Circular polarization of sunlight reflected by planetary atmospheres

Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined.     

Modeling the linear polarization of optical emission from red giants

We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N _d ∝ r ⁻², and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T _ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N _sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.     

Optical properties of spheroidal particles

A new exact solution of the diffraction problem for the homogeneous spheroid on the basis of the method of separation of variables is given. This solution is considerably more efficient than the one of Asano and Yamamoto from the computational point of view. The expressions for various characteristics of the scattered radiation are obtained. The radiation pressure on spheroidal particles is considered taking into account the radial and transversal components. The method of calculations and various tests, which were used to control the computer programs, are described. Numerical results for forward and arbitrary angles scattering by prolate and oblate spheroids with the refractive indices typical for ice and silicates are presented. The dependence of the results on the propagation direction and the polarization of the incident radiation, size of particle and its aspect ratio are examined. The asymptotics for the characteristics of the scattered radiation for the extremely prolate and extremely oblate spheroids are derived. The range of the validity of these approximations is studied. Astrophysical applications include: a) the calculations of the interstellar extinction, interstellar linear and circular polarization curves for the ensemble of partially oriented spheroidal grains, and b) the consideration of the profiles and polarization of the interstellar feature 2200 for the partially oriented graphite spheroids. Appendices contain the expressions for integrals of products of the angular spheroidal functions and the asymptotics for the oblate spheroidal functions.     

Polarization models of young stellar objects – II. Linear and circular polarimetry of R Coronae Australis

Near-infrared linear imaging polarimetry of the young stellar objects R CrA and T CrA in the J , H and K n bands, and circular imaging polarimetry in the H band, is presented. The data are modelled with the Clark and McCall scattering model. The R CrA and T CrA system is shown to be a particularly complex scattering environment. In the case of R CrA there is evidence that the wavelength dependence of polarization changes across the nebula. MRN dust grain models do not explain this behaviour. Depolarization by line emission is considered as an alternative explanation. The dust grain properties could also be changing across the nebula.
Although surrounded by reflection nebulosity, there is a region of particularly low polarization surrounding R CrA that is best modelled by the canonical bipolar outflow being truncated by an evacuated spherical cavity surrounding the star. The symmetry axis of the nebula appears inclined by 50° to the plane of the sky.
The H -band circular polarimetry of R CrA clearly shows a quadrupolar structure of positive and negative degrees of circular polarization that reach peak magnitudes of ∼5 per cent within our limited map. It is shown that spherical MRN grains are incapable of producing this circular polarization given the observed linear polarization of the R CrA system. Instead, scattering from aligned non-spherical grains is proposed as the operating mechanism.
T CrA is a more archetypical bipolar reflection nebula, and this object is modelled as a canonical parabolic reflection nebula that lies in the plane of the sky. The wavelength independence of linear polarization in the T CrA reflection nebula suggests that the scattering particles are Rayleigh sized. This is modelled with the MRN interstellar grain size distribution.     

Estimating the water content of hydrated minerals using reflectance spectroscopy: II. Effects of particle size

Visible-near infrared reflectance spectra for five particle size fractions of a Hawaiian palagonite (HWMK101) and a nontronite (ferruginous smectite, Clay Minerals Society source clay SWa-1) were measured under ambient, purged, and heated conditions to characterize the effects of surface and volume scattering on the relationship between absolute H₂O content and the strength of the 3 μm absorption feature. Both materials were ground and dry sieved to particle sizes of <25, 25-45, 45-75, 75-125, and 125-250 μm. Particles of the bulk palagonite have an approximate bimodal distribution consisting of small, amorphous particles <5 μm in diameter mixed with crystalline and glass particles <1 mm in diameter, whereas the nontronite particles are polycrystalline aggregates. We find that band parameters value relating the strength of the 3 μm hydration feature to water content increase with particle size for a given water content, regardless of whether reflectance or single scattering albedo spectra are used. Spectra generally increase in reflectance as particle size decreases, a result of the relative increase in volume to surface scattering. Spectra of large particles are commonly saturated in the 3 μm region due to an increase in optical path length, making an accurate estimate of water content indeterminate until the samples dehydrate to the volume-scattering regime. We find that the presence of fines in several of the size fractions of palagonite cause their spectra to be representative of the finest fraction rather than the mean particle size. The nontronite spectra appear to be representative of an effective particle size within the range of the sieved size fractions. Many planetary surfaces are expected to have a large number of small particles which can dominate their spectral signature. Our results for particles <45 μm provide a reasonable model for estimating the H₂O content of hydrated asteroids and regions of Mars.     

Non-Spherical Dust Grains in the Envelopes of Late-Type Giants

Effects of the grain shape on circumstellar dust dynamics and polarization of stellar radiation are analyzed. The grains are modeled by rotating prolate and oblate spheroids. It is shown that an asymmetry of the geometry of light scattering by non-spherical particles results in a component of the radiation pressure force perpendicular to the wave-vector of incident light. For silicate spheroids, this component can exceed 20 % of . For small metallic grains, the radiation pressure force for a spheroid can be 5–10 times greater than that for a sphere of the same volume. A simple light scattering consideration demonstrates that the distinction in the scattering geometry of aligned non-spherical grains can explain the observed wavelength variations of the positional angle of polarization. This revised version was published online in September 2006 with corrections to the Cover Date.     

Limits on the size of aerosols from measurements of linear polarization in Titan’s atmosphere

The Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe into the atmosphere of Titan yielded information on the size, shape, optical properties, and vertical distribution of haze aerosols in the atmosphere of Titan [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., 2008. Planet. Space Sci. 56, 669-707] from photometric and spectroscopic measurements of sunlight in Titan’s atmosphere. This instrument also made measurements of the degree of linear polarization of sunlight in two spectral bands centered at 491 and 934 nm. Here we present the calibration and reduction of the polarization measurements and compare the polarization observations to models using fractal aggregate particles which have different sizes for the small dimension (monomer size) of which the aggregates are composed. We find that the Titan aerosols produce very large polarizations perpendicular to the scattering plane for scattering near 90° scattering angle. The size of the monomers is tightly constrained by the measurements to a radius of 0.04 ± 0.01 μm at altitudes from 150 km to the surface. The decrease in polarization with decreasing altitude observed in red and blue light is as expected by increasing dilution due to multiple scattering at decreasing altitudes. There is no indication of particles that produce small amounts of linear polarization at low altitudes.     

Light scattering by nonspherical ice grains: An application to noctilucent cloud particles

The light scattered by noctilucent cloud particles is nearly fully polarized at scattering angles in the vicinity of 90 . This was one of the reasons to conclude that the upper limit of their sizes is not larger than about 0.12 m. Nevertheless, this estimate was made on the basis of the Mie scattering theory for spherical particles, whereas many investigators noted usefulness of highly aspherical shapes of noctilucent cloud particles. In this paper, we used rigorous light scattering theory for randomly oriented nonspherical particles to calculate the degree of linear polarization of the scattered light for ice grains of different shape. By comparing these calculations with rocket polarization measurements of noctilucent clouds, we show that, as for spherical particles, the upper limit of particle equal-volume radii for slightly flattened and elongated grains is of about 0.12 m, while for highly aspherical plate-like and needle-like particles this upper limit is substantially larger and is of about 0.18–0.20 m. We also report calculations of the volumetric scattering cross-section for particles of different shape and show that randomly oriented spheroids have (slightly) smaller scattering cross section per unit particle mass than equal-volume spherical grains. Nevertheless, if in noctilucent clouds plate-like and needle-like grains grow to much larger sizes than spherical particles, their scattering efficiency may be much greater.     

Chaotic zone boundary for low free eccentricity particles near an eccentric planet

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Through collisionless particle integration, we numerically find the location of the boundary of the chaotic zone in the planet's corotation region. We find that the distance in semimajor axis between the planet and boundary depends on the planet mass to the 2/7 power and is independent of the planet eccentricity, at least for planet eccentricities below 0.3. Our integrations reveal a similarity between the dynamics of particles at zero eccentricity near a planet in a circular orbit and with zero free eccentricity particles near an eccentric planet. The 2/7th law has been previously explained by estimating the semimajor at which the first-order mean motion resonances are large enough to overlap. Orbital dynamics near an eccentric planet could differ due to first-order corotation resonances that have strength proportional to the planet's eccentricity. However, we find that the corotation resonance width at low free eccentricity is small; also the first-order resonance width at zero free eccentricity is the same as that for a zero-eccentricity particle near a planet in a circular orbit. This accounts for insensitivity of the chaotic zone width to planet eccentricity. Particles at zero free eccentricity near an eccentric planet have similar dynamics to those at zero eccentricity near a planet in a circular orbit.     

Inferring asteroid surface properties from radar albedos and circular‐polarization ratios

We model electromagnetic scattering from varying closely packed random aggregates of spheres imitating piles of rocks on the surface of an asteroid. We utilize the Multiple Sphere T‐Matrix Method software to study how different parameters affect the radar albedo and the circular‐polarization ratio, for example, the size distribution and electric permittivities of the spherical particles forming the aggregates, and to see if the computed radar albedos and circular‐polarization ratios can be linked to the observational data of asteroids detected using radar. The results of the simulations show the radar albedo and the circular‐polarization ratio as a function of size parameter for different silicate minerals, including anorthosite, peridotite olivine, and basalt. A direct vacuum‐rock surface interface will be considered as well as an approximation for a case in which the rocks are covered by a layer of powdered material, that is, fine regolith. The promising results show values on the range of observed values and imply that the highest circular‐polarization values (μ_c > 1) are measurable only for targets with surface material of high electric permittivity (ε′ > 4.0). However, the asteroid surface model requires further development before more robust conclusions can be made of the surface chemical and structural composition.     

The vertical structure and thickness of Saturn's rings

We have considered the steady state vertical structure of Saturn's rings with regard to whether collapse to a monolayer due to collisions between particles, the end state predicted by Jeffreys (1947a), may be prevented by any of a variety of mechanisms. Given a broad distribution of particle sizes such as a typical power law n(R) = n₀R^?3, it is found that gravitational scattering of small particles by large particles maintains a true ring thickness of several times the radius of the largest particles, or many times the radius of the smallest particles. Thus the “many-particle-thick” condition which best satisfies optical observations, such as the opposition effect, may be reconciled with ongoing particle collisions. If we consider the obvious sources of energy available for such a process, we find that a ring thickness of only tens of meters may be sustained over the lifetime of the solar system. This implies a maximum particle size on the order of a few meters.     

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.     

X-ray polarization signatures of Compton scattering in magnetic cataclysmic variables

Compton scattering within the accretion column of magnetic cataclysmic variables (mCVs) can induce a net polarization in the X-ray emission. We investigate this process using Monte Carlo simulations and find that significant polarization can arise as a result of the stratified flow structure in the shock-ionized column. We find that the degree of linear polarization can reach levels up to ∼8 per cent for systems with high accretion rates and low white dwarf masses, when viewed at large inclination angles with respect to the accretion column axis. These levels are substantially higher than previously predicted estimates using an accretion column model with uniform density and temperature. We also find that for systems with a relatively low-mass white dwarf accreting at a high accretion rate, the polarization properties may be insensitive to the magnetic field, since most of the scattering occurs at the base of the accretion column where the density structure is determined mainly by bremsstrahlung cooling instead of cyclotron cooling.     

The profiles of polarized broad Hα lines in radio galaxies

We present spectropolarimetric observations of seven broad-line radio galaxies. We find significantly polarized broad Hα emission in four objects including two, Arp 102B and 3C 390.3, which have double-peaked line profiles. In these objects the prominent redshifted and blueshifted peaks of the broad Hα line have no clear counterparts in polarized flux. This conflicts with theoretical predictions for a relativistic line-emitting disc with an electron scattering atmosphere, one of the leading models advanced to account for the double-peaked lines. The shapes and widths of the polarized line profiles can be explained if, as expected in unified schemes, the scattering occurs near the poles of an obscuring torus. However, the observed polarization position angles favour geometries in which the scattering plane is perpendicular to the radio jet. A configuration in which Hα photons emitted by a biconical flow are scattered off the inner wall of the torus has this property, and would also produce a single-peaked scattered line profile. With the exception of 3C 227, the sample as a whole conforms to the general trend in powerful radio galaxies for the optical polarization to be aligned with the radio source axis, favouring toroidal rather than polar scattering.     

Observations Of Scattered Light From Cometary Dust And Their Interpretation

This review begins with a discussion of the techniques needed for observations of scattered light from cometary dust. After an introduction into the basic concepts of the scattering process, observations of the phase curves of brightness, colour and polarization are covered. Images of colour and polarization are presented and the observed relation of colour and polarization in jets and shells is discussed. The interpretation of the measurements is based on the power law size distributions of dust grains observed from space. The power index must lie between 2 and 4 to provide the mass budget and visibility of the dust coma in accordance with the basic facts of cometary physics. Application of mechanical (radiation pressure) theory to cometary images allows us to derive related power law distributions for comets not explored by spacecraft. Grain scattering models are presented and compared with observations. A prediction is made of the spatial distribution of Stokes parameters U and V in the presence of aligned particles. Up to now such patterns have not been observed. Future work should include the exploration of comets at small and possibly very small phase angles and a detailed comparison of polarization and colour images of comets with thermal images and with models based on mechanical theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

Polarization of Light Scattered by Solar System Bodies and the Aggregate Model of Dust Particles

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 m. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.     

Estimates of the size of the particles in the rings of saturn and their cosmogonic implications

Very low values of the radio brightness temperature of the rings of Saturn indicate that their high refar reflectivity is not simply due to a gain effect in the backscattering direction. These two sets of observations are consistent with the ring particles having a very high single scattering albedo at radio wavelenghts, with multiple scattering effects being important. Comparison of scattering calculations for ice and silicate particles with the radio and radar observations imply a mean particle radius of ～1 cm. The ice bands observed in the rings' near-infrared reflectivity spectra are formed by scattering within a microstructure on the surface of the ring particles, with the scattering centers being 25–125 μm in size. The Poynting-Robertson effect has caused a significant spiraling-in of the ring particles, probably resulting in a broadening of the rings. The inferred mean size is consistent with a model in which meteoroid impacts have caused a substantial reduction in the mean particle size from its initial value.     

Multispectral polarimetry as a tool to investigate texture and chemistry of lunar regolith particles

We report results of telescope polarimetric imaging of the Moon with a CCD LineScan Camera at large phase angles, near 88°. This allows measurements of the polarization degree with an absolute accuracy better than 0.3% and detection of features with polarization contrast as small as 0.1%. The measurements are carried out in two spectral bands centered near 0.65 and 0.42 μm. We suggest characterizing the lunar regolith with the parameter a(Pmax)A, where Pmax,A, and a are the degree of maximum polarization, albedo, and the parameter describing the linear regression of the correlation Pmax-A. The parameter bears significant information on the particle characteristic size and packing density of the lunar regolith. We also suggest characterizing the lunar regolith with color-ratio images obtained with a polarization filter at large phase angles. We here consider the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm). Using light scattering model calculations we show that the color-ratio images obtained with a polarization filter at large phase angles suggest a new tool to study the lunar surface. In particular, it turns out that the color-ratios C||(0.65/0.42 μm) and C_⊥(0.65/0.42 μm) are sensitive to somewhat different thicknesses of the surfaces of regolith particles. We consider the applicability of the Hubble Space Telescope, the Very Large Telescope (ESO), and a spacecraft on a lunar polar orbit for polarimetric observations of the lunar surface.     

Positive branch of asteroid polarization: Observational data and computer modeling

Observations of near-Earth asteroids at large phase angles made it possible to obtain a more complete (for ground-based observations) phase dependence of the polarization of the E-type asteroids’ radiation including the maximum of the positive branch of the linear polarization degree. It is shown that the position of the polarization maximum of high-albedo asteroids is noticeably shifted to the decrease of phase angles compared with S-type asteroids. Model calculations of polarimetric properties of random Gaussian particles that simulate dust particles on the regolith surface are carried out. Model calculations show a qualitatively similar behavior pattern of parameters of the positive polarization branch. The influence of the refractive index of individual scattering particles on the size and position of the maximum of the positive branch of the linear polarization degree is investigated within the considered model.     

Observations and interpretation of moving type IV solar radio bursts

Properties of 23 moving type IV bursts observed with the Culgoora Radioheliograph are summarized. Both shock and plasmoid models are examined. It is found that the theories invoking shocks have limited application and that plasmoid models have several problems with regard to plasmoid formation as well as with explanations for multiple sources and large values of circular polarization. While the synchrotron radiation mechanism is the most widely accepted for both shock and plasmoid models, it is possible that Langmuir wave emission processes may be important, at least in some events. To overcome some of the difficulties of the plasmoid theory, a new source model is proposed. This model involves synchrotron radiation from electror ; confined by rapid scattering through hydromagnetic wave particle interactions.Operated by the Association of Universities for Research in Astronomy, Inc. under contract AST-74-04129 with the National Science Foundation.