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The scattering properties of cometary dust
Journal of Quantitative Spectroscopy & Radiative Transfer 79–80 (2003) 695 – 705
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The scattering properties of cometary dust Martha S. Hanner∗ Jet Propulsion Laboratory, California Institute of Technology, Mail Stop 183-501, Pasadena, CA 91109, USA Received 11 June 2002; accepted 19 August 2002
Abstract The dust particles in di/erent comets exhibit generally similar scattering properties. Polarization is characterized by a small negative branch at scattering angles ¿ 160◦ and a maximum of 15 –25% near 90◦ in red light. The material is, on average, very dark, with geometric albedo of 3–5% at visual to near-infrared wavelengths for comets within 2:5 AU of the sun. The scattering properties are consistent with a mixture of silicate and carbonaceous material, as measured by the Halley space probes. In comparing comets, there is a correlation of stronger polarization, redder polarimetric color, higher albedo, stronger infrared silicate emission, and higher infrared color temperature. Aggregate particles having constituent grain size parameters X ¿ 1:5 show promise in matching the observed scattering properties. An enhancement in the abundance of small silicate grains with X ∼ 1:5–2 at 0:5 m wavelength may cause the higher polarization, higher albedo, and stronger silicate emission in comets such as Hale-Bopp. ? 2003 Elsevier Science Ltd. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Dust scattering properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Angular scattering function, albedo, and color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Thermal emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Silicate emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Correlations among observable parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Scattering by aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 ∗
Tel.: +818-354-4100; fax: +818-354-0966. E-mail address: [email protected] (M.S. Hanner).
0022-4073/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 3 1 5 - 1
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1. Introduction The scattering by cometary dust particles presents several challenges for modeling of light scattering by small particles, due to the heterogeneous composition, irregular structure, and broad size distribution of the particles. On the other hand, analysis of cometary dust scattering is relatively simple compared to other dusty environments in astrophysics, because the scattering geometry is known and the cometary dust coma is optically thin. Comet nuclei formed by accretion in the outer solar nebula where the temperatures were low. We expect comet dust to be a mixture of pre-existing interstellar dust, ices, and solar nebula condensates. Radial gradients in temperature and composition and the extent of mixing within the solar nebula at the epoch of comet formation should be evident today as di/erences in the dust properties among comets. Thus, a major goal of cometary dust studies is to look for trends in dust properties among comets that might correlate with their place of origin. While in situ measurements from the comet Halley space probes and the analysis of interplanetary dust particles (IDPs) captured in the Earth’s atmosphere provide some information about the physical properties of cometary dust, interpretation of remote sensing data is the only means for understanding the full range of dust properties and the di/erences among comets, as well as comparing cometary dust with interstellar dust. The dust impact detectors on the Giotto Halley probe recorded dust particles ranging in size from nanometers to millimeters [1]. The dust mass distribution indicated that the mass was concentrated in the large (mm–cm) particles, while the cross section (thus the observable scattering properties) was distributed across a broad size range, with 0.1–10 m particles contributing ¿ 50%. The Giotto Halley probe also carried a small photometer to record the intensity and polarization of the locally scattered light from the dust along Giotto’s trajectory [2]. Polarization at constant 107◦ scattering angle showed variations along the spacecraft track, indicating that the average size or physical properties of the dust varied with position in the coma. A comparison between the scattered light brightness and the dust impact mass distribution indicated that the density of the particles may be quite low, ¡ 0:5 g=cm3 , favoring Ju/y aggregate particles [3]. Although submicron sized grains released from comets are rapidly removed from the solar system by radiation pressure, larger cometary particles remain on bound orbits and may be swept up by the Earth. Interplanetary dust particles (IDPs) are routinely collected in the stratosphere for laboratory analysis [4]. The chondritic aggregate class of IDPs are thought to originate from comets because of their submicron grain size, heterogeneous mineral mixture, porous structure, and relatively high atmospheric entry speeds. Typical grain sizes within the aggregates are 0.1–0:5 m diameter, with some larger olivine and enstatite crystals [5]. The silicate grains are embedded in a dark, carbon-rich matrix. The heterogeneous composition of silicates, iron sulKdes, and carbonaceous material is consistent with the results from the dust composition analyzers on the Halley space probes [6]. These particles are very di/erent from the small, homogeneous symmetrical particles that are easy to model. First of all, these particles are not spheres. While some optical properties of small compact particles can be approximated by spherical particles, the polarization in particular is strongly dependent on particle shape. The modeling also requires treatment of inhomogeneous particles, either explicitly in a code such as DDA or by means of e/ective medium theory. Moreover, appropriate grain sizes have to be used. It is clear from the measured polarization and color, as well as from
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the dust mass distribution measured from Giotto, that grains ¡ 0:1 m do not play a signiKcant role in the scattering. This paper discusses the observations of scattering by cometary dust and their interpretation, with emphasis on the correlations among observable parameters that constrain the dust physical properties. 2. Dust scattering properties 2.1. Polarization The linear polarization as a function of scattering angle, P(), carries important information about the properties of the scattering particles. Since a comet can be observed at only one scattering angle on a given date, P() has to be built up by observing a comet over many months as the sun-comet– earth geometry changes or by combining observations from a number of comets. Polarization has the advantage that it is an intensity ratio, so that it is independent of temporal variations in the brightness of a comet. However, if the dust size distribution or other physical properties change with time, such as during an outburst, the degree of polarization can be a/ected. The P() assembled from numerous comets covering a wide range in activity level and heliocentric distance form a remarkably consistent pattern (see Fig. 2 in [7]). Negative polarization of order −2% is observed in the backscattering region at ¿ 160◦ . At ¡ 160◦ the polarization is positive, with a broad maximum near = 90◦ . Comets tend to divide into two classes with di/ering maximum polarization, Pmax ∼ 15% and ∼ 25%, respectively, at red wavelength = 0:684 m [8–10]. The comets with higher Pmax generally exhibit a strong scattered light continuum and a conspicuous infrared silicate feature. Polarization generally increases towards longer wavelength (red polarimetric color), but the overall shape of the polarization curve remains remarkably similar from 0.44 –1:6 m. The relatively low Pmax and presence of negative polarization tell us immediately that the optically dominant particles in the coma are not Rayleigh scatterers; rather, the particles must have a size parameter, X = 2 a= ¿ 1:5. Nor do the particles scatter like spheres. Shape e/ects for compact particles with 1 6 X 6 5 were studied by Yanamandra-Fisher and Hanner [11]. While silicate spheres with X = 2:5 exhibit negative polarization at all , the computed polarization for other regular shapes showed Pmax about 25% and negative polarization at ¿ c , where c ranged from 110 –160◦ . In contrast, the computed polarization for carbon particles with X = 2:5 displayed mainly positive polarization, with Pmax ∼ 50%; the phase angle of maximum polarization varied with particle shape. Phase matrices for shape distributions of dirty silicate spheroids with X = 3:5 were computed by Mishchenko [12]. As the axial ratio of the spheroids increased, the polarization at intermediate changed from negative (characteristic of spheres) to positive, leaving a negative branch at ¿ 150◦ . Thus, it appears that compact, non-spherical particles with dimensions comparable to the wavelength can reproduce the primary features of the cometary polarization curve. We know from other measurements that comet dust contains both silicate and carbonaceous material. A mixture of these particles could be compatible with P(); however, silicate particles are needed to give the negative polarization at ¿ 160◦ . For X ¡ 2 (but not 1), both absorbing and silicate grains generate red polarimetric color. For somewhat larger X , compact absorbing particles will display blue polarimetric color while silicate particles will have red polarimetric color [11]. The refractive index of the cometary material may be wavelength dependent, and this will inJuence polarimetric color. The
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similarity of the negative polarization branch from one comet to the next and over a broad wavelength range remains a challenge to interpret. A broad size distribution of aggregate particles may be the answer, as discussed in Section 4. 2.2. Angular scattering function, albedo, and color The angular scattering function of the dust is diPcult to determine, because the amount of dust in the coma contributing to the scattered light intensity does not remain constant over time. Two methods have been used to normalize the observed intensity. The Krst method is to assume that the ratio of the dust to gas production rates remains constant and normalize to the gas production rate (e.g. [13,14]). The second method is to compare the measured scattered light to the measured thermal emission from the same volume of the coma, under the assumption that the emitting properties of the dust are not changing [15–17]. The latter method is the only means for extracting an albedo for the dust. The resulting scattering function is relatively Jat from 100◦ to 145◦ [15–17] and rises by about a factor of 2 from 150◦ to 180◦ [13]. No evidence for an opposition surge ¿ 20% was seen in comet 1P/Halley at 171–178:6◦ [14]. Only two comets have been observed at 30◦ ¡ ¡ 60◦ , using the second method, and they display strong forward scattering [18,19]. The geometric albedo of a particle, Ap , is deKned as the ratio of the energy scattered at 180◦ to that scattered by a white Lambert disk of the same geometric cross section [20]. Since comets are rarely observed at 180◦ , it is convenient to deKne Ap () as the product of the geometric albedo and the normalized scattering function at scattering angle . Ref. [15] presented a plot of Ap () in the J bandpass (1:2 m) for 10 comets. The total dust cross section within the Keld of view was determined by Ktting a dust emission model to the thermal spectral energy distribution, then the total cross section was applied to the scattered intensity to derive an average albedo. The resulting albedos are typically very low, about 0.025 at = 100–145◦ and about 0.05 at ∼ 180◦ . There is some indication that Ap is higher for comets beyond 3 AU. The albedo was observed to increase by 50% in comet 1P/Halley’s coma during episodes of strong jet activity [16]. There may be several components of the dust, with di/ering albedos and temperatures; it has to be kept in mind that the average albedo may not represent the actual albedo of any of the components. However, the low average albedo rules out a large population of cold, bright grains that contribute to the scattered light but not to the thermal emission. The color of the scattered light is generally redder than the sun; the reJectivity gradient decreases with wavelength from 5 –18% per 0:1 m at wavelengths 0.35 –0:65 m to 0 –2% per 0:1 m at 1.6 –2:2 m [21]. The red color indicates that the particles are not Rayleigh scatterers; the coloring agent is most likely a refractory organic material. A less red color, suggesting an inJux of smaller particles, was associated with strong jet activity in comet P/Halley and with the spiral structures in comet Hale-Bopp. 2.3. Thermal emission In the infrared, the color temperature of the Planck function Kt to the 3–18 m thermal emission from the dust coma is 5 –20% higher than the temperature of a blackbody in equilibrium with the solar radiation. Dust particles having a wide range of temperatures contribute to the observed
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thermal emission. A temperature excess is typical of micron-sized and smaller absorbing particles in the solar radiation Keld because these small particles cannot radiate ePciently in the infrared at ¿ 10a, where a is the grain radius. For example, a radius a = 0:25 m carbon sphere will have T = 500 K at 1 AU, compared with TBB = 278 K [22]. The wavelength-dependent emissivity of these small grains will also cause departures from a Planckian curve. Larger particles will be signiKcantly hotter than a blackbody only if they are Ju/y and the constituent grain size is ¡ 1 m. Pure silicate particles, on the other hand, can be quite transparent at visual wavelengths while radiating ePciently in the infrared. Their temperature will depend on the Fe/Mg ratio and the extent to which they are physically associated with absorbing material [22]. The Giotto size distribution, with small adjustments in the slope for small particles, can provide a Kt to the thermal spectral energy distribution for a number of comets. However, the thermal emission at = 3–18 m is contributed mainly by the smaller particles, because they are warmer. Detection of dust thermal emission at ∼ 100 m from several comets is the best evidence for a broad size distribution of radiating dust particles [23–25]. 2.4. Silicate emission An emission feature near 10 m, attributed to the stretching mode vibration in small silicate grains, is seen in some, but not all, comets (see review in [26]). Spectral structure indicates that the emitting particles must be a mixture of crystalline and non-crystalline olivine and pyroxenes. The strength of the feature depends on the grain size and temperature. For a strong feature to be visible, the grains must be roughly micron-sized or smaller and their temperature must be comparable to a theoretical blackbody or warmer, in order for their radiation to be visible above the strong thermal continuum produced by featureless particles in the coma. Spectra of comet Hale-Bopp taken from the Infrared Space Observatory exhibited prominent silicate emission features also at 16 –35 m, corresponding to Mg-rich crystalline olivine [27]. 3. Correlations among observable parameters In order to separate the e/ects of particle size and composition, it is useful to look at the correlations among observable quantities. This is particularly important for polarization, which depends in a complex way on the size, composition, and morphology of the scattering particles. Comet Hale-Bopp (C/1995 O1) was an unusually large, active comet with copious dust production. Like P/Halley, it was well observed over many months. Table 1 compares the average observed properties in the inner coma of Hale-Bopp with similar measurements of comet P/Halley. There is a clear correlation of higher polarization, redder polarimetric color, higher albedo, stronger silicate feature, higher infrared color temperature, and enhanced 3–5 m thermal emission. Other comets follow similar trends. A correlation between infrared color temperature and silicate emission in comets was noted by [17]. All of these parameters show the same correlations when comparing spatially resolved measurements of the dust jets and spiral structures in Hale-Bopp with the background coma. Comet Hale-Bopp displayed stronger silicate emission than any other comet. The 10 m feature was already evident at 4:8 AU preperihelion and the total Jux/continuum ratio was ∼ 3 near perihelion [22]. The 3–5 m emission was also extremely high relative to that expected from a blackbody
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Table 1 Correlations among cometary dust scattering properties Hale-Bopp versus Halley
Possible explanations
Polarization
Higher
Polarimetric color
Redder
Albedo
Higher
Continuum
Stronger
Silicate feature
Stronger
Color temperature 3–5 m Jux
Higher Higher
More small grains, a ∼ 0:2 m More absorbing grains a ∼ , a ¿ More small grains, a ∼ 0:2 m More silicate grains, a ∼ More small grains, a ∼ 0:2 m More “clean” silicates More small grains More “clean” silicates Higher dust/gas ratio More small silicate grains, a 6 1 m Higher silicate/carbon abundance Warmer silicates More small absorbing grains, a 6 1 m More small absorbing grains, a 6 0:5 m
in equilibrium. The implied high grain temperatures exceed the temperatures predicted for dirty silicates or Fe-rich silicate and seem to imply a separate population of submicron sized absorbing grains [22,28]. In addition, Hale-Bopp displayed higher polarization than any other comet at comparable ; unfortunately, the geometry never allowed Pmax to be measured near 90◦ . Spatially resolved observations revealed di/erences in the negative branch with position in the coma, with values as low as −5% in the inner few thousand kilometers at = 173◦ [29]. Visible jets and arcs in the inner coma correlated with regions of higher polarization [29–32]. Do these correlations reJect changes in particle size or composition? Table 1 suggests that the scattering properties of dust in Hale-Bopp relative to P/Halley are consistent with an increase in abundance of both silicate and absorbing grains with e/ective grain radius of ∼ 0:15 m, comparable to the grain size in aggregate IDPs of probable cometary origin. First, let us consider the polarization. For regular, but non-spherical shapes, with X ∼ 2:5– 6, Pmax is higher for absorbing particles such as carbon than for silicate particles. As X increases from 2.5 to 5, Pmax decreases for silicate particles, but increases for carbon particles [11]. Thus, higher Pmax would imply more absorbing grains relative to silicate grains in the coma, in contradiction to the observed correlation between Pmax and silicate emission. If X 6 2, then a decrease in grain size would produce an increase in polarization for both silicate and absorbing grains, consistent with both the higher silicate feature and higher 3–5 m Jux. Thus, an increased abundance of grains with radius 0.1–0:2 m within a broad size distribution may explain the scattering properties in the comets with higher Pmax . These grains would also produce a redder polarimetric color. Small grains with e/ective radius 0.15 –0:2 m will not give negative polarization at ¿ 1 m. The measured polarization for Hale-Bopp was essentially 0% at = 2:2 m and = 12◦ [32]. For comets in the low Pmax group, Pmax ∼ 15% and the presence of negative polarization seem to require primarily silicate particles, despite the lack of a silicate feature in these comets, and this remains a puzzle.
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The higher average albedo measured for Hale-Bopp is also consistent with smaller grains, if the grains are not too absorbing. For compact, slightly or moderately absorbing grains (k 6 0:25), the single scattering albedo reaches a maximum at |m − 1|X ∼ 1:5, where m = n − ik is the refractive index. At = 0:5 m the maximum corresponds to an e/ective grain radius ∼ 0:2 m. Consequently, decreasing the mean grain size in the coma from micron-sized to a few tenths of a micron would tend to increase the albedo. (Since the albedo is measured at a speciKc phase angle, any change in the angular scattering function would a/ect the observed albedo also.) Loss of absorbing mantles on small silicate grains is another means of increasing the albedo. For fully absorbing grains, the albedo decreases with decreasing grain size and a shift to smaller grains would lower the albedo. The high 3–5 m thermal emission could be produced by an enhanced population of a ∼ 0:15 m grains only if they are strongly absorbing, while the strong silicate emission implies an increase in 0.1–1 m warm silicate grains. Interstellar silicate grains may have acquired organic refractory mantles through successive intervals of deposition in cold dense molecular clouds followed by irradiation in the di/use interstellar medium [33]. Since interstellar particles are likely to have been incorporated into comets, these core/mantle grains may play a role in the observed scattering properties. For example, an absorbing mantle would cause a core/mantle grain to be warmer than a pure silicate grain. Mantle sublimation may account for changes in the scattering properties with position in the coma [34]. 4. Scattering by aggregates Many of the larger cometary particles may be rather porous aggregates of small grains, as one sees in the chondritic aggregate class of IDPs. In recent years, improved numerical codes and laboratory measurements have allowed progress in understanding the scattering by aggregate particles. The degree of porosity makes a critical di/erence in the optical properties. For a very porous aggregate, the light interacts primarily with the individual structural units. The scattering properties of such aggregates, particularly the polarization, are determined to a large extent by the scattering properties of the constituent grains, as demonstrated by both DDA calculations and laboratory measurements [35,36]. The absorption cross section for an aggregate particle will have a less steep slope at long infrared wavelengths than a single sphere. Consequently, aggregates of absorbing grains in a comet coma will be cooler than isolated small grains, because the aggregate radiates more ePciently in the infrared. Xing and Hanner [37] found that 10-element aggregates of carbon grains had temperatures the same as a sphere with volume equivalent to the aggregate when the porosity was less than 60%. For a porosity of 80% or greater, the aggregate temperature was close to that of the isolated constituent grains. Thus, the high 3–5 m Jux observed in comet Hale-Bopp requires either isolated small absorbing grains or aggregates of these grains with porosity ¿ 80%. Calculations of the scattering function and polarization for aggregate particles composed of spheres with Xi ¿ 1 have been carried out by Petrova et al. [38]. Irregular aggregates with 15 –33 constituent silicate spheres of size Xi ∼ 1:65 exhibited a polarization phase curve similar to that of comets, including negative polarization at large scattering angles, and the scattering function showed a rise toward =180◦ . However, the shape of the polarization curve depended strongly on constituent grain
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size and the small negative branch quickly disappeared for other Xi [38]. These calculations were extended to study the spectral dependence by Petrova and Jockers [39]. They found that the color depended in a complex way on the particle size and scattering angle; resonances in the scattering by spherical particles are at least partly the cause of this complexity. Petrova and Jockers [39] also emphasized that color and polarimetric color will depend on the wavelength-dependent imaginary part of the refractive index in cometary dust. Ten-element aggregates with porosity ∼ 60% generated polarization intermediate between that of the constituent grains and that of a compact particle with size parameter equal to the aggregate size in DDA calculations by Xing and Hanner [37]. A mixture of silicate and carbon aggregates with porosity ∼ 60% and constituent tetrahedral grains of size Xi = 2:6 could produce a polarization curve similar to that of comet dust [37]. These results show promise for duplicating the polarization phase curve of cometary dust with aggregates of constituent grains having Xi ∼ 1:5–3; however, it is still the case that the model parameters have to be “Kne-tuned” to reproduce the Pmax and small negative branch. Finite resources of computer memory and CPU time have limited the numerical modeling to constituent grains of uniform size and shape. Most likely, cometary dust aggregates consist of irregular grains with a range of sizes, shapes, and refractive indices and the aggregates themselves have a range of porosities. For a broad power law size distribution of such aggregates, the weighted contribution to the scattered light may shift with wavelength, so that the optically dominant size parameter remains similar over a broad wavelength range. This could explain in part the very similar shape of the polarization curve from the blue to the near-infrared spectral regions. Particle shapes other than spheres, such as a shape distribution of silicate ellipsoids, can generate a negative polarization branch over a wider range of sizes and can avoid some of the problems of the resonances in scattering by spheres. The e/ect of porosity on the albedo of an aggregate particle will depend on the size and absorptivity of the constituent grains. Hage and Greenberg [40] have shown that, for aggregates having constituent grains with size parameter Xi ∼ 0:2, the albedo will decrease as the porosity increases, particularly for porosity ¿ 75%. In their aggregate model of cometary dust [41,42], the authors assume that the aggregates are composed of core–mantle interstellar grains with core radius 0:1 m and overall radius ∼ 0:14 m; for this model, the albedo will decrease as porosity increases. Only if the constituent grains had radii ¿ 0:2 m and k ¡ 0:25 would the albedo at = 0:5 m increase with increasing aggregate porosity. Laboratory scattering measurements o/er an alternative means for exploring the scattering properties of aggregates, particularly for structures too large or complex to be handled easily by computer simulations. Two of the approaches that have been applied are to levitate particles in microgravity and to conduct measurements scaled to the microwave domain. The PROGRA2 experiments make use of microgravity during parabolic airplane Jights to levitate particles in the path of a laser and measure P() [7,43,44]. These experiments have the advantage of using “natural” particle shapes, but the disadvantage that the aggregates are diPcult to describe precisely. In the recent experiments, the particles consist of submicron grains, radius ¡ 0:1 m forming Ju/y aggregates. The aggregates can agglomerate into very loose structures up to millimeter size. Although the Pmax is generally high because of the small constituent grain size, mixtures of silica and carbon aggregates show promise for reproducing the cometary polarization, including negative polarization at scattering angles ¿ 160◦ . Scattering measurements scaled to microwave wavelengths are a powerful tool for investigating the polarization properties of irregular aggregates, including particle size and shape and wavelength
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dependence [36]. The microwave scattering experiments have the advantage that the aggregate particle under study can be arbitrarily constructed and precisely deKned. Gustafson and Kolokolova [36] presented color and polarization data for aggregates of silicate and absorbing grains of size 0:5 ¡ X ¡ 20 and analyzed the trends of color and polarimetric color with grain size and composition. The e/ect of grain mantles on the scattering properties is also being studied, and this has potentially important application to cometary dust [34]. 5. Conclusions and future directions Optical and infrared observations of the dust coma of active comets yield the following average scattering properties for the ensemble of dust particles. The average geometric albedo at = 0:5 m is low, only 3–5%. The scattering function is fairly Jat from 90◦ to 150◦ scattering angle, then rises by about a factor of 2 from 150◦ to 180◦ . The color of the scattered light is neutral to slightly red. Polarization maximum of 10 –25% at = 0:5 m occurs near 90◦ , with negative polarization at scattering angles 160 –180◦ . Polarization is higher at longer wavelengths (red polarimetric color), but the overall shape of P() remains similar from 0:44 ¡ ¡ 2:2 m. In the infrared, the color temperature of the Planck function Ktted to the 3–18 m thermal emission is higher than the equilibrium blackbody temperature. Some (but not all) comets display an emission feature at 8–12:5 m due to small, optically thin silicate grains. These scattering properties are in qualitative agreement with a mixed dust population of silicate and carbonaceous material, as inferred from the dust experiments on the Halley space probes and IDPs of probable origin. The low average albedo indicates that silicates must be well mixed with absorbing material. (Only a small fraction of Knely dispersed absorbing material is needed to decrease the albedo of a silicate particle.) The red color is evidence that the particles are not Rayleigh scatterers; the coloring agent is most likely a refractory organic material. The relatively low maximum polarization implies a particle size parameter ¿ 1:5. The presence of silicate emission requires a population of micron-sized or smaller silicate particles and not so embedded in absorbing material that the feature contrast is masked. A color temperature above the equilibrium blackbody temperature requires particles that can absorb more ePciently at visual wavelengths than they radiate in the infrared; this requirement can be met by absorbing grains that are micron-sized or smaller. Larger particles can have elevated temperatures only if they are very porous and the constituent grains are micron-sized or smaller. A high 3–5 m thermal Jux is a particularly sensitive indicator of hot submicron sized absorbing grains (grain radius a 6 0:5 m). Aggregate particles may be particularly relevant to describing the scattering by cometary dust. The scattering behavior of aggregates depends on the porosity. For very porous particles, the scattering and emitting properties depend primarily on the those of the constituent grains. Flu/y aggregates composed of grains with size parameter X ¡ 1 have the high polarization typical of Rayleigh particles; thus, they are not a useful analogue for cometary dust. The persistence of the small negative polarization branch over a wide wavelength range remains an unsolved puzzle. Most numerical models require a Kne-tuning of the particle size and ratio of silicate to absorbing grains to match the −2% polarization. However, for a broad power law size distribution, the weighted contribution to the scattering may shift with wavelength, so that the optically dominant size/wavelength ratio remains similar.
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To make progress, future numerical modeling should focus on aggregates that contain a range in constituent grain sizes (size parameter 1 ¡ X ¡ 10) and move away from very regular shapes such as spheres or tetrahedra. For example, introducing a size and shape distribution of spheroids as the constituent grains would be an important step forward. Understanding the relative inJuence of the constituent grains versus the overall particle structure, as a function of the porosity, is an important goal for both modeling and scattering experiments. Acknowledgements This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration. References [1] McDonnell JAM, Lamy PL, Pankiewicz GS. Physical properties of cometary dust. In: Newburn RL, Neugebauer M, Rahe J, editors. Comets in the post Halley era. Dordrecht: Kluwer, 1991. p. 1043–73. [2] Levasseur-Regourd A-C, McBride N, Hadamcik E, Fulle M. Similarities between in situ measurements of local dust light scattering and dust Jux impact data within the coma of 1P/Halley. Astron Astrophys 1999;348:636–41. [3] Fulle M, Levasseur-Regourd A-C, McBride N, Hadamcik E. In situ dust measurements from within the coma of 1P/Halley: Krst-order approximation with a dust dynamical model. Astron J 2000;119:1968–77. [4] Bradley JP, Sandford SA, Walker RM. Interplanetary dust particles. In: Kerridge JF, Matthews MS, editors. Meteorites and the early solar system. Tucson: University of Arizona Press, 1988. p. 861–95. [5] Bradley JP, Humecki HJ, Germani MS. Combined infrared and analytical electron microscope studies of interplanetary dust particles. Astrophys J 1992;394:643–51. [6] Jessberger E. Rocky cometary particulates: their elemental, isotopic, and mineralogical ingredients. Space Sci Rev 1999;90:91–7. [7] Levasseur-Regourd AC, Hadamcik E. Light scattering by irregular particles in the solar system: observations and interpretation by laboratory measurements. JQSRT, 2002, this volume. [8] Chernova GP, Kiselev NN, Jockers K. Polarimetric characteristics of dust particles as observed in 13 comets: comparisons with asteroids. Icarus 1993;103:144–58. [9] Levasseur-Regourd AC, Hadamcik E, Renard JB. Evidence for two classes of comets from their polarimetric properties at large phase angles. Astron Astrophys 1996;313:327–33. [10] Kiselev NN, Velichko FP. Polarimetry and Photometry of Comet C/1996 B2 Hyakutake. Icarus 1998;133:286–92. [11] Yanamandra-Fisher PA, Hanner MS. Optical properties of nonspherical particles of size comparable to the wavelength of light: application to comet dust. Icarus 1999;138:107–28. [12] Mishchenko MI. Light scattering for size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength. Appl Opt 1993;32:4652–66. [13] Millis RL, A’Hearn MF, Thompson DT. Narrowband photometry of comet P/Stephan-Oterma and the backscattering properties of cometary grains. Astron J 1982;87:1310–7. [14] Meech KJ, Jewitt DC. Observations of comet P/Halley at minimum phase angle. Astron Astrophys 1987;187: 585–93. [15] Hanner MS, Newburn RL. Infrared photometry of comet Wilson (1986l) at two epochs. Astron J 1989;97:254–61. [16] Tokunaga AT, Golisch WF, Griep DM, Kaminski CD, Hanner MS. The NASA Infrared Telescope Facility comet Halley monitoring program I. Preperihelion results. Astron J 1986;92:1183–90. [17] Gehrz RD, Ney EP. 0.7–23 m photometric observations of P/Halley 1986 III and six recent bright comets. Icarus 1992;100:162–86. [18] Ney EP, Merrill KM. Comet West and the scattering function of cometary dust. Science 1976;194:1051–3.
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[19] Ney EP. Optical and infrared observations of bright comets in the range 0:5 m to 20 m. In: Wilkening LL, editor. Comets. Tucson: University of Arizona, 1982. p. 323–40. [20] Hanner MS, Giese RH, Weiss K, Zerull R. On the deKnition of albedo and application to irregular particles. Astron Astrophys 1981;104:42–6. [21] Jewitt D, Meech KJ. Cometary dust scattering versus wavelength, or, “what color is cometary dust?”. Astrophys J 1986;310:937–52. [22] Hanner MS, Gehrz RD, Harker DE, Hayward TL, Lynch DK, Mason CC, Russell RW, Williams DM, Wooden DH, Woodward CE. Thermal emission from the dust coma of comet Hale-Bopp and the composition of the silicate grains. Earth Moon Planets 1999;79:247–64. [23] Gruen E, Hanner MS, Peschke SB, et al. Broadband infrared photometry of comet Hale-Bopp with ISOPHOT. Astron Astrophys 2001;377:1098–118. [24] Walker RG, Aumann HH. IRAS observations of cometary dust. Adv Space Res 1984;4(9):197–201. [25] Lisse CM, A’Hearn MF, Hauser MG, Kelsall T, Lien DJ, Moseley SH, Reach WT, Silverberg RF. Infrared observations of comets by COBE. Astrophys J 1998;496:971–91. [26] Hanner MS. The silicate material in comets. Space Sci Rev 1999;90:99–108. [27] Crovisier J, Leech K, Bockelee-Morvan D, Brooke TY, Hanner MS, Altieri B, Keller HU, Lellouch E. The spectrum of comet Hale-Bopp (C/1995 O1) observed with the Infrared Space Observatory at 2.9 Astronomical Units from the Sun. Science 1997;275:1904–7. [28] Mason CG, Gehrz RD, Jones TJ, Woodward CE, Hanner MS, Williams DM. Observations of unusually small dust grains in the coma of comet Hale-Bopp C/1995 O1. Astrophys J 2001;549:635–46. [29] Hadamcik E, Levasseur-Regourd AC, Renard JB. CCD polarimetric imaging of comet Hale-Bopp (C/1995 O1). Earth Moon Planets 1999;78:365 –71. (See also: Hadamcik E. Contribution a une classiKcation des cometes a partir d’observations et de simulations en laboratoire. Ph.D. Dissertation, Universite Paris VI, 1999.). [30] Furusho R, Suzuki B, Yamamoto N, Kawakita H, Sasaki T, Shimizu Y, Kurakami T. Imaging polarimetry and color of the inner coma of comet Hale-Bopp (C/1995 O1). Publ Astron Soc Jpn 1999;51:367–73. [31] Jockers K, Rosenbush VK, Bonev T, Credner T. Images of polarization and color in the inner coma of comet Hale-Bopp. Earth Moon Planets 1999;78:373–9. [32] Jones TJ, Gehrz RD. Infrared imaging polarimetry of Comet C/1995 O1 (Hale-Bopp). Icarus 2000;143:338–46. [33] Greenberg JM. What are comets made of? A model based on interstellar dust. In: Wilkening LL, editor. Comets. Tucson: University of Arizona 1982; 131– 63. [34] Kolokolova L, Jockers K, Gustafson BAS, Lichtenberg G. Colors and polarization as indicators of comet dust properties. J Geophys Res 2001;106:10113–28. [35] West RA. Optical properties of aggregate particles whose outer diameter is comparable to the wavelength. Appl Opt 1991;30:5316–24. [36] Gustafson BAS, Kolokolova L. A systematic study of light scattering by aggregate particles using the microwave analog technique: angular and wavelength dependence of intensity and polarization. J Geophys Res 1999;104:31711. [37] Xing Z, Hanner MS. Light scattering by aggregate particles. Astron Astrophys 1997;324:805–20. [38] Petrova EV, Jockers K, Kiselev NN. Light scattering by aggregates with sizes comparable to the wavelength: an application to cometary dust. Icarus 2000;148:526–36. [39] Petrova EV, Jockers K. In: Gustafson B, Kolokolova L, Videen G, editors. On the Spectral Dependence of Intensity and Polarization of Light Scattered by Aggregate Particles, Electromagnetic and Light Scattering by Non-spherical Particles. Maryland: ARO, 2002. p. 259–62. [40] Hage JI, Greenberg JM. A model for the optical properties of porous grains. Astrophys J 1990;361:251–9. [41] Greenberg JM, Hage JI. From interstellar dust to comets: a uniKcation of observational constraints. Astrophys J 1990;361:260–74. [42] Li A, Greenberg JM. From interstellar dust to comets: infrared emission from comet Hale-Bopp. Astrophys J 1998;498:L83–7. [43] Worms JC, Renard JB, Hadamcik E, Levasseur-Regourd AC, Gayet JF. Results of the PROGRA2 experiment: an experimental study in microgravity of scattered polarised light by dust particles with large size parameter. Icarus 1999;142:281–97. [44] Hadamcik E, Renard JB, Worms JC, Levasseur-Regourd AC, Masson M. Polarization of light scattered by Ju/y particles (PROGRA2 experiment). Icarus 2002;155:497–508.
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The scattering properties of cometary dust Martha S. Hanner∗ Jet Propulsion Laboratory, California Institute of Technology, Mail Stop 183-501, Pasadena, CA 91109, USA Received 11 June 2002; accepted 19 August 2002
Abstract The dust particles in di/erent comets exhibit generally similar scattering properties. Polarization is characterized by a small negative branch at scattering angles ¿ 160◦ and a maximum of 15 –25% near 90◦ in red light. The material is, on average, very dark, with geometric albedo of 3–5% at visual to near-infrared wavelengths for comets within 2:5 AU of the sun. The scattering properties are consistent with a mixture of silicate and carbonaceous material, as measured by the Halley space probes. In comparing comets, there is a correlation of stronger polarization, redder polarimetric color, higher albedo, stronger infrared silicate emission, and higher infrared color temperature. Aggregate particles having constituent grain size parameters X ¿ 1:5 show promise in matching the observed scattering properties. An enhancement in the abundance of small silicate grains with X ∼ 1:5–2 at 0:5 m wavelength may cause the higher polarization, higher albedo, and stronger silicate emission in comets such as Hale-Bopp. ? 2003 Elsevier Science Ltd. All rights reserved.
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Dust scattering properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Angular scattering function, albedo, and color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Thermal emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Silicate emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Correlations among observable parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Scattering by aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions and future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
696 697 697 698 698 699 699 701 703
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 ∗
Tel.: +818-354-4100; fax: +818-354-0966. E-mail address: [email protected] (M.S. Hanner).
0022-4073/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 3 1 5 - 1
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1. Introduction The scattering by cometary dust particles presents several challenges for modeling of light scattering by small particles, due to the heterogeneous composition, irregular structure, and broad size distribution of the particles. On the other hand, analysis of cometary dust scattering is relatively simple compared to other dusty environments in astrophysics, because the scattering geometry is known and the cometary dust coma is optically thin. Comet nuclei formed by accretion in the outer solar nebula where the temperatures were low. We expect comet dust to be a mixture of pre-existing interstellar dust, ices, and solar nebula condensates. Radial gradients in temperature and composition and the extent of mixing within the solar nebula at the epoch of comet formation should be evident today as di/erences in the dust properties among comets. Thus, a major goal of cometary dust studies is to look for trends in dust properties among comets that might correlate with their place of origin. While in situ measurements from the comet Halley space probes and the analysis of interplanetary dust particles (IDPs) captured in the Earth’s atmosphere provide some information about the physical properties of cometary dust, interpretation of remote sensing data is the only means for understanding the full range of dust properties and the di/erences among comets, as well as comparing cometary dust with interstellar dust. The dust impact detectors on the Giotto Halley probe recorded dust particles ranging in size from nanometers to millimeters [1]. The dust mass distribution indicated that the mass was concentrated in the large (mm–cm) particles, while the cross section (thus the observable scattering properties) was distributed across a broad size range, with 0.1–10 m particles contributing ¿ 50%. The Giotto Halley probe also carried a small photometer to record the intensity and polarization of the locally scattered light from the dust along Giotto’s trajectory [2]. Polarization at constant 107◦ scattering angle showed variations along the spacecraft track, indicating that the average size or physical properties of the dust varied with position in the coma. A comparison between the scattered light brightness and the dust impact mass distribution indicated that the density of the particles may be quite low, ¡ 0:5 g=cm3 , favoring Ju/y aggregate particles [3]. Although submicron sized grains released from comets are rapidly removed from the solar system by radiation pressure, larger cometary particles remain on bound orbits and may be swept up by the Earth. Interplanetary dust particles (IDPs) are routinely collected in the stratosphere for laboratory analysis [4]. The chondritic aggregate class of IDPs are thought to originate from comets because of their submicron grain size, heterogeneous mineral mixture, porous structure, and relatively high atmospheric entry speeds. Typical grain sizes within the aggregates are 0.1–0:5 m diameter, with some larger olivine and enstatite crystals [5]. The silicate grains are embedded in a dark, carbon-rich matrix. The heterogeneous composition of silicates, iron sulKdes, and carbonaceous material is consistent with the results from the dust composition analyzers on the Halley space probes [6]. These particles are very di/erent from the small, homogeneous symmetrical particles that are easy to model. First of all, these particles are not spheres. While some optical properties of small compact particles can be approximated by spherical particles, the polarization in particular is strongly dependent on particle shape. The modeling also requires treatment of inhomogeneous particles, either explicitly in a code such as DDA or by means of e/ective medium theory. Moreover, appropriate grain sizes have to be used. It is clear from the measured polarization and color, as well as from
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the dust mass distribution measured from Giotto, that grains ¡ 0:1 m do not play a signiKcant role in the scattering. This paper discusses the observations of scattering by cometary dust and their interpretation, with emphasis on the correlations among observable parameters that constrain the dust physical properties. 2. Dust scattering properties 2.1. Polarization The linear polarization as a function of scattering angle, P(), carries important information about the properties of the scattering particles. Since a comet can be observed at only one scattering angle on a given date, P() has to be built up by observing a comet over many months as the sun-comet– earth geometry changes or by combining observations from a number of comets. Polarization has the advantage that it is an intensity ratio, so that it is independent of temporal variations in the brightness of a comet. However, if the dust size distribution or other physical properties change with time, such as during an outburst, the degree of polarization can be a/ected. The P() assembled from numerous comets covering a wide range in activity level and heliocentric distance form a remarkably consistent pattern (see Fig. 2 in [7]). Negative polarization of order −2% is observed in the backscattering region at ¿ 160◦ . At ¡ 160◦ the polarization is positive, with a broad maximum near = 90◦ . Comets tend to divide into two classes with di/ering maximum polarization, Pmax ∼ 15% and ∼ 25%, respectively, at red wavelength = 0:684 m [8–10]. The comets with higher Pmax generally exhibit a strong scattered light continuum and a conspicuous infrared silicate feature. Polarization generally increases towards longer wavelength (red polarimetric color), but the overall shape of the polarization curve remains remarkably similar from 0.44 –1:6 m. The relatively low Pmax and presence of negative polarization tell us immediately that the optically dominant particles in the coma are not Rayleigh scatterers; rather, the particles must have a size parameter, X = 2 a= ¿ 1:5. Nor do the particles scatter like spheres. Shape e/ects for compact particles with 1 6 X 6 5 were studied by Yanamandra-Fisher and Hanner [11]. While silicate spheres with X = 2:5 exhibit negative polarization at all , the computed polarization for other regular shapes showed Pmax about 25% and negative polarization at ¿ c , where c ranged from 110 –160◦ . In contrast, the computed polarization for carbon particles with X = 2:5 displayed mainly positive polarization, with Pmax ∼ 50%; the phase angle of maximum polarization varied with particle shape. Phase matrices for shape distributions of dirty silicate spheroids with X = 3:5 were computed by Mishchenko [12]. As the axial ratio of the spheroids increased, the polarization at intermediate changed from negative (characteristic of spheres) to positive, leaving a negative branch at ¿ 150◦ . Thus, it appears that compact, non-spherical particles with dimensions comparable to the wavelength can reproduce the primary features of the cometary polarization curve. We know from other measurements that comet dust contains both silicate and carbonaceous material. A mixture of these particles could be compatible with P(); however, silicate particles are needed to give the negative polarization at ¿ 160◦ . For X ¡ 2 (but not 1), both absorbing and silicate grains generate red polarimetric color. For somewhat larger X , compact absorbing particles will display blue polarimetric color while silicate particles will have red polarimetric color [11]. The refractive index of the cometary material may be wavelength dependent, and this will inJuence polarimetric color. The
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similarity of the negative polarization branch from one comet to the next and over a broad wavelength range remains a challenge to interpret. A broad size distribution of aggregate particles may be the answer, as discussed in Section 4. 2.2. Angular scattering function, albedo, and color The angular scattering function of the dust is diPcult to determine, because the amount of dust in the coma contributing to the scattered light intensity does not remain constant over time. Two methods have been used to normalize the observed intensity. The Krst method is to assume that the ratio of the dust to gas production rates remains constant and normalize to the gas production rate (e.g. [13,14]). The second method is to compare the measured scattered light to the measured thermal emission from the same volume of the coma, under the assumption that the emitting properties of the dust are not changing [15–17]. The latter method is the only means for extracting an albedo for the dust. The resulting scattering function is relatively Jat from 100◦ to 145◦ [15–17] and rises by about a factor of 2 from 150◦ to 180◦ [13]. No evidence for an opposition surge ¿ 20% was seen in comet 1P/Halley at 171–178:6◦ [14]. Only two comets have been observed at 30◦ ¡ ¡ 60◦ , using the second method, and they display strong forward scattering [18,19]. The geometric albedo of a particle, Ap , is deKned as the ratio of the energy scattered at 180◦ to that scattered by a white Lambert disk of the same geometric cross section [20]. Since comets are rarely observed at 180◦ , it is convenient to deKne Ap () as the product of the geometric albedo and the normalized scattering function at scattering angle . Ref. [15] presented a plot of Ap () in the J bandpass (1:2 m) for 10 comets. The total dust cross section within the Keld of view was determined by Ktting a dust emission model to the thermal spectral energy distribution, then the total cross section was applied to the scattered intensity to derive an average albedo. The resulting albedos are typically very low, about 0.025 at = 100–145◦ and about 0.05 at ∼ 180◦ . There is some indication that Ap is higher for comets beyond 3 AU. The albedo was observed to increase by 50% in comet 1P/Halley’s coma during episodes of strong jet activity [16]. There may be several components of the dust, with di/ering albedos and temperatures; it has to be kept in mind that the average albedo may not represent the actual albedo of any of the components. However, the low average albedo rules out a large population of cold, bright grains that contribute to the scattered light but not to the thermal emission. The color of the scattered light is generally redder than the sun; the reJectivity gradient decreases with wavelength from 5 –18% per 0:1 m at wavelengths 0.35 –0:65 m to 0 –2% per 0:1 m at 1.6 –2:2 m [21]. The red color indicates that the particles are not Rayleigh scatterers; the coloring agent is most likely a refractory organic material. A less red color, suggesting an inJux of smaller particles, was associated with strong jet activity in comet P/Halley and with the spiral structures in comet Hale-Bopp. 2.3. Thermal emission In the infrared, the color temperature of the Planck function Kt to the 3–18 m thermal emission from the dust coma is 5 –20% higher than the temperature of a blackbody in equilibrium with the solar radiation. Dust particles having a wide range of temperatures contribute to the observed
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thermal emission. A temperature excess is typical of micron-sized and smaller absorbing particles in the solar radiation Keld because these small particles cannot radiate ePciently in the infrared at ¿ 10a, where a is the grain radius. For example, a radius a = 0:25 m carbon sphere will have T = 500 K at 1 AU, compared with TBB = 278 K [22]. The wavelength-dependent emissivity of these small grains will also cause departures from a Planckian curve. Larger particles will be signiKcantly hotter than a blackbody only if they are Ju/y and the constituent grain size is ¡ 1 m. Pure silicate particles, on the other hand, can be quite transparent at visual wavelengths while radiating ePciently in the infrared. Their temperature will depend on the Fe/Mg ratio and the extent to which they are physically associated with absorbing material [22]. The Giotto size distribution, with small adjustments in the slope for small particles, can provide a Kt to the thermal spectral energy distribution for a number of comets. However, the thermal emission at = 3–18 m is contributed mainly by the smaller particles, because they are warmer. Detection of dust thermal emission at ∼ 100 m from several comets is the best evidence for a broad size distribution of radiating dust particles [23–25]. 2.4. Silicate emission An emission feature near 10 m, attributed to the stretching mode vibration in small silicate grains, is seen in some, but not all, comets (see review in [26]). Spectral structure indicates that the emitting particles must be a mixture of crystalline and non-crystalline olivine and pyroxenes. The strength of the feature depends on the grain size and temperature. For a strong feature to be visible, the grains must be roughly micron-sized or smaller and their temperature must be comparable to a theoretical blackbody or warmer, in order for their radiation to be visible above the strong thermal continuum produced by featureless particles in the coma. Spectra of comet Hale-Bopp taken from the Infrared Space Observatory exhibited prominent silicate emission features also at 16 –35 m, corresponding to Mg-rich crystalline olivine [27]. 3. Correlations among observable parameters In order to separate the e/ects of particle size and composition, it is useful to look at the correlations among observable quantities. This is particularly important for polarization, which depends in a complex way on the size, composition, and morphology of the scattering particles. Comet Hale-Bopp (C/1995 O1) was an unusually large, active comet with copious dust production. Like P/Halley, it was well observed over many months. Table 1 compares the average observed properties in the inner coma of Hale-Bopp with similar measurements of comet P/Halley. There is a clear correlation of higher polarization, redder polarimetric color, higher albedo, stronger silicate feature, higher infrared color temperature, and enhanced 3–5 m thermal emission. Other comets follow similar trends. A correlation between infrared color temperature and silicate emission in comets was noted by [17]. All of these parameters show the same correlations when comparing spatially resolved measurements of the dust jets and spiral structures in Hale-Bopp with the background coma. Comet Hale-Bopp displayed stronger silicate emission than any other comet. The 10 m feature was already evident at 4:8 AU preperihelion and the total Jux/continuum ratio was ∼ 3 near perihelion [22]. The 3–5 m emission was also extremely high relative to that expected from a blackbody
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Table 1 Correlations among cometary dust scattering properties Hale-Bopp versus Halley
Possible explanations
Polarization
Higher
Polarimetric color
Redder
Albedo
Higher
Continuum
Stronger
Silicate feature
Stronger
Color temperature 3–5 m Jux
Higher Higher
More small grains, a ∼ 0:2 m More absorbing grains a ∼ , a ¿ More small grains, a ∼ 0:2 m More silicate grains, a ∼ More small grains, a ∼ 0:2 m More “clean” silicates More small grains More “clean” silicates Higher dust/gas ratio More small silicate grains, a 6 1 m Higher silicate/carbon abundance Warmer silicates More small absorbing grains, a 6 1 m More small absorbing grains, a 6 0:5 m
in equilibrium. The implied high grain temperatures exceed the temperatures predicted for dirty silicates or Fe-rich silicate and seem to imply a separate population of submicron sized absorbing grains [22,28]. In addition, Hale-Bopp displayed higher polarization than any other comet at comparable ; unfortunately, the geometry never allowed Pmax to be measured near 90◦ . Spatially resolved observations revealed di/erences in the negative branch with position in the coma, with values as low as −5% in the inner few thousand kilometers at = 173◦ [29]. Visible jets and arcs in the inner coma correlated with regions of higher polarization [29–32]. Do these correlations reJect changes in particle size or composition? Table 1 suggests that the scattering properties of dust in Hale-Bopp relative to P/Halley are consistent with an increase in abundance of both silicate and absorbing grains with e/ective grain radius of ∼ 0:15 m, comparable to the grain size in aggregate IDPs of probable cometary origin. First, let us consider the polarization. For regular, but non-spherical shapes, with X ∼ 2:5– 6, Pmax is higher for absorbing particles such as carbon than for silicate particles. As X increases from 2.5 to 5, Pmax decreases for silicate particles, but increases for carbon particles [11]. Thus, higher Pmax would imply more absorbing grains relative to silicate grains in the coma, in contradiction to the observed correlation between Pmax and silicate emission. If X 6 2, then a decrease in grain size would produce an increase in polarization for both silicate and absorbing grains, consistent with both the higher silicate feature and higher 3–5 m Jux. Thus, an increased abundance of grains with radius 0.1–0:2 m within a broad size distribution may explain the scattering properties in the comets with higher Pmax . These grains would also produce a redder polarimetric color. Small grains with e/ective radius 0.15 –0:2 m will not give negative polarization at ¿ 1 m. The measured polarization for Hale-Bopp was essentially 0% at = 2:2 m and = 12◦ [32]. For comets in the low Pmax group, Pmax ∼ 15% and the presence of negative polarization seem to require primarily silicate particles, despite the lack of a silicate feature in these comets, and this remains a puzzle.
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The higher average albedo measured for Hale-Bopp is also consistent with smaller grains, if the grains are not too absorbing. For compact, slightly or moderately absorbing grains (k 6 0:25), the single scattering albedo reaches a maximum at |m − 1|X ∼ 1:5, where m = n − ik is the refractive index. At = 0:5 m the maximum corresponds to an e/ective grain radius ∼ 0:2 m. Consequently, decreasing the mean grain size in the coma from micron-sized to a few tenths of a micron would tend to increase the albedo. (Since the albedo is measured at a speciKc phase angle, any change in the angular scattering function would a/ect the observed albedo also.) Loss of absorbing mantles on small silicate grains is another means of increasing the albedo. For fully absorbing grains, the albedo decreases with decreasing grain size and a shift to smaller grains would lower the albedo. The high 3–5 m thermal emission could be produced by an enhanced population of a ∼ 0:15 m grains only if they are strongly absorbing, while the strong silicate emission implies an increase in 0.1–1 m warm silicate grains. Interstellar silicate grains may have acquired organic refractory mantles through successive intervals of deposition in cold dense molecular clouds followed by irradiation in the di/use interstellar medium [33]. Since interstellar particles are likely to have been incorporated into comets, these core/mantle grains may play a role in the observed scattering properties. For example, an absorbing mantle would cause a core/mantle grain to be warmer than a pure silicate grain. Mantle sublimation may account for changes in the scattering properties with position in the coma [34]. 4. Scattering by aggregates Many of the larger cometary particles may be rather porous aggregates of small grains, as one sees in the chondritic aggregate class of IDPs. In recent years, improved numerical codes and laboratory measurements have allowed progress in understanding the scattering by aggregate particles. The degree of porosity makes a critical di/erence in the optical properties. For a very porous aggregate, the light interacts primarily with the individual structural units. The scattering properties of such aggregates, particularly the polarization, are determined to a large extent by the scattering properties of the constituent grains, as demonstrated by both DDA calculations and laboratory measurements [35,36]. The absorption cross section for an aggregate particle will have a less steep slope at long infrared wavelengths than a single sphere. Consequently, aggregates of absorbing grains in a comet coma will be cooler than isolated small grains, because the aggregate radiates more ePciently in the infrared. Xing and Hanner [37] found that 10-element aggregates of carbon grains had temperatures the same as a sphere with volume equivalent to the aggregate when the porosity was less than 60%. For a porosity of 80% or greater, the aggregate temperature was close to that of the isolated constituent grains. Thus, the high 3–5 m Jux observed in comet Hale-Bopp requires either isolated small absorbing grains or aggregates of these grains with porosity ¿ 80%. Calculations of the scattering function and polarization for aggregate particles composed of spheres with Xi ¿ 1 have been carried out by Petrova et al. [38]. Irregular aggregates with 15 –33 constituent silicate spheres of size Xi ∼ 1:65 exhibited a polarization phase curve similar to that of comets, including negative polarization at large scattering angles, and the scattering function showed a rise toward =180◦ . However, the shape of the polarization curve depended strongly on constituent grain
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size and the small negative branch quickly disappeared for other Xi [38]. These calculations were extended to study the spectral dependence by Petrova and Jockers [39]. They found that the color depended in a complex way on the particle size and scattering angle; resonances in the scattering by spherical particles are at least partly the cause of this complexity. Petrova and Jockers [39] also emphasized that color and polarimetric color will depend on the wavelength-dependent imaginary part of the refractive index in cometary dust. Ten-element aggregates with porosity ∼ 60% generated polarization intermediate between that of the constituent grains and that of a compact particle with size parameter equal to the aggregate size in DDA calculations by Xing and Hanner [37]. A mixture of silicate and carbon aggregates with porosity ∼ 60% and constituent tetrahedral grains of size Xi = 2:6 could produce a polarization curve similar to that of comet dust [37]. These results show promise for duplicating the polarization phase curve of cometary dust with aggregates of constituent grains having Xi ∼ 1:5–3; however, it is still the case that the model parameters have to be “Kne-tuned” to reproduce the Pmax and small negative branch. Finite resources of computer memory and CPU time have limited the numerical modeling to constituent grains of uniform size and shape. Most likely, cometary dust aggregates consist of irregular grains with a range of sizes, shapes, and refractive indices and the aggregates themselves have a range of porosities. For a broad power law size distribution of such aggregates, the weighted contribution to the scattered light may shift with wavelength, so that the optically dominant size parameter remains similar over a broad wavelength range. This could explain in part the very similar shape of the polarization curve from the blue to the near-infrared spectral regions. Particle shapes other than spheres, such as a shape distribution of silicate ellipsoids, can generate a negative polarization branch over a wider range of sizes and can avoid some of the problems of the resonances in scattering by spheres. The e/ect of porosity on the albedo of an aggregate particle will depend on the size and absorptivity of the constituent grains. Hage and Greenberg [40] have shown that, for aggregates having constituent grains with size parameter Xi ∼ 0:2, the albedo will decrease as the porosity increases, particularly for porosity ¿ 75%. In their aggregate model of cometary dust [41,42], the authors assume that the aggregates are composed of core–mantle interstellar grains with core radius 0:1 m and overall radius ∼ 0:14 m; for this model, the albedo will decrease as porosity increases. Only if the constituent grains had radii ¿ 0:2 m and k ¡ 0:25 would the albedo at = 0:5 m increase with increasing aggregate porosity. Laboratory scattering measurements o/er an alternative means for exploring the scattering properties of aggregates, particularly for structures too large or complex to be handled easily by computer simulations. Two of the approaches that have been applied are to levitate particles in microgravity and to conduct measurements scaled to the microwave domain. The PROGRA2 experiments make use of microgravity during parabolic airplane Jights to levitate particles in the path of a laser and measure P() [7,43,44]. These experiments have the advantage of using “natural” particle shapes, but the disadvantage that the aggregates are diPcult to describe precisely. In the recent experiments, the particles consist of submicron grains, radius ¡ 0:1 m forming Ju/y aggregates. The aggregates can agglomerate into very loose structures up to millimeter size. Although the Pmax is generally high because of the small constituent grain size, mixtures of silica and carbon aggregates show promise for reproducing the cometary polarization, including negative polarization at scattering angles ¿ 160◦ . Scattering measurements scaled to microwave wavelengths are a powerful tool for investigating the polarization properties of irregular aggregates, including particle size and shape and wavelength
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dependence [36]. The microwave scattering experiments have the advantage that the aggregate particle under study can be arbitrarily constructed and precisely deKned. Gustafson and Kolokolova [36] presented color and polarization data for aggregates of silicate and absorbing grains of size 0:5 ¡ X ¡ 20 and analyzed the trends of color and polarimetric color with grain size and composition. The e/ect of grain mantles on the scattering properties is also being studied, and this has potentially important application to cometary dust [34]. 5. Conclusions and future directions Optical and infrared observations of the dust coma of active comets yield the following average scattering properties for the ensemble of dust particles. The average geometric albedo at = 0:5 m is low, only 3–5%. The scattering function is fairly Jat from 90◦ to 150◦ scattering angle, then rises by about a factor of 2 from 150◦ to 180◦ . The color of the scattered light is neutral to slightly red. Polarization maximum of 10 –25% at = 0:5 m occurs near 90◦ , with negative polarization at scattering angles 160 –180◦ . Polarization is higher at longer wavelengths (red polarimetric color), but the overall shape of P() remains similar from 0:44 ¡ ¡ 2:2 m. In the infrared, the color temperature of the Planck function Ktted to the 3–18 m thermal emission is higher than the equilibrium blackbody temperature. Some (but not all) comets display an emission feature at 8–12:5 m due to small, optically thin silicate grains. These scattering properties are in qualitative agreement with a mixed dust population of silicate and carbonaceous material, as inferred from the dust experiments on the Halley space probes and IDPs of probable origin. The low average albedo indicates that silicates must be well mixed with absorbing material. (Only a small fraction of Knely dispersed absorbing material is needed to decrease the albedo of a silicate particle.) The red color is evidence that the particles are not Rayleigh scatterers; the coloring agent is most likely a refractory organic material. The relatively low maximum polarization implies a particle size parameter ¿ 1:5. The presence of silicate emission requires a population of micron-sized or smaller silicate particles and not so embedded in absorbing material that the feature contrast is masked. A color temperature above the equilibrium blackbody temperature requires particles that can absorb more ePciently at visual wavelengths than they radiate in the infrared; this requirement can be met by absorbing grains that are micron-sized or smaller. Larger particles can have elevated temperatures only if they are very porous and the constituent grains are micron-sized or smaller. A high 3–5 m thermal Jux is a particularly sensitive indicator of hot submicron sized absorbing grains (grain radius a 6 0:5 m). Aggregate particles may be particularly relevant to describing the scattering by cometary dust. The scattering behavior of aggregates depends on the porosity. For very porous particles, the scattering and emitting properties depend primarily on the those of the constituent grains. Flu/y aggregates composed of grains with size parameter X ¡ 1 have the high polarization typical of Rayleigh particles; thus, they are not a useful analogue for cometary dust. The persistence of the small negative polarization branch over a wide wavelength range remains an unsolved puzzle. Most numerical models require a Kne-tuning of the particle size and ratio of silicate to absorbing grains to match the −2% polarization. However, for a broad power law size distribution, the weighted contribution to the scattering may shift with wavelength, so that the optically dominant size/wavelength ratio remains similar.
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To make progress, future numerical modeling should focus on aggregates that contain a range in constituent grain sizes (size parameter 1 ¡ X ¡ 10) and move away from very regular shapes such as spheres or tetrahedra. For example, introducing a size and shape distribution of spheroids as the constituent grains would be an important step forward. Understanding the relative inJuence of the constituent grains versus the overall particle structure, as a function of the porosity, is an important goal for both modeling and scattering experiments. Acknowledgements This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration. References [1] McDonnell JAM, Lamy PL, Pankiewicz GS. Physical properties of cometary dust. In: Newburn RL, Neugebauer M, Rahe J, editors. Comets in the post Halley era. Dordrecht: Kluwer, 1991. p. 1043–73. [2] Levasseur-Regourd A-C, McBride N, Hadamcik E, Fulle M. Similarities between in situ measurements of local dust light scattering and dust Jux impact data within the coma of 1P/Halley. Astron Astrophys 1999;348:636–41. [3] Fulle M, Levasseur-Regourd A-C, McBride N, Hadamcik E. In situ dust measurements from within the coma of 1P/Halley: Krst-order approximation with a dust dynamical model. Astron J 2000;119:1968–77. [4] Bradley JP, Sandford SA, Walker RM. Interplanetary dust particles. In: Kerridge JF, Matthews MS, editors. Meteorites and the early solar system. Tucson: University of Arizona Press, 1988. p. 861–95. [5] Bradley JP, Humecki HJ, Germani MS. Combined infrared and analytical electron microscope studies of interplanetary dust particles. Astrophys J 1992;394:643–51. [6] Jessberger E. Rocky cometary particulates: their elemental, isotopic, and mineralogical ingredients. Space Sci Rev 1999;90:91–7. [7] Levasseur-Regourd AC, Hadamcik E. Light scattering by irregular particles in the solar system: observations and interpretation by laboratory measurements. JQSRT, 2002, this volume. [8] Chernova GP, Kiselev NN, Jockers K. Polarimetric characteristics of dust particles as observed in 13 comets: comparisons with asteroids. Icarus 1993;103:144–58. [9] Levasseur-Regourd AC, Hadamcik E, Renard JB. Evidence for two classes of comets from their polarimetric properties at large phase angles. Astron Astrophys 1996;313:327–33. [10] Kiselev NN, Velichko FP. Polarimetry and Photometry of Comet C/1996 B2 Hyakutake. Icarus 1998;133:286–92. [11] Yanamandra-Fisher PA, Hanner MS. Optical properties of nonspherical particles of size comparable to the wavelength of light: application to comet dust. Icarus 1999;138:107–28. [12] Mishchenko MI. Light scattering for size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength. Appl Opt 1993;32:4652–66. [13] Millis RL, A’Hearn MF, Thompson DT. Narrowband photometry of comet P/Stephan-Oterma and the backscattering properties of cometary grains. Astron J 1982;87:1310–7. [14] Meech KJ, Jewitt DC. Observations of comet P/Halley at minimum phase angle. Astron Astrophys 1987;187: 585–93. [15] Hanner MS, Newburn RL. Infrared photometry of comet Wilson (1986l) at two epochs. Astron J 1989;97:254–61. [16] Tokunaga AT, Golisch WF, Griep DM, Kaminski CD, Hanner MS. The NASA Infrared Telescope Facility comet Halley monitoring program I. Preperihelion results. Astron J 1986;92:1183–90. [17] Gehrz RD, Ney EP. 0.7–23 m photometric observations of P/Halley 1986 III and six recent bright comets. Icarus 1992;100:162–86. [18] Ney EP, Merrill KM. Comet West and the scattering function of cometary dust. Science 1976;194:1051–3.
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