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Дата изменения: Fri Nov 19 12:07:18 2010
Дата индексирования: Tue Oct 2 00:00:32 2012
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Поисковые слова: п п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п р п п р п п р п п р п п р п п р п п р п п р п п р п п р п п р п п р п п р п
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Next: The 2175Å feature
Up: Extinction properties (transmitted radiation)
Previous: Extinction efficiencies: general behaviour
Wavelength dependence
Interpretation of the interstellar extinction involves
two tasks: explanation of the wavelength dependence and
fitting the absolute extinction.
The first task assumes the searching for chemical composition
and sizes of particles which give the wavelength dependence of
the extinction efficiencies close to the observed dependence of
.
Figure 7:
Wavelength dependence of the extinction efficiency factors
for homogeneous spherical particles of different sizes
consisting of astronomical silicate and amorphous carbon.
The dashed segment shows the approximate wavelength dependence of the mean
galactic extinction curve at optical wavelengths.
|
The average interstellar extinction curve in the visible-near UV
(
) presented in Fig. 13 in Voshchinnikov [2002]
can be approximated by the power law
.
This dependence is plotted in Figs. 7-9 as a dashed segment.
The Figures allow one to judge the influence of the size,
chemical composition, structure and shape of particles on the wavelength
dependence of extinction.
In all cases, the initial growth of extinction reflects the increase of
factors
at the interval from zero up to the first maximum.
As follows from Fig. 7, spheres of astrosil with
or slightly smaller spheres of AC1
can produce the dependence
resembling the observed one.
Evidently, the fraction of particles with these radii
in the size distribution must be considerable.
As was noted many times (e.g., Greenberg, [1978]),
a similar extinction occurs if the product of the typical
particle size
on the
particle refractive index is constant, i.e.
![\begin{displaymath}
\langle r \rangle \, \vert m-1\vert \approx {\rm const.}
\end{displaymath}](img75.gif) |
(5) |
Using the values of
from Table 3 in Voshchinnikov [2002]
and the results shown in Fig. 7,
it is possible to conclude that
the wavelength dependence of extinction
in the visible can be approximately
reproduced if one choose the particles of astrosil
with
,
particles of AC1 with
,
particles of iron with
, etc.
This illustrates that
from the wavelength dependence of extinction
one can determine only the product of the typical particle size
on refractive index but not the size or chemical composition of dust grains
separately.
Figure 8:
Wavelength dependence of the extinction efficiency factors
for spherical particles of astronomical silicate with radius
.
Calculations were made for homogeneous particles with the
refractive indices found from the Bruggeman
mixing rule with a different fraction of vacuum
(upper panel) and for hollow particles with different core size (lower panel).
The dashed segment shows the approximate wavelength dependence of
the mean galactic extinction curve at optical wavelengths.
|
The conclusion on the impossibility to identify exactly the structure of particles
can be done from Fig. 8 where the extinction for spheres with
a fraction of vacuum is presented.
The voids were included in two ways:
using the Bruggeman mixing rule
(see Table 4 in Voshchinnikov [2002]) and in the form
of the core in core-mantle
spheres.
In both cases, the ``effective'' refractive index of particles reduces, and
according to Eq. (5) to produce the observed extinction,
the particle radius over
must be increased.
It is interesting to note the similarity in behaviour of extinction
for particles with different internal structure.
This shows that the EMT is
not a totally hopeless matter.
Figure 9:
Wavelength dependence of the normalized extinction cross-sections
for spherical and spheroidal equivolume particles of astronomical silicate
with radius
.
Calculations were made for homogeneous spheroids with
in a fixed orientation
(
and
) and for 3D-orientation.
The dashed segment shows the approximate wavelength dependence of
the mean galactic extinction curve at optical wavelengths.
|
In Fig. 9, the normalized extinction cross-sections
for spheroids
(see Eqs. (2.43) and (2.44) in Voshchinnikov [2002]) and
spheres are plotted. The results for spheroids are shown for two
orientations of non-rotating particles (``picket fence'' alignment)
and for the case of the arbitrary orientation in space (3D alignment)
when the average cross-section is:
![\begin{displaymath}
\langle C_{\rm ext} \rangle^{\rm 3D} =
\int^{\pi /2}_0 \, \f...
...m TE}(\alpha) \right] G(\alpha) \,\sin\alpha \, {\rm d}\alpha.
\end{displaymath}](img86.gif) |
(6) |
Here
is the geometrical cross-section of a spheroid
(Eqs. (2.41) and (2.42) in Voshchinnikov [2002]) and the incident radiation is assumed
to be non-polarized.
Figure 9 shows that the shape of particles has a small
influence on the extinction at different wavelengths.
Certainly, the curves for spheroids in a fixed orientation differ
from those for spheres, and the difference increases with the
growth of
.
However, the wavelength dependence of extinction close to the observed
one can be obtained if the difference in the paths of the rays inside particles
with different orientation is taken into account.
It means that the particles with
smaller than 0.1
for
and larger than 0.1
for
for prolate (oblate) particles should be chosen.
Thus, neither chemical composition, nor structure, and shape of
dust particles can be uniquely deduced from the wavelength dependence
of the interstellar extinction.
Next: The 2175Å feature
Up: Extinction properties (transmitted radiation)
Previous: Extinction efficiencies: general behaviour
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2003-04-09