arXiv subjects

Derek C. Richardson

Publications and source records attributed to Derek C. Richardson.

At least 37 records · Page 2Linked to original sources

arXiv2020

Superparticle Method for Simulating Collisions

For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated to represent a collectively large collisional cross section of real particles. Here we develop a superparticle-based method that replicates the kinetic energy loss during real-world collisions, implement it in an $N$-body code and test it. The tests provide interesting insights into dynamics of self gravitating collisional systems. They show how particle systems evolve over several free fall timescales to form central concentrations and equilibrated outer shells. The superparticle method can be extended to account for the accretional growth of objects during inelastic mergers.

astro-ph.EP↗

arXiv2019

Reversibility of granular rotations and translations

We analyze reversibility of both displacements and rotations of spherical grains in three-dimensional compression experiments. Using transparent acrylic beads with cylindrical holes and index matching techniques, we are not only capable of tracking displacements but also, for the first time, analyze reversibility of rotations. We observe that for moderate compression amplitudes, up to one bead diameter, the translational displacements of the beads after each cycle become mostly reversible after an initial transient. By contrast, granular rotations are largely irreversible. We find a weak correlation between translational and rotational displacements, indicating that rotational reversibility depends on more subtle changes in contact distributions and contact forces between grains compared with displacement reversibility.

cond-mat.soft↗

arXiv2018

Fragment properties from large-scale asteroid collisions: I: Results from SPH/N-body simulations using porous parent bodies and improved material models

Understanding the collisional fragmentation and subsequent reaccumulation of fragments is crucial for studies of the formation and evolution of the small-body populations. Using an SPH / N-body approach, we investigate the size-frequency distributions (SFDs) resulting from the disruption of 100 km-diameter targets consisting of porous material, including the effects of pore-crushing as well as friction. Overall, the porous targets have a significantly higher impact strength (Q*D) than the rubble-pile parent bodies investigated previously (Benavidez et al., 2012) and show a behavior more similar to non-porous monolithic targets (Durda et al., 2007). Our results also confirm that for a given specific impact energy, the SFDs resulting from a parent body disruption are strongly dependent on the size scale.

astro-ph.EP↗

arXiv2018

The formation mechanism of 4179 Toutatis' elongated bi-lobed structure in a close Earth encounter scenario

The optical images of near-Earth asteroid 4179 Toutatis acquired by Chang'e-2 spacecraft show that Toutatis has an elongated contact binary configuration, with the contact point located along the long axis. We speculate that such configuration may have resulted from a low-speed impact between two components. In this work, we performed a series of numerical simulations and compared the results with the optical images, to examine the mechanism and better understand the formation of Toutatis. Herein we propose an scenario that an assumed separated binary precursor could undergo a close encounter with Earth, leading to an impact between the primary and secondary, and the elongation is caused by Earth's tide. The precursor is assumed to be a doubly synchronous binary with a semi-major axis of 4 $R_p$ (radius of primary) and the two components are represented as spherical cohesionless self-gravitating granular aggregates. The mutual orbits are simulated in a Monte Carlo routine to provide appropriate parameters for our \emph{N}-body simulations of impact and tidal distortion. We employ the \emph{pkdgrav} package with a soft-sphere discrete element method (SSDEM) to explore the entire scenarios. The results show that contact binary configurations are natural outcomes under this scenario, whereas the shape of the primary is almost not affected by the impact of the secondary. However, our simulations further provide an elongated contact binary configuration best-matching to the shape of Toutatis at an approaching distance $r_p$ = 1.4 $\sim$ 1.5 $R_e$ (Earth radius), indicative of a likely formation scenario for configurations of Toutatis-like elongated contact binaries.

astro-ph.EP↗

arXiv2017

Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides, or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ~0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.

astro-ph.EP↗

arXiv2017

Structural analysis of rubble-pile asteroids applied to collisional evolution

Solar system small bodies come in a wide variety of shapes and sizes, which are achieved following very individual evolutional paths through billions of years. This paper focuses on the reshaping process of rubble-pile asteroids driven by meteorite impacts. In our study, numerous possible equilibrium configurations are obtained via Monte Carlo simulation, and the structural stability of these configurations is determined via eigen analysis of the geometric constructions. The eigen decomposition reveals a connection between the cluster's reactions and the types of external disturbance. Numerical simulations are performed to verify the analytical results. The gravitational N-body code pkdgrav is used to mimic the responses of the cluster under intermittent non-dispersive impacts. We statistically confirm that the stability index, the total gravitational potential and the volume of inertia ellipsoid show consistent tendency of variation. A common regime is found in which the clusters tend towards crystallization under intermittent impacts, i.e., only the configurations with high structural stability survive under the external disturbances. The results suggest the trivial non-disruptive impacts might play an important role in the rearrangement of the constituent blocks, which may strengthen these rubble piles and help to build a robust structure under impacts of similar magnitude. The final part of this study consists of systematic simulations over two parameters, the projectile momentum and the rotational speed of the cluster. The results show a critical value exists for the projectile momentum, as predicted by theory, below which all clusters become responseless to external disturbances; and the rotation proves to be significant for it exhibits an "enhancing" effect on loose-packed clusters, which coincides with the observation that several fast-spinning asteroids have low bulk densities.

astro-ph.EP↗

arXiv2017

Creep stability of the proposed AIDA mission target 65803 Didymos: I. Discrete cohesionless granular physics model

As the target of the proposed Asteroid Impact & Deflection Assessment (AIDA) mission, the near-Earth binary asteroid 65803 Didymos represents a special class of binary asteroids, those whose primaries are at risk of rotational disruption. To gain a better understanding of these binary systems and to support the AIDA mission, this paper investigates the creep stability of the Didymos primary by representing it as a cohesionless self-gravitating granular aggregate subject to rotational acceleration. To achieve this goal, a soft-sphere discrete element model (SSDEM) capable of simulating granular systems in quasi-static states is implemented and a quasi-static spin-up procedure is carried out. We devise three critical spin limits for the simulated aggregates to indicate their critical states triggered by reshaping and surface shedding, internal structural deformation, and shear failure, respectively. The failure condition and mode, and shear strength of an aggregate can all be inferred from the three critical spin limits. The effects of arrangement and size distribution of constituent particles, bulk density, spin-up path, and interparticle friction are numerically explored. The results show that the shear strength of a spinning self-gravitating aggregate depends strongly on both its internal configuration and material parameters, while its failure mode and mechanism are mainly affected by its internal configuration. Additionally, this study provides some constraints on the possible physical properties of the Didymos primary based on observational data and proposes a plausible formation mechanism for this binary system. With a bulk density consistent with observational uncertainty and close to the maximum density allowed for the asteroid, the Didymos primary in certain configurations can remain geo-statically stable without including cohesion.

astro-ph.EP↗

arXiv2017

Numerical Simulations of Saturn's B Ring: Granular Friction as a Mediator between Self-Gravity and Viscous Overstability

We study the B ring's complex optical depth structure. The source of this structure may be the complex dynamics of the Keplerian shear and the self-gravity of the ring particles. The outcome of these dynamic effects depends sensitively on the collisional and physical properties of the particles. Two mechanisms can emerge that dominate the macroscopic physical structure of the ring: self-gravity wakes and viscous overstability. Here we study the interplay between these two mechanisms by using our recently developed particle collision method that allows us to better model the inter-particle contact physics. We find that for a constant ring surface density and particle internal density, particles with rough surfaces tend to produce axisymmetric ring features associated with the viscous overstability, while particles with smoother surfaces produce self-gravity wakes.

astro-ph.EP↗

arXiv2016

Hektor - an exceptional D-type family among Jovian Trojans

In this work, we analyze Jovian Trojans in the space of suitable resonant elements and we identify clusters of possible collisional origin by two independent methods: the hierarchical clustering and a so-called "randombox". Compared to our previous work (Brož and Rozehnal 2011), we study a twice larger sample. Apart from Eurybates, Ennomos and $1996\,\rm RJ$ families, we have found three more clusters --- namely families around asteroids (20961)~Arkesilaos, (624)~Hektor in the $L_4$ libration zone and (247341)~$2001\,\rm UV_{209}$ in $L_5$. The families fulfill our stringent criteria, i.e. a high statistical significance, an albedo homogeneity and a steeper size-frequency distribution than that of background. In order to understand their nature, we simulate their long term collisional evolution with the Boulder code (Morbidelli et al. 2009) and dynamical evolution using a modified SWIFT integrator (Levison and Duncan, 1994). Within the framework of our evolutionary model, we were able to constrain the the age of the Hektor family to be either 1 to 4 Gyr or, less likely, 0.1 to 2.5 Gyr, depending on initial impact geometry. Since (624) Hektor itself seems to be a bilobed--shape body with a satellite (Marchis et al. 2014), i.e. an exceptional object, we address its association with the D--type family and we demonstrate that the moon and family could be created during a single impact event. We simulated the cratering event using a Smoothed Particle Hydrodynamics (SPH, Benz and Asphaug, 1994). This is also the first case of a family associated with a D--type parent body.

astro-ph.EP↗

arXiv2016

The Role of the Kozai-Lidov Mechanism in Black Hole Binary Mergers in Galactic Centers

In order to understand the rate of merger of stellar-mass black hole binaries (BHBs) by gravitational wave (GW) emission it is important to determine the major pathways to merger. We use numerical simulations to explore the evolution of BHBs inside the radius of influence of supermassive black holes (SMBHs) in galactic centers. In this region the evolution of binaries is dominated by perturbations from the central SMBH. In particular, as first pointed out by Antonini and Perets, the Kozai-Lidov (KL) mechanism trades relative inclination of the BHB to the SMBH for eccentricity of the BHB, and for some orientations can bring the BHB to an eccentricity near unity. At very high eccentricities, GW emission from the BHB can become efficient, causing the members of the BHB to coalesce. We use a novel combination of two N-body codes to follow this evolution. We are forced to simulate small systems to follow the behavior accurately. We have completed 400 simulations that range from $\sim$ 300 stars around a $10^{3}$ M$_{\odot}$ black hole to $\sim$ 4500 stars around a $10^{4}$ M$_{\odot}$ black hole. These simulations are the first to follow the internal orbit of a binary near a SMBH while also following the changes to its external orbit self-consistently. We find that this mechanism could produce mergers at a maximum rate per volume of $\sim 100$ Gpc$^{-3}$ yr$^{-1}$ or considerably less if the inclination oscillations of the binary remain constant as the BHB inclination to the SMBH changes, or if the binary black hole fraction is small.

astro-ph.HE↗

arXiv2015

Collisional Formation and Modeling of Asteroid Families

In the last decade, thanks to the development of sophisticated numerical codes, major breakthroughs have been achieved in our understanding of the formation of asteroid families by catastrophic disruption of large parent bodies. In this review, we describe numerical simulations of asteroid collisions that reproduced the main properties of families, accounting for both the fragmentation of an asteroid at the time of impact and the subsequent gravitational interactions of the generated fragments. The simulations demonstrate that the catastrophic disruption of bodies larger than a few hundred meters in diameter leads to the formation of large aggregates due to gravitational reaccumulation of smaller fragments, which helps explain the presence of large members within asteroid families. Thus, for the first time, numerical simulations successfully reproduced the sizes and ejection velocities of members of representative families. Moreover, the simulations provide constraints on the family dynamical histories and on the possible internal structure of family members and their parent bodies.

astro-ph.EP↗

arXiv2014

Coupled Spin and Shape Evolution of Small Rubble-Pile Asteroids: Self-Limitation of the YORP Effect

We present the first self-consistent simulations of the coupled spin-shape evolution of small gravitational aggregates under the influence of the YORP effect. Because of YORP's sensitivity to surface topography, even small centrifugally driven reconfigurations of aggregates can alter the YORP torque dramatically, resulting in spin evolution that can differ qualitatively from the rigid-body prediction. One third of our simulations follow a simple evolution described as a modified YORP cycle. Two-thirds exhibit one or more of three distinct behaviors---stochastic YORP, self-governed YORP, and stagnating YORP---which together result in YORP self-limitation. Self-limitation confines rotation rates of evolving aggregates to far narrower ranges than those expected in the classical YORP cycle, greatly prolonging the times over which objects can preserve their sense of rotation. Simulated objects are initially randomly packed, disordered aggregates of identical spheres in rotating equilibrium, with low internal angles of friction. Their shape evolution is characterized by rearrangement of the entire body, including the deep interior. They do not evolve to axisymmetric top shapes with equatorial ridges. Mass loss occurs in one-third of the simulations, typically in small amounts from the ends of a prolate-triaxial body. We conjecture that YORP self-limitation may inhibit formation of top-shapes, binaries, or both, by restricting the amount of angular momentum that can be imparted to a deformable body. Stochastic YORP, in particular, will affect the evolution of collisional families whose orbits drift apart under the influence of Yarkovsky forces, in observable ways.

astro-ph.EP↗

arXiv2014

Low-speed Impact Simulations into Regolith in Support of Asteroid Sampling Mechanism Design I.: Comparison with 1-g Experiments

This study is carried out in the framework of sample-return missions to asteroids that use a low-speed projectile as the primary component of its sampling mechanism (e.g., JAXA's Hayabusa and Hayabusa2 missions). We perform numerical simulations of such impacts into granular materials using different projectile shapes under Earth's gravity. We then compare the amounts of ejected mass obtained in our simulations against what was found in experiments that used similar setups, which allows us to validate our numerical approach. For the targets, we consider 2 different monodisperse grain-diameter sizes: 5 mm and 3 mm. The impact speed of the projectile is 11 m s$^{-1}$ directed downward, perpendicular to the surface of the targets. Using an implementation of the soft-sphere discrete element method (SSDEM) in the $N$-Body gravity tree code PKDGRAV, previously validated in the context of low-speed impacts into sintered glass bead agglomerates, we find a noticeable dependence of the amount of ejected mass on the projectile shape. As found in experiments, in the case of the larger target grain size (5 mm), a conically shaped projectile ejects a greater amount of mass than do projectiles of other shapes, including disks and spheres. We then find that numerically the results are sensitive to the normal coefficient of restitution of the grains, especially for impacts into targets comprised of smaller grains (3 mm). We also find that static friction plays a more important role for impacts into targets comprised of the larger grains. As a preliminary demonstration, one of these considered setups is simulated in a microgravity environment. As expected, a reduction in gravity increases both the amount of ejected mass and the timescale of the impact process. Our methodology is also adaptable to the conditions of sampling mechanisms included in specific mission designs.

astro-ph.EP↗

arXiv2014

Numerical predictions of surface effects during the 2029 close approach of asteroid 99942 Apophis

Asteroid (99942) Apophis' close approach in 2029 will be one of the most significant small-body encounter events in the near future and offers a good opportunity for in situ exploration to determine the asteroid's surface properties and measure any tidal effects that might alter its regolith configuration. Resurfacing mechanics has become a new focus for asteroid researchers due to its important implications for interpreting surface observations, including space weathering effects. This paper provides a prediction for the tidal effects during the 2029 encounter, with an emphasis on whether surface refreshing due to regolith movement will occur. The potential shape modification of the object due to the tidal encounter is first confirmed to be negligibly small with systematic simulations, thus only the external perturbations are taken into account for this work (despite this, seismic shaking induced by shifting blocks might still play a weak role and we will look into this mechanism in future work). A two-stage approach is developed to model the responses of asteroid surface particles (the regolith) based on the soft-sphere implementation of the parallel N-body gravity tree code pkdgrav. A full-body model of Apophis is sent past the Earth on the predicted trajectory to generate the data of all forces acting at a target point on the surface. A sandpile constructed in the local frame is then used to approximate the regolith materials; all the forces the sandpile feels during the encounter are imposed as external perturbations to mimic the regolith's behavior in the full scenario. The local mechanical environment on the asteroid surface is represented in detail, leading to an estimation of the change in global surface environment due to the encounter. Typical patterns of perturbation are presented that depend on the asteroid orientation and sense of rotation at perigee.

astro-ph.EP↗

arXiv2014

The Brazil-nut effect and its application to asteroids

Out of the handful of asteroids that have been imaged, some have distributions of blocks that are not easily explained. In this paper, we investigate the possibility that seismic shaking leads to the size sorting of particles in asteroids. In particular, we focus on the so-called Brazil Nut Effect (BNE) that separates large particles from small ones under vibrations. We study the BNE over a wide range of parameters by using the N-body code PKDGRAV, and find that the effect is largely insensitive to the coefficients of restitution, but sensitive to friction constants and oscillation speeds. Agreeing with the previous results, we find that convection drives the BNE, where the intruder rises to the top of the particle bed. For the wide-cylinder case, we also observe a "whale" effect, where the intruder follows the convective current and does not stay at the surface. We show that the non-dimensional critical conditions for the BNE agree well with previous studies. We also show that the BNE is scalable for low-gravity environments and that the rise speed of an intruder is proportional to the square root of the gravitational acceleration. Finally, we apply the critical conditions to observed asteroids, and find that the critical oscillation speeds are comparable to the seismic oscillation speeds that are expected from non-destructive impacts.

astro-ph.EP↗

arXiv2014

Dependence of the outer density profiles of halos on their mass accretion rate

We present a systematic study of the density profiles of LCDM halos, focusing on the outer regions, 0.1 < r/Rvir < 9. We show that the median and mean profiles of halo samples of a given peak height exhibit significant deviations from the universal analytic profiles discussed previously in the literature, such as the Navarro-Frenk-White and Einasto profiles, at radii r > 0.5 R200m. In particular, at these radii the logarithmic slope of the median density profiles of massive or rapidly accreting halos steepens more sharply than predicted. The steepest slope of the profiles occurs at r ~ R200m, and its absolute value increases with increasing peak height or mass accretion rate, reaching slopes of -4 and steeper. Importantly, we find that the outermost density profiles at r > R200m are remarkably self-similar when radii are rescaled by R200m. This self-similarity indicates that radii defined with respect to the mean density are preferred for describing the structure and evolution of the outer profiles. However, the inner density profiles are most self-similar when radii are rescaled by R200c. We propose a new fitting formula that describes the median and mean profiles of halo samples selected by their peak height or mass accretion rate with accuracy < 10% at all radii, redshifts and masses we studied, r < 9 Rvir, 0 < z < 6 and Mvir > 1.7E10 Msun/h. We discuss observational signatures of the profile features described above, and show that the steepening of the outer profile should be detectable in future weak-lensing analyses of massive clusters. Such observations could be used to estimate the mass accretion rate of cluster halos.

astro-ph.CO↗

arXiv2013

Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests

We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular "atmosphere" that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to centrifuging as a function of rotation rate.

astro-ph.EP↗

arXiv2013

Numerical simulations of granular dynamics II. Particle dynamics in a shaken granular material

Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties. We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration. We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments.

astro-ph.EP↗