Analysing the New Saturnian Rings, R/2004 S1 and R/2004 S2

The Cassini-Huygens arrival into the Saturnian system brought a large amount of data about the satellites and rings. Two diffuse rings were found in the region between the A ring and Prometheus. R/2004 S1 is coorbital to Atlas and R/2004 S2 is close to Prometheus. In this work we analysed the closest approach between Prometheus and both rings. As a result we found that the satellite removes particles from R/2004 S2 ring. Long-term numerical simulations showed that some particles can cross the F ring region . The well known region of the F ring, where small satellites are present and particles are being taking from the ring, gains a new insight with the presence of particles from R/2004 S2 ring. The computation of the Lyapunov Characteristic Exponent reveled that the R/2004 S2 ring lies in a chaotic region while R/2004 S1 ring and Atlas are in a stable region. Atlas is responsible for the formation of three regimes in the R/2004 S1 ring, as expected for a satellite embedded in a ring.     

Hydrodynamical Simulations of Galaxy Clusters

In my contribution I discuss the relevance that hydrodynamical simulation of clusters can play to understand the ICM physics and to calibrate mass estimates from X-ray observable quantities. Using hydrodynamical simulations, which cover quite a large dynamical range and include a fairly advanced treatment of the gas physics (cooling, star formation and SN feedback), I show that scaling relations among X-ray observable quantities can be reproduced quite well. At the sametime, these simulations fail at accounting for several observational quantities, which are related to the cooling structure of the ICM: the fraction of stars, the temperature profiles and the gas entropy in central cluster regions. This calls for the need of introducing in simulations suitable physical mechanisms which should regulate the cooling structure of the ICM.     

Numerical simulations of the magnetic field distribution in a solar complex of activity

Powerful solar complexes of activity are supposed to result from the excitation of Rossby vortices within a thin layer beneath the convection zone. Numerical simulations demonstrate that Rossby vortices generate large-scale arc-like magnetic structures. It is shown that the most powerful complex of activity observed in June-July 1982 was likely to be a result of the excitation of a Rossby anticyclone rather than a cyclone.     

Simulations of dense planetary rings: IV. Spinning self-gravitating particles with size distribution

Previous self-gravitating simulations of dense planetary rings are extended to include particle spins. Both identical particles as well as systems with a modest range of particle sizes are examined. For a ring of identical particles, we find that mutual impact velocity is always close to the escape velocity of the particles, even if the total rms velocity dispersion of the system is much larger, due to collective motions associated to wakes induced by near-gravitational instability or by viscous overstability. As a result, the spin velocity (i.e., the product of the particle radius and the spin frequency) maintained by mutual impacts is also of the order of the escape velocity, provided that friction is significant. For the size distribution case, smaller particles have larger impact velocities and thus larger spin velocities, particularly in optically thick rings, since small particles move rather freely between wakes. Nevertheless, the maximum ratio of spin velocities between the smallest and largest particles, as well as the ratio for translational velocities, stays below about 5 regardless of the width of the size distribution. Particle spin state is one of the important factors affecting the temperature difference between the lit and unlit face of Saturn's rings. Our results suggest that, to good accuracy, the spin frequency is inversely proportional to the particle size. Therefore, the mixing ratio of fast rotators to slow rotators on the scale of the thermal relaxation time increases with the width of the particle size distribution. This will offer means to constrain the particle size distribution with the systematic thermal infrared observations carried by the Cassini probe.     

太阳大气中磁重联的MHD数值模拟

回顾了近３０年太阳大气中磁重联过程的ＭＨＤ数值模拟工作取得的进展。着重描述了在验证理论模型,解释观测现象,以及研究各种因素对重联的影响三个方面的成果,如快速磁重联,太阳耀斑机制及色球,日冕中的各种爆发现象等。指出了在数值模拟中应注意的几个问题,并对该领域今后的发展作了简要的展望。     

Simulations of spheroidal systems with substructure: trees in fields

We present a hybrid technique of N -body simulation to deal with collisionless stellar systems having an inhomogeneous global structure. We combine a treecode and a self-consistent field code such that each of the codes models a different component of the system being investigated. The treecode is suited to treatment of dynamically cold or clumpy components, which may undergo significant evolution within a dynamically hot system. The hot system is appropriately evolved by the self-consistent field code. This combined code is particularly suited to a number of problems in galactic dynamics. Applications of the code to these problems are briefly discussed.     

Oscillations In Galaxies

Oscillations in galaxies have been investigated by numerical simulations. The various models used have density distributions corresponding to that of polytrope of index n in the range 0 ≤ n ≤ 4 and their evolution has been followed for more than 70 crossing times. The kinetic energy shows regular and smooth oscillations for models with n = 0, 1 and 2 whereas in other models it shows noisy oscillation. The oscillation in kinetic energy is observed to have a period of 3 crossing time irrespective of the density and size of the galaxy. The amplitude of oscillation is seen to decrease as the central density of the galaxy increases. This revised version was published online in July 2006 with corrections to the Cover Date.     

New Trends in Numerical Simulation of the Motion of Small Bodies of the Solar System

A brief survey of the results obtained by the authors in the development and investigation of the algorithms of numerical simulation of the motion of solar system small bodies is given. New approaches to the construction of the algorithms of high-accuracy numerical simulation of the dynamics of small bodies and the methods of the determination of the domain of their possible motions are presented.     

Elements of spin motion

For use in numerical studies of rotational motion, a set of elements is introduced for the torque-free rotational motion of a rigid body around its barycenter. The elements are defined as the initial values of a modification of the Andoyer canonical variables. A computational procedure is obtained for determining these elements from the combination of the spin angular momentum vector and a triad defining the orientation of the rigid body. A numerical experiment shows that the errors of transformation between the elements and variables are sufficiently small. The errors increase linearly with time for some elements and quadratically for some others.     

The shape and dynamics of a heliotropic dusty ringlet in the Cassini Division

The so-called “Charming Ringlet” (R/2006 S3) is a low-optical-depth, dusty ringlet located in the Laplace gap in the Cassini Division, roughly 119,940 km from Saturn center. This ringlet is particularly interesting because its radial position varies systematically with longitude relative to the Sun in such a way that the ringlet’s geometric center appears to be displaced away from Saturn’s center in a direction roughly toward the Sun. In other words, the ringlet is always found at greater distances from the planet’s center at longitudes near the sub-solar longitude than it is at longitudes near Saturn’s shadow. This “heliotropic” behavior indicates that the dynamics of the particles in this ring are being influenced by solar radiation pressure. In order to investigate this phenomenon, which has been predicted theoretically but not observed this clearly, we analyze multiple image sequences of this ringlet obtained by the Cassini spacecraft in order to constrain its shape and orientation. These data can be fit reasonably well with a model in which both the eccentricity and the inclination of the ringlet have “forced” components (that maintain a fixed orientation relative to the Sun) as well as “free” components (that drift around the planet at steady rates determined by Saturn’s oblateness). The best-fit value for the eccentricity forced by the Sun is 0.000142 ± 0.000004, assuming this component of the eccentricity has its pericenter perfectly anti-aligned with the Sun. These data also place an upper limit on a forced inclination of 0.0007°. Assuming the forced inclination is zero and the forced eccentricity vector is aligned with the anti-solar direction, the best-fit values for the free components of the eccentricity and inclination are 0.000066 ± 0.000003 and 0.0014 ± 0.0001°, respectively. While the magnitude of the forced eccentricity is roughly consistent with theoretical expectations for radiation pressure acting on 10-to-100-μm-wide icy grains, the existence of significant free eccentricities and inclinations poses a significant challenge for models of low-optical-depth dusty rings.     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

A Geometric Interpretation of Integrable Motions

Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where Newtonian motions are seen as geodesics of suitable -mechanical- manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N = 2 Toda model, and for a modified Hénon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.     

Numerical investigation of the orbit of Interball‐1

We investigated the motion of the Earth's artificial satellite Interball‐1 by using a method suitable for the computation of large eccentricity orbits. Though the measured and the computed orbital elements differ from each other within the measured error bound, we found a slight tendency for secular decreasing in the semi‐major axis, caused probably by electromagnetic drag. We analysed the dominant role of the Moon in the variations of the orbital eccentricity, leading to zero perigee height and the end of the lifetime of the satellite. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monte Carlo Simulations of Oort Cloud Comets: the Influence of Mantle Blow-off on the Inclination Distribution of Jupiter Family

We have developed an efficient Monte Carlo method by which we can evaluate the evolution of comets. There are many poorly known evolutional parameters, and we have investigated the influence of these parameters on the final populations and the inclination distributions of short-period comets. We compare the observed and calculated inclination distributions of different comet populations and obtain a good fit for the inclinations of the Jupiter family comets by assuming a mantle blow-off and a sudden brightening of the comet when its perihelion distance is lowered in a major jump. This revised version was published online in July 2006 with corrections to the Cover Date.     

Physical collisions of moonlets and clumps with the Saturn's F-ring core

Since 2004, observations of Saturn's F-ring have revealed that the ring's core is surrounded by structures with radial scales of hundreds of kilometers, called “spirals” and “jets.” Gravitational scattering by nearby moons was suggested as a potential production mechanism; however, it remained doubtful because a population of Prometheus-mass moons is needed and, obviously, such a population does not exist in the F-ring region. We investigate here another mechanism: dissipative physical collisions of kilometer-size moonlets (or clumps) with the F-ring core. We show that it is a viable and efficient mechanism for producing spirals and jets, provided that massive moonlets are embedded in the F-ring core and that they are impacted by loose clumps orbiting in the F-ring region, which could be consistent with recent data from ISS, VIMS and UVIS. We show also that coefficients of restitution as low as ∼0.1 are needed to reproduce the radial extent of spirals and jets, suggesting that collisions are very dissipative in the F-ring region. In conclusion, spirals and jets would be the direct manifestation the ongoing collisional activity of the F-ring region.     

3D numerical models of magnetic field evolution in galaxies interacting with the ICM

A fully three-dimensional (3D) MHD model is applied to simulate the evolution of large-scale magnetic field in galaxies interacting with the intra-cluster medium (ICM). As the model input we use a time dependent velocity field of gas clouds (HI) resulting from 3D N-body sticky-particle model of a galaxy. These clouds are affected by ram pressure due to their rapid motion through the ICM. The gas evolves in an analytically given gravitational potential which includes a dark matter halo, a disk, and a bulge component. We found that due to the interaction with the ICM the resultant magnetic field correctly reproduces the observed structures of the magnetic field forming peculiar spiral arms and magnetic features widely observed in cluster spiral galaxies. This revised version was published online in September 2006 with corrections to the Cover Date.