Light Scattering by Aggregate Particles Comparable in Size to Wavelength: Application to Cometary Dust

Many naturally occurring particles (including, most likely, cometary dust) have an aggregate structure. We study the scattering properties of polydisperse independent aggregate particles (clusters) comparable in size to visible wavelengths. The sizes of the monomers constituting a cluster play a significant role in forming the angular dependences of intensity and linear polarization of the scattered light. Irregularly structured aggregates composed of a moderate number of spheres (<50) with size parameters 1.3–1.65 exhibit properties typical of cometary dust particles: a slight increase in backscattering intensity, a negative polarization at small phase angles, an inversion phase angle close to the observed one, an increase in brightness, and a linear polarization with increasing wavelength. In this case, the imaginary part of the refractive index for particles can increase with decreasing wavelength in the visible spectral range, which is typical of silicates with an admixture of iron or organic material. The spectral dependence of extinction efficiency for aggregates is less steep than that for equivalent spherical particles, and its maximum is shifted to larger size parameters. Therefore, when analyzing extinction measurements, the scatterer shape must be taken into account to avoid underestimation of the scattering-particle sizes.     

Theoretical polarimetric responses of fractal aggregates,in relation with experimental studies of dust in the solar system

Dust particles in the solar system (e.g. atmospheric hazes, cometary or interplanetary dust, regolith) are likely to be irregular aggregates whose light scattering properties (phase functions of polarization) are drastically different from those of Mie spheres. However, the observation of the light they scatter may provide informations on their physical properties. If the mechanisms which lead to aggregation are invariant with time, the aggregates are likely to be fractal particles made up from individual monomers. Computations, developped in relation with the CODAG experiment, are performed using a Discrete Dipole Approximation, and each monomer is described by one or more dipoles. When the particles are formed from a few monomers made up of numerous dipoles, the polarimetric response of the aggregate is similar to the one of the constituent monomer. When the particles are formed from many monomers made up of individual dipoles, the phase curves are similar to those observed in the solar system. Our calculations suggest that dust particles have a fractal dimension of the order of 2 (Ballistic Cluster-Cluster Aggregation), and that the values of the real and imaginary part of the complex refractive index of the constituent material are high. Those results are in agreement with laboratory measurements on samples representative of astronomical organics and minerals.     

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.     

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.     

Polarization of Light Scattered by Fluffy Particles (PROGRA Experiment)

This work was carried out with the PROGRA² experiment developed to measure the angular dependence of the polarization of light scattered by dust particles. The dust samples are fluffy aggregates (size range 0.01-1 mm) with constituent grains of about 10 nm. Various setups were used: samples deposited on surfaces, the same samples lifted under the effect of a draft, and particles levitating in microgravity conditions on board the CNES dedicated aircraft. For deposited particles, the maximum value of polarization (P_max) follows the Umov law. For a cloud of particles (P_max) near 100° phase angle decreases when: (i) multiple scattering between the particles—or between the grains inside the particles—increases, or (ii) the real part of the refractive index of the materials increases, or (iii) the size parameter of the constituent grains increases between 0.05 and 0.5. A negative branch in the polarization phase curve is found for deposited samples. For levitating particles made of a single material and a single size distribution, a positive increase of polarization appears at phase angles smaller than 20°; for mixtures of these materials the polarization is negative at the same phase angles. These results are compared to modeling results as well as to polarimetric observations of comets.     

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.     

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster owing to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z ∼0.5–3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, ∼0.1( τ /0.02) μK in the Rayleigh–Jeans part of the CMB spectrum ( τ being the Thomson optical depth across the cluster). This value exceeds the polarization introduced by the cluster transverse peculiar motion if v _t<1300 km s⁻¹. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of ( v _t c )² τ , ( v _t c ) τ ² and ( kT _e m _e c ²) τ ², as well as the polarization owing to the CMB quadrupole, were previously given by Sunyaev and Zel'dovich for the Rayleigh–Jeans part of the spectrum. We fully confirm their earlier results and present exact frequency dependences for all these effects. The polarization degree is considerably higher in the Wien region.     

Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.     

Cometary dust properties retrieved from polarization observations: Application to C/1995 O1 Hale-Bopp and 1P/Halley

The analysis of the polarized light scattered by cometary dust particles provides information on the physical properties of the solid component of cometary comae for C/1995 O1 Hale-Bopp and 1P/Halley. A model of light scattering by a size distribution of aggregates of up to 256 submicron-sized grains (spherical or spheroidal) mixed with single spheroidal particles has been developed, with its parameters adjusted to fit the phase angle and wavelength dependence of the polarization observations. The particles are built of two materials: a non-absorbing silicates-type material and a more absorbing organic-type material. The model reproduces accurately the inversion angle and the positive branch of the polarization phase curves from the visible to the near-infrared spectral domains. A negative branch of the polarization phase curves appears in our model, although the negative branch is not deep enough to reproduce accurately the observations. Significant differences are shown between the two comets, with dominance of small grains in the coma of Comet C/1995 O1 Hale-Bopp, well fitted by a distribution of the volume-equivalent diameter, a, following a^−3.0 with a lower cutoff around 0.20 μm and an upper cutoff of at least 40 μm. For 1P/Halley, the size distribution follows a^−2.8 with a lower cutoff around 0.26 μm and an upper cutoff of about 38 μm. The relative amount of organic-type particles is larger for 1P/Halley while the amount of aggregates, significant for both comets, is larger for C/1995 O1 Hale-Bopp.     

Radiation pressure on dust aggregates in circumstellar disks

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

Galileo Photopolarimetry of Jupiter at 678.5 nm

Brightness and linear polarization measurements at 678.5 nm for four south-north strips of Jupiter are studied. These measurements were obtained in 1997 by the Galileo photopolarimeter/radiometer. The observed brightness exhibits latitudinal variations consistent with the belt/zone structure of Jupiter. The observed degree of linear polarization is small at low latitudes and increases steeply toward higher latitudes. No clear correlations were observed between the degree of linear polarization and the brightness. The observed direction of polarization changes from approximately parallel to the local scattering plane at low latitudes to perpendicular at higher latitudes. For our studies, we used atmospheric models that include a haze layer above a cloud layer. Parameterized scattering matrices were employed for the haze and cloud particles. On a pixel-wise basis, the haze optical thickness and the single-scattering albedo of the cloud particles were derived from the observed brightness and degree of linear polarization; results were accepted only if they were compatible with the observed direction of polarization. Using atmospheric parameter values obtained from Pioneer 10 and 11 photopolarimetry for the South Tropical Zone and the north component of the South Equatorial Belt, this analysis yielded acceptable results for very few pixels, particularly at small phase angles. However, for almost all pixels, acceptable results were found when the parameterized scattering matrix of the cloud particles was adjusted to produce more negative polarization for single scattering of unpolarized light, especially at large scattering angles, similar to some laboratory measurements of ammonia ice crystals. Using this adjusted model, it was found that the derived latitudinal variation of the single-scattering albedo of the cloud particles is consistent with the belt/zone structure, and that the haze optical thickness steeply increases toward higher latitudes.     

Power spectra of CMB polarization by scattering in clusters

Mapping cosmic microwave background (CMB) polarization is an essential ingredient of current cosmological research. Particularly challenging is the measurement of an extremely weak B-mode polarization that can potentially yield unique insight on inflation. Achieving this objective requires very precise measurements of the secondary polarization components on both large and small angular scales. Scattering of the CMB in galaxy clusters induces several polarization effects whose measurements can probe cluster properties. Perhaps more important are levels of the statistical polarization signals from the population of clusters. Power spectra of five of these polarization components are calculated and compared with the primary polarization spectra. These spectra peak at multipoles  ℓ≥ 3000  , and attain levels that are unlikely to appreciably contaminate the primordial polarization signals.     

Light scattering by fluffy Mg-Fe-SiO and C mixtures as cometary analogs (PROGRA experiment)

Cometary particles mainly consist of silicates and carbon compounds; they seem to be fluffy aggregates of tiny grains, as found in some IDPs. The linear polarization of the scattered light is an efficient method to characterize their physical properties. Laboratory simulations of light scattering by cometary analog particles help to disentangle different physical parameters by comparison with observational data. We present here polarization laboratory results with nine samples levitating particles: five samples of vapor-condensed magnesiosilica, one ferrosilica smoke, a mixture of magnesio-ferrosilica smokes, one mixture of ferrosilica with carbon and one mixture of magnesio-ferrosilica with carbon. The phase curves are bell-shaped with a maximum polarization at a phase range of (80°-100°). A shallow negative branch can be present at phase angles smaller than 20°. The different characteristics of the phase curves are discussed considering the size and the structure of the constituent grains and the size of the particles. For the five magnesiosilica samples, the maximum in polarization is in the 40% range (close to cometary values), and no wavelength dependence is detected; the negative branch, whose presence seems to be linked to the presence of large aggregates of fine silica (SiO₂) grains, does not always exist. For the ferrosilica smoke, the maximum in polarization is about 30% in red light (632.8 nm) and 40% in green light (543.5 nm); the negative branch occurs for phase angles smaller than 20°. For the two mixtures with carbon black, the polarization spectral gradient is positive, as expected for cometary analog particles. Finally, the phase curves obtained for agglomerates of magnesio-ferrosilica and carbon (expected to be the main components of cometary particles) are comparable to those obtained by remote observations of dust in cometary comae.     

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.     

Photometry and polarimetry of Titan: Pioneer 11 observations and their implications for aerosol properties

The preliminary measurements by Pioneer 11 of the limb darkening and polarization of Titan at red and blue wavelenghts (M. G. Tomasko, 1980,J. Geophys. Res., 85, 5937–5942) are refined and the measurements of the brightness of the integrated disk at phase angles from 22 to 96° are reduced. At 28° phase, Titan's reflectivity in blue light at southern latitudes is as much as 25% greater than that at northern latitudes, comparable to the values observed by Voyager 1 (L. A. Sromovsky et al., 1981,Nature (London), 292, 698–702). In red light the reflectivity is constant to within a few percent for latitudes between 40°S and 60°N. Titan's phase coefficient between 22 and 96° phase angle averages about 0.014 magnitudes/degree in both colors—a value considerably greater than that observed at smaller phase from the Earth. Comparisons of the data with vertically homogeneous multiple-scattering models indicate that the single-scattering phase functions of the aerosols in both colors are rather flat at scattering angles between 80 and 150° with a small peak at larger scattering (i.e., small phase) angles. The models indicate that the phase integral, q, for Titan in both red and blue light is about 1.66 ± 0.1. Together with Younkin's value for the bolometric geometric albedo scaled to a radius of 2825 km, this implies an effective temperature in equilibrium with sunlight of 84 ± 2°K, in agreement with recent thermal measurements. The single-scattering polarizations produced by the particles at 90° scattering angle are quite large, >85% in blue light and >95% in red. A vertically homogeneous model in which the particles are assumed to scatter as spheres cannot simultaneously match the polarization observations in both colors for any refractive index. However, the observed polarizations are most sensitive to the particle properties near optical depth $\text{1}\text{2}$ in each color, and so models based on single scattering by spheres can be successful over a range of refractive indices if the size of the particles increases with depth and if the cross section of the particles increases sufficiently rapidly with decreasing wavelenght. For example, with n_r = 1.70, the polarization (and the photometry) are reproduced reasonably well in both colors when the area-weighted average radous of the particles, α, is given by α = (0.117 μm)(τ_red/0.5)^0.217. While this model does not reproduce the large increase in brightness from 129 to 160° phase observed by Voyager 1, the observed increase is determined by the properties of the particles in the top few hundredths of an optical depth. Thus the addition of a very thin layer of forward-scattering aerosols on top of the above model offers one way of satisfying both the Pioneer 11 and Voyager 1 observations. Of course, other models, using bimodal size distributions or scattering by nonspherical particles, may also be capable of reproducing these data.     

ω Cen – An ultra compact dwarf galaxy?

We study the merging of star clusters out of cluster aggregates similar to Knot S in the Antennae on orbits close to the one of ω Cen by carrying out high resolution numerical N-body simulations. We want to constrain the parameter space which is able to produce merger objects with similar properties as ω Cen. This revised version was published online in August 2006 with corrections to the Cover Date.     

Long slit spectropolarimetry of Jupiter and Saturn

We present ground-based limb polarization measurements of Jupiter and Saturn consisting of full disk imaging polarimetry for the wavelength 7300 Å and spatially resolved (long-slit) spectropolarimetry covering the wavelength range 5200-9350 Å.For the polar region of Jupiter we find for λ = 6000 Å a very strong radial (perpendicular to the limb) fractional polarization with a seeing corrected maximum of about +11.5% in the South and +10.0% in the North. This indicates that the polarizing haze layer is thicker at the South pole. The polar haze layers extend down to 58° in latitude. The derived polarization values are much higher than reported in previous studies because of the better spatial resolution of our data and an appropriate consideration of the atmospheric seeing. Model calculations demonstrate that the high limb polarization can be explained by strongly polarizing (p ≈ 1.0), high albedo (ω ≈ 0.98) haze particles with a scattering asymmetry parameter of g ≈ 0.6 as expected for aggregate particles of the type described by West and Smith (West, R.A., Smith, P.H. [1991]. Icarus 90, 330-333). The deduced particle parameters are distinctively different when compared to lower latitude regions.The spectropolarimetry of Jupiter shows a decrease in the polar limb polarization towards longer wavelengths and a significantly enhanced polarization in strong methane bands when compared to the adjacent continuum. This is a natural outcome for a highly polarizing haze layer above an atmosphere where multiple scatterings are suppressed in absorption bands. For lower latitudes the fractional polarization is small, negative, and it depends only little on wavelength except for the strong CH₄-band at 8870 Å.The South pole of Saturn shows a lower polarization (p ≈ 1.0-1.5%) than the poles of Jupiter. The spectropolarimetric signal for Saturn decrease rapidly with wavelength and shows no significant enhancements in the fractional polarization in the absorption bands. These properties can be explained by a vertically extended stratospheric haze region composed of small particles <100 nm as suggested previously by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2005]. Icarus 179, 195-221).In addition we find in the V- and R-band a previously not observed strong polarization feature (p = 1.5-2.0%) near the equator of Saturn. The origin of this polarization signal is unclear but it could be related to a seasonal effect.Finally we discuss the potential of ground-based limb polarization measurements for the investigation of the scattering particles in the atmospheres of Jupiter and Saturn.     

A Monte Carlo Code to Compute Energy Fluxes in Cometary Nuclei

A Monte Carlo model designed to compute both the input and output radiation fields from spherical-shell cometary atmospheres has been developed. The code is an improved version of that by H. Salo (1988, Icarus76, 253-269); it includes the computation of the full Stokes vector and can compute both the input fluxes impinging on the nucleus surface and the output radiation. This will have specific applications for the near-nucleus photometry, polarimetry, and imaging data collection planned in the near future from space probes. After carrying out some validation tests of the code, we consider here the effects of including the full 4×4 scattering matrix in the calculations of the radiative flux impinging on cometary nuclei. As input to the code we used realistic phase matrices derived by fitting the observed behavior of the linear polarization as a function of phase angle. The observed single scattering linear polarization phase curves of comets are fairly well represented by a mixture of magnesium-rich olivine particles and small carbonaceous particles. The input matrix of the code is thus given by the phase matrix for olivine as obtained in the laboratory plus a variable scattering fraction phase matrix for absorbing carbonaceous particles. These fractions are 3.5% for Comet Halley and 6% for Comet Hale-Bopp, the comet with the highest percentage of all those observed.The errors in the total input flux impinging on the nucleus surface caused by neglecting polarization are found to be within 10% for the full range of solar zenith angles. Additional tests on the resulting linear polarization of the light emerging from cometary nuclei in near-nucleus observation conditions at a variety of coma optical thicknesses show that the polarization phase curves do not experience any significant changes for optical thicknesses τ?0.25 and Halley-like surface albedo, except near 90° phase angle.     

Optical polarimetry of Comet West 1976 VI

The polarization of the continuum of Comet West 1976 VI was measured in four narrowband filters spanning the wavelengths 440–850 nm. The postperihelion observations indicated wavelength independent linear polarization on each of the three occasions on which it was measured. The wavelength independence is in agreement with other polarization measurements of this comet from the visible to the near-infrared, but it counters the general tendency in comets for the polarization to increase with wavelength. The magnitude of the polarization as a function of scattering angle, the wavelength independence, and the infrared and optical photometric properties suggests that dirty silicates (n₁≈0.05) with radii smaller than 5 μm but approaching this size may be responsible. No circular polarization was detected.