Rotation rate and velocity dispersion of planetary ring particles with size distribution: I. Formulation and analytic calculation

We derive an equation for the evolution of rotational energy of Keplerian particles in a dilute disk due to mutual collisions. Three-dimensional Keplerian motion of particles is taken into account precisely, on the basis of Hill's approximation. The Rayleigh distribution of particles' orbital eccentricities and inclinations, and the Gaussian distribution of their rotation rates are also taken into account. Performing appropriate variable transformation, we show that the equation can be expressed with two terms. The first term, which we call collisional stirring term, represents energy exchange between rotation and random motion via collisions. The second term, which we call rotational friction term, tends to equalize the mean rotational energy of particles with different sizes. The equation can describe the evolution of rotational energy of Keplerian particles with an arbitrary size distribution. We analytically evaluate the rates of stirring and friction for the random kinetic energy and rotational energy due to inelastic collisions, for non-gravitating particles in a dilute disk. Using these results, we discuss equilibrium states in a disk of spinning, non-gravitating Keplerian particles.     

A note on the puzzling spindown behavior of the Galactic center magnetar SGR J1745-2900

SGR J1745-2900 is a magnetar near the Galactic center. X-ray observations of this source found a decreasing X-ray luminosity accompanied by an enhanced spindown rate. This negative correlation between X-ray luminosity and spindown rate is hard to understand. The wind braking model of magnetars is employed to explain this puzzling spindown behavior. During the release of magnetic energy of magnetars,a system of particles may be generated. Some of these particles remain trapped in the magnetosphere and may contribute to the X-ray luminosity. The rest of the particles can flow out and take away the rotational energy of the central neutron star. A smaller polar cap angle will cause the decrease of X-ray luminosity and enhanced spindown rate of SGR J1745-2900. This magnetar is shortly expected to have a maximum spindown rate.     

Cosmic rays and galactic rotation curves

A theoretical basis for modifying Newtonian dynamics on a galactic scale can be obtained by postulating that cosmic rays interact with graviton exchanges between distant masses. This assumes that these charged particles move under the influence of local electromagnetic fields rather than the weak gravitational fields of distant matter. It leads to an enhancement of graviton exchanges between distant masses via an additional gravitational force term inversely proportional to distance. At planetary and local interstellar distances this predicts an extremely small additional gravitational force, but it can become significant on a galactic scale. The model is used here to predict rotational velocities in a wide range of galaxies including the Milky Way, Andromeda (M31) and some galaxies in the THINGS study. Results are obtained assuming a galactic cosmic ray density consistent with observations in the solar system. This approach is compared with the dark matter hypothesis and with Modified Newtonian Dynamics (MOND), the two primary postulates used to explain the constant rotational velocities observed in most galaxies.     

The ellipsoidal and dumbbell-shaped inclusions within particulate lunar globules

The centrifugal motion of liquid, solid, and gaseous particles within the symmetrical lunar dumbbell and prolate droplets is studied. The migration of dense particles away from the rotational axis and light particles towards the axis has been observed in many cases. A method for determining the temperatures of formation of the globules is presented which depends on the comparison between the prediction of simple models, and the observed position of the particles within a globule. The globules examined show initial formation temperatures in the range 1800–2000 K. The study strongly supports the hypothesis that most lunar globules result from meteorite impact.     

Numerical simulations of rotational bursting of F-coronal dust in eccentric orbits due to coronal mass ejections

Model calculations were carried out to determine the extent of the effects on the rotational bursting of F-coronal dust in eccentric orbits due to their interaction with the flow of coronal mass ejections (CMEs). The model included an initial limiting perihelion distance of 8 solar radii (R_S) for all particles used. The parameters of the CMEs (velocity and proton number density) along with the various parameters of the dust particles (size and median density) were taken into consideration. By keeping these parameters the same and varying one of them, it was found that the velocity of the CMEs protons plays a major role in determining at which heliocentric distance the particle bursts. To a lesser degree, the median density of the particle also had a similar effect. Depending on the values of the dust particles orbital eccentricity, limiting sizes of the dust particles were found beyond which the particles do not burst. More particles bursted in regions close to their perihelion passage, however very few particles bursted near 8R_S from which we conclude that the majority of the fragmented particles were outside the F-corona region. The results show that rotational bursting of the dust in eccentric orbits inside the F-corona forces the particles to fragment outside 8R_S.     

Effect of thermal conductivity on the gravitational instability of a magnetized rotating plasma through a porous medium in the presence of suspended particles

The self-gravitational instability of an ionized, thermally-conducting, magnetized, rotating plasma flow through a porous medium has been studied in the presence of suspended particles. The ionized gas-particle medium has been considered rotating along and perpendicular to the vertical magnetic field. Propagation of the plasma waves has been studied for the longitudinal and the transverse modes for both the cases of rotation. A general dispersion relation has been derived with the help of relevant perturbation equations, using the method of normal mode analysis. The Jeans criterion determines the condition of gravitational instability in all the cases with some modifications introduced by the various parameters considered. Thermal conductivity replaces the adiabatic sonic speed by the isothermal one. Considering the longitudinal mode of propagation with perpendicular rotational axis, for an inviscid plasma with adiabatic behaviour the effect of both, the rotation and the suspended particles has been removed by the magnetic field. For the transverse mode of propagation with the axis of rotation parallel to the magnetic field, the viscosity removes the effect of both, the rotation and the suspended particles. Porosity reduces the effect of both, the rotation and the magnetic field, whereas the concentration of the suspended particles reduces the rotational effect.     

Synchronization mechanism of sharp edges in rings of Saturn

We propose a new mechanism which explains the existence of enormously sharp edges in the rings of Saturn. This mechanism is based on the synchronization phenomenon due to which the epicycle rotational phases of particles in the ring, under certain conditions, become synchronized with the phase of external satellite, e.g. with the phase of Mimas in the case of the outer B ring edge. This synchronization eliminates collisions between particles and suppresses the diffusion induced by collisions by orders of magnitude. The minimum of the diffusion is reached at the centre of the synchronization regime corresponding to the ratio 2:1 between the orbital frequency at the edge of B ring and the orbital frequency of Mimas. The synchronization theory gives the sharpness of the edge in a few tens of meters that is in agreement with available observations.     

A new representation of theH-functions of radiative transfer

The energetics involved in the formation of neutron stars in close binaries as a result of supernova explosions are considered. The gravitational binding energy of the neutron star must find proper outlets. The mass ejection and cosmic ray particles can carry away only a small fraction (up to a few per cent) of this energy. Most of the binding energy goes into rotational kinetic energy, gravitational radiation and neutrino emissions. A scenario is considered in which most of the gravitational binding energy goes into rotational kinetic energy and is, ultimately, radiated away as gravitational waves.     

Systems of colliding bodies in a gravitational field: Evolution and role of the internal rotations

To emphasize the rotational effects of a simple friction between colliding bodies in a keplerian field we investigate numerically the evolution of the rotational energies in a three dimensional system of spherical particles interacting through inelastic collisions in a deterministic model. All the particles are made of the same material but they possibly have different sizes. Each collision reduces the relative surface velocity and there are exchanges between orbital energy and rotational energy. Our results are compared with some previous papers and our aim is to supply other probabilists models with simple basic references about mean dynamical properties.The rotational energy of the colliding bodies tends to reach an equilibrium state that depends only on the rate of energy loss in the collision process. Internal rotations prevent the complete flattening of the system. With this model, light and small particles spin faster than the massive and big ones. We observe an excess of prograde rotations on counterclockwise orbits. The ratio of rotational and orbital energies is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa% aaleaacaWGYbaabeaakiaac+cacaWGfbWaaSbaaSqaaiaadUgaaeqa% aOGaeyisISRaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaa% aaaa!3F83!\[E_r /E_k \approx 10^{ - 3} \] while the ratio of corresponding mean angular velocities is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaacq% aHjpWDaiaawMYicaGLQmcacaGGVaWaaaWaaeaacqGHPoWvaiaawMYi% caGLQmcacqGHijYUcaaIYaaaaa!4008!\[\left\langle \omega \right\rangle /\left\langle \Omega \right\rangle \approx 2\] These values depends strongly on the dimensional scale of the model.     

Penrose process in Kerr-Taub-NUT spacetime

Penrose process on rotational energy extraction of the black hole in the Kerr-Taub-NUT spacetime is studied. It has been shown that for the radial motion of particles NUT parameter slightly shifts the shape of the effective potential down. The dependence of the extracted energy from compact object on NUT parameter has been found.     

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.     

Extension of Cassini's Laws

We investigate the Cassini's laws which describe the rotational motion in a 1:1 spin-orbit resonance. When this rotational motion follows the conventional Cassini's laws, the figure axis coincides with the angular momentum axis. In this case we underline the differences between the rotational Hamiltonian for a 'slow rotating' body like the Moon and for a 'fast rotating' body like Phobos. Then, we study a more realistic rotational Hamiltonian where the angle J between the figure axis and the angular momentum axis could be different from zero. This Hamiltonian has not been studied before. We have found a new particular solution for this Hamiltonian which could be seen as an extension of the Cassini's laws. In this new solution the angle J is constant, which is not zero, and the precession of the angular momentum plane is equal to the mean motion of the argument of pericenter of the rotating body. This type of rotational motion is only possible when the orbital eccentricity of the rotating body is not zero. This new law enables describing in particular, the Moon mean rotational motion for which the mean value of the angle J is found to be equal to 103.9±0.7 s of arc.     

Vesicle dynamics during the atmospheric entry heating of cosmic spherules

Cosmic spherules are unique igneous objects that form by melting due to gas drag heating during atmospheric entry heating. Vesicles are an important component of many cosmic spherules since they suggest their precursors had finite volatile contents. Vesicle abundances in spherules decrease through the series porphyritic, glassy, barred, to cryptocrystalline spherules. Anomalous hollow spherules, with large off‐center vesicles occur in both porphyritic and glassy spheres. Numerical simulation of the dynamic behavior of vesicles during atmospheric flight is presented that indicates vesicles rapidly migrate due to deceleration and separate from nonporphyritic particles. Modest rotation rates of tens of radians s^?1 are, however, sufficient to impede loss of vesicles and may explain the presence of small solitary vesicles in barred, cryptocrystalline and glassy spherules. Rapid rotation at spin rates of several thousand radians s^?1 are required to concentrate vesicles at the rotational axis and leads to rapid growth by coalescence and either separation or retention depending on the orientation of the rotational axis. Complex rapid rotations that concentrate vesicles in the core of particles are proposed as a mechanism for the formation of hollow spherules. High vesicle contents in porphyritic spherules suggest volatile‐rich precursors; however, calculation of volatile retention indicates these have lost >99.9% of volatiles to degassing prior to melting. The formation of hollow spherules, by rapid spin, necessarily implies preatmospheric rotations of several thousand radians s^?1. These particles are suggested to represent immature dust, recently released from parent bodies, in which rotations have not been slowed by magnetic damping.     

Gravitational instability of a thermally-conducting plasma flowing through a porous medium in the presence of suspended particles

Magnetogravitational instability of a thermally-conducting, rotating plasma flowing through a porous medium with finite conductivity and finite Larmor radius in the presence of suspended particles has been investigated. The wave propagation has been considered for both parallel and perpendicular axes of rotation. Magnetic field is being taken in the vertical direction. A general dispersion relation has been derived through relevant linearized perturbation equations. It has been observed that the condition of instability is determined by the Jeans's criterion in its modifed form. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one. Rotation decreases the Larmor radius. Porosity decreases the Alfvén velocity. In case of a viscous medium the effects of FLR, rotation, and suspended particles are not observed in the Jeans's condition, for transverse propagation for rotational axis parallel to the magnetic field. The effects of rotation and FLR are decreased by the porosity and the suspended particles. Finite conductivity removes the Alfvén velocity from Jeans's condition.     

Electrostatic solitons in rotating dusty plasmas with anisotropic ion pressure

The Zakharov-Kuznetsov (ZK) equation is derived for electrostatic wave in a rotating magnetoplasma with anisotropic ion pressure and in the presence of stationary charged dust particles. The anisotropic ion pressure is defined using double adiabatic Chew-Golberger-Low (CGL) theory. The reductive perturbation method is employed to study the dynamics of obliquely propagating low frequency ion acoustic wave with adiabatic ions. It is found that the ion pressure anisotropy, polarity, density of the dust particles and rotational frequency have significant effects on the formation nonlinear structures in rotating magnetized dusty plasmas. The numerical results are also presented for illustration.     

The motion of charged dust particles in interplanetary space—I. The zodiacal dust cloud

The problem of electromagnetic perturbations of charged dust particle orbits in interplanetary space has been re-examined in the light of our better understanding of the large scale spatial and temporal interplanetary plasma and field topology. Using both analytical and numerical solutions for particle propagation it was shown that: (1) stochastic variations induced by electromagnetic forces are unimportant for the zodiacal dust cloud except for the lowest masses, (2) systemetic variations in orbit inclinations are unimportant if orbital radii are larger than 10 a.u. This is due to the solar cycle variation in magnetic polarity which tends to cancel out systematic effects, (3) systematic variations in orbital parameters (inclination, longitude of ascending node, longitude of perihel) induced by electromagnetic forces inside 1 a.u. tend to shift the plane of symmetry of the zodiacal dust cloud somewhat towards the solar magnetic equatorial plane, (4) inside 0.3 a.u. there is a possibility that dust particles may enter a region of “magnetically resonant” orbits for some time. Changes in orbit parameters are then correspondingly enhanced, (5) the observed similarity of the plane of symmetry of zodiacal light with the solar equatorial plane may be the effect of the interaction of charged interplanetary dust particles with the interplanetary magnetic field. Numerical orbit calculation of dust particles show that one of the results of this interaction is the rotation of the orbit plane about the solar rotational axis.     

Pulsars and the origin of cosmic rays

The capabilities and limitations of pulsars as sources of cosmic rays are reviewed in the light of experimental observations. Pulsars can supply the cosmic ray power if they have rotational velocities in excess of 700 rad s^?1 at birth. Though this is theoretically possible, there is no experimental proof for the same. Pulsars can accelerate particles to the highest energies of 10²⁰ eV, but in general, the spectra on simple considerations, turn out to be flatter than the observed cosmic ray spectrum. At the highest energies, absorption processes due to fragmentation and photodisintegration dominate for heavy nuclei. The existence of a steady flux of cosmic rays of energy greater than 10¹⁷ eV demands acceleration of particles to last over fifty years, the time interval between supernovae outbursts, whereas the expected period of activity is less than a few years. Finally, the problem of anisotropy with relevance to pulsars as sources and the possibility of observing pulsar accelerated particles from galactic clusters is considered.     

Magnetospheric environments of outer planet rings: Influence of Saturn's axially symmetric magnetic field

The Jovian and Uranian rings exist within severe energetic particle and plasma environments where magnetosphere-related losses of small ring particles and surface reflectance alteration by sputtering are likely to be important. In contrast, the main Saturnian rings exist within a zone where magnetospheric losses and surface alteration effects are negligible, primarily because of solid-body absorption of inwardly diffusing magnetospheric particles. It is shown here that solid-body absorption of radially diffusing ions is a much more efficient process in the inner Saturnian magnetosphere than in the inner Jovian and Uranian magnetospheres because of the near axial symmetry of the planetary magnetic field with respect to the rotational equatorial plane. This is especially true for continuous rings (as opposed to satellites) for which the approximate time scale against absorption is the particle bounce period in an axially symmetric field, whereas it is the particle drift period in an asymmetric field. Assuming comparable diffusion rates, inward transport of magnetospheric particles is much more strongly inhibited in the inner Saturnian magnetosphere than in the inner magnetospheres of Jupiter and Uranus. This remains true when only rings of comparable widths and optical depths are considered (e.g., the F ring at Saturn and the ϵ ring at Uranus). The most extreme possible consequence of this difference in solid-body absorption efficiency may have been the preferential development of a radially extensive, optically thick ring system at Saturn where magnetospheric losses are minimized in comparison to those at Jupiter and Uranus. A more definite consequence is that the Uranian rings are most probably directly exposed to nearly the same proton fluxes measured at Voyager 2's closest approach. Exposure of ring particle surfaces to radiation belt ion fluxes therefore remains as a viable explanation for the low albedos of the Uranian rings.     

Solar wind and spin of small interplanetary particles

The action of the solar corpuscular radiation on the rotational properties of small interplanetary dust particles is investigated. It is shown that the solar wind increases the angular momentum (spin) of the particle. Analytic solutions are presented for dominant terms in which quantities of the orders (v/u) ⁿ ,n 1, are neglected (v is the orbital velocity of dust particle around the Sun andu is the speed of the solar wind particles).