Interaction of particles in the near field and opposition effects in regolith-like surfaces

The explanation of the opposition effects observed in brightness and polarization in different celestial bodies and laboratory samples is still far from being complete. The shadow hiding and coherent backscattering mechanisms are mentioned most frequently in this connection. In the present work, we consider one more scattering mechanism—the interaction of particles in the near field—and its influence on the brightness and polarization of light scattered by ensembles of particles at small phase angles. First, we analyze two manifestations of this mechanism: the field inhomogeneity in the vicinity of the scatterers and the shielding of particles by each other at distances compared with their sizes. Then, we use the model regolith described as an ensemble of clusters as constituents and compare the contributions of the coherent backscattering and the near-field effect to the intensity and polarization of light when the porosity of the ensemble is varied. The modeling confirms that the phase dependences of the intensity and polarization of light scattered by complex structures in the backscattering domain is mainly caused by these two mechanisms. The coherent backscattering works more effectively in sparse media, while the near-field effect manifests itself in more compact ensembles of wavelength-sized particles. However, it is difficult to distinguish quantitatively their contributions, even in models of simple structures. A number of observations, especially of moderate- and low-albedo objects, can be explained only by invoking the near-field effect.     

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.     

Coherent backscattering and opposition effects observed in some atmosphereless bodies of the solar system

The results of photometric and polarimetric observations carried out for some bright atmosphere-less bodies of the Solar system near the zero phase angle reveal the simultaneous existence of two spectacular optical phenomena, the so-called brightness and polarization opposition effects. In a number of studies, these phenomena were explained by the influence of coherent backscattering. However, in general, the interference concept of coherent backscattering can be used only in the case where the particles are in the far-field zones of each other, i.e., when the scattering medium is rather rarefied. Because of this, it is important to prove rigorously and to demonstrate that the coherent backscattering effect may also exist in densely packed scattering media like regolith surface layers of celestial bodies. From the results of the computer modeling performed with the use of numerically exact solutions of the macroscopic Maxwell equations for discrete random media with different packing densities of particles, we studied the origin and evolution of all the opposition phenomena predicted by the coherent backscattering theory for low-packing-density media. It has been shown that the predictions of this theory remain valid for rather high packing densities of particles that are typical, in particular, of regolith surfaces of the Solar system bodies. The results allow us to conclude that both opposition effects observed simultaneously in some high-albedo atmosphereless bodies of the Solar system are caused precisely by coherent backscattering of solar light in the regolith layers composed of microscopic particles.     

Ocean Worlds in the Outer Regions of the Solar System (Review)

There is an astonishing variety of celestial bodies in the outer regions of the Solar System: Europa, with its bizarre surface features, Enceladus, small but geologically active, Titan, the only moon with a significant atmosphere, Pluto, with its nitrogen glaciers, and many others. Over the past 25 years, measurements from spacecraft have shown that many of these celestial bodies are ocean worlds with large volumes of liquid water trapped under icy surfaces. This new group of celestial bodies, ocean worlds, is important for research for several reasons, but the most convincing and at the same time the simplest reason is that they can be potential habitats. Life, as we know it, requires liquid water in addition to energy, nutrients, and a sustainable environment. All these requirements can be met for some of these celestial bodies. The moons of the giant planets on which the presence of the subsurface ocean is established (Europa, Ganymede, Titan, and Enceladus) and their astrobiological potential are discussed.     

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.     

Characteristics of Light Scattering at Small Phase Angles by Surfaces Consisting of Spherical Particles

We present the results of measurements of the phase dependences of brightness and of the polarization and depolarization characteristics for surfaces consisting of spherical glass particles in the phase-angle range from 0.1° to 5.0°. The measurements are performed using the laboratory photometer/polarimeter of Kharkov Astronomical Observatory and the photometer of Jet Propulsion Laboratory. An optically thick layer of transparent-glass spheres with mean size of about 57 m and refractive index of 1.44 exhibits a strong opposition effect due to single scattering. The contribution of interparticle scattering is nearly independent of the phase angle. At an angle of 0.4°, the spheres exhibit a glory ring that manifests itself in the phase behavior of all characteristics investigated. Small details are seen on the curves when a monochromatic radiation source is used for measurements. Their occurrence is confirmed by calculations based on the Mie theory. The unusual behavior of the phase dependences of reflectivity, degree of polarization, and color index for layers composed of spherical particles can be used to search for sites of possible deposits of spherical glass (or ice) particles in regoliths of atmosphereless celestial bodies.     

The Opposition Effect and Negative Polarization of Structural Analogs for Planetary Regoliths

To better understand the negative polarization and brightness opposition effects observed on airless celestial bodies, we carried out simultaneous photometric and polarimetric measurements of laboratory samples that simulate the structure of planetary regoliths. Computer modeling of shadow-hiding and coherent backscatter in regolith-like media are also presented. The laboratory investigations were carried out with a photometer/polarimeter at phase angles covering 0.2°-4° and wavelengths of 0.63 and 0.45 μm. We studied samples that characterize a variety of microscopic structures and albedos. A particle-size dependence of the negative branch of polarization for powdered dielectric surfaces was found. Colored samples such as a powder Fe₂O₃ exhibit a very prominent wavelength dependence of the photometric and polarimetric opposition phenomena. Metallic powders usually exhibit a wide branch of the negative polarization independent of the size of particles. For fine dielectric powders, both opposition phenomena become more prominent when the samples were compressed. Our computer modeling based on ray tracing in particulate media shows that shadow-hiding affects the negative polarization only in combination with the coherent backscatter enhancement. Modeling reveals that scattering orders higher than second contribute to negative polarization even in dark particulate surfaces. Our model qualitatively reproduces the effects of varying sample-compression that we observed in the laboratory. Our experimental and computer modeling studies mutually confirm that the degree of polarization for highly reflective dielectric surfaces depends not only on phase angle but also on surface tilt. Even at exactly zero phase the degree of polarization for tilted surfaces can be nonzero. A tilt of the surface normal to the scattering plane gives a parallel shift of the negative polarization branch to large values of |P|. The tilt in the perpendicular plane gives the same shift in the direction of positive polarization. At exactly zero phase angle, a celestial body of irregular shape can exhibit nonzero polarization even in integral polarimetric observations.     

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.     

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.     

Regolith Surface Reflectance: A New Attempt to Model

The reflectance coefficient of the regolith layer of celestial bodies has been studied in relation to the physical properties of regolith particles (size, refractive index, and packing density) on the basis of an accurate numerical radiative-transfer algorithm for a semi-infinite flat layer. Using the geometric-optics approximation, we have found that a shape mixture of randomly oriented spheroids can successfully model the single-scattering phase function of independent soil grains. In order to take into account the effect of packing density in a regolith layer, the concept of the so-called static structure factor was used. The main effect of increasing packing density is to suppress the forward-scattering peak of the phase function and to increase the albedo of the reflecting surface. We also investigated the influence of fine dust on the reflected light. An addition of small particles not only increases the surface albedo, but also changes the brightness profile and enhances the backscattering. Although the problem of unique solution, which is inherent in the retrieval of the properties of a medium from the measurements of the intensity of light scattered by this media, cannot be removed in the proposed model, the procedure used here, in contrast to widely used approximations, allows us to fit observational data with a set of real characteristics of the regolith. Semiempirical approaches are able to fit the measurements well with a small number of free parameters, but they do not explicitly contain crucial physical characteristics of the regolith such as grain sizes or the refractive index. We compared the numerical solution of the radiative-transfer equation with the Hapke approximation, which is most often used by investigators. The errors introduced by the Hapke model are small only for near-isotropic scattering by isolated particles. However, independent regolith grains are known to scatter light mainly in the forward direction.     

Arecibo radar observations of Rhea, Dione, Tethys, and Enceladus

We have measured the bulk radar reflectance properties of the mid-size saturnian satellites Rhea, Dione, Tethys, and Enceladus with the Arecibo Observatory's 13 cm wavelength radar system during the 2004 through 2007 oppositions of the Saturn system. Comparing to the better studied icy Galilean satellites, we find that the total reflectivities of Rhea and Tethys are most similar to Ganymede while Dione is most similar to Callisto. Enceladus' reflectivity falls between those of Ganymede and Europa. The mean circular polarization ratios of the saturnian satellites range from ∼0.8 to 1.2, and are on average lower than those of the icy Galilean satellites at this wavelength although still larger than expected for single reflections off the surface. The ratio for the trailing hemisphere of Enceladus may be the exception with a value ?0.56. The 13 cm wavelength radar albedos and polarization ratios may be systematically lower than similar results from the Cassini orbiter's RADAR instrument at 2.2 cm wavelength [Ostro, S.J., and 19 colleagues, 2006. Icarus 183, 479-490]. Overall, these reflectivities and polarization properties, together with the shapes of the echo spectra, suggest subsurface multiple scattering to be the dominant reflection mechanism although operating less efficiently than on the large icy moons of Jupiter. All these saturnian moons and icy jovian moons are atmosphere-less, low temperature water ice surfaces, and any differences in radar properties may be indicative of differences in composition or the effects of various processes that modify the regolith structure. The degree of variation in radar properties with wavelength on each satellite may constrain the thickness and efficiency of the scattering layer.     

Laboratory Studies of Icy Regoliths in Relation to Observations of Minor Bodies in the Outer Solar System

Observing the properties of solar lightscattered by TNOs is (up to now) the only way to obtain information on the physical properties of their surfaces. As such observations, performed near backscattering, become available, it is important to stress the significance of the phase angle and wavelength dependences of the linear polarization of the scattered light. At small phase angles, a narrow spike in brightness and a significantly negative polarization could be typical of icy regoliths, actually expected to be formed by alteration of icy bodies surfaces. Accurate experimental simulations of icyaggregates and regoliths formation that should take place with the ICAPS facility on board the ISS are presented, with emphasis on light scattering measurements providing a link between remote observations of TNOs and physical properties of their surfaces.     

The Structure of the Surface of Mercury's Regolith from Remote Sensing Data

Long experience of ground-based and cosmic studies of the Moon has shown that space-weathering processes play a key role in the formation of the surface layers of atmosphereless bodies. Undoubtedly, the surface of Mercury, which is subjected to the same processes, is covered by a mantle of shattered rocks—the regolith. The structure of the reflecting layer determines the photometric and polarization characteristics of the surface of a planetary body. Despite the general similarity of the integral optical properties of the surfaces of Mercury and the Moon, specific characteristics of the media of these celestial bodies manifest themselves as certain differences in the details of the measured parameters. Moreover, the similarity to the Moon permits in-depth interpretation of the results of remote observations of Mercury, such as integral polarimetry and integral spectropolarimetry. The data obtained suggest that the general structure of the surface layer of the Mercurian regolith is very similar to the structure of the lunar soil, although it is somewhat smoother and probably has a greater amount of the fine-grained fraction. The soil maturity matches the content of about 80% of the secondary particles. At the same time, the exposure age of the soil, which has the same degree of maturity, is less than the age of the soil formed under lunar conditions.     

Saturn's icy satellites: Thermal and structural models

Thermal histories of the small icy Saturnian satellites Mimas, Tethys, Dione, Rhea, and Iapetus are constructed by assuming that they formed as homogeneous ice-silicate mixtures. The models include effects of radiogenic and accretional heating, conductive and subsolidus convective heat transfer, and lithospheric growth. Accretional heating is unlikely to have melted the water ice in the interiors of these bodies and solid state creep of the predominately ice material precludes melting by radiogenic heating. Mimas is so small that its thermal evolution is essentially purely conductive; at present it is a cold, nearly isothermal body. Any subsolidus convection or thermal activity in Mimas would have been confined to a brief period in its early history and would have been due to a warm formation. The four largest satellites are big enough and contain sufficient heat-producing silicates that solid state convection beneath a rigid lithosphere is inevitable independent of initial conditions. Dione and Rhea have convective interiors for most of their thermal histories, while Tethys and Iapetus have mainly conductive thermal histories with early periods of convective 0activity. The thermal histories of the five satellites for the last 4 by are independent of initial conditions; at present they have cold, conductive interiors. The model thermal histories are qualitatively consistent with the appearances of these satellites: Mimas has an ancient heavily cratered surface, Tethys and probably Iapetus have both heavily cratered and more lightly cratered areas, and Dione and Rhea have extensively modified surfaces. Because of their similar sizes and densities, Mimas and Enceladus are expected to have similar surfaces and thermal histories, but instead Enceladus has the most modified surface of all the small icy Saturnian satellites. Our results suggest a heat source for Enceladus, in addition to radiogenic and accretional heating; tidal dissipation is a possibility. Because the water ice in these bodies does not melt, resurfacing must be accomplished by the melting of a low-melting-temperature minor component such as ammonia hydrate.     

Prospects for Estimating the Properties of a Loose Surface from the Phase Profiles of Polarization and Intensity of the Scattered Light

It has been shown that the model of a scattering medium composed of clusters located in the far zones of each other allows some properties of regolith-like surfaces to be quantitatively estimated from the phase dependences of intensity and polarization measured in the backscattering domain. From the polarization profiles, the sizes of particles, the structure and porosity of the medium, and a portion of the surface area covered with a disperse material can be determined. At the same time, the intensity profiles of the scattered light weakly depend on the sizes and structure of particles; they are mainly controlled by the concentration of scatterers in the medium and the shadow-hiding contribution at small phase angles. Since the latter effect is beyond the considered model, a good agreement between the model and the measured intensity cannot be achieved. Nevertheless, if a portion of the surface that participates in coherent backscattering has been found from the phase profile of polarization, the present model makes it possible to determine the relative contribution of the shadow-hiding effect to the brightness surge measured at zero phase angle. This, in turn, may allow the roughness of the scattering surface to be estimated. The model contains no free parameters, but there is currently no possibility to verify it comprehensively by the data obtained in laboratory measurements of the samples with thoroughly controlled characteristics, because such measurements are rare for a wide range of the properties of particles in a medium, their packing density, and phase angles.

     

Search for and limits on plume activity on Mimas, Tethys, and Dione with the Cassini Visual Infrared Mapping Spectrometer (VIMS)

Cassini Visual Infrared Mapping Spectrometer (VIMS) observations of Mimas, Tethys, and Dione obtained during the nominal and extended missions at large solar phase angles were analyzed to search for plume activity. No forward scattered peaks in the solar phase curves of these satellites were detected. The upper limit on water vapor production for Mimas and Tethys is one order of magnitude less than the production for Enceladus. For Dione, the upper limit is two orders of magnitude less, suggesting this world is as inert as Rhea (Pitman, K.M., Buratti, B.J., Mosher, J.A., Bauer, J.M., Momary, T., Brown, R.H., Nicholson, P.D., Hedman, M.M. [2008]. Astrophys. J. Lett. 680, L65-L68). Although the plumes are best seen at ∼2.0 μm, Imaging Science Subsystem (ISS) Narrow Angle Camera images obtained at the same time as the VIMS data were also inspected for these features. None of the Cassini ISS images shows evidence for plumes. The absence of evidence for any Enceladus-like plumes on the medium-sized saturnian satellites cannot absolutely rule out current geologic activity. The activity may below our threshold of detection, or it may be occurring but not captured on the handful of observations at large solar phase angles obtained for each moon. Many VIMS and ISS images of Enceladus at large solar phase angles, for example, do not contain plumes, as the active “tiger stripes” in the south pole region are pointed away from the spacecraft at these times. The 7-year Cassini Solstice Mission is scheduled to gather additional measurements at large solar phase angles that are capable of revealing activity on the saturnian moons.     

Plasma, plumes and rings: Saturn system dynamics as recorded in global color patterns on its midsize icy satellites

New global maps of the five inner midsize icy saturnian satellites, Mimas, Enceladus, Tethys, Dione, and Rhea, have been constructed in three colors (UV, Green and near-IR) at resolutions of 1 km/pixel. The maps reveal prominent global patterns common to several of these satellites but also three major color features unique to specific satellites or satellite subgroups. The most common features among the group are first-order global asymmetries in color properties. This pattern, expressed on Tethys, Dione and Rhea, takes the form of a ∼1.4-1.8 times enhancement in redness (expressed as IR/UV ratio) of the surface at the center of the trailing hemisphere of motion, and a similar though significantly weaker IR/UV enhancement at the center of the leading hemisphere. The peak in redness on the trailing hemisphere also corresponds to a known decrease in albedo. These double hemispheric asymmetries are attributable to plasma and E-ring grain bombardment on the trailing and leading hemispheres, respectively, for the outer three satellites Tethys, Dione and Rhea, whereas as E-ring bombardment may be focused on the trailing hemisphere of Mimas due to its orbital location interior to Enceladus. The maps also reveal three major deviations from these basic global patterns. We observe the previously known dark bluish leading hemisphere equatorial band on Tethys but have also discovered a similar band on Mimas. Similar in shape, both features match the surface patterns expected for irradiation of the surface by incident MeV electrons that drift in a direction opposite to the plasma flow. The global asymmetry on Enceladus is offset ∼40° to the west compared to the other satellites. We do not consider Enceladus in detail here, but the global distribution of bluish material can be shown to match the deposition pattern predicted for plume fallback onto the surface (Kempf, S., Beckmann, U., Schmidt, S. [2010]. Icarus 206, 446-457. doi:10.1016/j.icarus.2009.09.016). E-ring deposition on Enceladus thus appears to mask or prevent the formation of the lenses and hemispheric asymmetries we see on the other satellites. Finally, we observe a chain of discrete bluish splotches along the equator of Rhea. Unlike the equatorial bands of Tethys and Mimas, these splotches form a very narrow great circle ?10-km wide (north-to-south) and appear to be related to surface disruption, exposing fresh, bluish ice on older crater rims. This feature is unique to Rhea and may have formed by impact onto its surface of orbiting material.     

Optical reflectance polarimetry of Saturn's globe and rings: IV. Aerosols in the upper atmosphere of Saturn

From 1958 to 1976 the degree and direction of polarization of the light at Saturn's disk center were measured in orange light over 74 nights and at five wavelenghts over 19 nights. Measurements were also recorded at limb, terminator, and pole. In addition, extensive regional polarization measurements were collected over Saturn's disk and several polarization maps were produced. These data were analyzed on the basis Mie scattering theory and of transfer theory in planetary atmospheres. A model of the Saturn upper atmosphere aerosol structure is derived in which the top part of the the main cloud layer is composed of spherical transparent particles of radius 1.4 μm and refractive index 1.44. Above this layer, a fine haze of submicron-sized grains was detected by its production of a component of polarization which is always directed poleward; this upper haze is interpreted as having nonspherical particles which are systematically oriented. This upper haze layer covers approximately the whole planet uniformly but varies in thickness from year to year. The clear gas above the cloud layer has an optical thickness of around 0.1.     

Light scattering by morphologically complex objects and opposition effects (a review)

Over the last decade, considerable progress has been achieved in the theory of light scattering by morphologically complex objects, which extends the potential of correct interpretation of photometric and polarimetric observations. This especially concerns the backscattering domain, where the opposition effects in brightness and polarization are observed. Although the equations of radiative transfer and weak localization (coherent backscattering) are rigorously valid only for sparse media, the results of exact computer solutions of the Maxwell equations for a macroscopic volume filled with randomly positioned particles show that their application area can be wider. In particular, the observations can be correctly interpreted if the packing density of particles in the medium reaches 20–30%. The recently suggested approximate solution of the coherent backscattering problem allowed interesting effects in the spectra of Saturn’s satellites to be explained. In the densely packed media, the effects that are impossible in the sparse media and caused by the near-field contribution can be observed. To calculate the characteristics of radiation reflected by such a medium, it is not sufficient to solve the radiative transfer and weak localization equations, even if they are written in a form without the far-zone limitations. Nowadays, the influence of the interaction of particles in the near field can be analyzed only for the restricted ensembles of particles. It shows that the substantial increase of the packing density essentially changes the phase functions of intensity and polarization in the backscattering domain. This allows the packing density of particles in the medium and their absorbing properties to be estimated from the shape of the phase curves measured. However, the task of quantitative interpretation of the measurements of radiation reflected by a densely packed medium, in terms of sizes of particles, their refractive index, and packing density, still remains unsolved.     

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.