ARTICLE IN PRESS
Planetary and Space Science 55 (2007) 1010–1020 www.elsevier.com/locate/pss
Physical properties of cometary and interplanetary dust A. Chantal Levasseur-Regourda,, T. Mukaib, J. Lasuea, Y. Okadab a
Universite´ Pierre et Marie Curie-Paris6, Ae´ronomie CNRS-IPSL, BP 3, 91371 Verrie`res, France b Graduate School of Science and Technology, Kobe University, Nada, Kobe 657-8501, Japan Accepted 22 March 2005 Available online 6 February 2007
Abstract In the absence of numerous in situ studies, physical properties of cosmic dust may be derived from observations of their light scattering and thermal properties, through numerical simulations making use of realistic assumptions. Estimations about cometary and interplanetary dust composition, structure, size, as well as about their light scattering and thermal properties, are first summarized. We then present and discuss the numerical simulations we have performed with different types of particles: core-mantle submicron-sized elongated grains (having contributed to the formation of cometary dust), fractal aggregates of such grains (found in cometary comae and in the interplanetary dust cloud), and fractal aggregates of large dust grains (found in cometary dust trails). A very satisfactory fit to the numerous polarimetric observations of comet Hale-Bopp is obtained for a mixture with about 33–60% of organics in mass, with a power law size distribution with an index of (3) and a radius of 20 mm for the upper cut-off. For the lessconstrained polarimetric observations of interplanetary dust near 1 AU, a fit is obtained for a mixture with about 40% of organics in mass, with a similar size distribution and a radius of about 50 mm for the upper cut-off. The ensemble of results obtained for the interplanetary dust strongly suggest that its light scattering and thermal properties stem from the presence of compact and fluffy particles, with compositions ranging from silicates to more absorbing materials, whose contribution decreases with decreasing distance to the Sun. r 2006 Elsevier Ltd. All rights reserved. Keywords: Aggregates particles; Cometary dust; Interplanetary dust; Light scattering; Numerical simulations; Thermal emission
1. Introduction Understanding the physical properties of dust particles in cometary comae and trails and in the interplanetary dust cloud, as well as their changes with e.g. the distances to the nucleus and to the Sun, is mandatory to assess the main processes that have shaped their evolution. A significant amount of information is provided by in situ studies and remote spectroscopic observations. The physical properties of the particles vary from one comet to another, from one region within a comet to another, and from one region within the interplanetary cloud to another. They can be characterized, through appropriate simulations (with realistic assumptions about the composition, the structure and the sizes of the particles) by studying how they scatter light, how the scattering depends upon the geometry and the Corresponding author. Tel.: +33 1 6447 4293; fax: +33 1 6929 2999.
E-mail address:
[email protected] (A.C. Levasseur-Regourd). 0032-0633/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2006.11.014
wavelength of the observations, and how they re-emit the absorbed thermal energy (see e.g. Levasseur-Regourd and Hadamcik, 2003; Kolokolova et al., 2004). 1.1. Composition and structure The composition is revealed by in situ observations, by remote infrared spectroscopy, and by laboratory analysis of samples of IDPs, i.e. interplanetary dust particles collected in the Earth atmosphere. As summarized in Hanner and Bradley (2004), cometary dust is an unequilibrated, heterogeneous mixture of high- and lowtemperature condensates. Major constituents are amorphous and crystalline silicate minerals (e.g. forsterite, enstatite) and organic refractory materials. The similarity between these properties and those of anhydrous chondritic IDPs (fine-grained and complex mixtures of numerous mineral and amorphous components) strongly suggests that comets are the source of such fragile and highly
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porous particles. IDPs actually mostly belong to the chondritic class, with either anhydrous (pyroxene, olivine) or hydrated (layer silicate) constituents, somehow matching the abundances of CI chondrites (see e.g. Brownlee, 1996; Jessberger et al., 2001). Relatively high abundances in silicates may be the result of high melting point favoring atmospheric entry. It should be added that, as compared to the IDPs (collected in the ecliptic at 1 AU, after they have suffered space weathering and atmospheric entry), the samples collected by the Stardust mission in the coma of comet 81P/Wild 2 are to provide an un-biased sample. The existence in cometary dust of crystalline olivine particles, formed in a hot (41000 K) environment, poses the problem of the trapping of minerals produced at high temperatures in comets (Brucato et al., 1999). A recent 10 mm spectroscopic survey of Herbig Ae star discs by van Boekel et al. (2005) has suggested that crystalline silicates are produced or reprocessed. In the proto-planetary disc of our solar system, the olivine particles could have been generated in the hot region near the proto-Sun, and transported to the cold region of formation of comets. Some comets actually show a silicate emission feature near 10 mm, while other ones do not have such a feature. In addition, comets exhibiting this emission feature may show a double peak, implying the existence of crystalline silicates, or a single broad peak, suggesting the existence of amorphous silicate (see e.g. Honda et al., 2004). The relationships between silicate band strength and structure among comet families are discussed in Sitko et al. (2004). It should be added that recent extensive infrared spectroscopy of comets from Spitzer (Woodward et al., 2005) should provide evidence for the mineralogy of dust grains in comets. Cometary dust particles are likely to have low densities—about 100 kg m3 for comet 1P/Halley (Fulle et al., 2000)—and to consist of easily fragmenting aggregates (see e.g. Desvoivres et al., 2000; Clark et al., 2004). Together with the D/H enrichment noticed in an IDP (Keller et al., 2000) and with laboratory experiments on ballistic agglomeration (Blum et al., 2000), such results are in excellent agreement with the hypothesis developed by Greenberg (1982): cometary dust particles could be ‘‘birdnest’’, i.e. porous aggregates of partly photo-chemically processed submicronic interstellar elongated dust grains, with possibly silicates cores and organics mantles. 1.2. Sizes distributions and cut-offs Dust ejected by comets spans a broad size range, from sub-micrometer to millimetre or larger. From measurements of Giotto spacecraft at comet Halley, most of the mass is concentrated in large particles, while submicron and micron-sized particles dominate the extinction and scattering properties of comets in the visual to near infrared wavelength range. The sizes certainly vary from comet to comet, as well as within the coma, because of dynamical effects, evaporation and fragmentation (see e.g.
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Kolokolova et al., 2004). As far as interplanetary dust is concerned, although a similar wide size range has been derived from lunar microcraters measurements, physical processes occurring within the dust cloud, i.e. sublimation, collisions, sputtering and charging, may induce significant changes with changing solar distances and inclinations of the particles (see e.g. Mukai et al., 2001). Size distributions are mostly derived from space probes data, obtained during a cometary coma flyby or a cruise through the interplanetary dust cloud. They are usually described with (as) power laws, where a is the effective radius of the particle, and s the power law index. An index of (2.670.2) has been derived for 1P/Halley (Fulle et al., 2000), from a fit with a dust dynamical model of the local brightness and dust flux data on board Giotto (LevasseurRegourd et al., 1999). More recently, a cumulative mass distribution has been obtained for comet 81P/Wild 2 from the dust flux monitor on board Stardust (Green et al., 2004), leading to an index of (3.171.2). It may be noticed that such power laws are not too different from the canonical (a3) law, expected for grain–grain collision shattering (Hellyer, 1970). Finally, for the interplanetary dust cloud, lunar micro-craters analyses and measurements by in situ space probes suggest indices of about 3.5 for very small particles (radius below approximately 0.1 mm), 2.3 for medium sized particles, and 4.4 for particles with a radius of about 10 mm and above (Gru¨n et al., 2001). The existence of silicon nanoparticles, introduced as one hypothesis to explain the extended red emission (ERE) within the 540–950 nm spectral range in dust-rich objects, is questioned today, since many other hypotheses do exist to explain it (see e.g. Witt et al., 2006). The presence of such nanoparticles, predicted in solar coronal holes (Habbal et al., 2003) from polarization measurements in the Fe XIII line at 1074.7 nm obtained during a total solar eclipse, has been rejected for the solar corona from spectroscopic coronal observations around 1074.7 nm, which did not provided indication of any emission due to their fluorescence (Singh et al. 2004), and from theoretical studies of their sublimation sequence in the vicinity of the Sun (Mann and Murad, 2005). The presence of large particles in comets had been suspected from the observation of antitails pointing towards the Sun, under particular viewing geometries. It is now recognized that comets supply a huge amount of large (above millimetre sized) particles, based on the observations of comet trails (Ishiguro et al., 2003; Reach, 2005). The sizes have been estimated from the fact that the observed trails show good fits with syndyne curves for particles with a b-value of about 104, where b is the ratio of solar radiation pressure to solar gravity on the particle. The next paragraph summarizes the available observations and the approaches previously developed to interpret scattered light and thermal emission observations. The last two paragraphs present new numerical simulations, making use, not only of spheroidal core-mantle particles, but also of porous aggregates of small grains (silicates and
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organics), and of big aggregates of large grains (crystalline silicate and amorphous carbon). The simulations allow us to derive specific results about the physical properties of dust in comets and in the interplanetary dust cloud. 2. Available observations and models 2.1. Light scattering observations
a observer α
Sun
Scattering plane
b
Scattering plane Dust particles along line-of-sight R Sun
20
10
0
The solar light scattered by optically thin media is linearly polarized, with the electromagnetic wave predominantly oscillating perpendicular or parallel to the scattering plane (Fig. 1a). The linear polarization of the scattered light, thereafter called polarization, is a ratio (theoretically comprised between 1 and 1), which only depends upon the phase angle a, the wavelength and the physical properties of the dust particles. To obtain significant results on cometary dust, it is necessary to avoid contamination by the gaseous emissions and thus to perform observations through narrow filters. Significant results about interplanetary dust polarization are even more difficult to obtain: since observations correspond to solar light scattered all along the line-of-sight over a wide range of phase angles (from the observer to the outer solar system, see Fig. 1b), local information is derived if and only if an inversion is possible. Fig. 2 (updated from Levasseur-Regourd and Hadamcik, 2003) presents the data obtained through narrow-band red filters for various comets and averaged on the projected coma. The cometary polarization versus phase angle dependence is characterized by smooth phase curves, with a shallow negative branch in the backscattering region, an inversion near 201, an almost linear increase in the 20–601 range, and a near 90–1001 maximum (in the 15–30% range). Polarization at a given phase angle (within the 20–901 range) usually increases with the wavelength (at
Dust particle
Red filter
30 Polarization (%)
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α observer
Ecliptic plane
Fig. 1. Geometry of the observations of solar light scattered by dust in the solar system. (a) general case; (b) interplanetary dust.
0
20
40
60
80
100
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Phase angle (˚)
Fig. 2. Linear polarization (through narrow-band red filters, averaged on the projected coma) versus phase angle for various comets, including C/1999 O1 Hale-Bopp (from Levasseur-Regourd and Hadamcik, 2003).
least in the visible to near-infrared domain and outside the innermost coma). This trend, first noticed for 1P/Halley (Dollfus et al., 1988), has been extensively documented for C/1999 O1 Hale-Bopp, the polarization of which was the highest ever observed (Levasseur-Regourd, 1999; Kolokolova et al., 2004). It should be added that the polarization at a given phase angle and for a given wavelength is not constant all over the coma, due to temporal evolution (e.g. by fragmentation, evaporation) in the physical properties of the dust particles ejected by the nucleus (Levasseur-Regourd et al., 1999; Furusho et al., 1999; Hadamcik and Levasseur-Regourd, 2003). The local polarization of interplanetary dust, as obtained through inversion techniques (see e.g. Dumont and Levasseur-Regourd, 1988; Lumme, 2000; LevasseurRegourd et al., 2001), is also characterized by a smooth phase curve, with an inversion angle possibly by 151, and a near 901 maximum of about 30% near 1 AU in the near-ecliptic symmetry surface of the cloud. From data currently available, it is impossible to draw any definitive conclusion about the wavelength dependence of the local polarization. However, the variation with solar distance of the local polarization at 901 is also derived; it decreases with decreasing solar distance R, approximately with a (R+0.570.1) power law, indicating changes in the physical properties of the dust particles. Such changes might result from e.g. sublimation and sputtering of the particles, while their orbits evolve under dissipative forces. The above-mentioned smooth polarimetric phase curves confirm that cometary and interplanetary dust mostly consist of irregular particles and aggregates, with a size greater than or equal to the observational wavelength. 2.2. Light scattering numerical simulations for individual grains Numerical simulations have been developed for interstellar grains, assuming them to have various compositions (see e.g. Mathis et al., 1977). Results of simulations with
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cylinders or spheroids, with a silicate core coated by an organic refractory mantle and an elongation of about 2, are in good agreement with the observed interstellar polarization and extinction (Li and Greenberg, 1997). Simulations have also been developed for cometary and interplanetary dust particles. Shortly after 1P/Halley flybys, Mukai et al. (1987) have succeeded to fit the polarimetric observations (retrieved up to about 651 phase angle, in the visible and near-infrared domains) by applying Mie calculations to spheres with a size distribution spectrum estimated from the Vega spacecraft data. The derived complex refractive index (m ¼ 1.385+0.035i at 620 nm) was found to slightly decrease with the wavelength for the real part and to increase with it for the imaginary part, as could be expected for a mixture of ices, silicates and organics. Since the cometary and interplanetary dust particles have no reason to be spherical, attempts have also been made to develop numerical simulations for spheroids, polyhedral solids and stochastically rough convex or concave particles (see e.g. Lumme, 2000). 2.3. Light scattering numerical simulations for aggregates Fractal aggregates of grains (Meakin, 1983) are more likely to reproduce the porosity and mechanisms of aggregation of cometary dust particles in the proto-solar nebula. Numerical simulations of the scattering properties of cometary dust aggregates have been initiated in the late 1990s, making use of the Discrete Dipole Approximation (DDA) code developed by Draine and Flatau (2000). Results, for aggregates of 512 grains (small enough to be individual dipoles) and for the above-mentioned complex refractive index from Mukai et al. (1987), have suggested that the observational polarimetric phase curves could be obtained for aggregates with a fractal dimension of about 2 (Levasseur-Regourd et al., 1997). Increasing the real part of the index would decrease the maximum, while increasing the imaginary part would induce a trend towards a negative polarization (Haudebourg et al., 1999). With aggregates of up to 27,000 grains (also represented by dipoles), Nakamura and Okamoto (1999) have reproduced the shallow negative branch typical of the near backscattering polarization. Some simulations have also been developed with aggregates of spheres, tetrahedra, cubes, cylinders and parallelepipeds (Xing and Hanner, 1997; Yanamandra-Fisher and Hanner, 1999). Simulations with aggregates of spheres provide polarimetric phase curves reminiscent of the cometary data. For spheres with radii in the 0.08 to 0.2 mm range and for a complex refractive index representative of astronomical silicates, the negative branch is less pronounced when particles are fluffier or when the wavelength is higher (Petrova et al., 2000; Tishkovets et al., 2004). Simulations with fractal aggregates of spheres, built up of mixtures of silicates, organics, carbon, metal, and with an index of
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(1.98+0.48i) at 600 nm, suggest that the spheres are submicron-sized and that the equivalent radius (i.e. the radius of a sphere having the same volume as the aggregate of interest) of the aggregates is above 0.6 mm (Kimura et al., 2003; Mann et al., 2004). 2.4. Temperature from infrared observations of the thermal emission The temperature of dust particles in thermal equilibrium is determined by equalling the solar energy absorbed and the thermal energy emitted when the other energy sources (e.g. the energy loss due to the sublimation) are negligible (see e.g. Kolokolova et al., 2004). Comets temperatures display a dependence upon the solar distance R. With R given in AU, the temperature derived for 1P/Halley (Tokunaga et al., 1988) corresponds to a (315.5 R0.5) law, but some different trends have been noticed for other comets. Continuum emission at sub-millimetre wavelengths indicates the presence of millimetre-sized particles (see e.g. Jewitt and Matthews, 1999). From an inversion of the infrared zodiacal thermal emission, the dependence of the local temperature upon the solar distance (in the near-ecliptic symmetry surface) is found to be less steep than expected in the blackbody case (Dumont and Levasseur-Regourd, 1988). Below 1.5 AU in the near-ecliptic symmetry surface of the interplanetary dust cloud, the best fit (see e.g. Reach, 1991; Renard et al., 1995) is obtained for (R0.3670.02). 3. Numerical simulations with core-mantle elongated grains and porous irregular aggregates of submicron grains We have developed systematic numerical simulations for grains of silicates and organics, and for rather small aggregates thereof, which could somehow represent the shape and composition of dust particles in cometary comae, and possibly in the interplanetary dust cloud. Optical indices of amorphous silicates (Dorschner et al., 1995) and of crystalline silicates (Ja¨ger et al., 1998) are rather similar in the visible; we have chosen to take the value of Mg-rich pyroxene near 550 nm (m ¼ 1.62+0.003i), since it is the major constituent of cometary silicates (Wooden et al., 1999, Hayward et al., 2000). The optical indices of organics in comets are less constrained; we have taken the value of organic residues of ices processed by energetic particles near 550 nm (m ¼ 1.88+ 0.1i), as obtained by laboratory experiments simulating processes in the diffuse interstellar medium (Jenniskens, 1993; Li and Greenberg, 1997). Our aim is to estimate, from the observational constraints, the sizes (distribution and cut-offs) and the silicates to organics ratio in a cometary coma or in the interplanetary cloud. As far as cometary simulations are concerned, more details about the particles properties, the numerical codes and the results can be found in Lasue and Levasseur-Regourd (2006).
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3.1. Light scattering simulations for core-mantle elongated grains
3.2. Light scattering simulations for aggregates of spheroidal grains
Simulations have been developed for spheres and for prolate spheroids (great to small axis ratio typically equal to 2), to tentatively reproduce the shape of interstellar grains, as defined by e.g. Li and Greenberg (1997). The size parameter x, equal to (2pa/l), where a is the equivalent radius and l the wavelength of the light, could be in the 1–2 range for most interstellar grains. These grains may be mono-disperse and made of either astronomical silicates or organics. Computations for small mono-disperse spheres and spheroids are made with T-matrix, while computations with large mono-disperse grains are made with Ray-tracing codes (as developed, respectively, by Mishchenko and Travis, 1998 and Macke and Mishchenko, 1996). The small grains may also, as illustrated in Fig. 3, be built of a silicates core and an organics mantle. From interstellar dust values extrapolated to the protosolar cloud stage and constrained by solar abundances, a silicates to organics ratio of about 1 in mass is derived (Greenberg and Hage, 1990), i.e. a ratio of the equivalent radius of the core to the equivalent width of the mantle of about 2.4. For such small core-mantle spheres, polarization phase curves are found to follow closely those of organics grains of identical size and shape (Lasue and Levasseur-Regourd, 2006). For small core-mantle spheroids (more representative of interstellar grains), with radii typically ranging between 0.1 and 1 mm and with ratios of the core radius to mantle width of similar orders of magnitude, computations performed with DDA code (Draine and Flatau, 2000), for two concentric spheroids of different optical indices, lead to the same results. Light scattering numerical computations for mono-disperse spheres or spheroids made of organics can thus be used to simulate the properties of grains of interstellar origin, formed of a silicates core coated with an organics mantle.
We have also performed simulations with DDA code for fractal Ballistic Cluster-Cluster Aggregates (BCCA) and Ballistic Particle-Cluster Aggregates (BPCA) of up to 128 spherical or spheroidal grains, so-called monomers (Fig. 3). Each monomer is described by at least 500 dipoles and each calculation is averaged over more than 1500 different orientations. For 128 grains, the fractal dimensions are 1.5 and 2.9. Fig. 4 presents, as an example, typical polarization maps for BCCA or BPCA of 64 silicates spheroids or organics spheroids, with orientations randomized inside the aggregate. Each grey-coded map provides the polarization as a function of the phase angle and of the size parameter of the constituting grains. Taking into account the above-mentioned results about silicate core-organics mantle grains, the polarization maps obtained for organics spheroids are also representative of those of core-mantle spheroids (with a width of the mantle comparable to the radius of the core). The main results about the number of monomers, the porosity and the composition are as follows (Lasue and Levasseur-Regourd, 2006). The trends, from 32 to 128 grains, are similar, with the negative branch usually occurring for a grain size parameter above 1, although the maximum in polarization slightly decreases with increasing number of monomers. The differences between the polarization values for BPCA and fluffier BCCA are not very important, although the maximum in polarization is higher for the fluffier particles, within which a reduced amount of multiple scattering is taking place. The overall features on the map for silicates are somehow shifted towards smaller values of the size parameter for organics. Similar analyses performed with aggregates of singlesized spheres lead to values of the minimum in polarization generally more negative than for spheroids. However, the results are quite comparable for aggregates of spheres with a Gaussian size distribution (FWHM of about 40% of the mean radius) and for spheroids, indicating that this latter approach fairly represents an average over shapes and orientations of the grains inside the particle. The range of grains size parameters corresponding to a polarimetric behaviour representative of cometary or interplanetary dust in the visible and near-infrared domains corresponds to x about 1.3–1.8, indicating that the effective radius of the grains within the aggregate remains in the 0.08–0.3 mm range. 3.3. Results for comet Hale-Bopp
Fig. 3. Schematic image of a fractal aggregate built up of small spheroidal grains (silicates core and organics mantle), with effective radii of the order of the wavelength.
Taking into account the fact that the wavelength dependence of the polarization is very well documented for comet C/1999 O1 Hale-Bopp, it is also possible to compare the observations and the simulations obtained with a mixture of silicates and organics aggregates, assuming a power law size distribution for the small grains,
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Fig. 4. Polarization maps presenting the linear polarization as a function of the phase angle (abscissa) and the size parameter of the grains (ordinate) for BPCA (upper part) and BCCA (lower part) particles of 64 small spheroids. Left, silicates; right, organics.
their aggregates, and some larger spheroids. A very satisfactory fit (Fig. 5a, from Lasue and LevasseurRegourd, 2006) is obtained for a power law size distribution with an index of (3), radii of about 0.1 mm for the lower cut-off and of 20 mm for the upper cut-off, and a mixture ratio with a significant amount of organics, with about 50–75% in total volume, i.e. about 33–60% in mass. Kolokolova et al. (2001) had been using Mie computations for grains with a silicates core and an organics mantle, assuming the interactions between the constituting grains of a fluffy aggregate to be negligible. Their best fit for Hale-Bopp corresponds to small particles with a silicate core radius of about 0.05 mm, a core/mantle mass ratio of 1–2, a power law size distribution index of about 3, and a refractive index of (1.5+0.5i) for the core and (1.7+0.5i) for the mantle. Min et al. (2005), using hollow spheres to reproduce the properties of fluffy particles, had derived a size distribution index of 3.48 and suggested a composition of about 54% amorphous silicates, 4% crystalline silicates, 24% carbon and 18% iron or iron sulphur. It may be added that indices in the 3 to 3.9 range had been derived from mid-infrared spectra (Harker et al., 2002; Moreno et al., 2003), assuming that the particles are in the 0.2–200 mm size range. Our results, which rely on more realistic assumptions for the shape of the cometary particles, are in agreement with the previous ones for the
size distribution or the composition, and allow a fair determination of the cut-off sizes. 3.4. Results for interplanetary dust For the (rather poorly constrained) interplanetary dust data in the near-ecliptic symmetry surface, satisfactory fits for the phase angle dependence can be obtained with spheroids, for usual power law size distributions and for the Gru¨n et al. (2001) size distribution. In both cases, the presence of a mixture (with a poorly constrained ratio) of silicates, allowing the apparition of the negative branch, and of organics, allowing the decrease of the maximum in polarization, is necessary. The decrease with solar distance in the polarization at maximum (Levasseur-Regourd et al., 2001) may be fitted by increasing either the ratio of silicates when getting closer to the Sun (if the sizes remain unchanged), or the contribution of small grains, i.e. a steeper size distribution (if the silicates to organics ratio is constant), or most likely by a combination of both effects. These results strongly suggest that the decrease in local polarization originates in the weathering (sublimation, sputtering, charging, fragmentation of the particles) of the particles of cometary (and asteroidal) origin, which are either spiralling towards the Sun or escaping from the inner solar system.
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Fig. 5. Best fits between local observations and models, for a mixture of aggregates of up to 128 small spheroidal grains and larger spheroids (with a power law size distribution) composed of astronomical silicates and absorbing organics. (a) Comet Hale-Bopp: size distribution index of (3), radii of about 0.1 and 20 mm respectively for the lower and upper cut-offs, about 33 to 60% of organics in mass (from Lasue and Levasseur-Regourd, 2006). (b) Interplanetary dust particles near 1 AU: size distribution index of (3.1), radii of about 0.1 and 50 mm, respectively, for the lower and upper cut-offs, about 40% of organics in mass.
An attempt to fit the data, as previously done for comets, with a mixture of small grains, their aggregates and some larger spheroids, suggests that the contribution of aggregates is lower in the interplanetary dust cloud than in cometary comae. A good fit (Fig. 5b) is obtained for a size distribution with a power law index of (3.1), radii of about 0.1 mm for the lower cut-off and of 50 mm for the upper cut-off, and a silicates and organics mixture with about 30% to 55% of organics in mass. One main trend observed for interplanetary dust temperature is its solar distance variation, with a gradient of about (0.36). There is a better agreement for organics or carbon (with a gradient of about 0.35 to 0.37) than for silicates. For fluffy aggregates, the trend is similar; however, the value of the temperature is lower and its size dependence is less pronounced. These results, together with fits obtained for the polarization of scattered light, strongly suggest that both organics and silicates contribute significantly to the interplanetary dust cloud composition. For the F-corona, Mann et al. (1994) had shown that fluffy aggregates of silicates with a slight amount of absorbing material can reproduce the temperature dependence, and suggested that the amount of aggregates is lower in the interplanetary dust than in cometary dust, with a higher upper size cut-off. Our results are in agreement with these results, and extend them to the interplanetary dust cloud, at least up to 1 AU in the near-ecliptic symmetry surface. 4. Numerical simulations for large dust grains Further analysis of dust particles properties in cometary trails, i.e. colour, temperature, and b-value, requires the knowledge of light scattering properties of larger particles, taking into account their shape and structure.
Fig. 6. Schematic image of the light absorption (based on geometrical optics, GO) by a fractal aggregate of large spherical grains, with radii much larger than the wavelength.
4.1. Light scattering simulations of fractal aggregates composed from large sized grains When the particle size is much larger than the wavelength of interest, light scattering simulations based on geometrical optics (GO) are applicable (Macke, 1993; Muinonen et al., 1996), with the incident light treated as a bundle of rays. The public code Siris was developed by Muinonen et al. (1996) to calculate through GO the scattering properties of large irregularly shaped particles. The code has been modified by Okada et al. (2006) to calculate the absorption/radiation pressure efficiencies of millimetre-sized dust aggregates (BPCA). That is, the incident rays are traced through their reflection, refraction and absorption by the monomer of the aggregate recursively (see Fig. 6).
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GO is applicable for a size parameter x of the monomer much larger than the wavelength of interest, e.g. x above 100, while for smaller x, Maxwell–Garnett effective medium theory (MG-EMT) is used together with Mie theory (MG-Mie) (Mukai et al., 1992). MG-EMT is applicable for inclusions smaller than the wavelength of interest and with a volume fraction lower than that of the host medium (Chy’lek and Srivastava, 1983). In MG-Mie method, the scattering properties of the aggregates are calculated using Mie theory for a hypothetical sphere with a characteristic radius and an effective refractive index m* (where m* is determined from MG-EMT) based on the volume fraction of grain material to vacuum in the aggregate of interest. 4.2. Temperature of large aggregates To derive the energy gain and loss by the grain, we need the absorption efficiencies of the grain over a wide range of wavelengths, i.e. from short (e.g. 200 nm) to long (e.g. 500 mm) wavelengths. For the aggregate, we apply GO to deduce the absorption efficiencies for a size parameter x of the monomer above 100, while we use MG-Mie for x smaller or equal to 100. Fig. 7 shows the size dependence of the dust temperature calculated for crystalline silicate (1.48+0.000028i near 550 nm) and amorphous carbon (mE1.88+0.77i near 550 nm) with the refractive indices listed, respectively, in Mukai (1989) and Preibisch et al. (1993). For the three sizes of large aggregates, with equivalent radius a of 2, 5 and 10 mm, the temperature are derived using GO for x greater than 100 and MG-Mie for x smaller or equal to 100. For comparison, the temperature derived by MG-Mie alone is shown by a solid line. It is found that the dust temperatures derived by above two different calculations are very similar with a difference of up to 5%. This result confirms the applicability of MG-Mie for large aggregates to derive the temperature of BPCA, as shown for small aggregates in Mann et al. (1994). For the investigation of the influence of the shape of aggregates (i.e. spherical and non-spherical particles), the
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dust temperature of the equal volume sphere based on absorption efficiencies calculated from Mie theory is also presented. As the size of monomer increases, the dust temperature of the sphere goes down to minimum values around 10 mm in radius, and then approaches the blackbody temperature. On the other hand, the temperature of the BPCA approaches the blackbody temperature without showing minimum values around 10 mm in radius of the equal volume sphere. 4.3. Solar radiation pressure forces on large aggregates The b-value, i.e. the solar radiation pressure to solar gravity ratio, plays an important role in the dynamical evolution of dust particles. For example, the presence of mm-sized grains in cometary trails is predicted by the fact that the observed trails show good fits with syndyne curves with a value of about 104 (Ishiguro et al., 2003). The radiation pressure efficiency is calculated as [Qpr ¼ Qext/gSQsca], where Qext and Qsca are the extinction and the scattering efficiencies and /gS is an asymmetry parameter. The result of b-value derived by MG-Mie method alone is discussed for the aggregates with a wide range of radii of the equal volume sphere. Fig. 8 shows b-values of BPCA calculated for crystalline silicate and amorphous carbon as used in Fig. 7. In this figure, two types of equal volume BPCA with different number of monomers (i.e. 2048 and 16384) are calculated. These two aggregates almost show the same value of b with the condition of equal volumes. Therefore, we can conclude that the b-value for the aggregate does not depend upon the number N of monomers, at least for N ¼ 2048 and 16,384, when the volume of aggregate is fixed. The b-value for equal volume sphere is also presented to compare with results for BPCA. For smaller sizes of aggregates, b for BPCA is smaller than that of the sphere, in agreement with the results shown in Kimura et al. (2002). On the other hand, for larger sizes of aggregates, b for BPCA becomes larger than that of the sphere. It is predicted that a mm-sized grain shows optical properties similar to those expected for a black body, and
Fig. 7. Temperature at 1 AU of dust aggregates of (a) silicates or (b) amorphous carbon, built up of 2048 monomers.
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Fig. 8. b ratio (radiation pressure to gravity force) for a BPCA aggregate of large grains, compared to a sphere of equivalent volume. (a) silicates, (b) amorphous carbon.
thus that no significant dependence of the b value on its composite materials appears. It is found, however, that the aggregates consisting of large individual grains still keep their dependence of b value on the materials, at least for carbon and silicate. This result implies that a possible selective segregation between materials due to radiation pressure forces may occur in the dust tails, even in large (mm-sized) grains. 5. Conclusions Numerical simulations are proposed, to represent the light scattering and thermal properties of dust in cometary comae and tails and in the interplanetary dust cloud. Different types of particles are used: core-mantle submicron elongated grains, fractal aggregates of such grains, and fractal aggregates of larger dust grains. The main results are as follows. (1) Light scattering properties of submicron spheroidal grains with an astronomical silicates core and an organics mantle are comparable to those of similar organics grains, for a silicates to organics ratio typical of the protosolar cloud. (2) Polarimetric properties of fluffy fractal aggregates are compatible with effective radii of the submicron grains building up the aggregates in the 0.08 to 0.3 mm range. (3) The numerous polarimetric observations of comet Hale-Bopp are nicely fitted with a mixture of individual grains and aggregates, corresponding to about 33% to 60% of organics in mass, to a power law size distribution with an index of (3), and an upper cutoff radius by 20 mm. (4) The less-constrained polarimetric observations of interplanetary dust near 1 AU can be fitted with a mixture of individual grains and aggregates with less aggregates, corresponding to about 40% of organics in mass, a similar size distribution and an upper cut-off radius by 50 mm. (5) The interplanetary dust light scattering and thermal properties are indicative of the presence of both compact and fluffy particles, with compositions ranging
from silicates to more absorbing material (such as organics compounds and amorphous carbon). (6) A possible segregation between materials may occur for the large aggregates present in dust tails.
References Blum, J., Wurm, G., Kempf, S., Poppe, T., Klahr, H., Kosaka, T., Rott, M., Henning, T., Dorschner, J., Schra¨pler, R., Keller, H.U., Markiewicz, W.J., Mann, I., Gustafson, B.A.S., Giovane, F., Neuhaus, D., Fechtig, H., Gru¨n, E., Feuerbacher, B., Kochran, H., Ratke, L., El Goresy, A., Morfill, G., Weidenschilling, S.J., Schwehm, G., Metzler, K., Ip, W.H., 2000. Growth and form of planetary seedlings: results from a microgravity aggregation experiment. Phys. Rev. Lett. 85, 2426–2429. van Boekel, R., Min, M., Waters, L.B.F.M, de Koter, A., Dominik, C., van den Ancker M.E., Bouwman, J., 2005. A 10 mm spectroscopic survey of Herbig Ae star disks: Grain growth and crystallization. Astron. Astrophys. 437, 189–208. Brownlee, D.E., 1996. The elemental composition of interplanetary dust, In: Gustafson, B., Hanner, M.S. (Eds.), Physics, Chemistry and Dynamics of Interplanetary Dust. A.S.P. Conferences Series, pp. 261–264. Brucato, J.R., Colangeli, L., Mennella, V., Palumbo, P., Bussoletti, E., 1999. Mid-infrared spectral evolution of thermally annealed amorphous pyroxene. Astron. Astrophys. 348, 1012–1019. Chy’lek, P., Srivastava, V., 1983. Dielectric constant of a composite inhomogeneous medium. Phys. Rev. B 27, 5098–5106. Clark, B.C., Green, S.F., Economou, T.E., Sandford, S.A., Zolensky, M.E., McBride, N., Brownlee, D.E., 2004. Release and fragmentation of aggregates to produce heterogeneous, lumpy coma streams. J. Geophys. Res. 109 (E12S03), 1–13. Desvoivres, E., Klinger, J., Levasseur-Regourd, A.C., 2000. Modeling the dynamics of fragments of cometary nuclei: Application to comet C/1996 B2 Hyakutake. Icarus 144, 172–181. Dollfus, A., Bastien, P., Le Borgne, J.L., Levasseur-Regourd, A.C., Mukai, T., 1988. Optical polarimetry of P/Halley: Synthesis of the measurements in the continuum. Astron. Astrophys. 206, 348–356. Dorschner, J., Begemann, B., Henning, Th., Ja¨ger, C., Mutschke, H., 1995. Steps towards interstellar silicate mineralogy. II. Study of Mg–Fe-silicate glasses of variable composition. Astron. Astrophys. 300, 506–520. Draine, B.T., Flatau, P.J., 2000. User Guide for the Discrete Dipole Approximation Code DDSCAT, /http://arxiv.org/abs/astro-ph/ 008151v4S. Dumont, R., Levasseur-Regourd, A.C., 1988. Properties of interplanetary dust from infrared and optical observations. Astron. Astrophys. 191, 154–160.
ARTICLE IN PRESS A.C. Levasseur-Regourd et al. / Planetary and Space Science 55 (2007) 1010–1020 Fulle, M., Levasseur-Regourd, A.C., McBride, N., Hadamcik, E., 2000. In-situ dust measurements from within the coma of 1P/Halley: first order approximation with a dust dynamical model. Astron. J. 119, 1968–1977. Furusho, R., Suzuki, B., Yamamoto, N., Kawakita, H., Sasaki, T., Shimizu, Y., Kurakami, T., 1999. Imaging polarimetry and color of the inner coma of comet Hale-Bopp (C/1995 O1). Publ. Astron. Soc. Jpn. 51, 367–373. Green, S.F., McDonnell, J.A.M., McBride, N., Colwell, M.T.S.H., Tuzzolino, A.J., Economou, T.E., Tsou, P., Clark, B.C., Brownlee, D.E., 2004. The dust mass distribution of comet 81P/Wild 2. J. Geophys. Res. 109 (E12S04), 1–13. Greenberg, J.M., 1982. What are comets made of? A model based on interstellar dust. In: Wilkening, L.L. (Ed.), Comets. University of Arizona Press, pp. 131–163. Greenberg, J.M., Hage, J.I., 1990. From interstellar dust to comets: a unification of observational constraints. Astrophys. J. 361, 260–274. Gru¨n, E., Baguhl, M., Svedhem, H., Zook, H.A., 2001. In situ measurements of cosmic dust. In: Gru¨n, E., Gustafson, B., Dermott, S., Fechtig, H. (Eds.), Interplanetary Dust. Springer, Berlin, pp. 295–346. Habbal, S.R., Arndt, M.B., Nayfeh, M.H., Arnaud, J., Johnson, J., Hegwer, S., Woo, R., Ene, A., Habbal, F., 2003. On the detection of the signature of silicon nanoparticle dust grains in coronal holes. Astrophys. J. 592, L87–L90. Hadamcik, E., Levasseur-Regourd, A.C., 2003. Dust evolution of comet C/1995 O1 (Hale-Bopp) by imaging polarimetric observations. Astron. Astrophys. 403, 757–768. Hanner, M.S., Bradley, J.P., 2004. Composition and mineralogy of cometary dust. In: Festou, M.C., Keller, H.U., Weaver, H.A. (Eds.), Comets II. University of Arizona Press, pp. 555–564. Harker, D.E., Wooden, D.H., Woodward, C.E., Lisse, C.M., 2002. Grain properties of comet C/1995 O1 (Hale-Bopp). Astrophys. J. 580, 579–597. Haudebourg, V., Cabane, M., Levasseur-Regourd, A.C., 1999. Theoretical polarimetric responses of fractal aggregates, in relation with experimental studies of dust in the solar system. Phys. Chem. Earth C 24, 603–608. Hayward, T.L., Hanner, M.S., Sekanina, Z., 2000. Thermal infrared imaging and spectroscopy of Comet Hale-Bopp (C/1995 O1). Astrophys. J. 538, 428–455. Hellyer, B., 1970. The fragmentation of asteroids. Mon. Not. R. Astr. Soc. 148, 383–390. Honda, M., Watanabe, J., Yamashita, T., Kataza, H., Okamoto, Y.K., Miyata, T., Sako, S., Fujiyoshi, T., Kawakita, H., Furusho, R., Kinoshita, D., Sekiguchi, T., Ootsubo, T., Onaka, T., 2004. The 10 micron spectra of comet C/2002 V1 (NEAT) and C/2001 RX14 (LINEAR). Astrophys. J. 601, 577–582. Ishiguro, M., Kwon, S.M., Sarugaku, Y., Hasegawa, S., Usui, F., Nishiura, S., Nakada, Y., Yano, H., 2003. Discovery of the dust trail of the stardust comet sample return mission target: 81P/Wild 2. Astrophys. J. 589, L101–L104. Ja¨ger, C., Molster, F.J., Dorschner, J., Henning, T., Mutschke, H., Waters, L.B.F.M., 1998. Steps toward interstellar silicate mineralogy: IV. The crystalline revolution. Astron. Astrophys. 339, 904–916. Jenniskens, P., 1993. Optical constants of organic refractory residue. Astron. Astrophys. 274, 653–661. Jessberger, E.K., Stephan, T., Rost, D., Arndt, P., Maetz, M., Stadermann, F.J., Brownlee, D.E., Bradley, J.P., Kurat, G., 2001. Properties of interplanetary dust: information from collected samples. In: Gru¨n, E., Gustafson, B., Dermott, S., Fechtig, H. (Eds.), Interplanetary Dust. Springer, Berlin, pp. 253–294. Jewitt, D., Matthews, H., 1999. Particulate mass loss from comet HaleBopp. Astron. J. 117, 1056–1062. Keller, L.P., Messenger, S., Bradley, J.P., 2000. Analysis of a deuterium rich interplanetary dust particle and implications for presolar material in IDPs. J. Geophys. Res. 10, 10397–10402.
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Kimura, H., Okamoto, H., Mukai, T., 2002. Radiation pressure and the Poynting–Robertson effect for fluffy dust particles. Icarus 157, 349–361. Kimura, H., Kolokolova, L., Mann, I., 2003. Optical properties of cometary dust: constraints from numerical studies on light scattering by aggregate particles. Astron. Astrophys. Lett. 407, L5–L8. Kolokolova, L., Jockers, K., Gustafson, B.A.S., Lichtenberg, G., 2001. Color and polarization as indicators of comet dust properties and evolution in the near-nucleus coma. J. Geophys. Res. 106 (E5), 10113–10127. Kolokolova, L., Hanner, M.S., Levasseur-Regourd, A.C., Gustafson, B.A.S., 2004. Physical properties of cometary dust from light scattering and thermal emission. In: Festou, M.C., Keller, H.U., Weaver, H.A. (Eds.), Comets II. University of Arizona Press, pp. 577–604. Lasue, J., Levasseur-Regourd, A.C., 2006. Porous irregular aggregates of sub-micron sized grains to reproduce cometary dust light scattering observations. J. Quant. Spectros. Radiat. Transfer 100, 220–236. Levasseur-Regourd, A.C., 1999. Polarization of light scattered by cometary dust particles. Space Sci. Rev. 90, 163–168. Levasseur-Regourd, A.C., Hadamcik, E., 2003. Light scattering by irregular dust particles in the solar system: observations and interpretation by laboratory measurements. J. Quant. Spectros. Radiat. Transfer 79, 903–910. Levasseur-Regourd, A.C., Cabane, M., Worms, J.C., Haudebourg, V., 1997. Physical properties of dust in the solar system: relevance of the computational approach and of measurements under microgravity conditions. Adv. Space Res. 20, 1585–1594. Levasseur-Regourd, A.C., McBride, N., Hadamcik, E., Fulle, M., 1999. Similarities between in situ measurements of local dust scattering and dust flux impact data within the coma of 1P/Halley. Astron. Astrophys. 348, 636–641. Levasseur-Regourd, A.C., Mann, I., Dumont, R., Hanner, M.S., 2001. Optical and thermal properties of interplanetary dust. In: Gru¨n, E., Gustafson, B., Dermott, S., Fechtig, H. (Eds.), Interplanetary Dust. Springer, Berlin, pp. 57–94. Li, A., Greenberg, J.M., 1997. A unified model of interstellar dust. Astron. Astrophys. 323, 566–584. Lumme, K., 2000. Scattering properties of interplanetary dust particles. In: Mishchenko, M.I., Hovenier, J.W., Travis, L.D. (Eds.), Light Scattering by Non Spherical Particles. Academic Press, New York, pp. 555–583. Macke, A., 1993. Scattering of light by polyhedral ice crystals. Appl. Opt. 32, 2780–2788. Macke, A., Mishchenko, M.I., 1996. Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles. App. Opt. 35, 4291–4296. Mann, I., Murad, E., 2005. On the existence of silicon nanodust near the Sun. Astrophys. J. 624, L125–L128. Mann, I., Okamoto, H., Mukai, T., Kimura, H., Kitada, Y., 1994. Fractal aggregate analogues for near solar dust properties. Astron. Astrophys. 291, 1011–1018. Mann, I., Kimura, H., Kolokolova, L., 2004. A comprehensive model to describe light scattering properties of cometary dust. J. Quant. Spectros. Radiat. Transfer 89, 291–301. Mathis, J.S., Rumpl, W., Nordsieck, K.H., 1977. The size distribution of interstellar grains. Astrophys. J. 217, 425–433. Meakin, P., 1983. Formation of fractal clusters and networks by irreversible diffusion-limited aggregation. Phys. Rev. Lett. 51, 1119–1122. Min, M., Hovenier, J.W., de Koter, A., Waters, L.B.F.M., Dominik, C., 2005. The composition of the dust in the coma of comet Hale-Bopp. Icarus 179, 158–173. Mishchenko, M.I., Travis, L.D., 1998. Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers. J. Quant. Spectrosc. Radiat. Transfer 60, 309–324.
ARTICLE IN PRESS 1020
A.C. Levasseur-Regourd et al. / Planetary and Space Science 55 (2007) 1010–1020
Moreno, F., Munoz, O., Vilaplana, R., Molina, A., 2003. Irregular particles in comet C/1995 O1 Hale-Bopp inferred from its mid-infrared spectrum. Astrophys. J. 595, 522–530. Muinonen, K., Nousiainen, T., Fast, P., Lumme, K., Peltoniemi, J., 1996. Light scattering by Gaussian random particles: ray optics approximation. J. Quant. Spectros. Radiat. Transfer 55, 577–601. Mukai, T., 1989. Cometary dust and interplanetary particles. In: Bonetti, A., Greenberg, J.M., Aiello, S.A. (Eds.), Evolution of Interstellar Dust and Related Topics. Elsevier, Amsterdam, pp. 397–445. Mukai, T., Mukai, S., Kikuchi, S., 1987. Complex refractive index of grain material deduced from the visible polarimetry of comet P/Halley. Astron. Astrophys. 187, 650–652. Mukai, T., Ishimoto, H., Kozasa, T., Blum, J., Greenberg, J.M., 1992. Radiation pressure forces of fluffy porous grains. Astron. Astrophys. 262, 315–320. Mukai, T., Blum, J., Nakamura, A.M., Johnson, R.E., Havnes, O., 2001. Physical processes on interplanetary dust. In: Gru¨n, E., Gustafson, B., Dermott, S., Fechtig, H. (Eds.), Interplanetary Dust. Springer, Berlin, pp. 445–507. Nakamura, R., Okamoto, H., 1999. Optical properties of fluffy aggregates as analogues of interplanetary dust particles. Adv. Space Res. 23, 1209–1212. Okada, Y., Nakamura, A.M., Mukai, T., 2006. Light scattering by particulate media of irregularly shaped particles: Laboratory measurements and numerical simulations. J. Quant. Spectros. Radiat. Transfer 100, 295–304 (2006). Petrova, E.V., Jockers, K., Kiselev, N.N., 2000. Light scattering by aggregates with sizes comparable to the wavelength: an application to cometary dust. Icarus 148, 526–536. Preibisch, T., Ossenkopf, V., Yorke, H.W., Henning, T., 1993. The influence of ice-coated grains on protostellar spectra. Astron. Astrophys. 279, 577–588. Reach, W.T., 1991. Zodiacal emission: II. Dust near ecliptic. Astrophys. J. 369, 529–543. Reach, W.T., 2005. Spitzer observations of comets and zodiacal light, 2005. American Astronomical Society Meeting 206, #28.17.
Renard, J.B., Levasseur-Regourd, A.C., Dumont, R., 1995. Properties of interplanetary dust from infrared observations. Astron. Astrophys. 304, 602–608. Singh, J., Sakurai, T., Ichimoto, K., Hagino, M., Yamamoto, T.T., 2004. Existence of nanoparticle dust grains in the inner solar corona? Astrophys. J. 608, L69–L72. Sitko, M.L., Lynch, D.K., Russell, R.W., Hanner, M.S., 2004. 3-14 micron spectroscopy of comets C/2002 O4 (Ho¨nig), C/2002 V1 (NEAT), C/2002 X5 (Kudo-Fujikawa), C/2002 Y1 (Juels-Holvorcem), and 69P/Taylor and the relationships among grain temperature, silicate band strength, and structure among comet families. Astrophys. J. 612, 576–587. Tishkovets, V.P., Petrova, E.V., Jockers, K., 2004. Optical properties of aggregate particles comparable in size to the wavelength. J. Quant. Spectros. Radiat. Transfer 86, 241–265. Tokunaga, A., Golish, W., Griep, D., Kaminski, C., Hanner, M., 1988. The NASA infrared telescope facility comet Halley monitoring programme. Astron. J. 96, 1971–1976. Witt, A.N., Gordon, K.D., Vijh, U.P., Sell, P.H., Smith, T.L., Xie, R.-H., 2006. The excitation of extended red emission: new constraints on its carrier from Hubble Space Telescope observations of NGC 7023. Astrophys. J. 636, 303–315. Wooden, D.H., Harker, D.E., Woodward, C.E., Butner, H.M., Koike, C., Witteborn, F.C., McMurtry, C.W., 1999. Silicate mineralogy of the dust in the inner coma of comet C/1995 O1 (Hale-Bopp) pre and post-perihelion. Astrophys. J. 517, 1034–1058. Woodward, C.E., Kelley, M.S., Harker, D.E., Wooden, D.H., Reach, W.T., Gehrz, R.D., Spitzer GO Comet Team, 2005. Astromineralogy of Solar System Comets from Spitzer, American Astronomical Society, DPS meeting #37, #16.16. Xing, Z., Hanner, M.H., 1997. Light scattering by aggregate particles. Astron. Astrophys. 324, 805–820. Yanamandra-Fisher, P.A., Hanner, M.S., 1999. Optical properties of nonspherical particles of size comparable to the wavelength of light: application to comet dust. Icarus 138, 107–128.
