Perihelion motion of small irregular dust particles due to radiation forces

Perihelion motion, i.e. a secular change of longitude of perihelion, of interplanetary dust particles is investigated under the action of solar gravity and solar electromagnetic radiation. As for spherical particle [Kla?ka, J., 2004. Electromagnetic radiation and motion of a particle. Cel. Mech. Dynam. Astron. 89, 1-61]: (i) perihelion motion is of the order ( is heliocentric velocity of the meteoroid and c is the speed of light in vacuum), if a component of electromagnetic radiation acceleration is considered as a part of central acceleration; (ii) perihelion motion is of the first order in if the total electromagnetic radiation force is considered as a disturbing force. The new facts presented in this paper concern irregular dust particles. Detailed numerical calculations were performed for the grains ejected at aphelion of comet Encke. Perihelion motion for irregular interplanetary dust particles exists already in the first order in for both cases of central accelerations. Moreover, perihelion motion of irregular particles exhibits both positive and negative directions during the particle orbital motion. Irregularity of the grains causes not only perihelion motion, but also dispersion of the dust in various directions, also normal to the orbital plane of the parent body.     

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.     

Motion of dust particles under the influence of a latitudinally dependent force

The Kelperian motion of dust particles in the solar system is mainly influenced by the electromagnetic and plasma Poynting-Robertson drag. The first force is isotropic while the second one shows latitudinal variations due to the observed differences of the solar wind parameters in the ecliptic plane and over the solar poles. Close to the Sun other effects become important, e.g. sublimation and sputtering, as well as for submicron particles Lorentz scattering has to be taken into account. These forces are very weak for dust grains of moderate size (10–100 µ) not too close (>0.03 AU) to the Sun and are neglected here. Assuming that the general form of the latidudinally dependent force is a series expansion in Legendre polynomials, we have studied the averaged equations of motion for the classical elements and found the first integral of them. The general character of motion is the same as for the classical Poynting-Robertson drag: particles spiral towards the Sun. The new features in the orbital evolution under the latitudinally dependent force as compared with the isotropic Poynting-Robertson drag are:

1. not only the semimajor axisa and the eccentricity ε but also the argument of the perihelion ω varies with time,
2. the rate of change ofa, ε, ω depends on the inclination.

An example of particle trajectories in the phase space of elements is presented.     

Factors affecting the motion of interplanetary dust particles

In this paper the dynamics of individual dust particles and the effects on their motion caused by insolation and consequent evaporation is considered. Evaporation rates and the radii of dust-free zones have been computed using thermodynamic data from various sources. Some doubt is thrown on the validity of the process of matching observed thermal emission peaks with theoretical evaporation zone radii.     

Temperature-influenced dynamics of small dust particles

The motion of spherical dust particles under the action of gravity, electromagnetic radiation force and Lorentz force (LF) is studied theoretically for materials with temperature-dependent dielectric functions in the visible (VIS) spectral range. Even a weak variation of the optical constants with heliocentric distance may influence predominately a long-term dynamical behaviour of submicron-sized and small micron-sized dust grains. It is shown that the lifetime of carbonaceous or Si particles may change by several tens of per cent because of the temperature dependence of particle refractive indices. The orbital inclination is the most evident difference between the evolution of a dust particle with temperature-dependent optical properties and one without. While carbonaceous 2-μm-sized particles with optical constants independent of temperature may evolve in orbits with inclinations greater than an initial value, grains of the same size with variable refractive indices will be spread along orbits characterized with inclinations lower than the initial one. Here the temperature works as a separation factor for particles having slightly different temperature dependences of the optical constants.     

A numerical study of the contributions of dust source regions to the global dust budget

Contributions of the nine potential dust source regions (North and South Africa, the Arabian Peninsula, Central Asia, eastern and western China, North and South America, and Australia) to the global dust budget are investigated with a global dust transport model. A six-year simulation (1990 to 1995) indicates that the greatest contributor to the global dust budget is found to be North Africa (the Sahara Desert), which accounts for 58% of the total global dust emission and 62% of the total global dust load in the atmosphere. Australian dust dominates the southern hemisphere. The dust emission and atmospheric dust load originating from East Asia (eastern and western China) are estimated to be 214 Tg yr^− 1 and 1.1 Tg, respectively, which are 11% and 6% of the total global dust emission and dust load. Dust from East Asia dominates the atmospheric load over China and Mongolia (about 70%), Korea (60%), Japan (50%), and the North Pacific Ocean (40%). The contribution of dust originating from regions other than East Asia to the dust load over these East Asian countries and the North Pacific Ocean cannot be ignored. The simulated total dust deposition flux on Greenland suggests a possible overestimation of the Saharan dust and an underestimation of the East Asian dust in the Arctic region, which may be a common problem with global dust transport models. Possible reasons for the underestimation of the East Asian dust are discussed.     

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.     

Effects of random solar-wind variations in the motion of small particles in the solar system

The evolution of the orbit of a small particle affected by regular and irregular components of the solar wind is examined. If the irregularity is taken into account, the pattern of motion may qualitatively change on large time scales, because the general integrals of motion are not conserved. The diffusion along the eccentricity of the orbit is most important. In certain cases, it can lead to the escape of a particle from the solar region. Corresponding numerical estimates are given.     

Two-body motion under the inverse square central force and equivalent geodesic flows

In this paper the fixed energy surfaces for the two-body problem for parabolic and, in particular, hyperbolic motion are completely, determined by utilizing an earlier work of J. Moser. The characterization of these fixed energy manifolds yields the explicit solutions to the above problems in an elementary way for arbitrary dimensions.     

The capture of interstellar dust: the Lorentz force case

The capture of arbitrarily shaped interstellar dust in the Solar System is investigated. Electromagnetic radiation and gravitational forces of the Sun and Lorentz force generated by interplanetary magnetic field are considered. The capture conditions appear to be very sensitive to the particle shape. Non-spherical particles as well as their spherical equivalents are captured only when they are moving initially in the vicinity of ecliptic plane. Capture of non-charged non-spherical dust typically occurs in the region , where R_Sun is solar radius and impact parameter b is defined as the smallest distance between the particle and the Sun if no forces existed. In contrast, charged particles are typically captured at b>150 R_Sun. The total amount of captured non-spherical sub-micron particles differs significantly from the corresponding amount of spherical dust grains. However, both amounts are comparable in the micron-sized range. It is shown that a certain mass of captured non-spherical particles may survive in the Solar System, while captured spherical ones hit the Sun or sublimate in its vicinity. Only a negligible amount of spherical particles can survive. Consideration of solar wind within around of yields that 20% of the captured non-spherical particles of the effective radius survive; the corresponding percentage for particles of the radius is 7%. The total mass of the surviving charged particles is about two orders of magnitude larger than the mass of the surviving non-charged particles. As a result, the sub-micron-sized particles are candidates to contribute to the density increase of the circumsolar dust cloud.     

Magnetothermal condensation modes including the effects of charged dust particles

We study thermal instability in a magnetized and partially ionized plasma with charged dust particles. Our linear analysis shows that the growth rate of the unstable modes in the presence of dust particles strongly depends on the ratio of the cooling rate and the modified dust-cyclotron frequency. If the cooling rate is less than the modified dust-cyclotron frequency, then the growth rate of the condensation modes does not modify due to the existence of the charged dust particles. But, when the cooling rate is greater than (or comparable to) the modified dust-cyclotron frequency, the growth rate of unstable modes increases because of the dust particles. Also, the wavenumber of the perturbations corresponding to the maximum growth rate shifts to the smaller values (larger wavelengths) as the cooling rate becomes larger than the modified dust-cyclotron frequency. We show that the growth rate of the condensation modes increases with the electrical charge of the dust particles.     

Lagrangian and Hamiltonian for the motion of charged particles up to the fourth-order terms

It is known that a special case of the Lagrangian of two identical charged particles up to fourth order terms has been found. The object of this paper is to derive the generalized Lagrangian by a scheme which is somewhat different from the one known. On the other hand one can then proceed to give the Hamiltonian form up to the same order.     

Considerations about the absorption efficiency of dust particles in the infrared

Analytical approximations used often in the literature for calculating energy rates emitted by dust grains in infrared are discussed. Comparisons with correct complete formulations are made for three grain models: (1) pure graphite, (2) ice mantle-graphite core, (3) silicates. ^-1 and ^-1 dependences for the average effective emissivity of such grains are used. We find that for silicate and graphite grains the simplified approximations are valid only when accuracies between 10% and 50% are required and only for grain temperatures higher than 80 K. At lower temperatures the validity of the approximations fails for the graphite particle while it is variable for the silicate dust grain. The ice core mantle particles can instead be treated with approximated formulae without introducing appreciable errors.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July, 1974.     

Charging and motion of dust grains near the terminator of the moon

We discuss the formation of strong local electric fields near minicraters or hills in the vicinity of the terminator. Electrons, having large thermal velocity compared to the solar wind speed can easily penetrate into the shadowed part of a minicrater. At the same time only protons with velocities much higher than their thermal speed can reach such regions. This results in the formation of a strong local negative potential whose magnitude depends on the steepness of the shadowed slope of the minicrater. The extremely small conductivity of the lunar regolith at the shadowed side of the crater prevents any significant electric discharge and thus supports the formation of a strong potential difference at scales much smaller than the Debye radius. Our estimates show that the created local electric fields are sufficiently strong enough to elevate dust grains with the sizes of the order of above the surface. The suggested mechanism is efficient only after sunset rather close to the terminator. Far away from the terminator at the dark side the fluxes of charged particles hitting the surface are so small that the process of dust elevation becomes too weak.     

Construction of the semi-analytical and numerical solutions to the problem of rotational motion of the moon

New high-precision, semianalytical and numerical solutions to the problem of the rotational motion of the Moon are obtained, for use in the long 418.9-year time frame. The dynamics of the rotational motion of the Moon is studied numerically using the Rodrigues-Hamilton parameters, relative to the fixed ecliptic for the epoch J2000. The results of the numerical solution to the problem under study are compared with a compiled semianalytical theory of Moon rotation (SMR). The initial conditions for the numerical integration have been taken from the SMR. The comparative discrepancies derived from the comparison between the numerical solutions and the SMR do not exceed 1.5″ on the time-scale of 418.9 yr. The investigation of the comparative discrepancies between the numerical and semianalytical solutions is performed using the least squares and spectral analysis methods in the Newtonian case. All the periodic terms describing the behavior of the comparative discrepancies are interpreted as the corrections to the semianalytical SMR theory. As a result, the series are constructed to describe the rotation of the Moon (MRS2010) in the time interval under study. The numerical solution for the Moon’s rotation has been obtained anew, with new initial conditions calculated using MRS2010. The discrepancies between the new numerical solution and MRS2010 do not exceed 20 arc milliseconds on the time-scale of 418.9 years. The results of the comparison suggest that that the MRS2010 series describe the rotation of the Moon more correctly than the SMR series.     

Investigation of the electrostatic charging of dust particles in a Paul-trap

Dust particles (glass, tungsten, and nickel) with sizes ranging from 0.25 to 3m were levitated in a Paul-trap and charged by ions or electrons. For ions the particle potential is limited at field strength of about 1×10⁹ V m^–1 by a temperature-dependent discharge mechanism. The particles interaction with 2 to 20 keV electrons always leads to positive surface potentials which can be explained in terms of a decreased absorption of electrons by small particles. Micrometer sized agglomerates were used for the investigation of the electrostatic fragmentation. Fragmentation takes place in a twofold manner: small surface flufl can be removed or the parent particle can be disrupted into smaller agglomerates.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

General Lagrangian approach to the equations of motion for test particles with internal structure

The equations of motion for test particles with internal structure are derived from a general Lagrange principle. The internal structure of the particles is described by sets of unspecified geometric objects, which transform homogeneously both under coordinate and under gauge transformations. Most of the Lagrangian approaches known in the literature are special cases of our general formalism.