Koordinationschemie Perhalogenierter Cyclopentadine und Alkine, XV

Coordination Chemistry of Perhalogenated Cyclopentadienes and Alkynes, XV[1]. - Systematic Generation of Fivefold Ring-Silylated Cyclopentadienyl Manganese Complexes from [C5Br5]Mn(CO)3. Molecular Structure of [C5Br3(SiMe3)2]Mn(CO)3 [C5Br5]Mn(CO)3 reacts in a sequence of alternate bromine-lithium exchange reactions and electrophilic silylations by SiMe3Cl or SiMe3OSO2CF3 to give [C5Br5-n(SiMe3)n]Mn(CO)3, where n = 1 (1), 2 (2), or 3 (3). A crystal structure determination of 2 shows the two silyl substituents in the relative 1,3-orientation. Addition of one or two equivalents of BuLi and SiMe2HCl to a solution of 3 yields [C5Br2-n(SiMe3)3-(SiMe2H)n]Mn(CO)3 with n = 1 (4) and 2 (5), respectively. If 1 is treated twice with 2 eq. of BuLi and then 2 eq. of SiMe2HCl, a further pentasilylated compound, [C5(SiMe3)(SiMe2H)4]-Mn(CO)3 (6), is obtained. In situ chlorination of [C5(SiMe2H)5]Mn(CO)3 or 6 with PdCl2, followed by addition of MeMgCl, yields after chromatography an inseparable mixture of [C5(SiMe3)4X]Mn(CO)3 compounds, where X = H (7a), SiMe2H (7b), and SiMe3 (7c)

SPH calculations of asteroid disruptions: The role of pressure dependent failure models

We present recent improvements of the modeling of the disruption of strength dominated bodies using the Smooth Particle Hydrodynamics (SPH) technique. The improvements include an updated strength model and a friction model, which are successfully tested by a comparison with laboratory experiments. In the modeling of catastrophic disruptions of asteroids, a comparison between old and new strength models shows no significant deviation in the case of targets which are initially non-porous, fully intact and have a homogeneous structure (such as the targets used in the study by Benz&Asphaug (1999). However, for many cases (e.g. initially partly or fully damaged targets, rubble-pile structures, etc.) we find that it is crucial that friction is taken into account and the material has a pressure dependent shear strength. Our investigations of the catastrophic disruption threshold $Q^*_{D}$ as a function of target properties and target sizes up to a few 100 km show that a fully damaged target modeled without friction has a $Q^*_{D}$ which is significantly (5-10 times) smaller than in the case where friction is included. When the effect of the energy dissipation due to compaction (pore crushing) is taken into account as well, the targets become even stronger ($Q^*_{D}$ is increased by a factor of 2-3). On the other hand, cohesion is found to have an negligible effect at large scales and is only important at scales $\lesssim$ 1km. Our results show the relative effects of strength, friction and porosity on the outcome of collisions among small ($\lesssim$ 1000 km) bodies. These results will be used in a future study to improve existing scaling laws for the outcome of collisions (e.g. Leinhardt&Stewart, 2012).Comment: Accepted for publication in Planetary and Space Scienc

Formation of bi-lobed shapes by sub-catastrophic collisions: A late origin of comet 67P/C-G's structure

The origin of the particular shape of a small body like comet 67P/Churyumov-Gerasimenko (67P/C-G) is a topic of active research. How and when it acquired its peculiar characteristics has distinct implications on the origin of the solar system and its dynamics. We investigate how shapes like the one of comet 67P/C-G can result from a new type of low-energy, sub-catastrophic impacts involving elongated, rotating bodies. We focus on parameters potentially leading to bi-lobed structures. We also estimate the probability for such structures to survive subsequent impacts. We use a smooth particle hydrodynamics (SPH) shock physics code to model the impacts, the subsequent reaccumulation of material and the reconfiguration into a stable final shape. The energy increase as well as the degree of compaction of the resulting bodies are tracked in the simulations. Our modelling results suggest that the formation of bi-lobed structures like 67P/C-G is a natural outcome of the low energy, sub-catastrophic collisions considered here. Sub-catastrophic impacts have the potential to alter the shape of a small body significantly, without leading to major heating or compaction. The currently observed shapes of cometary nuclei, such as 67P/C-G, maybe a result of such a last major shape forming impact.Comment: Astronomy & Astrophysics, accepted pending minor revision

SPH calculations of Mars-scale collisions: the role of the Equation of State, material rheologies, and numerical effects

We model large-scale ($\approx$2000km) impacts on a Mars-like planet using a Smoothed Particle Hydrodynamics code. The effects of material strength and of using different Equations of State on the post-impact material and temperature distributions are investigated. The properties of the ejected material in terms of escaping and disc mass are analysed as well. We also study potential numerical effects in the context of density discontinuities and rigid body rotation. We find that in the large-scale collision regime considered here (with impact velocities of 4km/s), the effect of material strength is substantial for the post-impact distribution of the temperature and the impactor material, while the influence of the Equation of State is more subtle and present only at very high temperatures.Comment: 24 pages, 11 figures; accepted for publication in Icaru

Global Scale Impacts

Global scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, dilatation, stripping of mantle and crust, and seismic degradation. Deciphering the complicated record of global scale impacts, in asteroids and meteorites, will lead us to understand the original planet-forming process and its resultant populations, and their evolution in time as collisions became faster and fewer. We provide a brief overview of these ideas, and an introduction to models.Comment: A chapter for Asteroids IV, a new volume in the Space Science Series, University of Arizona Press (Patrick Michel, Francesca E. DeMeo, William F. Bottke, Eds.

Modeling asteroid collisions and impact processes

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision.Comment: Chapter to appear in the Space Science Series Book: Asteroids IV. Includes minor correction

Small-body deflection techniques using spacecraft: techniques in simulating the fate of ejecta

We define a set of procedures to numerically study the fate of ejecta produced by the impact of an artificial projectile with the aim of deflecting an asteroid. Here we develop a simplified, idealized model of impact conditions that can be adapted to fit the details of specific deflection-test scenarios, such as what is being proposed for the AIDA project. Ongoing studies based upon the methodology described here can be used to inform observational strategies and safety conditions for an observing spacecraft. To account for ejecta evolution, the numerical strategies we are employing are varied and include a large N-Body component, a smoothed-particle hydrodynamics (SPH) component, and an application of impactor scaling laws. Simulations that use SPH-derived initial conditions show high-speed ejecta escaping at low angles of inclination, and very slowly moving ejecta lofting off the surface at higher inclination angles, some of which re-impacts the small-body surface. We are currently investigating the realism of this and other models' behaviors. Next steps will include the addition of solar perturbations to the model and applying the protocol developed here directly to specific potential mission concepts such as the proposed AIDA scenario.Comment: 19 pages, 11 figures, accepted for publication in Advances in Space Research, Special Issue: Asteroids & Space Debri

How primordial is the structure of comet 67P/C-G? Combined collisional and dynamical models suggest a late formation

There is an active debate about whether the properties of comets as observed today are primordial or, alternatively, if they are a result of collisional evolution or other processes. We investigate the effects of collisions on a comet with a structure like 67P/C-G. We develop scaling laws for the critical specific impact energies required for a significant shape alteration. These are then used in simulations of the combined dynamical and collisional evolution of comets in order to study the survival probability of a primordially formed object with a shape like 67P/C-G. The effects of impacts on comet 67P/C-G are studied using a SPH shock physics code. The resulting critical specific impact energy defines a minimal projectile size which is used to compute the number of shape-changing collisions in a set of dynamical simulations. These simulations follow the dispersion of the trans-Neptunian disk during the giant planet instability, the formation of a scattered disk, and produce 87 objects that penetrate into the inner solar system with orbits consistent with the observed JFC population. The collisional evolution before the giant planet instability is not considered here. Hence, our study is conservative in its estimation of the number of collisions. We find that in any scenario considered here, comet 67P/C-G would have experienced a significant number of shape-changing collisions, if it formed primordially. This is also the case for generic bi-lobe shapes. Our study also shows that impact heating is very localized and that collisionally processed bodies can still have a high porosity. Our study indicates that the observed bi-lobe structure of comet 67P/C-G may not be primordial, but might have originated in a rather recent event, possibly within the last 1 Gy. This may be the case for any kilometer-sized two-component cometary nuclei.Comment: Astronomy & Astrophysics, accepted pending minor revision

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

Numerical simulations of asteroid break-ups, 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 Q*D, 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 Q*D 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 Q*D, 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 Q*D 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. We then propose some power-law relationships between Q*D and both target's size and impact speed that can be used in collisional evolution models.Comment: 18 pages, 19 Figures. Accepted for publication in Icaru