results on large (20 cm diameter and up to 10 cm high) samples of gas-laden amorphous ice. The mechanical ∼tensile strength inferred for Tempel-1: ∼65 Pa is 30 to 60 times smaller than our experimental findings of 2-4 kPa. This means that Tempel-1 is even fluffier than our very fluffy, talcum like, ice sample. The thermal inertia: is very close to our value of 80. The density of , is close to our value of 250-300 kg m⁻³, taking into account an ice/silicate ratio of 1 in the comet, while we study pure ice. Surface morphological features, such as non-circular depressions, chaotic terrain and smooth surfaces, were observed in our experiments. The only small increase in the gas/water vapor ratio pre- and post-impact, suggest that in the area excavated by the impactor, the 135 K front did not penetrate deeper than a few meters. Altogether, the agreement between the findings of Deep Impact and our experimental results point to a loose agglomerate of ice grains (with a silicate-organic core), which was formed by a very gentle aggregation of the ice grains, without compaction.     

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.     

On the collisional disruption of porous icy targets simulating Kuiper belt objects

We present results from 27 impact experiments using porous (porosity ranging from 0.39 to 0.54) ice targets and solid ice projectiles at impact speeds ranging from 90 to 155 m/s. These targets were designed to simulate Kuiper Belt Objects (KBOs) in structure. We measured a specific energy for shattering, , of 2.1×¹⁰⁵ erg/g for those snowball targets hit by intact ice projectiles; this is of the same order as that measured for solid ice targets. The fragment mass distribution follows a power law, although the exponent is not simply related to the largest fragment size as assumed by fragmentation models. We provide the first measurement of the three-dimensional mass-velocity distribution for disrupted ice targets and find that fragment speeds range from ∼2 to ∼20 m/s. The fraction of collisional kinetic energy that is partitioned into ejecta speeds is between 1 and 15% (although it should be noted that the lower limit is more reliable than the upper).     

Full numerical simulations of catastrophic small body collisions

The outcome of collisions between small icy bodies, such as Kuiper belt objects, is poorly understood and yet a critical component of the evolution of the trans-neptunian region. The expected physical properties of outer Solar System materials (high porosity, mixed ice-rock composition, and low material strength) pose significant computational challenges. We present results from catastrophic small body collisions using a new hybrid hydrocode to N-body code computational technique. This method allows detailed modeling of shock propagation and material modification as well as gravitational reaccumulation. Here, we consider a wide range of material strengths to span the possible range of Kuiper belt objects. We find that the shear strength of the target is important in determining the collision outcome for 2 to 50-km radius bodies, which are traditionally thought to be in a pure gravity regime. The catastrophic disruption and dispersal criteria, , can vary by up to a factor of three between strong crystalline and weak aggregate materials. The material within the largest reaccumulated remnants experiences a wide range of shock pressures. The dispersal and reaccumulation process results in the material on the surfaces of the largest remnants having experienced a wider range of shock pressures compared to material in the interior. Hence, depending on the initial structure and composition, the surface materials on large, reaccumulated bodies in the outer Solar System may exhibit complex spectral and albedo variations. Finally, we present revised catastrophic disruption criteria for a range of impact velocities and material strengths for outer Solar System bodies.     

Dynamical erosion of the asteroid belt and implications for large impacts in the inner Solar System

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.     

A derivation of the luminosity function of the Kuiper belt from a broken power-law size distribution

We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 30<Db<90 km via a maximum-likelihood fit of our model to the observed luminosity function. We also confirm that the observed luminosity function for m(R)∼21-28 is consistent with a broken power-law size distribution, and exhibits a break at .     

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

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

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].     

Modelling meteor ablation in the venusian atmosphere

A comparative study of meteor ablation in the atmospheres of the Earth and Venus is presented. The classical single body meteor ablation model is extended to incorporate a heat penetration depth estimate allowing the simulation of larger meteoroids, than would an isothermal model. The ablation of icy and rocky meteoroids, with densities of 1.0 and 3.4 g cm⁻³, respectively, and initial radii of up to for rock and for ice (equivalent to an initial mass of in both cases), was simulated in both atmospheres. In general venusian meteors are brighter than terrestrial equivalents. Large, slow, rocky objects may be up to 0.7 mag brighter on Venus, while small, icy particles with entry speeds in the range 30-60 km s⁻¹, are found to be upwards of 2.7 mag brighter than at the Earth. Venusian meteors reach maximum brightness at greater altitudes than would similar particles at the Earth. Rocky meteoroids have their points of maximum brightness some 15-35 km higher up at Venus, between 90 and 120 km, whereas, for icy particles this altitude difference is about 5-25 km higher up than at the Earth, in the range 100-125 km. These findings agree, for the most part, with recent analytical studies. Venusian meteors, which last from 100 ms to , tend to be shorter-lived than terrestrial meteors, with correspondingly shorter visible trails. Large (), slow () icy particles reach a maximum magnitude of ∼−2 at Venus and remain visible for about one second, with a large section of the smaller faster meteoroids simulated here remaining visible for several hundred milliseconds. In light of recent space-based meteor observations at the Earth [Jenniskens, P., Tedesco, E., Muthry, J., Laux, C.O., Price, S., 2002. Meteorit. Planet. Sci. 37, 1071-1078], such brightness, height and duration estimates as suggested in this work, may be used in developing future observational campaigns to be carried out from Venus orbit.     

R-band light curve of Comet 9P/Tempel 1 during the Deep Impact event

We present high-speed CCD photometry of Comet 9P/Tempel 1 during the Deep Impact event on 2005 July 4 UT. Approximately 2 h and 50 min of R-band data were acquired at Mount Laguna Observatory with a temporal resolution of 5.5 s. The flux increased by 9% in the first minute after impact. This was followed by a more gradual two-part linear rise, with a change in slope at 9.2 min post-impact, at which time the rate of brightening increased from ∼ to ∼. An analysis of the light curve obtained with the guide camera on the United Kingdom Infrared Telescope and yields very similar results. These findings are mildly in disagreement with the 3-part linear rise found by Fernández et al. (2007) in that we do not find any evidence for a change at 4 min post-impact. We interpret the linear rise phase as due to solar illumination of the edge of an expanding optically thick dust ejecta plume. After approximately 20 min, the light curves begin to flatten out, perhaps coincident with the start of the transition to becoming optically thin. In the large apertures (>10^″) the light curve continues to gradually rise until the end of the observations. In smaller apertures, the light curves reach a peak at approximately 50 min, then decrease back towards the pre-impact flux level. The drop in flux in the smaller apertures may be caused by the ejecta expanding beyond the edge of the photometric aperture, and if so, we can use this timescale to infer an expansion velocity of ∼, consistent with previous published estimates.     

Oxygen ion escape at Mars in a hybrid model: High energy and low energy ions

We have studied the escape and energization of several O⁺ populations and an population at Mars by using a hybrid model. The quasi-neutral hybrid model, HYB-Mars model, included five oxygen ion populations making it possible to distinguish photoions from oxygen ions originating from charge exchange processes and from the ionosphere.We have identified two high-energy ion components and one low-energy ion component of oxygen. They have different spatial and energy distributions near Mars. The two high-energy oxygen ion components, consisting of a high-energy “beam” and a high-energy “halo”, have different origins. (1) The high-energy (>∼100 eV) “beam” of O⁺ and ions are originating from the ionosphere. These ions form a highly asymmetric spatial distribution of escaping oxygen ions with respect to the direction of the convective electric field in the solar wind. (2) The high-energy (>∼100 eV) “halo” component contains O⁺ ions which are formed from the oxygen neutral exosphere by extreme ultraviolet radiation (EUV) and by charge exchange processes. These energetic halo ions can be found all around Mars. (3) The low energy O⁺ and ions (<∼100 eV) form a relatively symmetric spatial distribution around the Mars-Sun line. They originate from the ionosphere and from charge exchange processes between protons and exospheric oxygen atoms.The existence of the low- and the high-energy oxygen components is in agreement with recent in situ plasma measurements made by the ASPERA-3 instrument on the Mars Express mission. The analysis of the escaping oxygen ions suggests that the global energization of escaping planetary ions in the martian tail is controlled by the convective electric field.     

Low-speed impacts between rubble piles modeled as collections of polyhedra

We present results of modeling rubble piles as collections of polyhedra. The use of polyhedra allows more realistic (irregular) shapes and interactions (e.g. collisions), particularly for objects of different sizes. Rotational degrees of freedom are included in the modeling, which may be important components of the motion. We solved the equations of rigid-body dynamics, including frictional/inelastic collisions, for collections of up to several hundred elements. As a demonstration of the methods and to compare with previous work by other researchers, we simulated low-speed collisions between km-scale bodies with the same general parameters as those simulated by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151]. High-speed collisions appropriate to present-day asteroid encounters require additional treatment of shock effects and fragmentation and are the subject of future work; here we study regimes appropriate to planetesimal accretion and re-accretion in the aftermath of catastrophic events. Collisions between equal-mass objects at low speeds () were simulated for both head-on and off-center collisions between rubble piles made of a power-law mass spectrum of sub-elements. Very low-speed head-on collisions produce single objects from the coalescence of the impactors. For slightly higher speeds, extensive disruption occurs, but re-accretion produces a single object with most of the total mass. For increasingly higher speeds, the re-accreted object has smaller mass, finally resulting in complete catastrophic disruption with all sub-elements on escape trajectories and only small amounts of mass in re-accreted bodies. Off-center collisions at moderately low speeds produce two re-accreted objects of approximately equal mass, separating at greater than escape speed. At high speed, complete disruption occurs as with the high-speed head-on collisions. Head-on collisions at low to moderate speeds result in objects of mostly oblate shape, while higher speed collisions produce mostly prolate objects, as do off-center collisions at moderate and high speeds. Collisions carried out with the same dissipative coefficients (coefficient of restitution ?n=0.8, zero friction) as used by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151] result in a value for specific energy for disruption , somewhat lower than the value of 2 J/kg found by them, while collisions with a lower coefficient of restitution and friction [?n=0.5, ?t=0, μ=0.5, similar to those used by Michel, et al. [Michel, P., Benz, W., Richardson, D.C., 2004. Planet. Space Sci. 52, 1109-1117] for SPH + N-body calculations] yield .     

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.     

Calculation of the enrichment of the giant planet envelopes during the “late heavy bombardment”

The giant planets of our solar system possess envelopes consisting mainly of hydrogen and helium but are also significantly enriched in heavier elements relatively to our Sun. In order to better constrain how these heavy elements have been delivered, we quantify the amount accreted during the so-called “late heavy bombardment”, at a time when planets were fully formed and planetesimals could not sink deep into the planets. On the basis of the “Nice model”, we obtain accreted masses (in terrestrial units) equal to for Jupiter, and for Saturn. For the two other giant planets, the results are found to depend mostly on whether they switched position during the instability phase. For Uranus, the accreted mass is with an inversion and without an inversion. Neptune accretes in models in which it is initially closer to the Sun than Uranus, and otherwise. With well-mixed envelopes, this corresponds to an increase in the enrichment over the solar value of 0.033±0.001 and 0.074±0.007 for Jupiter and Saturn, respectively. For the two other planets, we find the enrichments to be 2.1±1.4 (w/ inversion) or 1.2±0.7 (w/o inversion) for Uranus, and 2.0±1.2 (w/ inversion) or 2.7±1.6 (w/o inversion) for Neptune. This is clearly insufficient to explain the inferred enrichments of ∼4 for Jupiter, ∼7 for Saturn and ∼45 for Uranus and Neptune.