arXiv subjects

Derek C. Richardson

Publications and source records attributed to Derek C. Richardson.

42 records · Page 3Linked to original sources

arXiv2010

Formation of Kuiper Belt Binaries by Gravitational Collapse

A large fraction of 100-km-class low-inclination objects in the classical Kuiper Belt (KB) are binaries with comparable mass and wide separation of components. A favored model for their formation was capture during the coagulation growth of bodies in the early KB. Instead, recent studies suggested that large objects can rapidly form in the protoplanetary disks when swarms of locally concentrated solids collapse under their own gravity. Here we examine the possibility that KB binaries formed during gravitational collapse when the excess of angular momentum prevented the agglomeration of available mass into a solitary object. We find that this new mechanism provides a robust path toward the formation of KB binaries with observed properties, and can explain wide systems such as 2001 QW322 and multiples such as (47171) 1999 TC36. Notably, the gravitational collapse is capable of producing 100% binary fraction for a wide range of the swarm's initial angular momentum values. The binary components have similar masses (80% have the secondary-over-primary radius ratio >0.7) and their separation ranges from ~1,000 to ~100,000 km. The binary orbits have eccentricities from e=0 to ~1, with the majority having e<0.6. The binary orbit inclinations with respect to the initial angular momentum of the swarm range from i=0 to ~90 deg, with most cases having i<50 deg. Our binary formation mechanism implies that the primary and secondary components in each binary pair should have identical bulk composition, which is consistent with the current photometric data. We discuss the applicability of our results to the Pluto-Charon, Orcus-Vanth, (617) Patroclus-Menoetius and (90) Antiope binary systems.

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arXiv2009

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.

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arXiv2009

An analytic parameterization of self-gravity wakes in Saturn's rings, with application to occultations and propellers

We have developed a semi-analytic method of parameterizing N-body simulations of self-gravity wakes in Saturn's rings, describing their properties by means of only 6 numbers: 3 optical depths and 3 weighting factors. These numbers are obtained using a density-estimation procedure that finds the frequencies of various values of local density within a simulated ring patch. Application of our parameterization to a suite of N-body simulations implies that the distribution of local optical depths is trimodal, rather than bimodal as previous authors have assumed. Rings dominated by self-gravity wakes appear to be mostly empty space. The implications of this result for the analysis of occultation data are more conceptual than practical. The only adjustment needed is that the model parameter $τ_{gap}$ should be interpreted as representing the area-weighted average optical depth within the gaps (or inter-wake regions). The most significant consequence of our results applies to the question of why "propeller" structures observed in the mid-A ring are seen as relative-bright features, even though the most prominent features of simulated propellers are regions of relatively low density. We find preliminary quantitative support for the hypothesis that propellers would be bright if they involve a local and temporary disruption of self-gravity wakes, flooding the region with more "photometrically active" material (i.e., material that can contribute to the rings' local optical depth) even though the overall density is lower, and thus raising their apparent brightnesses in agreement with observations. We suggest that this mechanism be tested by future detailed numerical models.

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arXiv2009

Collisional and Rotational Disruption of Asteroids

Asteroids are leftover pieces from the era of planet formation that help us understand conditions in the early Solar System. Unlike larger planetary bodies that were subject to global thermal modification during and subsequent to their formation, these small bodies have kept at least some unmodified primordial material from the solar nebula. However, the structural properties of asteroids have been modified considerably since their formation. Thus, we can find among them a great variety of physical configurations and dynamical histories. In fact, with only a few possible exceptions, all asteroids have been modified or completely disrupted many times during the age of the Solar System. This picture is supported by data from space mission encounters with asteroids that show much diversity of shape, bulk density, surface morphology, and other features. Moreover, the gravitational attraction of these bodies is so small that some physical processes occur in a manner far removed from our common experience on Earth. Thus, each visit to a small body has generated as many questions as it has answered. In this review we discuss the current state of research into asteroid disruption processes, focusing on collisional and rotational mechanisms. We find that recent advances in modeling catastrophic disruption by collisions have provided important insights into asteroid internal structures and a deeper understanding of asteroid families. Rotational disruption, by tidal encounters or thermal effects, is responsible for altering many smaller asteroids, and is at the origin of many binary asteroids and oddly shaped bodies.

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arXiv2009

N-Body Simulations of Growth from 1 km Planetesimals at 0.4 AU

We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 solar mass star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate; therefore, we model a sample patch of the disk. Although this greatly reduces the number of bodies, we still track in excess of 10^5 particles. We consider three initial velocity distributions and monitor the growth of the planetesimals. The masses of some particles increase by more than a factor of 100. Additionally, the escape speed of the largest particle grows considerably faster than the velocity dispersion of the particles, suggesting impending runaway growth, although no particle grows large enough to detach itself from the power law size-frequency distribution. These results are in general agreement with previous statistical and analytical results. We compute rotation rates by assuming conservation of angular momentum around the center of mass at impact and that merged planetesimals relax to spherical shapes. At the end of our simulations, the majority of bodies that have undergone at least one merger are rotating faster than the breakup frequency. This implies that the assumption of completely inelastic collisions (perfect accretion), which is made in most simulations of planetary growth at sizes 1 km and above, is inappropriate. Our simulations reveal that, subsequent to the number of particles in the patch having been decreased by mergers to half its initial value, the presence of larger bodies in neighboring regions of the disk may limit the validity of simulations employing the patch approximation.

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arXiv2008

Formes d'astéroïdes et formation de satellites : rôle de la réaccumulation gravitationnelle

Asteroid shapes and satellites: role of gravitational reaccumulation. Following current evidences, it is widely accepted that many asteroids would be "gravitational aggregates", i.e. bodies lacking internal cohesion. They could mainly be originated during the catastrophic disruption of some parent bodies, through the gravitational reaccumulation of the resulting fragments. The same events produced the dynamical families that we observe. In this work we address the problem of the origin of shapes of gravitational aggregates, that could contain signatures of their origin. We use a N-body code to simulate the collapse of a cloud of fragments, with a variety of initial velocity distributions and total angular momentum. The fragments are treated as inhelastic spheres, that rapidly accumulate to form rotating aggregates. The resulting shapes and rotational properties are compared with theoretical predictions. The results show that only a precise category of shapes (flattened spheroids) are created via this mechanism. This may provide interesting constraints on the evolution of asteroid shapes, in particular for those with one or more satellites.

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