Catastrophic disruption of asteroids and family formation: a review of numerical simulations including both fragmentation and gravitational reaccumulations

In the last few years, thanks to the development of sophisticated numerical codes, a major breakthrough has been achieved in our understanding of the processes involved in small body collisions. In this review, we summarize the most recent results provided by numerical simulations, accounting for both the fragmentation of an asteroid and the gravitational interactions of the generated fragments. These studies have greatly improved our knowledge of the mechanisms that are at the origin of some observed features in the asteroid belt. In particular, the simulations have demonstrated that, for bodies larger than several kilometers, the collisional process not only involves the fragmentation of the asteroid but also the gravitational interactions between the ejected fragments. This latter mechanism can lead to the formation of large aggregates by gravitational reaccumulation of smaller fragments, and helps explain the presence of large members within asteroid families. Numerical simulations of the complete process have thus reproduced successfully for the first time the main properties of asteroid families, each formed by the disruption of a large parent body, and provided information on the possible internal structure of the parent bodies. A large amount of work remains necessary, however, to understand in deeper detail the physical process as a function of material properties and internal structures that are relevant to asteroids, and to determine in a more quantitative way the outcome properties such as fragment shapes and rotational states.     

A small‐strain overlay model

The paper begins with a discussion of the phenomenon of small‐strain stiffness and presents the small‐strain overlay model, a simple model that takes into account the non‐linear stiffness of soils at small strains. The new model can enhance already established elastoplastic formulations for non‐linear stiffness variation at small strains in a similar way that intergranular strain enhances the hypoplastic model. The overlay model is driven by the material's strain history and only two additional material constants, both with clear physical meaning. Therefore, the proposed model is a step towards the incorporation of small‐strain stiffness into routine design. In this paper, the new small‐strain overlay model is formulated. Its ability to take into account the influence of various strain histories on soil stiffness is illustrated in several examples. Copyright © 2008 John Wiley & Sons, Ltd.     

The gravity field of a dipping plate in Greece

Summary. The surface gravity anomalies for a three-dimensional density model of a dipping lithospheric plate under the Aegean island arc and the Aegean Sea in Greece in the eastern Mediterranean Sea have been calculated. Such a dipping plate has been suggested in geophysical investigations. The calculated gravity maximum over the dipping plate is located in the area of the largest observed Bouguer anomalies inside the island arc. It is suggested that this should be taken into account in studies of crustal structure and gravity in the area.     

The formation of the Baptistina family by catastrophic disruption: Porous versus non‐porous parent body

Abstract— In this paper, we present numerical simulations aimed at reproducing the Baptistina family based on its properties estimated by observations. A previous study by Bottke et al. (2007) indicated that this family is probably at the origin of the K/T impactor, is linked to the CM meteorites and was produced by the disruption of a parent body 170 km in size due to the head‐on impact of a projectile 60 km in size at 3 km s^?1. This estimate was based on simulations of fragmentation of non‐porous materials, while the family was assumed to be of C taxonomic type, which is generally interpreted as being formed from a porous body. Using both a model of fragmentation of non‐porous materials, and a model that we developed recently for porous ones, we performed numerical simulations of disruptions aimed at reproducing this family and at analyzing the differences in the outcome between those two models. Our results show that a reasonable match to the estimated size distribution of the real family is produced from the disruption of a porous parent body by the head‐on impact of a projectile 54 km in size at 3 km s^?1. Thus, our simulations with a model consistent with the assumed dark type of the family requires a smaller projectile than previously estimated, but the difference remains small enough to not affect the proposed scenario of this family history. We then find that the break‐up of a porous body leads to different outcomes than the disruption of a non‐porous one. The real properties of the Baptistina family still contain large uncertainties, and it remains possible that its formation did not involve the proposed impact conditions. However, the simulations presented here already show some range of outcomes and once the real properties are better constrained, it will be easy to check whether one of them provides a good match.     

Der nacheiszeitliche Bergsturz im Kandertal (Schweiz): Alter und Auswirkungen auf die damalige Umwelt

Zusammenfassung. Beim Bau des neuen AlpTransit Lötschberg Basistunnels wurden unter murgangartig verschwemmten Ablagerungen der alten Bergsturzmasse des Kandertals Stillwasserablagerungen mit zahlreichen organischen Resten und Torflagen gefunden. Die ¹⁴C-datierten Resultate der Pollen, Makrorest-, Holz- und Holzkohleanalysen ermöglichten eine Rekonstruktion der lokalen bis regionalen Umweltgeschichte. Ein Gewässer, vermutlich ein kleiner See, begann beim Tellenfeld in Frutigen um 8800 kal. Jahre v. Chr. zu verlanden. In der näheren Umgebung wuchs von 8800 v. Chr. bis 8000 v. Chr. ein Föhrenwald (Pinus silvestris), der reichlich mit Hasel (Corylus avellana) und anderen wärmeliebenden Gehölzen (Ulmen, Linden, Eichen; Ulmus, Tilia, Quercus) und Birken (Betula) durchsetzt war. Diese für die Nordalpen sehr frühe Bedeutung der Hasel ist durch ¹⁴C-datierte Corylus-Nussfragmente (9310±50 ¹⁴C BP, 8722–8337 v. Chr.) belegt. Nach 8500 v. Chr. drängte die Hasel die Waldföhre allmählich zurück. Auf Grund der paläoökologischen Resultate muss angenommen werden, dass die Wälder um 7600 v. Chr. durch ein katastrophales Ereignis stark gestört wurden. Als Reaktion darauf kam es zu einer starken Zunahme der Waldbrände und es breiteten sich zuerst Farne und Gräser sowie wenig später Waldföhren aus. Das Gewässer wurde um 7100 v. Chr. durch verschwemmtes Bergsturzmaterial zerstört. Der geomorphologische Befund deutet darauf hin, dass diese Ereignisse in engem Zusammenhang mit dem Hauptbergsturz im Kandertal stehen, der aussergewöhnliche Ausmasse hatte (ca. 800 Millionen m³). Die Zerstörung der lokalen ökosysteme als Folge des Bergsturzes um 7600–7100 v. Chr. fiel in ein frühes holozänes Wärme- und Sonneneinstrahlungsmaximum, in dem es, wie vorgängige Untersuchungen in den Alpen und in anderen Gebirgen belegen, zu überdurchschnittlich vielen Hanginstabilitäten kam.

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During the construction of the new AlpTransit railway line wetland sediments containing numerous fossils and peat layers were found below rockfall masses transported by debris flows. Radiocarbon-dated results of pollen, macrofossils, wood, and charcoal along with radiocarbon dating analysis were used to reconstruct the environmental history of the site. The wetland, originally probably a small lake, started to accumulate sediments at about 8800 cal. yr BC at Frutigen Tellenfeld. A pine forest (Pinus silvestris) admixed with hazel (Corylus avellana), other thermophilous arboreal taxa (Ulmus, Tilia, Quercus) and birch (Betula) grew in the surroundings of the lake. This very early importance of hazel is documented by ¹⁴C-dated Corylus nut fragments (9310±50 ¹⁴C yr BP, 8722–8337 yr BC). After 8500 BC hazel expanded on the costs of pine. The palaeo records suggest that the forests were severely disturbed by a catastrophic event at around 7600 BC. In response, forest fires strongly increased and ferns and grasses expanded and then pine stands established. At ca. 7100 BC the lake was abruptly destroyed by rockfall masses transported by a debris flow. The geomorphic situation suggests that these events were closely related with the main Kander valley rockfall, which had an exceptional size (800 millions m³). Local environmental catastrophes as a consequence of the rockfall at 7600–7100 BC occurred during an early Holocene thermal and solar irradiation maximum. As documented by previous investigations, this period was characterised by pronounced slope instabilities in the Alps and elsewhere.

Manuskript eingegangen 9. Februar 2004 Revidierte Fassung angenommen 17. Januar 2005     

Formation of Asteroid Families by Catastrophic Disruption: Simulations with Fragmentation and Gravitational Reaccumulation

This paper builds on preliminary work in which numerical simulations of the collisional disruption of large asteroids (represented by the Eunomia and Koronis family parent bodies) were performed and which accounted not only for the fragmentation of the solid body through crack propagation, but also for the mutual gravitational interaction of the resulting fragments. It was found that the parent body is first completely shattered at the end of the fragmentation phase, and then subsequent gravitational reaccumulations lead to the formation of an entire family of large and small objects with dynamical properties similar to those of the parent body. In this work, we present new and improved numerical simulations in detail. As before, we use the same numerical procedure, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational reaccumulation phase. However, this reaccumulation phase is now treated more realistically by using a merging criterion based on energy and angular momentum and by allowing dissipation to occur during fragment collisions. We also extend our previous studies to the as yet unexplored intermediate impact energy regime (represented by the Flora family formation) for which the largest fragment's mass is about half that of the parent body. Finally, we examine the robustness of the results by changing various assumptions, the numerical resolution, and different numerical parameters. We find that in the lowest impact energy regime the more realistic physical approach of reaccumulation leads to results that are statistically identical to those obtained with our previous simplistic approach. Some quantitative changes arise only as the impact energy increases such that higher relative velocities are reached during fragment collisions, but they do not modify the global outcome qualitatively. As a consequence, these new simulations confirm previous main results and still lead to the conclusion that: (1) all large family members must be made of gravitationally reaccumulated fragments; (2) the original fragment size distribution and their orbital dispersion are respectively steeper and smaller than currently observed for the real families, supporting recent studies on subsequent evolution and diffusion of family members; and (3) the formation of satellites around family members is a frequent and natural outcome of collisional processes.     

Synchrotron or plasma emission in solar microwave flares?

The spectral indices of microwave and hard X-ray emissions of a solar flare are found to correlate. Their observed values are in agreement with the expected relation from synchrotron and bremsstrahlung theory. These results are considered as strong evidence for the synchrotron mechanism in the microwave flare, contrary to recent alternative suggestions.     

Numerical simulations of catastrophic disruption: recent results

Numerical simulations have been used to study high velocity two-body impacts. In this paper a two-dimensional Lagrangian finite difference hydrocode and a three-dimensional smooth particle hydrocode (SPH) are described and initial results reported.

The 2D hydrocode has successfully reproduced both the fragment size distribution and the mean fragment velocities from laboratory impact experiments using basalt and cement mortar. Further, the hydrocode calculations have determined that the energy needed to fracture a body has a much stronger dependence on target size than predicted from most scaling theories. In addition, velocity distributions obtained (using homogeneous targets at impact velocities around 2 km s⁻¹) indicate that mean ejecta speeds resulting from large-body collisions do not generally exceed escape velocities.

The SPH model provides a fully three-dimensional framework for studying impacts, so that phenomena such as oblique collisions or impacts into non-spherical targets may be studied. The gridless code allows for arbitrary levels of distortion, and is hence appropriate for modeling the large-scale deformations which accompany most impact events. Because fragments are modeled explicitly, greater numerical accuracy is achieved in the regions of large fragments than with the purely statistical approach of the 2D model. Of course, this accuracy comes at the expense of significantly greater computational requirements.

These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.     

Seasonal variations of helium,radon, and uranium in lake waters near the Key Lake uranium deposit,Saskatchewan

To test the usefulness of the He method for the detection of buried U ore, a lake-water survey of the Key Lake area was carried out during March 1977 and repeated in June 1977. A set of 87 lake-water samples from 37 sites in eight different lakes were collected from the same sites in each survey. These samples were analyzed for He, Rn, O₂, Eh, pH, conductivity, alkalinity, and U.In the lakes the highest He concentrations, of nearly four times atmospheric equilibrium concentrations, were obtained during the winter survey. This was under the ice in two bottom lake samples where the sandy overburden extends for some 50 m directly to the ore zone. Radon and U values at these sites were also anomalous, but the highest values of Rn and U were obtained in a shallow lake about 2 km south of the ore zone where concentrations of radioactive boulders occur.The average net He and Rn contents dropped from 21 standard nanolitres/litre (nl/l) and 25 picocuries/litre (pCi/l) in the winter under the ice to 3 nl/l and 8 pCi/l in the summer, respectively. Average U and conductivity dropped from 2.3 ppb and 15 μmho/cm to 1.5 ppb and 11 μmho/cm, respectively, in the same suites of samples. The drop in the ionic species probably reflects the effect of snow and ice meltwater dilution and the much larger drop in the dissolved He and Rn reflects the combined effects of meltwater dilution, wind turbulence over ice-free lakes, and change in thermal gradients.The He results must be viewed with guarded optimism until a detailed investigation is completed to ascertain what fraction of the detected He is from the ore, what fraction from basement He that may have found its way into the lakes via the fracture zone in which the ore is located, and what effect drilling has had on the He flow into the lakes from the ore zone.