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Optical effects of irregular cosmic dust particle U2015 B10
Journal of Quantitative Spectroscopy & Radiative Transfer 63 (1999) 1}14
Optical e!ects of irregular cosmic dust particle U2015 B10 Miroslav Kocifaj *, Igor Kapis\ inskyH , Frantis\ ek Kundracik Department of Interplanetary, Astronomical Institute, Slovak Academy of Sciences, Matter, Du& bravska& cesta 9, 842 28 Bratislava, Slovak Republic Faculty of Mathematics and Physics, Department of Radiophysics, Universitas Comeniana, Mlynska& dolina F2, 842 15 Bratislava, Slovak Republic Received 6 July 1998
Abstract The radiation e!ects of nonspherical really shaped cosmic dust particles are studied in this paper. A correlation between particle shape and estimated lifetime of a particle in the solar system was studied also. The discrete dipole approximation is utilized to calculate e$ciency factors for scattering, absorption, extinction and radiation pressure, respectively, and scattering phase functions. Chemical and physical properties of our sample particle U2015 B10 are obtained by laboratory analyses. The model of particle constructed using computer techniques is compared with the real photos. Results of calculations show that Poyinting}Robertson drag used to simulate the particle motion in interplanetary space leads to incorrect results because the spherical shape of particle is proposed here. Therefore, for instance, a stability of zodiacal cloud cannot be explained in this manner. On the other hand, any asphericity or irregularities in particle shape will be re#ected in the increase of energy scattered in nonradial (non forward) direction. This fact is directly connected with the lifetime of the particle in solar system * i.e. the smaller the energy scattered forwardly the greater possibility of increasing the particle lifetime. Stability of zodiacal cloud could be then explained also by particle shape * e.g. if zodiacal cloud consists mainly of particles similar to our sample (which is very probable). The mean bulk density of our particle (about 1.83 g cm\) correlates well with material of carboneous chondrites of density about 2.1 g cm\ (from asteroids or comets, too). This particle could belong also to the debris (remnants) of Population I, i.e. to large grains with density approx. 2}3 g cm\. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Cosmic dust particles; Irregularly shaped particles; Mean e!ective; Refractive index; Scattering; Radiation
***** * Corresponding author. Tel.: 004217 378 2727; fax: 004217 375 157; e-mail: [email protected]. 0022-4073/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 8 ) 0 0 1 3 0 - 7
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1. Introduction Interplanetary dust particles (IDPs) for a long time have been the focus of attention because they are a very valuable resource for fundamental data on small and the smallest bodies in our Solar System, such as comets, asteroids, meteoroids and especially micrometeoroids. Particle size and shape are important factors in theory of particle spiral motion towards the Sun, and in constituting of the zodiacal cloud. By comparing the model results with IRAS observations in the 25 lm wave band, it was found that the observed shape of the zodiacal cloud can be accounted for by a combination of about to asteroidal dust and about to cometary dust. Cometary particles do not have a well-de"ned source in comparison with asteroidal particles. It is not de"nitely clear if they are produced by one highly active comet, several active comets, or by all the known short periodic comets or by comets in the Kuiper belt. Therefore any knowledge about particle properties may clarify the problem of stability of the zodiacal cloud. The well-known Pointing} Robertson e!ect is often utilized to estimate lifetime of the dust particles in solar system. For example, the PR drag lifetime of Encke-type 9 lm-sized particles (near to our studied particle) was estimated about 5000 years [1]. However, this result was obtained under assumption of perfectly spherical silicate and here Mie's theory was applied. For highly aspherical particles, spherical/nonspherical di!erences are signi"cant and make the Mie theory completely inapplicable [2]. An ideal sphere (larger than incident wavelength) is strongly forwarded scattering, but irregularities redirect rays from forward peak into other phase angles. This has the e!ect of increasing the scattering e$ciency in nonradial directions and leads to inadequate results for lifetime of such particles in the solar system assuming the PR drag for spheres. Therefore attention should be concentrated on the possibility of getting more precise model of the real-shaped particle. The better the particle model the better are the results of calculation. Many direct and/or indirect methods are used to get the reliable information about particle characteristics. The best conditions to "nd the complete structural properties of the particles is laboratory study of the directly collected particles. IDPs have been collected in a variety of terrestrial environments (e.g. deep-sea sediments, ice cores) but also in the stratosphere. Very small particles ((50 lm in diameter) are routinely collected in the Earth's stratosphere between 18 and 20 km altitude through the NASA Johnson Space Center (JSC) Cosmic Dust Program since 1981. However, all these collections of IDPs may be also contaminated by many kinds of natural terrestrial and anthropogenic materials. But a statistical analysis of this collection experiment over roughly 15 years show that the percentage of true cosmic dust is approximately 30% [3]. The properties of IDPs collected from the stratosphere should predominantly re#ect the properties of the main-belt asteroid parent bodies [4], but the question is more complicated (see Discussion also). These particles are the best available samples of IDPs (see e.g. [5]) and they are also very suitable for studying their detailed physical and optical properties mainly for a dust dynamics purpose. We have performed analytical electron microscopy (AEM) studies of 12 NASA stratospheric IDPs [6}8]. According to the results of these analyses we have chosen the cosmic dust particle U2015 B10. The selection looks on the nature of individual samples and paper intention which deals with mainly theoretical modeling. This cosmic particle was retrieved from the collection surface U2015 #own aboard the NASA U-2 aircraft during a series of #ights that were made along the west coast of North America from 22 June 1983 to 18 August, 1983. An inertial-compact collectors were mounted underneath the wings of high-#ying aircraft. The total of 39.6 h of
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Fig. 1. (a) Particle U2015 B10 at angle !603. (b) Model of the particle U2015 B10 at angle !603.
stratospheric exposure by usual manner was accumulated. According to preliminary original analysis including data obtained by optical AEM studies published in the Cosmic Dust Catalog, Vol. 5, No. 1 on p. 10 of Ref [9], the chosen particle is 9;13 lm in size, irregularly shaped, with opaque or translucent transparency and pale yellow to brown colour. The size coincides with the results of mid-infrared spectropolarimetry of the interstellar grains obtained by Hildebrand and Dragovan [10], i.e. that grains are oblate and the best "t for a ratio of particle axes 2 : 3. The luster is characterized as subvitreous or vitreous (see also Figs. 1a, 2a and 3a). The NASA analysis shows a high peak for Si and relatively lower peaks for Mg, Al, S, Ca and Fe in energy-dispersive X-ray (EDX) spectrum. Our own EDX analysis unambiguously con"rmed the cosmic origin of U2015 B10 sample. We also have found that in particle composition dominates the enstatite, composition of which is near to Mg Fe'' SiO . Our analysis did not reveal the further elements in comparison with the original analysis besides the content of oxygen which was naturally assumed. We also assume that the minor amounts of calcium and aluminum can be bound to calcium aluminosilicate (anortite) dispersed uniformly between the grains of enstatite, which have the size from 0.5 up to 3 lm. According to planary distribution it seems that sulphur is localized more in the core of grain, and not on its edge. From the morphological point of view it is remarkable that the U2015 B10 sample has probably a cavity in its center (for further details see [7]). Because of majority of the mineral enstatite in composition of U2015 B10 the mean refractive index of the particle can be in su$cient accuracy "tted by the enstatite optical properties. In meteoritic astronomy enstatite chondrites (or E chondrites) represent only 1.0% of all falls. They have the highest free metal and sul"de content (23}35% by weight) and the lowest oxidation state of all chondrites. Their silicate phase is almost purely enstatite (MgSiO ), an iron-free form of pyroxene.
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Fig. 2. (a) Particle U2015 B10 at angle #303. (b) Model of the particle U2015 B10 at angle #303.
Fig. 3. (a) Particle U2015 B10 at angle 03. (b) Model of the particle U2015 B10 at angle 03.
2. Radiation e4ects by irregular particles The great amount of the particles #oating in the upper Earth's atmosphere have nearly a constant mixing ratio, which indicates their extraterrestrial source. The cosmic dust particles collected by NASA in the stratosphere are characterized by their own size distribution, refractive
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index, shape and so on. Their in#uence on solar radiation is a little bit di!erent in comparison with atmospheric aerosol system. However, an &&in"nitesimal'' number of particles could be only assigned as spherical in both systems and this fact should be taken into account in any radiation model. Polydisperse spherical}nonspherical di!erences in the angular distribution of the scattered intensity can be large. In this case, Mie theory should not be used because of high errors. All the elements of the polydisperse scattering matrix are complicated functions of particle shape and, for di!erent nonspherical particles of equal size, may di!er in magnitude and even sign. Because all elements of the scattering matrix are strongly size dependent, they are sensitive indicators of particle size and asphericity. The informations about particle shape and refractive index are necessary for a more reliable estimation of the optical characteristics of true IDPs. As a matter of fact, the percentage of irregularly shaped cosmic dust particles is roughly 87. A partial concavity of particle shape may have a pronounced e!ect on light scattering. The discrete dipole approximation (DDA) method is used to calculate optical e!ects by irregular particles. DDA is a #exible and powerful tool for computing scattering and absorption by arbitrary targets and was described e.g. by Draine [11, 12]. DDA method is applicable for concave particles and can be successfully used for small particles. In comparison with well-known ¹-matrix method, the DDA is slower for large particles [2, 13]. We had applied DDA method for calculation of light scattering by some model particles [14]. It was shown that approximation of particle shape by sphere of identical volume may lead to inadequate evaluation of particle spiraling in interplanetary space. Calculations were performed for six model particles (sphere, cylinder, ellipsoid, hexagonal prism, rectangular target, tetrahedron) in di!erent orientations. Wavelength of j"0.55 lm of an incident radiation and e!ective radius of the particle 0.5 lm were used for calculation. Complete equation of motion was derived by Kl'ac\ ka and Kocifaj [15]. The following integrals are important for particle motion in solar system (they represent the projections of intensity vector of scattered radiation into each of three perpendicular axes of coordinate system): G "Q !Q G "Q G "Q
L L
L
p (h , u ) cos h d) ,
p (h , u ) sin h cosu d) , p (h , u ) sin h sin u d) , Q
where Q and Q are factors of e$ciency for extinction and scattering, p (h ,u ) is the phase function, h , u and ) are scattering, azimuth and solid angle, respectively. It was shown that motion of a real particle will be di!erent in comparison with the motion of the sphere when the values of G and/or G are at least at level 10\ of G . The greater the di!erence between isoline pro"les of p (h , u ) for real-shaped particle and partially symmetrical particle, the greater the ratios G /G or G /G . The motion of small particles in the interplanetary space is strongly dependent on given ratios G /G (i"1,2). A variability of p(h , u ) over wide range (several orders) can produce G the isoline structure with partially radial symmetry. It is because the greatest amount of scattered
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radiation energy is always in the forward direction. We found a cylindrical particle as a good candidate for the atypical motion in comparison with a sphere of identical volume. This indicates an enlargement of lifetime of such particle in solar system and increases the stability of zodiacal cloud.
3. The cosmic particle U2015 B10 and processing methods For a numerical simulation we have used the model of irregularly shaped particle which is su$ciently representative (true cosmic dust sample) and which is closest to the reality also. Therefore, for the model there was chosen the NASA particle U2015 B10 of which we have gained a sequence of "ve photos (images) made at di!erent angles (!60, !30, 0, #30, #603). The particle was washed of silicone oil with hexane and mounted on porous substrates. Because the technical problems did not allow to separate the sample from the substrates (made of porous boron and coated with carbon), the mentioned images represent approximately 80% of the particle surface. The shape of the missing 20% of surface we have modeled by design engineer, where the transparency of the particle was very helpful in this process. The result is a cube model of the particle. Edge of the cube was about 0.23 lm and total volume of the particle +187 lm. Particle model consists of 14 154 cubes, where the position of zero point inside the coordinate system (geometric center of the particle) is [27, 16, 16]. Center of gravity referred to this geometric center is [0, 1, !5]. The model was rendered using ray-tracing method. Program 3D-Studio MAX fy Kinetix was used. The particle U2015 B10 was de"nitely classi"ed as a cosmic particle which consists mainly of enstatite. Its refractive m"n !i.n can be expressed by simply formulae for a visible spectrum: P G n "1.735!0.26j, n (10\ P G using data published by Egan and Hilgeman [16]. Similarly as in Kocifaj and Kapis\ inskyH [14] we have studied an interaction of the particle with monochromatic solar radiation at the wavelength j"0.55 lm, which coincides with the maximum intensity in the solar spectrum. The corresponding refractive index of enstatite is then 1.59 for a given wavelength. Figs. 1}3 show the views of model together with the corresponding photos. It was not used in the same direction of illumination in both cases, for real and model particle. Our model consists of cubes, where surface re#ects the light by a di!erent way as a real-shaped particle. In this case we do not see some details of the model surface due to shadows of the cubes. Therefore, we have chosen such orientation of the particle in radiation "eld, for which the shapes of both, real particle and its model, may be correctly compared. The "gures demonstrate coincidence between the model and real particle. The DDA routine developed by Draine and Flatau [11] was used for calculation of the radiation characteristics such as phase function or e$ciency factors for extinction and scattering. Su$ciently accurate results can be guaranteed by this method if some conditions are ful"lled, for example if mkd(1,
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where m is particle refractive index, k"2n/j is a wave vector, and d is a lattice spacing expressed as follows: a , d" (3N/4n) where N is total number of cubes in the model and a is e!ective radius of a sphere of equivalent volume. We have developed numerical codes for processing of measured data (particle geometry), where the "ne-model (1) or coarse-model (2) procedures are included as additional functionality. This is helpful if the last condition is not ful"lled and we need to increase the number of cubes (1). Shape of an examined particle is not changed, but we can replace one cube by a 4, 9, etc. smaller cubes (subcubes). On the other hand, the calculation may be rapidly accelerated by decreasing of number of cubes (2) (using backtracking procedure, i.e. 4,9, 2 cubes are replaced by one cube of the same volume), but constraints cannot be violated (e.g. mkd should be smaller than 1). Unfortunately, DDA method needs to allocate too long a memory piece if characteristic size of a particle is much greater than a wavelength of an incident radiation. The computer memory expected for our particle U2015 B10 is about some hundreds of megabytes. However, the particle size is not so important for our study, because a set of IDPs consists of a wide spectrum of particle sizes and therefore we can also examine an interaction of radiation "eld with a small particle of the same shape. Such a study describes real conditions if a particle size lies inside the size range of a given particle set. Of course the scattered radiation is strongly dependent on the particle size. But we concentrate here on the radiation e!ects by a really &&shaped'' particle (excepting any degree of its shape symmetry) which characterize a real particle in the IDPs set. Each of six particle models studied in our previous paper [14] has its own degrees of symmetry (e.g. center point symmetry, or axially symmetry etc.). It can be expected that the values of G and G will not be so critical for these particles in comparison with the real-shaped particle. On the base of the facts discussed above and in agreement with our "rst paper we have chosen the e!ective particle radius to be equal to 0.5 lm. The particles of the size comparable to the incident wavelength are good example for a study of many e!ects because they are near the maximum scattering e$ciency, i.e. they are very sensitive to the incident radiation. The explanation of important radiation e!ects by the cosmic dust particle U2105 B10 is based on comparison of results obtained for both our particle and sphere of the identical volume and optical properties.
4. Calculation and results Results of calculation are presented in the Table 1. The factor of e$ciency of radiation pressure Q was calculated as a next important parameter of a particle motion in the interplanetary space. Values of Q depends on particle orientation in relation to the direction of incident radiation for the sphere. Of course, Q is independent of orientation for sphere. The greater the variability of Q , the greater the particle asphericity that can be expected. For example, we found the range of NP Q from 0.16 to 0.74 for a rectangular particle model (ratio of a edge was 1 : 4 : 12). Discussed range was also wide for a cylindrical particle (from 0.39 to 1.21). This particle was evaluated as the best candidate from six particle models for a long lifetime in a solar system. The values of Q for our
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Table 1 Results of the calculations for sphere and cosmic particle U2015B10 Parameter
Sphere
Q Q NP G G /G G /G
2.075 1.350 1.389 0.000 0.000
U2015B10 h"03 2.449 0.989 1.031 !0.007 0.320
U2015B10 h"603 4.084 1.120 1.203 0.316 !0.326
U2015B10 h"903 4.603 0.939 1.066 !0.050 !0.290
cosmic dust particle vary over small closed interval (from 0.9 to 1.1), which is caused by the nearly spherical shape of the particle. Here we should recall that the measurements of an interstellar polarization give lower and upper limits of particle axes ratio from 0.3 to 0.9 for interstellar grain (assuming the spheroidal shape, where particles are not too oblate/elongated). It means, if we do not like to study only a special set of the IDPs, the main interest should be in statistically important IDP systems, which may consist of aspherical particles similar to our sample. Q for an IDP U2015 B10 is nearly constant but the components G and G are comparable to the value G . This fact is re#ected in increasing of a lifetime of such a particle in a solar system. It is caused by slow spiraling due to signi"cant level of nonradial components G and G in comparison with radial component G . Such particle cannot be simply replaced by totally re#ecting target or equivalent sphere as it was often assumed in PR e!ect studies. Of course, it was expected. This result contributes to explanation of observed (relative) constancy of zodiacal light, which directly
Fig. 4. Isolines of the phase function for light scattering by spherical particle at orientation h"03.
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Fig. 5. (a) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"03. (b) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"603. (c) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"903.
depends on the stability of zodiacal cloud. Discussed conclusion of the calculations is con"rmed by Figs. 4 and 5, where isolines of the phase function of scattered radiation are presented. Source of incident radiation is behind the particle, which is situated in the center of the picture. The pictures are drawn in polar system of coordinates, where polar angle (equals to scattering angle) is calculated from 0 rad (central point) to n/2 (circle), and azimuth angle is calculated from 0 rad (eastern point) to 2n in counter-clockwise direction. The displayed curves are in log-scale because
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Fig. 6. (a) Isolines of the phase function for light scattering by cylindrical particle at orientation h"03. Particle radius: 0.5 km, wavelength of an incident radiation: 0.55 lm. (b) Isolines of the phase function for light scattering by cylindrical particle at orientation h"603. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm. (c) Isolines of the phase function for light scattering by cylindrical particle at orientation h"903. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm.
of the variability of phase function values over several orders. However, p vary over only 2}3 magnitudes, which is substantially less than for model particles. That is the reason of high values of G or G , respectively. In comparison with the results published in our previous paper [14] we do not see any symmetry of the isolines of phase function for arbitrary orientation of the particle U2015 B10 (Figs. 4 and 5). On the other hand, calculation results for the selected particle models (cylinder and hexagonal
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Fig. 7. (a) Isolines of the phase function for light scattering by hexagonal particle at orientation h"03. Particle radius: 0.5 km, wavelength of an incident radiation: 0.55 lm. (b) Isolines of the phase function for light scattering by hexagonal particle at orientation h"603. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm. (c) Isolines of the phase function for light scattering by hexagonal particle at orientation h"903. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm.
prism) clearly demonstrate an axially symmetry of a scattered radiation "eld (Figs. 6 and 7). The mirroring of the isolines over an axis of symmetry causes the signi"cant decreasing of one from the component G or G . Intensity of scattered radiation near to the forward direction (in small scattering angle approximation) depends not on whole particle surface but mainly on cross section pro"le. Therefore, the isolines close to the central point of the picture correspond to the particle shape in the current orientation. The values of G /G and G /G are built by a structure of the isolines. It means, both, the symmetry and absolute values of p are important. The greater the
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gradient of p (h , u ) for small scattering angles h , the smaller are the ratios G /G (i"1,2). The G isolines of p are axially symmetrical for the cylindrical particle, but discussed gradient is much smaller than for hexagonal prism. Therefore the ratios G /G for cylinder are greater than for G hexagonal particle. This fact coincides with lifetime of inspiraling of the given particle in the solar system. The greater the gradient, the greater is the density of the isolines. Each picture presented here contains the same number of isolines to make a simple comparison of the results. One can see that our cosmic dust particle is characterized by the smallest gradient of p (for a small scattering angle), which results in the greatest values of G /G . Besides, the values of p for this particle vary G over smallest interval * it is only two magnitudes for orientation h"03 and three magnitudes for orientation h"903$. For example, this interval covers seven orders for the hexagonal prism. 5. Conclusions and their discussions The radiation e!ects by the really shaped particle was studied for the model of cosmic dust particle situated in the interplanetary space. Our sample particle U2015 B10 was collected by aircraft in Earth's stratosphere during NASA experiment. Preparing the particle model and including it with the calculation procedure the optical}physical properties were obtained such as scattering phase function, e$ciency factors for absorption, extinction and radiation pressure, etc. Our aim was to check an important level of the particle shape in the problem of estimation of particle lifetime in the solar system. Attained conclusions were based on comparison with the relevant results for sphere of an identical volume. Some particle models (such as rectangular target, hexagonal prism, cylinder, ellipsoid, tetrahedron) were studied in our previous paper. Each particle model used in the calculation was characterized by its own degree of symmetry. That is the problem of simulation of radiation transfer through model particle * the symmetry always produce the increasing of radiation energy scattered in forward direction and of course the small amount of energy is scattered to other (perpendicular) directions. Based on discrete dipole approximation method (DDA) we found the signi"cant di!erences between radiation e!ects by sphere and our cosmic particle. Well-known Poyinting}Robertson drag (PR e!ect) is assumed to be representative for particle motion and its spiraling in interplanetary space. Basic formula for PR e!ect assumes the spherical particles. Unfortunately, this assumption can lead to inadequate evaluation of particle motion in solar system, which is a serious problem. Namely, the stability of zodiacal light cannot be explained by PR drag for spheres. Results of calculation for particle U2015 B10 show that signi"cant level of nonradial components G or G (in comparison with radial component G ) leads to slow spiraling of examined particle. This fact directly in#uences the lifetime of the particle. This conclusion contributes to the explanation of stability of zodiacal cloud. It was also shown that both the symmetry and absolute values of scattering phase function p can in#uence the motion of the particle and its lifetime. The greater the gradient of p (h, u), the smaller the ratio G /G . An G important result of this study is therefore the very transparent-dependence radiation e!ects (and particle motion) on particle shape symmetry. Generally, any degree of symmetry in particle shape contribute to forward scattering and results in decreasing of nonradial components of G . Therefore G an asphericity, unconcavities and any irregularities in particle shape can de"nitely change its motion in interplanetary space in comparison with PR e!ect and increase a lifetime of the particle in some magnitudes.
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Table 2 Volume percentages of individual elements in particle U2015B10 Element
O
Mg
Al
Si
S
Ca
Fe
Vol. %
40.60
17.49
3.21
24.40
2.31
1.82
10.17
According to our previous paper [7] the chemical analysis of studied particles was also made. Based on particle composition presented in Table 2 we have derived the mean particle density (about 1.83 g cm\). What concerns this calculated value of bulk density of investigated particle U2015 B10, it is suitable to mention some remarks with respect to the probable origin of the studied sample. Despite the fact that considering the origin of the particle only according to its density is not quite adequate, at least it is possible to mention that the parent bodies of investigated microparticle cover several kinds of interplanetary and interstellar material such as cometary (dust) ejecta, asteroidal debris, meteoritic material, possible interstellar grains, intermingling material, etc. With respect to the density of the mentioned sample and its potential parent body we can probably exclude very soft cometary material produced mainly by short period comets with very low bulk density (about 0.27 g cm\) as well as regular cometary material (long-period comets * density about 0.75 g cm\). It seems that the dense cometary material with density about 1 g cm\ produced by the inner part of comets is also inconvenient. Material of carboneous chondrites with density about 2.1 g cm\ (from asteroids or comets too) "ts well with the density of the U2015 B10 sample. It is not necessary to consider the higher density values of achondritic material (approx. 3.2 g cm\) and of ordinary chondrites (approx. 3.7 g cm\). Naturally from the same reasons as the soft cometary material, the stony-iron meteoritic material (density 4.7}5.6 g cm\) as well as iron meteorites (7.7 g cm\) have to be excluded from this consideration (see e.g. [17}19] etc.). Several years ago Sergeant and Lamy [20] published conception of the two-component dust population with di!erent mean size and density. From this point of view our sample could belong to the debris (remnants) of Population I, i.e. to large grains with diameter greater than 3 lm and density approx. 2}3 g cm\. The Population II consists of small particles (d(3 lm) having higher densities (+8 g cm\) with a minor component of silicates. In this connection it is also interesting that Brownlee et al. [21] published their conclusions based principally on their collection experiments. They concluded that the collected grains (such as cosmic sample U2015 B10) are compact aggregates of very small particles and their bulk density is about 2 g cm\. In the quoted paper authors emphasize that these conclusions are further supported by the microcraters, analyses and other numerous experiments. But generally it can be said that the results of the bulk density determinations of dust particles (or their parent bodies) are still controversial.
Acknowledgements This work has been supported by a Grant No 4174/97 of the Slovak Academy of Sciences. The authors are also very grateful to Dr. B.T. Draine and P.J. Flatau for their DDSCAT code and to Mrs. Z. Kapis\ inskaH for technical assistance in some parts of paper.
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References [1] Liou JC, Dermott SF, Xu YL. The contribution of cometary dust to the zodiacal cloud. Planet Space Sci 1995;43/6:717}722. [2] Mishchenko MI. Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength. Appl Opt 1993;32/24:4652}66. [3] Kapis\ inskyH I. The statistical and astronomical view of the decennium of the NASA Cosmic Dust Program. Contrib Astron Obs SkalnateH Pleso 1992;22:215}26. [4] Flynn GJ, Interplanetary dust particles collected from the stratosphere: physical, chemical, and mineralogical properties and implications for their sources. Planet Space Sci 1994;42/12:1151}61. [5] Walker RM. Laboratory studies of interplanetary dust. NASA Conf. Publication 2403 &&Interrelationships Among Circumstellar Interstellar, and Interplanetary Dust''. Maryland, 1985:55}69. [6] Kapis\ inskyH I, Figusch V, Hajduk A, Ivan J, Iz\ dinskyH K. Reanalysis of four NASA stratospheric particles. Earth Moon Planets 1994;64:273}80. [7] Kapis\ inskyH I, Figusch V, Hajduk A, Ivan J, Iz\ dinskyH K. The analysis of four cosmic dust particles. Earth Moon Planets 1995;68:347}60. [8] Kapis\ inskyH I, Figusch V, Hajduk A, Ivan J, Iz\ dinskyH K. Determination of origin of NASA stratospheric particles. Earth. Moon Planets 1996;73:7}14. [9] Clanton VS, Gooding JL, McKay DS, Robinson GA, Warren JL, Watts LA, editors. Picture in: Cosmic Dust Catalog (Particles from collection #ag U2015), vol. 5. NASA, Johnson Space Center, Houston, Texas, (1):10,1984. [10] Hildebrand RH, Dragovan M. The shapes and alignment properties of interstellar dust grains. Astrophys J 1995;450:663}6. [11] Draine BT, Flatau PJ. Discrete-dipole approximation for scattering calculations. J Opt Soc Amer A, 1994;11/4:1491}9. [12] Draine BT. The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys J 1988;333:848}72. [13] Mishchenko MI, Travis LD. Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation. Appl Opt 1994;33/30:7206}25. [14] Kocifaj M, Kapis\ inskyH I. Optical e!ects of dust particles of di!erent shapes. Contrib Astron Obs SkalnateH Pleso 1997;27:5}14. [15] Kl'ac\ ka J, Kocifaj M. Electromagnetic radiation and equation of motion for a dust particle. Proc. Conf. on Astrometry and Celestial Mechanics. Pozna 13}17 September 93,1994;187}90. [16] Egan WG, Hilgeman T. The interstellar medium: UV complex index of refraction of several candidate materials. Astron J 1975;80/8:587}94.. [17] Fechtig H, Rahe J. Comets and ESA's Space Mission Giotto to Halley's Comet. Naturwissenschaften Vol. 71. Berlin: Springer, 1984:275}93. [18] Lamy PL. Some remarks on the density of interplanetary dust grains. In: Properties and Interactions of Interplanetary dust, Giese RH, Lamy P. editors. Dordrecht: Reidel, 1985;137}40. [19] Ceplecha Z. Numbers and masses of di!erent populations of sporadic meteoroids from photographic and television records. In: Ceplecha Z, Lamy P, editors. The 10th European Regional Astronomy Meeting of the IAU. Prague, 24}29 August 1987:211}15. [20] Le Sergeant LB, Lamy PL. On the size distribution and physical properties of interplanetary dust grains. Icarus, 1980; 43: 350}72. [21] Brownlee DE, HoK rz, F, Tomandl DA, Hodge PW: Physical properties of interplanetary grains. 962}81, The Study of Comets, IAU Colloquium No. 25, NASA SP-393, 1976.
Optical e!ects of irregular cosmic dust particle U2015 B10 Miroslav Kocifaj *, Igor Kapis\ inskyH , Frantis\ ek Kundracik Department of Interplanetary, Astronomical Institute, Slovak Academy of Sciences, Matter, Du& bravska& cesta 9, 842 28 Bratislava, Slovak Republic Faculty of Mathematics and Physics, Department of Radiophysics, Universitas Comeniana, Mlynska& dolina F2, 842 15 Bratislava, Slovak Republic Received 6 July 1998
Abstract The radiation e!ects of nonspherical really shaped cosmic dust particles are studied in this paper. A correlation between particle shape and estimated lifetime of a particle in the solar system was studied also. The discrete dipole approximation is utilized to calculate e$ciency factors for scattering, absorption, extinction and radiation pressure, respectively, and scattering phase functions. Chemical and physical properties of our sample particle U2015 B10 are obtained by laboratory analyses. The model of particle constructed using computer techniques is compared with the real photos. Results of calculations show that Poyinting}Robertson drag used to simulate the particle motion in interplanetary space leads to incorrect results because the spherical shape of particle is proposed here. Therefore, for instance, a stability of zodiacal cloud cannot be explained in this manner. On the other hand, any asphericity or irregularities in particle shape will be re#ected in the increase of energy scattered in nonradial (non forward) direction. This fact is directly connected with the lifetime of the particle in solar system * i.e. the smaller the energy scattered forwardly the greater possibility of increasing the particle lifetime. Stability of zodiacal cloud could be then explained also by particle shape * e.g. if zodiacal cloud consists mainly of particles similar to our sample (which is very probable). The mean bulk density of our particle (about 1.83 g cm\) correlates well with material of carboneous chondrites of density about 2.1 g cm\ (from asteroids or comets, too). This particle could belong also to the debris (remnants) of Population I, i.e. to large grains with density approx. 2}3 g cm\. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Cosmic dust particles; Irregularly shaped particles; Mean e!ective; Refractive index; Scattering; Radiation
***** * Corresponding author. Tel.: 004217 378 2727; fax: 004217 375 157; e-mail: [email protected]. 0022-4073/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 8 ) 0 0 1 3 0 - 7
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1. Introduction Interplanetary dust particles (IDPs) for a long time have been the focus of attention because they are a very valuable resource for fundamental data on small and the smallest bodies in our Solar System, such as comets, asteroids, meteoroids and especially micrometeoroids. Particle size and shape are important factors in theory of particle spiral motion towards the Sun, and in constituting of the zodiacal cloud. By comparing the model results with IRAS observations in the 25 lm wave band, it was found that the observed shape of the zodiacal cloud can be accounted for by a combination of about to asteroidal dust and about to cometary dust. Cometary particles do not have a well-de"ned source in comparison with asteroidal particles. It is not de"nitely clear if they are produced by one highly active comet, several active comets, or by all the known short periodic comets or by comets in the Kuiper belt. Therefore any knowledge about particle properties may clarify the problem of stability of the zodiacal cloud. The well-known Pointing} Robertson e!ect is often utilized to estimate lifetime of the dust particles in solar system. For example, the PR drag lifetime of Encke-type 9 lm-sized particles (near to our studied particle) was estimated about 5000 years [1]. However, this result was obtained under assumption of perfectly spherical silicate and here Mie's theory was applied. For highly aspherical particles, spherical/nonspherical di!erences are signi"cant and make the Mie theory completely inapplicable [2]. An ideal sphere (larger than incident wavelength) is strongly forwarded scattering, but irregularities redirect rays from forward peak into other phase angles. This has the e!ect of increasing the scattering e$ciency in nonradial directions and leads to inadequate results for lifetime of such particles in the solar system assuming the PR drag for spheres. Therefore attention should be concentrated on the possibility of getting more precise model of the real-shaped particle. The better the particle model the better are the results of calculation. Many direct and/or indirect methods are used to get the reliable information about particle characteristics. The best conditions to "nd the complete structural properties of the particles is laboratory study of the directly collected particles. IDPs have been collected in a variety of terrestrial environments (e.g. deep-sea sediments, ice cores) but also in the stratosphere. Very small particles ((50 lm in diameter) are routinely collected in the Earth's stratosphere between 18 and 20 km altitude through the NASA Johnson Space Center (JSC) Cosmic Dust Program since 1981. However, all these collections of IDPs may be also contaminated by many kinds of natural terrestrial and anthropogenic materials. But a statistical analysis of this collection experiment over roughly 15 years show that the percentage of true cosmic dust is approximately 30% [3]. The properties of IDPs collected from the stratosphere should predominantly re#ect the properties of the main-belt asteroid parent bodies [4], but the question is more complicated (see Discussion also). These particles are the best available samples of IDPs (see e.g. [5]) and they are also very suitable for studying their detailed physical and optical properties mainly for a dust dynamics purpose. We have performed analytical electron microscopy (AEM) studies of 12 NASA stratospheric IDPs [6}8]. According to the results of these analyses we have chosen the cosmic dust particle U2015 B10. The selection looks on the nature of individual samples and paper intention which deals with mainly theoretical modeling. This cosmic particle was retrieved from the collection surface U2015 #own aboard the NASA U-2 aircraft during a series of #ights that were made along the west coast of North America from 22 June 1983 to 18 August, 1983. An inertial-compact collectors were mounted underneath the wings of high-#ying aircraft. The total of 39.6 h of
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Fig. 1. (a) Particle U2015 B10 at angle !603. (b) Model of the particle U2015 B10 at angle !603.
stratospheric exposure by usual manner was accumulated. According to preliminary original analysis including data obtained by optical AEM studies published in the Cosmic Dust Catalog, Vol. 5, No. 1 on p. 10 of Ref [9], the chosen particle is 9;13 lm in size, irregularly shaped, with opaque or translucent transparency and pale yellow to brown colour. The size coincides with the results of mid-infrared spectropolarimetry of the interstellar grains obtained by Hildebrand and Dragovan [10], i.e. that grains are oblate and the best "t for a ratio of particle axes 2 : 3. The luster is characterized as subvitreous or vitreous (see also Figs. 1a, 2a and 3a). The NASA analysis shows a high peak for Si and relatively lower peaks for Mg, Al, S, Ca and Fe in energy-dispersive X-ray (EDX) spectrum. Our own EDX analysis unambiguously con"rmed the cosmic origin of U2015 B10 sample. We also have found that in particle composition dominates the enstatite, composition of which is near to Mg Fe'' SiO . Our analysis did not reveal the further elements in comparison with the original analysis besides the content of oxygen which was naturally assumed. We also assume that the minor amounts of calcium and aluminum can be bound to calcium aluminosilicate (anortite) dispersed uniformly between the grains of enstatite, which have the size from 0.5 up to 3 lm. According to planary distribution it seems that sulphur is localized more in the core of grain, and not on its edge. From the morphological point of view it is remarkable that the U2015 B10 sample has probably a cavity in its center (for further details see [7]). Because of majority of the mineral enstatite in composition of U2015 B10 the mean refractive index of the particle can be in su$cient accuracy "tted by the enstatite optical properties. In meteoritic astronomy enstatite chondrites (or E chondrites) represent only 1.0% of all falls. They have the highest free metal and sul"de content (23}35% by weight) and the lowest oxidation state of all chondrites. Their silicate phase is almost purely enstatite (MgSiO ), an iron-free form of pyroxene.
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Fig. 2. (a) Particle U2015 B10 at angle #303. (b) Model of the particle U2015 B10 at angle #303.
Fig. 3. (a) Particle U2015 B10 at angle 03. (b) Model of the particle U2015 B10 at angle 03.
2. Radiation e4ects by irregular particles The great amount of the particles #oating in the upper Earth's atmosphere have nearly a constant mixing ratio, which indicates their extraterrestrial source. The cosmic dust particles collected by NASA in the stratosphere are characterized by their own size distribution, refractive
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index, shape and so on. Their in#uence on solar radiation is a little bit di!erent in comparison with atmospheric aerosol system. However, an &&in"nitesimal'' number of particles could be only assigned as spherical in both systems and this fact should be taken into account in any radiation model. Polydisperse spherical}nonspherical di!erences in the angular distribution of the scattered intensity can be large. In this case, Mie theory should not be used because of high errors. All the elements of the polydisperse scattering matrix are complicated functions of particle shape and, for di!erent nonspherical particles of equal size, may di!er in magnitude and even sign. Because all elements of the scattering matrix are strongly size dependent, they are sensitive indicators of particle size and asphericity. The informations about particle shape and refractive index are necessary for a more reliable estimation of the optical characteristics of true IDPs. As a matter of fact, the percentage of irregularly shaped cosmic dust particles is roughly 87. A partial concavity of particle shape may have a pronounced e!ect on light scattering. The discrete dipole approximation (DDA) method is used to calculate optical e!ects by irregular particles. DDA is a #exible and powerful tool for computing scattering and absorption by arbitrary targets and was described e.g. by Draine [11, 12]. DDA method is applicable for concave particles and can be successfully used for small particles. In comparison with well-known ¹-matrix method, the DDA is slower for large particles [2, 13]. We had applied DDA method for calculation of light scattering by some model particles [14]. It was shown that approximation of particle shape by sphere of identical volume may lead to inadequate evaluation of particle spiraling in interplanetary space. Calculations were performed for six model particles (sphere, cylinder, ellipsoid, hexagonal prism, rectangular target, tetrahedron) in di!erent orientations. Wavelength of j"0.55 lm of an incident radiation and e!ective radius of the particle 0.5 lm were used for calculation. Complete equation of motion was derived by Kl'ac\ ka and Kocifaj [15]. The following integrals are important for particle motion in solar system (they represent the projections of intensity vector of scattered radiation into each of three perpendicular axes of coordinate system): G "Q !Q G "Q G "Q
L L
L
p (h , u ) cos h d) ,
p (h , u ) sin h cosu d) , p (h , u ) sin h sin u d) , Q
where Q and Q are factors of e$ciency for extinction and scattering, p (h ,u ) is the phase function, h , u and ) are scattering, azimuth and solid angle, respectively. It was shown that motion of a real particle will be di!erent in comparison with the motion of the sphere when the values of G and/or G are at least at level 10\ of G . The greater the di!erence between isoline pro"les of p (h , u ) for real-shaped particle and partially symmetrical particle, the greater the ratios G /G or G /G . The motion of small particles in the interplanetary space is strongly dependent on given ratios G /G (i"1,2). A variability of p(h , u ) over wide range (several orders) can produce G the isoline structure with partially radial symmetry. It is because the greatest amount of scattered
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radiation energy is always in the forward direction. We found a cylindrical particle as a good candidate for the atypical motion in comparison with a sphere of identical volume. This indicates an enlargement of lifetime of such particle in solar system and increases the stability of zodiacal cloud.
3. The cosmic particle U2015 B10 and processing methods For a numerical simulation we have used the model of irregularly shaped particle which is su$ciently representative (true cosmic dust sample) and which is closest to the reality also. Therefore, for the model there was chosen the NASA particle U2015 B10 of which we have gained a sequence of "ve photos (images) made at di!erent angles (!60, !30, 0, #30, #603). The particle was washed of silicone oil with hexane and mounted on porous substrates. Because the technical problems did not allow to separate the sample from the substrates (made of porous boron and coated with carbon), the mentioned images represent approximately 80% of the particle surface. The shape of the missing 20% of surface we have modeled by design engineer, where the transparency of the particle was very helpful in this process. The result is a cube model of the particle. Edge of the cube was about 0.23 lm and total volume of the particle +187 lm. Particle model consists of 14 154 cubes, where the position of zero point inside the coordinate system (geometric center of the particle) is [27, 16, 16]. Center of gravity referred to this geometric center is [0, 1, !5]. The model was rendered using ray-tracing method. Program 3D-Studio MAX fy Kinetix was used. The particle U2015 B10 was de"nitely classi"ed as a cosmic particle which consists mainly of enstatite. Its refractive m"n !i.n can be expressed by simply formulae for a visible spectrum: P G n "1.735!0.26j, n (10\ P G using data published by Egan and Hilgeman [16]. Similarly as in Kocifaj and Kapis\ inskyH [14] we have studied an interaction of the particle with monochromatic solar radiation at the wavelength j"0.55 lm, which coincides with the maximum intensity in the solar spectrum. The corresponding refractive index of enstatite is then 1.59 for a given wavelength. Figs. 1}3 show the views of model together with the corresponding photos. It was not used in the same direction of illumination in both cases, for real and model particle. Our model consists of cubes, where surface re#ects the light by a di!erent way as a real-shaped particle. In this case we do not see some details of the model surface due to shadows of the cubes. Therefore, we have chosen such orientation of the particle in radiation "eld, for which the shapes of both, real particle and its model, may be correctly compared. The "gures demonstrate coincidence between the model and real particle. The DDA routine developed by Draine and Flatau [11] was used for calculation of the radiation characteristics such as phase function or e$ciency factors for extinction and scattering. Su$ciently accurate results can be guaranteed by this method if some conditions are ful"lled, for example if mkd(1,
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where m is particle refractive index, k"2n/j is a wave vector, and d is a lattice spacing expressed as follows: a , d" (3N/4n) where N is total number of cubes in the model and a is e!ective radius of a sphere of equivalent volume. We have developed numerical codes for processing of measured data (particle geometry), where the "ne-model (1) or coarse-model (2) procedures are included as additional functionality. This is helpful if the last condition is not ful"lled and we need to increase the number of cubes (1). Shape of an examined particle is not changed, but we can replace one cube by a 4, 9, etc. smaller cubes (subcubes). On the other hand, the calculation may be rapidly accelerated by decreasing of number of cubes (2) (using backtracking procedure, i.e. 4,9, 2 cubes are replaced by one cube of the same volume), but constraints cannot be violated (e.g. mkd should be smaller than 1). Unfortunately, DDA method needs to allocate too long a memory piece if characteristic size of a particle is much greater than a wavelength of an incident radiation. The computer memory expected for our particle U2015 B10 is about some hundreds of megabytes. However, the particle size is not so important for our study, because a set of IDPs consists of a wide spectrum of particle sizes and therefore we can also examine an interaction of radiation "eld with a small particle of the same shape. Such a study describes real conditions if a particle size lies inside the size range of a given particle set. Of course the scattered radiation is strongly dependent on the particle size. But we concentrate here on the radiation e!ects by a really &&shaped'' particle (excepting any degree of its shape symmetry) which characterize a real particle in the IDPs set. Each of six particle models studied in our previous paper [14] has its own degrees of symmetry (e.g. center point symmetry, or axially symmetry etc.). It can be expected that the values of G and G will not be so critical for these particles in comparison with the real-shaped particle. On the base of the facts discussed above and in agreement with our "rst paper we have chosen the e!ective particle radius to be equal to 0.5 lm. The particles of the size comparable to the incident wavelength are good example for a study of many e!ects because they are near the maximum scattering e$ciency, i.e. they are very sensitive to the incident radiation. The explanation of important radiation e!ects by the cosmic dust particle U2105 B10 is based on comparison of results obtained for both our particle and sphere of the identical volume and optical properties.
4. Calculation and results Results of calculation are presented in the Table 1. The factor of e$ciency of radiation pressure Q was calculated as a next important parameter of a particle motion in the interplanetary space. Values of Q depends on particle orientation in relation to the direction of incident radiation for the sphere. Of course, Q is independent of orientation for sphere. The greater the variability of Q , the greater the particle asphericity that can be expected. For example, we found the range of NP Q from 0.16 to 0.74 for a rectangular particle model (ratio of a edge was 1 : 4 : 12). Discussed range was also wide for a cylindrical particle (from 0.39 to 1.21). This particle was evaluated as the best candidate from six particle models for a long lifetime in a solar system. The values of Q for our
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Table 1 Results of the calculations for sphere and cosmic particle U2015B10 Parameter
Sphere
Q Q NP G G /G G /G
2.075 1.350 1.389 0.000 0.000
U2015B10 h"03 2.449 0.989 1.031 !0.007 0.320
U2015B10 h"603 4.084 1.120 1.203 0.316 !0.326
U2015B10 h"903 4.603 0.939 1.066 !0.050 !0.290
cosmic dust particle vary over small closed interval (from 0.9 to 1.1), which is caused by the nearly spherical shape of the particle. Here we should recall that the measurements of an interstellar polarization give lower and upper limits of particle axes ratio from 0.3 to 0.9 for interstellar grain (assuming the spheroidal shape, where particles are not too oblate/elongated). It means, if we do not like to study only a special set of the IDPs, the main interest should be in statistically important IDP systems, which may consist of aspherical particles similar to our sample. Q for an IDP U2015 B10 is nearly constant but the components G and G are comparable to the value G . This fact is re#ected in increasing of a lifetime of such a particle in a solar system. It is caused by slow spiraling due to signi"cant level of nonradial components G and G in comparison with radial component G . Such particle cannot be simply replaced by totally re#ecting target or equivalent sphere as it was often assumed in PR e!ect studies. Of course, it was expected. This result contributes to explanation of observed (relative) constancy of zodiacal light, which directly
Fig. 4. Isolines of the phase function for light scattering by spherical particle at orientation h"03.
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Fig. 5. (a) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"03. (b) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"603. (c) Isolines of the phase function for light scattering by cosmic dust particle U2015 B10 at orientation h"903.
depends on the stability of zodiacal cloud. Discussed conclusion of the calculations is con"rmed by Figs. 4 and 5, where isolines of the phase function of scattered radiation are presented. Source of incident radiation is behind the particle, which is situated in the center of the picture. The pictures are drawn in polar system of coordinates, where polar angle (equals to scattering angle) is calculated from 0 rad (central point) to n/2 (circle), and azimuth angle is calculated from 0 rad (eastern point) to 2n in counter-clockwise direction. The displayed curves are in log-scale because
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Fig. 6. (a) Isolines of the phase function for light scattering by cylindrical particle at orientation h"03. Particle radius: 0.5 km, wavelength of an incident radiation: 0.55 lm. (b) Isolines of the phase function for light scattering by cylindrical particle at orientation h"603. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm. (c) Isolines of the phase function for light scattering by cylindrical particle at orientation h"903. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm.
of the variability of phase function values over several orders. However, p vary over only 2}3 magnitudes, which is substantially less than for model particles. That is the reason of high values of G or G , respectively. In comparison with the results published in our previous paper [14] we do not see any symmetry of the isolines of phase function for arbitrary orientation of the particle U2015 B10 (Figs. 4 and 5). On the other hand, calculation results for the selected particle models (cylinder and hexagonal
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Fig. 7. (a) Isolines of the phase function for light scattering by hexagonal particle at orientation h"03. Particle radius: 0.5 km, wavelength of an incident radiation: 0.55 lm. (b) Isolines of the phase function for light scattering by hexagonal particle at orientation h"603. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm. (c) Isolines of the phase function for light scattering by hexagonal particle at orientation h"903. Particle radius: 0.5 lm, wavelength of an incident radiation: 0.55 lm.
prism) clearly demonstrate an axially symmetry of a scattered radiation "eld (Figs. 6 and 7). The mirroring of the isolines over an axis of symmetry causes the signi"cant decreasing of one from the component G or G . Intensity of scattered radiation near to the forward direction (in small scattering angle approximation) depends not on whole particle surface but mainly on cross section pro"le. Therefore, the isolines close to the central point of the picture correspond to the particle shape in the current orientation. The values of G /G and G /G are built by a structure of the isolines. It means, both, the symmetry and absolute values of p are important. The greater the
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gradient of p (h , u ) for small scattering angles h , the smaller are the ratios G /G (i"1,2). The G isolines of p are axially symmetrical for the cylindrical particle, but discussed gradient is much smaller than for hexagonal prism. Therefore the ratios G /G for cylinder are greater than for G hexagonal particle. This fact coincides with lifetime of inspiraling of the given particle in the solar system. The greater the gradient, the greater is the density of the isolines. Each picture presented here contains the same number of isolines to make a simple comparison of the results. One can see that our cosmic dust particle is characterized by the smallest gradient of p (for a small scattering angle), which results in the greatest values of G /G . Besides, the values of p for this particle vary G over smallest interval * it is only two magnitudes for orientation h"03 and three magnitudes for orientation h"903$. For example, this interval covers seven orders for the hexagonal prism. 5. Conclusions and their discussions The radiation e!ects by the really shaped particle was studied for the model of cosmic dust particle situated in the interplanetary space. Our sample particle U2015 B10 was collected by aircraft in Earth's stratosphere during NASA experiment. Preparing the particle model and including it with the calculation procedure the optical}physical properties were obtained such as scattering phase function, e$ciency factors for absorption, extinction and radiation pressure, etc. Our aim was to check an important level of the particle shape in the problem of estimation of particle lifetime in the solar system. Attained conclusions were based on comparison with the relevant results for sphere of an identical volume. Some particle models (such as rectangular target, hexagonal prism, cylinder, ellipsoid, tetrahedron) were studied in our previous paper. Each particle model used in the calculation was characterized by its own degree of symmetry. That is the problem of simulation of radiation transfer through model particle * the symmetry always produce the increasing of radiation energy scattered in forward direction and of course the small amount of energy is scattered to other (perpendicular) directions. Based on discrete dipole approximation method (DDA) we found the signi"cant di!erences between radiation e!ects by sphere and our cosmic particle. Well-known Poyinting}Robertson drag (PR e!ect) is assumed to be representative for particle motion and its spiraling in interplanetary space. Basic formula for PR e!ect assumes the spherical particles. Unfortunately, this assumption can lead to inadequate evaluation of particle motion in solar system, which is a serious problem. Namely, the stability of zodiacal light cannot be explained by PR drag for spheres. Results of calculation for particle U2015 B10 show that signi"cant level of nonradial components G or G (in comparison with radial component G ) leads to slow spiraling of examined particle. This fact directly in#uences the lifetime of the particle. This conclusion contributes to the explanation of stability of zodiacal cloud. It was also shown that both the symmetry and absolute values of scattering phase function p can in#uence the motion of the particle and its lifetime. The greater the gradient of p (h, u), the smaller the ratio G /G . An G important result of this study is therefore the very transparent-dependence radiation e!ects (and particle motion) on particle shape symmetry. Generally, any degree of symmetry in particle shape contribute to forward scattering and results in decreasing of nonradial components of G . Therefore G an asphericity, unconcavities and any irregularities in particle shape can de"nitely change its motion in interplanetary space in comparison with PR e!ect and increase a lifetime of the particle in some magnitudes.
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Table 2 Volume percentages of individual elements in particle U2015B10 Element
O
Mg
Al
Si
S
Ca
Fe
Vol. %
40.60
17.49
3.21
24.40
2.31
1.82
10.17
According to our previous paper [7] the chemical analysis of studied particles was also made. Based on particle composition presented in Table 2 we have derived the mean particle density (about 1.83 g cm\). What concerns this calculated value of bulk density of investigated particle U2015 B10, it is suitable to mention some remarks with respect to the probable origin of the studied sample. Despite the fact that considering the origin of the particle only according to its density is not quite adequate, at least it is possible to mention that the parent bodies of investigated microparticle cover several kinds of interplanetary and interstellar material such as cometary (dust) ejecta, asteroidal debris, meteoritic material, possible interstellar grains, intermingling material, etc. With respect to the density of the mentioned sample and its potential parent body we can probably exclude very soft cometary material produced mainly by short period comets with very low bulk density (about 0.27 g cm\) as well as regular cometary material (long-period comets * density about 0.75 g cm\). It seems that the dense cometary material with density about 1 g cm\ produced by the inner part of comets is also inconvenient. Material of carboneous chondrites with density about 2.1 g cm\ (from asteroids or comets too) "ts well with the density of the U2015 B10 sample. It is not necessary to consider the higher density values of achondritic material (approx. 3.2 g cm\) and of ordinary chondrites (approx. 3.7 g cm\). Naturally from the same reasons as the soft cometary material, the stony-iron meteoritic material (density 4.7}5.6 g cm\) as well as iron meteorites (7.7 g cm\) have to be excluded from this consideration (see e.g. [17}19] etc.). Several years ago Sergeant and Lamy [20] published conception of the two-component dust population with di!erent mean size and density. From this point of view our sample could belong to the debris (remnants) of Population I, i.e. to large grains with diameter greater than 3 lm and density approx. 2}3 g cm\. The Population II consists of small particles (d(3 lm) having higher densities (+8 g cm\) with a minor component of silicates. In this connection it is also interesting that Brownlee et al. [21] published their conclusions based principally on their collection experiments. They concluded that the collected grains (such as cosmic sample U2015 B10) are compact aggregates of very small particles and their bulk density is about 2 g cm\. In the quoted paper authors emphasize that these conclusions are further supported by the microcraters, analyses and other numerous experiments. But generally it can be said that the results of the bulk density determinations of dust particles (or their parent bodies) are still controversial.
Acknowledgements This work has been supported by a Grant No 4174/97 of the Slovak Academy of Sciences. The authors are also very grateful to Dr. B.T. Draine and P.J. Flatau for their DDSCAT code and to Mrs. Z. Kapis\ inskaH for technical assistance in some parts of paper.
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