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.     

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.     

On the secular decrease in the semimajor axis of Lageos's orbit

The semimajor axis of the Lageos satellite's orbit is decreasing secularly at the rate of 1.1 mm day^–1. Ten possible mechanisms are investigated to discover which one (s), if any, might be causing the orbit to decay. Six of the mechanisms, resonance with the Earth's gravitational field, gravitational radiation, the Poynting-Robertson effect, transfer of spin angular momentum to the orbital angular momentum, drag from near-earth dust, and atmospheric drag by neutral hydrogen are ruled out because they are too small or require unacceptable assumptions to account for the observed rate of decay. Three other mechanisms, the Yarkovsky effect, the Schach effect, and terrestrial radiation pressure give perturbations whose characteristic signatures do not agree with the observed secular decrease (terrestrial radiation pressure appears to be too small in any case); hence they are also ruled out. Charged particle drag with the ions at Lageos's altitude is probably the principal cause of the orbital decay. An estimate of charged particle drag based upon laboratory experiments and satellite measurements of ion number densities accounts for 60 percent of the observed rate of decrease in the semimajor axis, assuming a satellite potential of –1V. This figure is in good agreement with other estimates based on charge drag theory. A satellite potential of –1.5V will explain the entire decay rate. Atmospheric drag from neutral hydrogen appears to be the next largest effect, explaining about 10 percent of the observed orbital decay rate.     

Combined solar radiation pressure and drag effects on the orbits of artificial satellites

A semi analytical theory is proposed to study the joint effects of direct solar radiation pressure and atmospheric drag on the orbit of an artificial Earth satellite. Making the solar radiation pressure equal to zero the problem is reduced to one already solved by Brouwer and Hori. The solutions are not equivalent, however, since in the Brouwer and Hori theory one has spurious Poisson terms.     

Natural highways for end-of-life solutions in the LEO region

We present the main findings of a dynamical mapping performed in the Low Earth Orbit region. The results were obtained by propagating an extended grid of initial conditions, considering two different epochs and area-to-mass ratios, by means of a singly averaged numerical propagator. It turns out that dynamical resonances associated with high-degree geopotential harmonics, lunisolar perturbations and Solar radiation pressure can open natural deorbiting highways. For area-to-mass ratios typical of the orbiting intact objects, these corridors can be exploited only in combination with the action exerted by the atmospheric drag. For satellites equipped with an area augmentation device, we show the boundary of application of the drag, and where the Solar radiation pressure can be exploited.     

The two-body problem with drag and radiation pressure

The Kepler problem including radiation pressure and drag is treated. The equation of the orbit is derived and the scalar and vector integrals of motion are obtained by direct operation on the vector form of the equation of motion.     

The motion of axisymmetric satellite with drag and radiation pressure

The axisymmetric satellite problem including radiation pressure and drag is treated. The equations of motion of the satellite are derived. The energy-like and Laplace-like invariants of motion have been derived for a general drag force function of the polar angle, and the Laplace-like invariant is used to find the orbit equation in the case of a spherical satellite. Then using the small parameter, the orbit of the satellite is determined for an axisymmetric satellite.     

On the formation of Saturn's rings

It is shown that the formation of Saturn's ring C can be explained by the action of solar radiation pressure on the small ring particles. If the age of the rings is 1.6×10⁸ yr, the predicted optical thickness of ring C, as a function of the distance from the planet, can then be shown to be in agreement with the measured one. The disruption of a solid satellite as the origin of the rings is shown to be quite plausible. If, in Roche's limit, the molecular cohesion is taken into account, the disruption distance of a satellite having the mass of the rings seems to be in agreement with the average distance of the ring system.     

On the production of suprathermal grains by radiation pressure

The physical conditions under which suprathermal grains can be produced when they are accelerated by radiation pressure against the drag of the ambient gas are investigated. It is found that in general it is very difficult to produce such grains though there are regions where their existence is probable.     

A study of non-collinear libration points under the combined effects of radiation pressure and Stokes drag

We study the non-collinear libration points in the frame work of photo-gravitational circular restricted three-body problem with Stokes drag acting as a dissipative force and considering the more massive primary as a radiating body and the less massive primary as a triaxial rigid body. The combined effects of radiation pressure and Stokes drag on the existence and stability of non-collinear libration points is analyzed. It is found that there exist two non-collinear libration points and are asymptotically stable in the interval 0.6149 ≤ q ≤ 1 for μ = 0.01, where q and μ are the radiation factor and mass ratio, respectively.     

Equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag

We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.     

Two stages of dust delivery from satellites to planetary rings

Faint rings of micrometre-sized dust particles embrace many planets in the Solar system. As a rule, they are replenished by ejecta from embedded atmosphereless moons. On a number of occasions, the ejecta are generated by hypervelocity meteoroid impacts into the moons. Small ejecta fragments are then swiftly shifted into rings by an array of non-gravitational forces, e.g. radiation pressure or plasma drag. A significant fraction of ejecta mass, however, is contained in relatively big, multi-micrometre fragments which are subject to gravity only. Having escaped from the satellite, they stay close to its orbit and form a belt around planet. This belt is itself a source of ring dust through collisional disruption of its particles. Here the contributions of belts to the respective rings are estimated for selected satellites of Jupiter and Saturn. The belts under review could supply substantially more dust to rings than the direct ejecta from satellites and should be taken into account when estimating ring dust budgets. The belts are very difficult to observe, however, and some of them remain a theoretical proposition. We find an appealing evidence for the belts due to Amalthea and Thebe around Jupiter, and for the belt due to Enceladus around Saturn.     

Radiation drag driven mass accretion in a clumpy interstellar medium: implications for the supermassive black hole-to-bulge relation

We quantitatively scrutinize the effects of the radiation drag arising from the radiation fields in a galactic bulge in order to examine the possibility that the radiation drag could be an effective mechanism to extract angular momentum in a spheroidal system like a bulge and allow plenty of gas to accrete on to the galactic centre. For this purpose, we numerically solve the relativistic radiation hydrodynamical equation coupled with accurate radiative transfer, and quantitatively assess the radiation drag efficiency. As a result, we find that in an optically thick regime the radiation drag efficiency is sensitively dependent on the density distributions of the interstellar medium (ISM). The efficiency drops according to     in an optically thick uniform ISM, where τ _T is the total optical depth of the dusty ISM , whereas the efficiency remains almost constant at a high level if the ISM is clumpy . Hence, if bulge formation begins with a star formation event in a clumpy ISM, the radiation drag will effectively work to remove the angular momentum and the accreted gas may form a supermassive black hole. As a natural consequence, this mechanism reproduces a putative linear relation between the mass of a supermassive black hole and the mass of a galactic bulge, although further detailed modelling for stellar evolution is required for a more precise prediction.     

Poynting–Robertson (P–R) drag and oblateness effects on motion around the triangular equilibrium points in the photogravitational R3BP

This paper investigates the motion of a test particle around the triangular equilibrium points under the effects of radiation pressure of the second primary and its Poynting–Robertson (P–R) effect when the first primary is an oblate spheroid. It is seen that triangular points are influenced by the presence of these parameters: radiation pressure from the secondary and the incidental P–R effect and the oblateness of the first primary. The linear stability of the problem is studied and applied to the binary system RXJ 0450.1-5856, the triangular points are unstable due to positive roots in the Lyapunov sense when P–R effect is considered as against their conditional stability in the absence of P–R drag effect.     

Dust ring formation due to ice sublimation of radially drifting dust particles under the Poynting-Robertson effect in debris disks

In a disk with a low optical depth, dust particles drift radially inward by the Poynting-Robertson (P-R) drag rather than are blown out by stellar radiation pressure following destructive collisions. We investigate the radial distribution of icy dust composed of pure ice and refractory materials in dust-debris disks taking into account the P-R drag and ice sublimation. We find that icy dust particles form a dust ring by their pile-ups at the edge of their sublimation zone, where they sublime substantially at the temperature 100-110 K. The distance of the dust ring is 20-35 AU from the central star with its luminosity L_??30L_⊙ and 65(L_?/100L_⊙)^1/2 AU for L_??30L_⊙, where L_⊙ is the solar luminosity. The effective optical depth is enhanced by a factor of 2 for L_??100L_⊙ and more than 10 for L_??100L_⊙. The optical depth of the outer icy dust disk exceeds that of the inner disk filled with refractory particles, namely, the residue of ice sublimation, which are further subjected to the P-R effect. As a result, an inner hole is formed inside the sublimation zone together with a dust ring along the outer edge of the hole.     

Alfvén drag for satellites orbiting in Jupiter's plasmasphere

According to a mechanism discovered by S. D. Drell, H. M. Foley, and M. A. Ruderman ((1965). J. Geophys. Res.70, 3131–3145), a satellite orbiting around a planet having a strong magnetic field and a dense ionospheric plasma dissipates orbital energy via radiation of Alfvén waves. The dissipation process is effective for objects larger than a minimum size and made of material exceeding a minimum electrical conductivity. It is shown that the corresponding drag effect could have influenced in a significant way the orbital evolution of the small natural moons orbiting inside or in proximity of Jupiter's ring. In particular this mechanism could explain the absence in the ring of objects in the size range from ～0.1 to ～10 km.     

Efficient numerical routines to find the averaged motion of small dust particles under the Poynting-Robertson force

The orbit-averaged differential equations of motion of dust particles under gravity, radiation pressure and Poynting-Robertson drag were given by Wyatt and Whipple (1950). An integral of motion enables the system of two equations in semi-major axis a and eccentricity e to be reduced to one equation, the solution of which is presented here in terms of analytical formulae. An efficient numerical algorithm to compute the solution is given. Listings of two FORTRAN routines are included.     

Dust in jupiter''s magnetosphere: Physical processes

The physical processes acting on charged microscopic dust grains in the Jovian magnetosphere are examined. Such small dust grains are believed to be injected continuously into the magnetosphere via volcanic activity on Io. It is shown that electromagnetic forces dominate the dust particle dynamics, and that these particles behave adiabatically, in the sense that the guiding centre approximation to their motion applies. Based on this fact, the diffusion across field lines, caused by random charge fluctuations of the dust grains, can be determined. This diffusion is the major cross field transport mechanism and determines the dispersion of dust grains from Io throughout the inner Jovian magnetosphere. Other physical processes (radiation pressure drag, Coulomb drag, sputtering) are also examined regarding their importance for particle transport.     

Physical processes in Jupiter's ring: Clues to its origin by Jove!

The particles making up the Jovian ring may be debris which has been excavated by micrometeoroids from the surfaces of many unseen (R ? 1 km) parent bodies (or “mooms” as we will occasionally call them) residing in the ring. A distribution of particle sizes exists: large objects are sources for the small visible ring particles and also account for the absorption of charged particles noted by Pioneer; the small grains are generated by micrometeoroid impacts, by jostling collisions among different-sized particles, and by self-fracturing due to electrostatic stresses. The latter are most effective in removing surface asperities to thereby produce smooth and crudely equidimensional grains. The presence of intermediate-sized (radius of several to several hundred microns) objects is also expected; these particles will have a total area comparable to the area of the visible ring particles. The nominal size (?2 μm) of the visible particles derived from their forward-scattering characteristics is caused, at least in part, by a selection effect but may also reflect a fundamental grain size or the preferential generation of certain sizes along with the destruction of others. The tiny ring particles have short lifetimes (?10²?10³ years) limited by erosion due to sputtering and meteoroid impacts. Plasma drag significantly modifies orbits in ～10² years but Poynting-Robertson drag is not effective (T_PR ～ 10⁵ years) in removing debris. The ring width is influenced by the distribution of source satellites, by the initial ejection velocity off them, by electromagnetic scattering, and by solar radiation forces. In the absence of electromagnetic forces, debris will reimpact a mother satellite or collide with another particle in about 10 years. A relative drift between different-sized particles, caused by a lessened effective gravity due to the Lorentz force, will substantially shorten these times to less than a month. The ring thickness is determined by a balance between initial conditions (abetted perhaps by electromagnetic scattering) and collisional damping; existence of the “halo” over the diffuse disk compared to its relative absence over the bright ring indicates the presence of mooms in the bright ring but not in the faint disk. Small satellites (R ? 1 km) will not reaccumulate colliding dust grains whereas satellites having the size of J14 or J16 may be able to do so, depending upon their precise shape, size, density, and location. Visible ring structure could indicate separate source satellites. The particles in the faint inner disk are delivered from the bright ring by orbital evolution principally under plasma drag. The halo is comprised of small particles (～0.1 μm) partially drawn out of the faint disk by interactions with the tilted Jovian magnetic field.     

Radiatively driven mass accretion on to galactic nuclei by circumnuclear starbursts

We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation–hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by M ˙ ( r )= η ( L _*/ c ²)( r / R )² (Δ R / R )(1 −  e ^−τ) at radius r , where the efficiency η ranges from 0.2 up to 1, L _* and R are respectively the bolometric luminosity and the radius of the starburst ring, Δ R is the extent of the emission regions, and τ is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to ∼ parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation–hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.