In literature, one of the widely adopted opacities is that of Hildebrand [26]:
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Hildebrand [26]
arrived at the above values from first estimating
abs(125
µm) and then assuming
1 for
< 250 µm
and
2 for
> 250 µm.
He estimated the 125 µm opacity from
abs(125
µm) = 3Qabs(125 µm) /
(4a
) =
3 / (4a
)
[Qabs(125 µm) / Qext(UV)]
Qext(UV) by taking a = 0.1 µm,
= 3 g
cm-3, Qext(UV) = 3, and
Qext(UV) / Qabs(125 µm)
= 4000, where Qext(UV) is the ultraviolet extinction
efficiency at
~ 0.15-0.30
µm.
The most recent silicate-graphite-PAHs interstellar dust model for the diffuse ISM (Li & Draine [41]) gives
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while abs(
)
4.6 ×
105(
/
µm)-2 cm2 g-1
for the classical
Draine & Lee [19]
silicate-graphite model. The fluffy composite dust model of
Mathis & Whiffen [48]
has
abs(
)
2.4 ×
105(
/
µm)-1.6 cm2 g-1
in the wavelength range of 100 µm <
< 1000 µm.
The silicate core-carbonaceous mantle dust model of
Li & Greenberg [44]
gives
abs(
)
1.8 ×
105(
/
µm)-2 cm2 g-1 for
30 µm <
< 1000 µm. We see that these
abs values
differ by over one order-of-magnitude; e.g., the 1350
µm opacity calculated from the composite model
[
abs(1350
µm)
2.35 cm2 g-1;
Mathis & Whiffen [48]]
is higher than that from the silicate-graphite-PAHs model
[
abs(1350
µm)
0.20 cm2 g-1;
Li & Draine [41]]
by a factor of ~ 12.
While the Mathis & Whiffen [48] composite dust model predicts an IR emission spectrum too flat to be consistent with the COBE-FIRAS observational spectrum, and the dust IR emission has not been calculated for the Li & Greenberg [44] core-mantle model which focuses on the near-IR to far-UV extinction and polarization, the silicate-graphite-PAHs model has been shown successful in reproducing the infrared emission spectra observed for the Milky Way (Li & Draine [41]), the Small Magellanic Cloud (Li & Draine [42]), and the ringed Sb galaxy NGC7331 (Regan et al. [57], Smith et al. [60]). Therefore, at this moment the dust opacity calculated from the silicate-graphite-PAHs model is preferred.
It has recently been suggested that the long wavelength opacity can be estimated from the comparison of the visual or near-IR optical depth with the (optically thin) far-IR, submm and mm dust emission measured for the same region with high angular resolution, assuming that both the short wavelength extinction and the long wavelength emission are caused by the same dust (e.g. see Alton et al. [2, 3], Bianchi et al. [5, 6], Cambrésy et al. [12], Kramer et al. [30, 31])
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where V is the
visual optical depth,
S(
) is the
surface brightness at wavelength
, and
Qext(V) is the extinction efficiency in
the V-band
(
= 5500Å).
With the dust temperature T determined from a modified black-body
-
B
(T) fit to the far-IR dust emission spectrum
(
is not
treated as a free parameter but taken to be a chosen number),
Qabs(
)
can be calculated from the far-IR, submm, or mm surface density
S(
), and the
measured visual optical depth
V
[if what is measured is the near-IR color-excess,
say E(H - K), instead of
V, one can derive
V from
V
14.6E(H
- K)]. In so doing,
Qext(V) is usually taken to be
1.5.
The long wavelength
abs values
recently determined
using this method (Eq. [12]) are generally higher
than those predicted from the dust models for the diffuse ISM.
Although this can be explained by the fact that we are
probably looking at dust in dense regions where the dust
has accreted an ice mantle and coagulated into fluffy
aggregates for which a higher
abs is expected
(e.g. see
Krügel & Siebenmorgen
[34],
Pollack et al. [52],
Ossenkopf & Henning [51],
Henning & Stognienko [25],
Li & Lunine [46]),
the method itself is subject to large uncertainties:
(1) the grains responsible for the visual/near-IR
extinction may not be the same as those responsible for
the far-IR, submm and mm emission; the latter is more
sensitive to large grains while the former is dominated
by submicron-sized grains; (2) the dust temperature T
may have been underestimated if the actual
is larger
than chosen; and (3) the fact that in many cases the IRAS
(Infrared Astronomical Satellite) 60 µm photometry
was included in deriving the dust temperature T results
in appreciable uncertainties since the 60 µm emission is
dominated by stochastically heated ultrasmall grains;
ignoring the temperature distributions of those grains
would cause serious errors in estimating the dust mass
(see Draine [16])
and therefore also in deriving the long wavelength opacity
abs. These
problems could be solved by a detailed radiative transfer treatment
of the interaction of the dust with starlight (e.g.
Popescu et al. [53],
Tuffs et al. [62])
together with a physical interstellar dust model
(e.g. the silicate-graphite-PAHs model; see
Li & Draine [41,
42]).
Based on the laboratory measurements of the far-IR
and mm absorption spectra of both amorphous and crystalline
silicates as well as disordered carbon dust as a function
of temperature,
Agladze et al. [1] and
Mennella et al. [49]
found that not only the wavelength dependence exponent index
but also the
absolute values of the absorption
are temperature dependent: the far-IR and mm opacity
systematically decreases (almost linearly) with decreasing
temperature to T ~ 10-15 K and then increases with
decreasing temperature at very low temperature. While the linear
dependence of
abs on
T at T > 10-15 K was interpreted by
Mennella et al. [49]
in terms of two-phonon difference processes, the inverse-temperature
dependence of
abs on
T at very low temperature was attributed to a two-level
population effect
(Agladze et al. [1]).
Agladze et al. [1] and
Mennella et al. [49]
also found that the far-IR and mm opacity of amorphous
materials are larger than that of their crystalline
counterparts. This is because for amorphous materials,
the loss of long-range order of the atomic arrangement
leads to a relaxation of the selection rules that govern
the excitation of vibrational modes so that all modes are
infrared active, while for crystalline solids, only a small
number of lattice vibrations are active.