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Дата изменения: Fri Nov 19 12:07:22 2010 Дата индексирования: Tue Oct 2 00:14:03 2012 Кодировка: Поисковые слова: rho ophiuchi |
The behaviour of the polarization efficiency (see Eq. (14))
for non-absorbing
and absorbing spheroids is shown in Fig. 11
for the case when a maximum polarization is expected (PF
alignment,
). The chosen refractive indices are typical for water ice and soot. The
In Table 1, the values of the parameter
at which the polarization cross section
reach a maximum are presented for icy
particles at
.
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Prolate spheroid | |||||||
1.5 | 3.45 | 0.1036 | 0.057 | 0.30 | 0.26 | 3.40 | 0.99 |
2.0 | 3.44 | 0.1536 | 0.092 | 0.30 | 0.23 | 3.41 | 0.99 |
3.0 | 3.15 | 0.2036 | 0.157 | 0.28 | 0.19 | 3.42 | 1.08 |
5.0 | 3.71 | 0.3510 | 0.241 | 0.32 | 0.19 | 3.76 | 1.01 |
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1.94 | 0.3552 | 0.184 | -- | 0.19 | 2.00 | 1.03 |
Oblate spheroid | |||||||
1.5 | 3.05 | 0.1210 | 0.067 | 0.27 | 0.31 | 2.97 | 0.97 |
2.0 | 3.01 | 0.2237 | 0.124 | 0.26 | 0.34 | 3.05 | 1.01 |
3.0 | 3.39 | 0.4052 | 0.176 | 0.30 | 0.43 | 3.38 | 1.00 |
5.0 | 3.34 | 0.6342 | 0.298 | 0.29 | 0.50 | 3.41 | 1.02 |
It is also seen from Fig. 11
that relatively large particles produce
no polarization independently of their shape.
For absorbing particles, it occurs at smaller values
than for non-absorbing ones. However, the position at which the ratio
reaches a maximum is rather stable in every panel of Fig. 11
independently of
.
Thus, it should be emphasized that
for particles larger than the radiation wavelength,
the linear polarization is expected to be rather small. This does not
allow one to distinguish between the particle properties like refractive index,
shape, orientation. Even in the case of ideal (PF) orientation,
large particles (possibly available in dark clouds, -
see Fig. 32 and discussion in Sect. 3.3.1 in Voshchinnikov [2002])
do not polarize the transmitted radiation.
So, the decrease of the ratio with the rise
of
like found by Clayton and Cardelli ([1988])
should imply only that large grains are not efficient at producing
polarization and is not connected with the change of grain shape
or their less efficient alignment.
However, there is a possibility of reducing of the polarization efficiency
associated with growth of the spherical icy mantles on non-spherical
cores in dark clouds. In Fig. 14,
this effect is illustrated for spheroidal particles
with astrosil core and water ice mantle.
The influence of variations of the mantle shape for particles of different
sizes is shown.
The shape of the core was fixed and for each curve the shape of the mantle remains
the same. In this case, the
ratio of the core volume to that of the particle
does not change. For the values of (core) used, it is rather small
(from 0.11 to 0.004) and, therefore, the core's influence appears for
particles of small radii only. For particles larger than
,
the polarization seems to be mainly determined by the shape of the
particle mantle.
Values of the ratio presented in Figs. 11-14
are usually much larger than the upper limit for the interstellar polarization given by
Eq. (3.42) in Voshchinnikov [2002]:
.
In order to reduce the ratio
, the imperfect orientation of dust
grains should be considered. Note that the PDG orientation
(in comparison with PF)
should reduce the polarization of prolate grains only
as PF and PDG orientations for oblate grains are equivalent
(see Eq. (16)).
It is interesting that the polarization efficiency
created by rotating ellipsoidal particles is lower than that of oblate spheroids
and sometimes even prolate spheroids (Fig. 15)4.
Taking into account the problems with grain alignment in dark
clouds (e.g., Lazarian et al., [1997]), the hope to solve the problem
of the origin of polarization with the aid of more complex three-dimensional
particles looks like unfounded.