Scattering properties of a moonlet (satellite) embedded in a particle ring: Application to the rings of Saturn

The gravitational influence of moonlets or satellites on the radial structure of the rings of Saturn has been calculated numerically. A drastic change in the surface mass density is obtained even after a single scattering process of the ring particles on a moonlet (satellite). The final surface density shows a significant radial structure, which has been used to estimate the radius and the mass of moonlets or satellites embedded in rings of low optical depth (E ring, Cassini division, C ring).     

Scattering of waves in a magnetoactive plasma

A general theory of scattering of waves in a magnetoactive plasma by particles of arbitrary energy is presented. The cross-section for the scattering of magnetoionic waves by thermal particles is derived and discussed. Conditions under which the effect of the spiralling motion of the scattering electron can be neglected in treating inverse Compton radiation are found.     

Small-Amplitude Disturbances in a Radiating and Scattering Grey MediumIII. Gravitational Effects on the Solutions of Given Real Wave Number k

We study the fundamental modes of radiation hydrodynamic linear waves that arise from one-dimensional small-amplitude initial fluctuations with wave number k in a radiating and scattering grey medium by taking into account the gravitational effects. The equation of radiative acoustics is derived from three hydrodynamic equations, Poisson’s equation, and two moment equations of radiation, by assuming a spherical symmetry for the matter and radiation and by using the Eddington approximation. We solve the dispersion relation as a quintic function of angular frequency ω, the wave number k being a real parameter. Numerical results reveal that wave patterns of five solutions are distinguished into three types: the radiation-dominated, type 1, and type 2 matter-dominated cases. In the case of no gravitaional effects (Kaneko et al., 2005), the following wave modes appear: radiation wave, conservative radiation wave, entropy wave, Newtonian-cooling wave, opacity-damped and cooling-damped waves, constant-volume and constant-pressure diffusions, adiabatic sound wave, cooling-damped and drag-force-damped isothermal sound waves, isentropic radiation-acoustic wave, and gap mode. Meanwhile, the gravitaional effects being taken into account, the growing gravo-diffusion mode newly arises from the constant-pressure diffusion at the point that k agrees with Jeans’ wave number specified by the isothermal sound speed. This mode changes to the growing radiation-acoustic gravity mode near the point that k becomes Jeans’ wave number specified by the isentropic radiation-acoustic speed. In step with a transition between them, the isentropic radiation-acoustic wave splits into the damping radiation-acoustic gravity mode and constant-volume diffusion. The constant-volume diffusion emerges twice if the gravitational effects are taken into account. Since analytic solutions are derived for all wave modes, we discuss their physical significance. The critical conditions are given which distinguish between radiation-dominated and type 1 matter-dominated cases, and between type 1 and type 2 matter-dominated cases. Waves in a self-gravitating scattering grey medium are also analyzed, which provides us some hints for the effects of energy and momentum exchange between matter and radiation.     

Scattering properties of planetary regolith analogs

The physics of scattering of electromagnetic waves by media in which the particles are in contact, such as planetary regoliths, has been thought to be relatively well understood when the particles are larger than the wavelength. However, this is not true when the particles are comparable with or smaller than the wavelength. We have measured the scattering parameters of planetary regolith analogs consisting of suites of well-sorted abrasives whose particles ranged from larger to smaller than the wavelength. We measured the variation of reflectance as the phase angle varied from 0.05° to 140°. The following parameters of the media were then deduced: the single scattering albedo, single scattering phase function, transport mean free path, and scattering, absorption, and extinction coefficients. A scattering model based on the equation of radiative transfer was empirically able to describe quantitatively the variation of intensity with angle for each sample. Thus, such models can be used to characterize scattering from regoliths even when the particles are smaller than the wavelength. The scattering parameters were remarkably insensitive to particle size. These results are contrary to theoretical predictions, but are consistent with earlier measurements of alumina abrasives that were restricted to small phase angles. They imply that a basic assumption made by virtually all regolith scattering models, that the regolith particles are the fundamental scattering units of the medium, is incorrect. Our understanding of scattering by regoliths appears to be incomplete, even when the particles are larger than the wavelength.     

Gravitational lensing by stars in a galaxy halo: Theory of combined weak and strong scattering

The theory of gravitational lensing of background quasars by stars in the halo of a galaxy is considered. In the limiting case of small ‘optical depth’, only one star is close enough to the beam to cause strong scattering, and the effect of all the other stars is treated as a perturbation with both systematic and random components. The perturbation coming from weak scattering can increase the number of images and the amplification in those cases where the amplification is already high; such events are preferentially selected in flux limited observations. The theory is applicable to the apparent association of background quasars with foreground galaxies. A comparison with earlier work on the same problem is given. The relevance of these results to gravitational lensing by galaxies as perturbed by random inhomogeneities surrounding the ray path is also briefly discussed.     

Line Formation in a Purely Scattering, Optically Thick Atmosphere

A model problem in the theory of line formation in an optically thick, purely scattering, stellar atmosphere is considered. The integral equation of radiation transfer at line frequencies is solved numerically for a two-level atom in the approximation of complete frequency redistribution in scattering. The numerical results are compared with those calculated from equations of the asymptotic theory. On the basis of the asymptotic theory, the positions of intensity maxima in a line are found for different absorption profiles.     

On the interaction of jet plasma with dark matter subhaloes in active galaxies

The interaction of fragmented plasma of active galactic nuclei jets with galactic haloes via gravitational scattering and lensing by dark matter subhaloes is studied using analytical calculations and numerical Monte-Carlo method. The lensing of jet radiation by halo masses is found to be negligible and unobservable. Moving through a galactic halo jet plasma fragments are sequentially deflected on hyperbolic orbits by gravitational field of subhaloes and deviates at some angles when leaving halo, causing widening of the jet. Based on this model jet opening angles are calculated numerically for various values of jet and halo characteristics. Though these angles are very small, gravitational scattering by halo masses results in specific radial profile of jet radiation intensity, that does not depend on halo mass distribution and jet properties. The intensity of jet radiation, obeying the derived profile, decreases by reasonable observable factors giving possibility to probe the presence of dark matter subhaloes.     

Polarization Models for Rayleigh Scattering Planetary Atmospheres

We present Monte Carlo simulations for the polarization of light reflected from planetary atmospheres. We investigate dependencies of intensity and polarization on three main parameters: single scattering albedo, optical depth of a scattering layer, and albedo of a Lambert surface underneath. The main scattering process considered is Rayleigh scattering, but isotropic scattering and enhanced forward scattering on haze particles are also investigated. We discuss disk integrated results for all phase angles and radial profiles of the limb polarization at opposition. These results are useful to interpret available limb polarization measurements of solar system planets and to predict the polarization of extra-solar planets as a preparation for VLT/SPHERE. Most favorable for a detection are planets with an optically thick Rayleigh-scattering layer. The limb polarization of Uranus and Neptune is especially sensitive to the vertically stratified methane mixing ratio. From limb polarization measurements constraints on the polarization at large phase angles can be set.     

Scattering of Light by Composite Particles in a Planetary Surface

It has been proposed that composite particles containing internal scatterers may provide the explanation for the fact that most photometric studies of planetary surfaces based on Hapke's model of bidirectional reflectance have found the planetary particles to exhibit moderately backscattering phase functions. However, an implicit assumption made in this explanation is that the scattering by composite particles containing multiple internal inclusions in a planetary surface can still be adequately computed using standard radiative transfer theory assuming the composite particles to be the fundamental individual scatterers even though such particles are necessarily in close proximity to each other. In this paper, this assumption is explored by examining the effects of close packing on the light scattering by spherical particles containing isotropic internal scatterers using a Monte Carlo routine. As expected, classical radiative transfer (assuming a random distribution of scattering particles) coupled with the assumption that the composite particle is the fundamental scatterer provides a good approximation in the high porosity limit. However, even for porosities as high as 90% the effects of close packing are clearly seen with the radiative transfer calculation underestimating the scattering by ∼10% at high incidence, emission, and phase angles. As the porosity is lowered further, the discrepancy becomes more severe and can reach 50% or more. In contrast, assuming the individual scatterer properties in the radiative transfer calculation leads to a substantial overestimate of the scattering even for porosities as low as 27.5%. This suggests that parameters derived using the classical radiative transfer theory will yield results intermediate between those of the composite as a whole and those of the internal scatterers. Thus, one should exercise caution in interpreting the results of models based on classical radiative transfer theory in terms of the physical properties of the surface particles and, where possible, the bidirectional reflectance of densely packed composite particles should be computed using more accurate methods such as the stochastic radiative transfer theory.     

Polarization of the CMB Photons Crossing the Galaxy Clusters

In this paper, I investigate a local effect of polarization of the Cosmic Microwave Background (CMB) in clusters of galaxies, induced by the Thomson scattering of an anisotropic radiation. A local anisotropy of the CMB is produced by some scattering and gravitational effects, as, for instance, the Sunyaev Zel‘dovich effect, the Doppler shift due to the cluster motion and the gravitational lensing. The resulting anisotropy ΔI/I depends on the physical properties of the clusters, in particular on their emissivity in the X band on their size, on their gravitational potential and on the peculiar conditions characterizing the gas they contain. By solving the Boltzmann radiative transfer equation in presence of such anisotropies I calculate the average polarization at the centre of some clusters, namelyA2218, A576 and A2163, whose properties are quite well known. I prove that the gravitational effects due to the contraction or to the expansion have some importance, particularly for high density structures; moreover, the peculiar motion of the cluster, considered as a gravitational lens, influences the propagation of the CMB photons by introducing a particular angular dependence in the gravitational anisotropy and in the scattering integrals. Thus, the gravitational and the scattering effects overally produce an appreciable local average polarization of the CMB, may be observable through a careful polarization measurements towards the centres of the galaxy clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scattering of radiation by a large particle with a random rough surface

Intensity and polarization of scattered light by an absorbing spherical particle with a random rough surface and with a radius larger than the wavelength of radiation are investigated. Multiple reflections of incident light on the rough surface are treated based on the multiple scattering theory.Within the limits of our approximation the model gives good agreement with typical scattering features by irregular shaped particles derived by microwave analogue experiments and laser measurements, namely a backward enhancement of the intensity, and a reduction of magnitude of polarization.Our treatment will be provide a powerful tool for studying scattering problems of interstellar and/or interplanetary grains as well as those of asteroids and the Moon.     

Scattering physics

The theory of polarized scattering in a stellar atmosphere is formulated, first within the framework of classical physics, then in terms of quantum mechanics. The expression for the redistribution matrix that describes partial redistribution in polarization and frequency is derived for the general case when the magnetic field is of arbitrary strength. The special cases of weak fields (the Hanle limit) and zero fields (non-magnetic scattering) are discussed. Observational examples of spectral signatures in linear polarization are presented, which show effects of hyperfine structure, interference between fine structure components, and molecular scattering.     

Scattering Properties and Composition of Cometary Dust

Composition of the Comet dust obtained by the dust impact analyzer on the Halley probes indicated that the comet dust is a mixture of silicate and carbonaceous material. The collected interplanetary dust particles (IDP's) are fluffy and composite, having grains of several different types stuck together. Using discrete dipole approximation (DDA) we study the scattering properties of composite grains. In particular, we study the angular distribution of the scattered intensity and linear polarization of composite grains. We assume that the composite grains are made up of a host silicate sphere/spheroid with the inclusions of graphite. Results of our calculations on the composite grains show that the angle of maximum polarization shifts, and the degree of polarization varies with the volume fraction of the inclusions. We use these results on the composite grains to interpret the observed scattering in cometary dust.     

Low-Angle Thomson Scattering Experiment for Determination of Plasma Electron Density and Temperature

In this work we show results of measurements of the electron density n_e and temperature T_e by using small-angle Thomson scattering in a theta-pinch plasma. The method of measurement and analysis developed here is based on integration of only two ranges of the scattering profile. This method simplifies the experimental set up, because it needs only two detectors for simultaneous determination of n_e and T_e, instead of the commonly 5–7 detectors used in 90° experiments.The results obtained for low-angle scattering are compared with the measurements at 90° using single pass and multipass under the same plasma conditions.     

Radial diffusion rate of planetesimals due to gravitational encounters

We study the rate of radial diffusion of planetesimals due to mutual gravitational encounters under Hill’s approximations in the three-body problem. Planetesimals orbiting a central star radially migrate inward and outward as a result of mutual gravitational encounters and transfer angular momentum. We calculate the viscosity in a disk of equal-sized planetesimals due to their mutual gravitational encounters using three-body orbital integrations, and obtain a semianalytic expression that reproduces the numerical results. We find that the viscosity is independent of the velocity dispersion of planetesimals when the velocity dispersion is so small that Kepler shear dominates planetesimals’ relative velocities. On the other hand, in high-velocity cases where random velocities dominate the relative velocities, the viscosity is a decreasing function of the velocity dispersion, and is found to agree with previous estimates under the two-body approximation neglecting the solar gravity. We also calculate the rate of radial diffusion of planetesimals due to gravitational scattering by a massive protoplanet. Using these results, we discuss a condition for formation of nonuniform radial surface density distribution of planetesimals by gravitational perturbation of an embedded protoplanet.     

Orbital Decay of a Binary System Consisting of Spin-Down Neutron Stars

{W}e consider the gravitational radiation from two time variable mass stars, orbiting around each other under the influence of gravity. The total rates of the variation of the energy, angular momentum, semimajor axis, eccentricity and orbital period are obtained. The results could be important for the understanding of general relativistic effects in the case of the variation of the gravitational mass due to spinning down of the compact stars, which sensitively depends on the equations of state. The cases of the binary systems PSR 1913+16 and PSR 1534+12 are analyzed in detail, and, for different equations of state of nuclear matter, the corrections to the orbital decay due to gravitational radiation and to the spinning down of the pulsars are calculated. The results show that a future significant improvement in the observational techniques could lead to the observation of the specific general relativistic effect of mass variation of pulsars due to spinning down, via the study of orbital decay, even in slowly rotating binary systems.     

Wave Transformation and Scattering on Stationary Charged Particles in a Magnetoactive Plasma. I

The scattering and transformation of natural waves of a magnetoactive plasma on a heavy charged particle lying at a plane plasma—vacuum boundary is considered. The angular distribution and cross section for scattering (transformation) of high-frequency ordinary and extraordinary waves are investigated.     

On a repelling force between particles in a bath of thermal radiation

In an optically thin medium two particles in a bath of thermal radiation repel each other with a force directly proportional to the product of their cross sections and inversely proportional to the square of the distance between them. This force, which is mediated by the scattered photons, was in the past much larger than the gravitational attraction between scattering particles, and could have played a role in the formation of the first gravitationally bound systems.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

Light Scattering and Extinction in M 82

Published low-resolution measurements of colour and polarisation over the face of M82 are discussed to separate the contribution of starlight and scattered light. We show that in all places of the middle and outer halo the scattered light comes predominantly from a central source of very high ultraviolett excess, the contribution of the disc is negligble there. The projected distributions of H_α-light and scattered continuum are of considerable similarity. Major extinction occurs in the southern half of the main body and of the inner halo; the northern half of the bright body, and the northern halo, are free of extinction, excluding some regions near the minor axis. The light of the central source is reddened only before it is scattered in the halo. The variation of the true degree of polarisation (after correction for starlight) is interpreted in terms of the variation of the mean scattering angle. From this, conclusions can be drawn concerning the location of the dust and the geometry of the illumination. The high brightness of the scattered light near the minor axis is caused axis is caused by a bright illuminating beam there, strengthened in some places by comparatively low scattering angles (45°) and a higher (projected) density of the scattering material. The stellar populations seen in M82 are different in the northern and in the southern halfs of the galaxy. The main body and the region of the northern “halo” consist of an old population of normal metal content (pop. I); the colours of the southern parts – which are partly considerably influenced by extinction – can be due to either metal poor F-stars (pop. II) or to young B-stars. To solve the latter ambiguity and at the same time the question in what direction the plane of the galaxy is tilted, good spectra of the faint southern parts of M82 outside the minor axis are needed.