O n t h e o p t i c a l c o n s t a n t s
o f c o s m i c d u s t a n a l o g s
Optical constants of materials in space These constants (the complex refractive index, dielectric function or permittivity, etc.) are macroscopic quantities that characterize the interaction of radiation with solids. The quantities being actually wavelength dependent appear when the Maxwell equations are supplemented with the material equations (see, e.g., [1] for more details). For molecules and clusters of molecules (PAHs, etc.), this approach is not applicable, and one must use quantum mechanical consideration [1].
The materials of astronomical interst can be divided generally into two groups: those whose optical properties are typical of dielectrics (ices, silicates, etc.) and those typical of metals (metals, carbon, etc.) -- see, for example, the values of the refractive index of different cosmic dust analog materials in visual given in the table.
The optical constants can depend on temperature and for metallic particles also on the size of granular? structure. The temperature effects have been more or less well studied in laboratories. The size-dependent effects in visual and near-IR being important for small clusters of some metals (e.g., silver) are negligible for pure iron possibly presented in space [2].
However, combined effects of these kinds are expected to occur for graphite particles of radius comparable to or smaller than the mean free path of electrons or holes in the bulk material. According to [3], the dielectric function eperp for the case of orientation of the electric field perpendicular to the basal? plane of graphite is expected to be appreciably modified in the IR. The effect appears for particles with the radius smaller than the critical one rc = 1.9/(1+0.322T+0.000137T2) micron, where T is the dust temperature. For T=20K, the difference in e_perp values becomes noticeable when lambda > 5 micron [4].
Available data Various terrestrial analogs of cosmic solids have been studied extensively in laboratories and for different extra-terrestrial and artificial materials the optical constants have been determined as well. However, many of these experiments neither took into account the specifics of cosmic dust materials (composion, lattice structure, processing, etc.), nor covered the wavelength intervals of current astrophysical interest. Note also that these data are mainly in the form of tables and graphics in papers and free WWW resources are generally limitted by several collections of refractive indices for a few materials. The only attempt to develop an universal site was the Jena-St.Petersburg Datadbase of Optical Constants for astronomy (JPDOC) based on original data obtained in Jena Laboratory (see the description of the JPDOC here).
Most of the materials studied in Jena are synthetic compounds prepared especially for the purpose of spectroscopic investigation. They include silicates in both amorphous and crystalline state, oxides of magnesium, iron, and aluminum, sulfides, and carbon in different forms. Chemical and physical analytical methods were generally applied to confirm the homogeneity, composition, and crystal structure of the products prior to the spectroscopic measurements. Further, some natural crystals (oxides and silicates) have been included in the studies. If necessary, data have been determined for the different crystallographic axes. For part of the compounds, data are available at cryogenic temperatures. In the following we give some examples of the data and their possible applications. A Postscript version of these exapmles please find in the paper.
Silicate minerals. Silicate minerals of the olivine and pyroxene classes have been shown to be present in outflows of evolved stars as well as in comets and protoplanetary disks. The positions of the infrared emission bands produced by these minerals are diagnostic for the crystal structure as well as for the chemical composition, especially the iron content. Comparison of the laboratory data with observed features can constrain the conditions in these environments which have led to the formation or processing of the dust grains.
We have used the infrared optical constants of forsterite contained in the database for calculating the absorption cross sections of spherical and non-spherical particles in the Rayleigh limit (see Fig.1). The spectra are obtained by averaging the cross sections calculated for the three different crystallographic directions. The spectra show resonances due to surface modes which shift very strongly in dependence on the aspect ratio of the particles. This effect probably is very important for the identification of emission features in astronomical spectra [6,7]. Interstellar polarization measurements and laboratory experiments on the growth of silicate particles [8] support the presence of elongated grains in astrophysical environments. Information about the grain shape may provide constraints for the formation mechanism of crystalline silicate grains, i.e. the role of direct condensation vs. processing of previously amorphous material.
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| Figure 1: Left panel: Imaginary part of the refractive index for crystalline forsterite (Mg2SiO4) in the three different crystallographic directions. Right panel: Mass-normalized absorption cross section (MAC) of prolate spheroidal forsterite particles (rotationally averaged) with different axis ratios. The dots and asterisks below the spectra indicate positions of astronomically observed emission bands (after [5]). |
Amorphous magnesium silicate. About 85-90% of the dust condensing in the envelopes of oxygen-rich evolved stars consist of amorphous magnesium or magnesium-iron silicates [5]. Optical constants (n,k) of stoichiometric and nonstoichimetric magnesium silicates with Mg/Si ratios from 0.7 to 2.4 produced by the sol-gel method have been derived from reflection measurements by a combination of Kramers-Kronig analysis (KKR) and Lorentz-oscillator fit method (see Fig.2). The calculated absorption coefficients show that MgO influences the position of the 10 and 20 micron band. With increasing MgO content the 10 micron band is shifted to longer wavelengths whereas the 20 micron band is shifted in the opposite direction.
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| Figure 2: Left panel: Imaginary part of the refractive index for amorphous Mg0.7SiO2.7 (dotted line) and Mg2.4SiO4.4 (solid line). Right panel: Absorption efficiency normalized by particle radius calculated for a continuous distribution of ellipsoidal grain shapes (CDE) composed of the same materials. |
The comparison between differently produced magnesium silicates demonstrates the existence of varying amorphous magnesium silicates material with differences in the internal structures. Based upon these results one has to conclude that the amorphous state of any magnesium silicate is not unique but there exist different possibilities for structural arrangements of subunits in the amorphous silicate structure, similar to the varying structures of amorphous carbon [9].
The astrophysical usefulness of these sol-gel silicates was tested by comparison of optically thin model spectra based on the new optical data with the dust emissivity derived from ISO-SWS spectra of AGB stars in the range between 8--30 micron. The dust emissivity derived from TY Dra, an evolved dust forming star, can excellently be reproduced by the models, sugessting that the dust grains consist indeed of pure amorphous Mg silicate.
Magnesium-aluminium oxide (spinel). Magnesium-aluminium spinel (MgAl2O4) has been considered as a primary condensate in the outflows of oxygen-rich AGB stars and as a potential carrier of the 13 micron emission band observed in the spectra of these stars [10]. Therefore, in the Jena laboratory, a systematic study of the infrared properties of Mg-Al oxides of both synthetic and natural origin was performed in order to derive the optical constants of these materials. This led to the discovery of two accompanying features in the astronomical spectra at larger wavelengths, thereby strongly supporting the idea of spinel condensates in AGB star outflows (see Fig.3, [11]). Recently, the experiments have been extended in the direction of Ca-Al oxide minerals [12] and condensation studies of oxide grains in low-presure oxygen-rich atmospheres.
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| Figure 3: Left panel: Imaginary part of the refractive index for synthetic and natural magnesium-aluminium spinels. Right panel: Calculated normalized absorption spectra for small particles composed of natural spinel (smooth solid line) and synthetic MgAl2O4 (dotted line) in comparison to the band profile of the newly discovered 32 micron feature [11]. |
Hydrogenated amorphous carbon. Amorphous carbonaceous materials can show a great diversity of optical properties due to the variability in their microstructure. Especially in the infrared range, the optical constants can differ by orders of magnitude according to the conducting or insulating electrical behavior of the material. The amorphous-carbon data contained in the database cover a wide range of these properties as is illustrated by Fig.4. The differently pyrolized celluloses are representative for a suit of carbonaceous material ranging from strongly disordered (insulating) to graphitized (conducting) material.
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| Figure 4: Complex refractive index of hydrogenated amorphous carbon prepared by pyrolysis (annealing) of cellulose at different temperatures. |
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| Figure 5: Absorption coefficient calculated for Spheres and a CDE in vacuum from the optical data of Fig.4 for at 400 and 1000oC pyrolized cellulose |
Especially interesting for astronomy is the calculations of the absorption and scattering cross sections of small particles in vacuum. In Fig.5, the strongly disordered material pyrolized at a temperature of 400oC shows an absorption efficiency in the wavelength region between 0.6 and 100 micron which is smaller by 3 orders of magnitude compared to the other carbon materials. The absorption efficiency normalized by the particle radius of carbonaceous particles in the far infrared follows a power law (Qabs/a ~ lambda-beta). The spectral index beta depends strongly on the internal structure of the carbon materials. The spectral index beta in the long wavelength tail is considerably lower for the highly disordered material than the exponents of the carbon material pyrolized at higher temperature [13]. There is a gradual increase of beta for spherical grains with increasing graphitization due to higher pyrolysis temperature.
Our calculations for different particle shapes show that there is no morphological effect on the spectral index for the low-temperature samples in contrast to the more graphitic materials. For the latter materials we find a significantly lower index in the case of broad shape distributions (CDE) compared to spherical grain shapes. This is caused by percolation effects, present in the more graphitized samples which contain free charge carriers. We should note that the results of the CDE calculations serve as an illustrative example. For a more realistic calculation, one has to assume a special aggregate structure and/or shape distribution of the individual particles [14]. For extreme values of the refractive indices, computational methods for the calculation of the absorption by aggregates or elongated particles meet their limits.
References:
- 1.
- Kruegel E. (2003) Physics of Interstellar Dust. IOP, London.
- 2.
- Kreibig U. and Vollmer M. (1995) Optical Properties of Metal Clusters. Springer, Berlin.
- 3.
- Draine B.T. and Lee H.M. (1984) Astrophys. J. 285, 89.
- 4.
- Draine B.T. (1985) Astrophys. J. Suppl. 57, 587.
- 5.
- Molster M.J., Waters B.L.F.M., Tielens A.G.G.M. (2002) Astron. Astrophys. 382, 222.
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- Fabian D., Henning Th., Jaeger C., Mutschke H., Dorschner J., and Werhan O. (2001) Astron. Astrophys. 378, 228.
- 7.
- Henning Th., and Mutschke H. (2000) in: M.L. Sitko, A.L. Sprague, D.K. Lynch (eds.) Thermal Emission Spectroscopy and Analysis of Dust, Disks, and Regoliths, ASP Conf. Ser. 196, 253.
- 8.
- Tsuchiyama A. (1998) Mineral. J. 20, 59.
- 9.
- Jaeger C., Dorschner J., Posch Th., and Henning Th. (2002), Astron. Astrophys., submitted.
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- Fabian D., Posch Th., Mutschke H., Kerschbaum F., and Dorschner J. (2001) Astron. Astrophys. 373, 1125.
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- Mutschke H., Posch Th., Fabian D., and Dorschner J. (2002) Astron. Astrophys., submitted.
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- Jaeger C., Mutschke H., Dorschner J., and Henning Th. (1998) Astron. Astrophys. 332, 291.
- 14.
- Quinten M., Kreibig U., Henning Th., and Mutschke H. (2002) Appl. Opt., submitted.
Table. The refractive index for cosmic dust analog materials at lambda=0.55 micron
| G r o u p: m a t e r i a l | m = n + ki | Reference |
|---|---|---|
| Silicates: | ||
| glassy pyroxene: Mg0.5Fe0.5SiO3 | 1.61 + 1.65 10-3i | [1] |
| glassy olivine: MgFeSiO4 | 1.758 + 8.44 10-2i | [1] |
| Silicon and silicon oxides: | ||
| silicon: Si | 4.07 + 2.84 10-2i | [2] |
| quartz: alpha-SiO2 | 1.546 + 0.0 i | [3] |
| Metals: Fe | 2.59 + 3.62 i | [4] |
| Oxides | ||
| FeO | 2.380 + 0.6897 i | [5] |
| MgO | 2.380 + 0.6897 i | [6] |
| Sulfides: FeS2 | 2.60 + 3.12 i | [7] |
| Carbides: SiC | 2.52 + 0.908 10-3 i | [8] |
| Carbonaceous species: | ||
| amorphous carbon: AC1 | 1.98 + 0.232 i | [9] |
| Organics: organic refractory | 1.953 + 0.290 i | [10] |
| Ices: water ice | 1.306 + 3.11 10-9i | [11] |
| Space materials: astrosil | 1.679 + 0.030 i | [8] |
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