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
Introduction.
Nanometer- and micrometer-sized solid particles are distributed
in the interstellar medium and play an important role for
astrophysical processes such as star and planet formation.
These particles show a rich chemistry and mineralogy as has been
revealed by spectroscopic astronomical observations in the last decades.
Many new observational data have been measured in the last years,
e.g. by the Infrared Space Observatory (ISO) in 1995--1998, and
interpretation of these spectroscopic data is still in progress.
This requires large volume of data on the optical constants of
"analog materials".
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]).
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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.
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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].
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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
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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.
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- Draine B.T. and Lee H.M. (1984)
Astrophys. J. 285, 89.
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- Draine B.T. (1985)
Astrophys. J. Suppl. 57, 587.
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Astron. Astrophys. 382, 222.
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and Werhan O. (2001)
Astron. Astrophys. 378, 228.
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- 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.
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- 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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Dorschner J., and Hron J. (1999)
Astron. Astrophys. 352, 609.
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Dorschner J. (2001)
Astron. Astrophys. 373, 1125.
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Astron. Astrophys., submitted.
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Astron. Astrophys. 332, 291.
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- 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: |
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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] |
References: [1] Dorschner et al.(1995) Astron. Astrophys. 300, 503
[2] Geist (1998) Handbook of Optical Constants of Solids,III, ed. by E.D.Palik, Acad.Press, NY, p.519
[3] Philipp (1985) Handbook of Optical Constants of Solids, ed. by E.D.Palik, Acad.Press, NY, p.719
[4] Leksina, Penkina (1967) Fizika metallov i metaloved. 23, 344
[5] Henning et al. (1995) Astron. Astrophys. Suppl. 112, 143
[6] Roessler, Huffman (1991) Handbook of Optical Constants of Solids, II, ed. by E.D.Palik, Acad.Press, NY, p.949
[7] Palik (1998) Handbook of Optical Constants of Solids, III, ed. by E.D.Palik, Acad.Press, NY, p.507
[8] Laor, Draine (1993) Astrophys.J. 402, 441
[9] Rouleau, Martin (1991) Astrophys.J. 377, 526
[10] Greenberg, Li (1996) Astron. Astrophys. 309, 258
[11] Warren (1984) Appl. Opt. 23, 1206
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