Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

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.     

Discriminating contamination from particle components in spectra of Cassini's dust detector CDA

The Chemical Analyser subsystem of the Cosmic Dust Analyser (CDA) aboard the Cassini spacecraft performs in situ measurements of the chemical composition of dust in space. The instrument records time-of-flight mass spectra of cations, extracted from the impact cloud that is created by high-velocity particle impacts onto the detector target. Thus, the spectra not only show signals of particle components but also of ions from the target material and target contamination. The aim of this work is to determine which non-particle ions are to be expected in the spectra obtained in space operation at Saturn.We present an analysis of the contamination state of the instrument's impact target. Beside investigations of the purity of the rhodium target surface, spectra from CDA calibration experiments at the dust accelerator facility are evaluated with regard to contamination signatures. Furthermore, contamination mass lines in spectra obtained by impacts of Jovian and Saturnian dust stream particles are analysed. Due to their small size and high speed, stream particle impacts predominantly produce ions from the target material and therefore the spectra are excellent probes of the contamination state of the target operating in space. With the exception of adsorbed hydrogen and carbon, the level of contamination is very low.Implications for CDA spectra of Saturnian E ring particle impacts are derived. The findings confirm the published interpretations. The low level of alkali metal contamination implies a significant sodium contribution in the composition of E ring ice particles. Additionally, ionisation thresholds for the occurrence of contamination mass lines can be utilised to set limits for the impact velocity.     

Analytical potential–density pairs for flat rings and toroidal structures

The Kuzmin–Toomre family of discs is used to construct potential–density pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular orbits are calculated for these structures. A few examples of three-dimensional potential–density pairs of 'inflated' flat rings (toroidal mass distributions) are presented.     

E ring dust sources: Implications from Cassini's dust measurements

The Enceladus flybys of the Cassini spacecraft are changing our understanding of the origin and sustainment of Saturn's E ring. Surprisingly, beyond the widely accepted dust production caused by micrometeoroid impacts onto the atmosphereless satellites (the impactor-ejecta process), geophysical activities have been detected at the south pole of Enceladus, providing an additional, efficient dust source. The dust detector data obtained during the flyby E11 are used to identify the amount of dust produced in the impactor-ejecta process and to improve related modeling [Spahn, F., Schmidt, J., Albers, N., Hörning, M., Makuch, M., Seiß, M., Kempf, S., Srama, R., Dikarev, V.V., Helfert, S., Moragas-Klostermeyer, G., Krivov, A.V., Sremčević, M., Tuzzolino, A., Economou, T., Grün, E., 2006. Cassini dust measurements at Enceladus: implications for Saturn's E ring. Science, in press]. With this, we estimate the impact-generated dust contributions of the other E ring satellites and find significant differences in the dust ejection efficiency by two projectile families—the E ring particles (ERPs) and the interplanetary dust particles (IDPs). Together with the Enceladus south-pole source, the ERP impacts play a crucial role in the inner region, whereas the IDP impacts dominate the particle production in the outer E ring, possibly accounting for its large radial extent. Our results can be verified in future Cassini flybys of the E ring satellites. In this way poorly known parameters of the dust particle production in hypervelocity impacts can be constrained by comparison of the data and theory.     

Dust ring formation due to sublimation of dust grains drifting radially inward by the Poynting-Robertson drag: An analytical model

Dust particles exposed to the stellar radiation and wind drift radially inward by the Poynting-Robertson (P-R) drag and pile up at the zone where they begin to sublime substantially. The reason they pile up or form a ring is that their inward drifts due to the P-R drag are suppressed by stellar radiation pressure when the ratio of radiation pressure to stellar gravity on them increases during their sublimation phases. We present analytic solutions to the orbital and mass evolution of such subliming dust particles, and find their drift velocities at the pileup zone are almost independent of their initial semimajor axes and masses. We derive analytically an enhancement factor of the number density of the particles at the outer edge of the sublimation zone from the solutions. We show that the formula of the enhancement factor reproduces well numerical simulations in the previous studies. The enhancement factor for spherical dust particles of silicate and carbon extends from 3 to more than 20 at stellar luminosities L_?=0.8-500L_⊙, where L_⊙ is solar luminosity. Although the enhancement factor for fluffy dust particles is smaller than that for spherical particles, sublimating particles inevitably form a dust ring as long as their masses decrease faster than their surface areas during sublimation. The formulation is applicable to dust ring formation for arbitrary shape and material of dust in dust-debris disks as well as in the Solar System.     

Dynamical evolution of Saturn's F ring dust particles

Saturn's F ring has been the subject of study due to its peculiar structure and the proximity to two satellites, named Prometheus (interior) and Pandora (exterior to the ring), which cause perturbations to the ring particles. Early results from Voyager data have proposed that the ring is populated with centimetre- and micrometre-sized particles. The Cassini spacecraft also detected a less dense part in the ring with width of 700 km. Small particles suffer the effects of solar radiation. Burns et al. showed that due to effects of one component of the solar radiation, the Poynting–Robertson drag, a ring particle will decay in the direction of the planet in a time much shorter than the age of the Solar system. In this work, we have analysed a sample of dust particles (1, 3, 5 and 10 μm) under the effects of solar radiation, the Poynting–Robertson drag and the radiation pressure components and the gravitational effects of the satellites Prometheus and Pandora. In this case, the high increase of the eccentricity of the particles leads almost all of them to collide with the outer edge of the A ring. The inclusion of the oblateness of Saturn in this system significantly changes the outcome, since the large variation of the eccentricity is reduced by the oblateness effect. As a result, there is an increase in the lifetime of the particle in the envelope region. Our results show that even the small dust particles, which are very sensitive to the effects of solar radiation, have an orbital evolution similar to larger particles located in the F ring. The fate of all particles is a collision with Prometheus or Pandora in less than 30 years. On the other hand, collisions of these particles with moonlets/clumps present in the F ring could change this scenario.     

The effect of long-lived vortical circulation on the dynamics of dust particles in the mid-plane of a protoplanetary disc

We investigate the response of dust particles in the mid-plane of a protoplanetary disc to the turbulent velocity field of long-lived, large-scale vortical circulation. The dynamical problem is studied through numerical integrations of the equations of motion for individual particles (the sizes of which range from centimetres to metres) subject to the solar gravity and the friction drag of the nebular gas. It is found, neglecting the thickness of the disc, that the particles do not drift inwards to the central star as occurs in a standard symmetrical nebula. Vortices tend to capture a large number of the particles. The effectiveness of this size-selective concentration mechanism depends not only on the value of the drag and the distance from the Sun, but also on the elongation of the vortex and its characteristic lifetime. Typical anticyclonic vortices with exponential decay times of 30 orbital periods and semi-axis ratios of 4 can increase the local surface density by a factor of 4 in a lifetime and accumulate 0.03–0.3 Earth masses. If the elongation is significant (>7), the vortex cannot concentrate any significant amount of solid material. Vortices with an elongation of about 2 are the most effective as regards trapping of dust. We have also found analytical expressions for the capture time as well as capture constraints as a function of the friction parameter, the elongation of the vortex and the impact parameter. By increasing the lifetime and the surface density of the solid particles, this confining mechanism can make the agglomeration of the solid material of the nebula (through collisional aggregation or gravitational instabilities) much more efficient than previously believed. This offers new possibilities for the formation of the planetesimals and the giant planet cores, and may explain the rapid formation of extrasolar giant planets.     

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.     

Microbeam Analysis of Four Chondritic Interplanetary Dust Particles for Major Elements,Carbon and Oxygen

Abstract— Chemical compositions determined using electron excited x-rays are reported for four interplanetary dust particles collected in the stratosphere. These analyses include measurements of carbon and oxygen abundances which are important elements in these primitive materials. Spot analyses show very heterogeneous compositions on a micrometer scale although average composition approaches that of C1 carbonaceous chondrites. While the spot analyses show intermediate compositions between cometary dust and carbonaceous chondrites, the heterogeneity more closely resembles that of comet Halley dust particles.     

A model for the formation of spokes in Saturn's ring

We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.     

The total number of giant planets in debris discs with central clearings

Infrared spectra from the Spitzer Space Telescope ( SSC ) of many debris discs are well fit with a single blackbody temperature which suggest clearings within the disc. We assume that clearings are caused by orbital instability in multiple planet systems with similar configurations to our own. These planets remove dust-generating planetesimal belts as well as dust generated by the outer disc that is scattered or drifts into the clearing. From numerical integrations, we estimate a minimum planet spacing required for orbital instability (and so planetesimal and dust removal) as a function of system age and planet mass. We estimate that a 10⁸ yr old debris disc with a dust disc edge at a radius of 50 au hosted by an A star must contain approximately five Neptune mass planets between the clearing radius and the iceline in order to remove all primordial objects within it. We infer that known debris disc systems contain at least a fifth of a Jupiter mass in massive planets. The number of planets and spacing required is insensitive to the assumed planet mass. However, an order of magnitude higher total mass in planets could reside in these systems if the planets are more massive.     

Formation of fine dust on Saturn's rings as suggested by the presence of spokes

The common interpretation of spokes on the B ring of Saturn is that they are the result of light scattered by electrostatically levitated micrometer- and submicrometer-size dust particles. The origin of this dust in terms of radiation-induced thermal fatigue and collisions between the particles of the ring as well as meteoritic bombardment is investigated.     

Radiation pressure on dust aggregates in circumstellar disks

We apply the ballistic particle-cluster and cluster-cluster aggregation of spherical monomers identical in size and material composition to study the effect of the particle's shape and structure on the radiation pressure force acting on circumstellar dust particles. Furthermore, the influence of the material composition on the radiation pressure is investigated based on the assumption that the constituents of dust aggregates are composed of either silicate or carbon.We show that the ratio of radiation pressure to stellar gravity in the radial direction from a star is weaker for aggregates than for homogeneous spherical grains in the radius range of submicron or less. Therefore fluffy dust particles of submicron radius have a longer dynamical lifetime, compared to compact spherical particles. We also show that the nonradial component of the radiation pressure force can reach the same order of magnitude as the radial component of the radiation pressure reduced by stellar gravity for aggregates of submicron or less in size. This non-radial component of the radiation pressure may yield a component of random motion along the trajectories of the particles.     

对金斯定则的几点认识

用物理学基本定律可导出金斯经验定则,它似应称为金斯定则,该定则的速度、高度或能量等表述完全等效,可随意选用,用能量观点更容易解释此定则,满足金斯定则只是给定的粒子成为具有稠密大气的行星或卫星的主要大气成分的必要条件,该定则的适应范围可用方程或其图像表示,也能用诺模图确定,它适用于太阳系内的行星,卫星,小行星,流星体和像柯伊伯带天体与半人马族星这样的外太阳系天体,此定则现在仍有普遍的现实意义。     

SCUBA imaging of the NGC 7331 dust ring

We present observations of the spiral galaxy NGC 7331 using the Submillimetre Common User Bolometer Array (SCUBA) on the James Clark Maxwell Telescope. We have detected a dust ring of 45 arcsec radius (3.3 kpc) at wavelengths of 450 and 850 μm. The dust ring is in good correspondence with other observations of the ring in the mid-infrared (MIR), CO and radio continuum, suggesting that the observed dust is associated with molecular gas and star formation. A B  −  K colour map shows an analogous ring structure with an asymmetry about the major axis, consistent with the extinction being produced by a dust ring. The derived temperature of the dust lies between 16 and 31 K and the gas-to-dust ratio lies between 150 and 570, depending on the assumed dust emission efficiency index (β = 1.5 or 2).     

The effects of metallicity and grain growth and settling on the early evolution of gaseous protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large (∼1 AU) and internal temperatures are low (<2000 K). The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of isolated, non-accreting planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.     

Dust formation in primordial Type II supernovae

We have investigated the formation of dust in the ejecta of Type II supernovae (SNe), mostly of primordial composition, to answer the question of where the first solid particles are formed in the Universe. However, we have also considered non-zero progenitor metallicity values up to Z = Z_⊙ . The calculations are based on standard nucleation theory, and the scheme has been tested for the first time on the well-studied case of SN1987A, yielding results that are in agreement with the available data. We find that: (i) the first dust grains are predominantly made of silicates, amorphous carbon (AC), magnetite and corundum; and (ii) the largest grains are the AC ones, with sizes around 300 Å, whereas the other grain types have smaller radii, around 10–20 Å . The grain size distribution depends somewhat on the thermodynamics of the ejecta expansion, and variations in the results by a factor ≈2 might occur within reasonable estimates of the relevant parameters. Also, and for the same reason, the grain size distribution is essentially unaffected by metallicity changes. The predictions on the amount of dust formed are very robust: for Z =0 , we find that SNe with masses in the range (12–35) M_⊙ produce about 0.08 M_⊙≲ M _d≲0.3 M_⊙ of dust per supernova. The above range increases by roughly three times as the metallicity is increased to solar values. We discuss the implications and the cosmological consequences of the results.     

The role of Kelvin–Helmholtz instability in dusty and partially ionized outflows

We investigate the linear theory of Kelvin–Helmholtz instability at the interface between a partially ionized dusty outflow and the ambient material analytically. We model the interaction as a multifluid system in a planar geometry. The unstable modes are independent from the charge polarity of the dust particles. Although our results show a stabilizing effect for charged dust particles, the growth time-scale of the growing modes gradually becomes independent of the mass or charge of the dust particles when the magnetic-field strength increases. We show that growth time-scale decreases with increasing the magnetic field. Also, as the mass of the dust particles increases, the growth time-scale of the unstable mode increases.     

Dynamical determination of the mass of the Kuiper Belt from motions of the inner planets of the Solar system

In this paper we determine dynamically the mass of the Kuiper Belt Objects by exploiting the latest least-squares determinations of the extra rates of perihelia of the inner planets of the Solar system. By modelling classical Kuiper Belt Objects as an ecliptic ring of finite thickness, we obtain 0.033 ± 0.115 in units of terrestrial masses. For resonant Kuiper Belt Objects, a two-ring model yields 0.018 ± 0.063. These values are consistent with recent determinations obtained using ground- and space-based optical techniques. Some implications for precise tests of Einsteinian and post-Einsteinian gravity are briefly discussed.