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Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
Speckle interferometry and radiative transfer modelling of the
Wolf­Rayet star WR118
B. Yudin 1 , Y. Balega 2 , T. Bl˜ocker 3 , K.­H. Hofmann 3 , D. Schertl 3 , and G. Weigelt 3
1 Sternberg Astronomical Institute, Universitetskii pr. 13, 119899 Moscow, Russia
2 Special Astrophysical Observatory, Nizhnij Arkhyz, Zelenchuk region, Karachai--Cherkesia, 35147, Russia (balega@sao.ru)
3 Max--Planck--Institut f˜ur Radioastronomie, Auf dem H˜ugel 69, D--53121 Bonn, Germany
(bloecker@mpifr­bonn.mpg.de, hofmann@mpifr­bonn.mpg.de, schertl@mpifr­bonn.mpg.de, weigelt@mpifr­bonn.mpg.de)
final version edp: September 17, 2001
Abstract. WR 118 is a highly evolved Wolf­Rayet star of the WC10 subtype surrounded by a permanent dust shell absorbing
and re­emitting in the infrared a considerable fraction of the stellar luminosity. We present the first diffraction­limited 2.13 m
speckle interferometric observations of WR 118 with 73 mas resolution. The speckle interferograms were obtained with the 6 m
telescope at the Special Astrophysical Observatory. The two­dimensional visibility function of the object does not show any
significant deviation from circular symmetry. The visibility curve declines towards the diffraction cut­off frequency to  0:66
and can be approximated by a linear function. Radiative transfer calculations have been carried out to model the spectral energy
distribution, given in the range of 0.5­25 m, and our 2.13 m visibility function, assuming spherical symmetry of the dust
shell. Both can be fitted with a model containing double­sized grains (``small'' and ``large'') with the radii of a = 0.05 m and
0.38m, and a mass fraction of the large grains greater than 65%. Alternatively, a good match can be obtained with the grain
size distribution function n(a)  a 3 , with a ranging between 0.005m and 0.6m. At the inner boundary of the modelled
dust shell (angular diameter  in = (17  1) mas), the temperature of the smallest grains and the dust shell density are 1750 K
 100 K and (1  0:2)
10 19 g/cm 3 , respectively. The dust formation rate is found to be (1:3  0:5)
10 7 M /yr, assuming
Vwind = 1200 km/s.
Key words. Techniques: image processing --- Circumstellar matter --- Stars: individual: WR 118 --- Stars: mass--loss --- Stars:
Wolf­Rayet --- Infrared: stars
1. Introduction
The Wolf­Rayet star WR 118 (= CRL 2179 = IRAS 18289­
1001) in the catalog of WR stars of van der Hucht (2001) be­
longs to the latest subtypes of the carbon­rich sequence (WC).
It is classified as WC9­10 (Allen et al. 1977, Massey & Conti
1983). Its very prominent IR excess is attributed to the thermal
emission of a warm carbon dust shell. No remarkable varia­
tions in the dust emission have been registered over the last two
decades (Williams et al. 1987, van der Hucht et al. 1996) and it
has been designated as a ``persistent'' dust­maker (Williams &
van der Hucht 2000). While the dust grains are momentum­
coupled to the fast stellar wind, fresh dust grains should be
steadily condensing at a definite distance from the star, i.e. the
dust formation rate is generally constant on the time scale of
several decades.
Among the known galactic WR stars, WR 118 is one of the
optically faintest objects, but one of the brightest ones in the
infrared regime. This is naturally explained by its heavy inter­
stellar reddening and the obscuration by its conspicuous dust
Send offprint requests to: B. Yudin (yudin@sai.msu.ru)
shell. A strong interstellar 9.7 m silicate feature is observed
in its spectrum with an optical depth of  9:7m  0:7 (Roche
& Aitken 1984, van der Hucht et al. 1996). Using the rela­
tion A V = 9:7m  21:5 (Schutte et al. 1998), an extinction
of A V  15 can be derived. Allen et al. (1977) and Williams et
al. (1987) list A V  15 and  12:8, respectively. In the optical
region, the brightness of WR 118 is only roughly known.
From spectrophotometry, Massey & Conti (1983) estimate
the v narrow­band magnitude to be approximately 22, and
Cohen &Vogel (1978) list a V broad­band magnitude of  20.
Williams et al. (1987) modelled the IR spectral energy distribu­
tion (SED) of the WC stars, finding that they could be well fit­
ted with an optically thin shell consisting of small ( 0:01 m)
amorphous carbon grains with a density distribution of  /
r 2 . The absence of the silicon carbide feature at 11.3 m in
the spectra of WR stars exclude SiC to be a constituent of
their dust shells. In this paper we present diffraction­limited 73
mas speckle interferometric observations of the dust shell of
WR 118. Radiative transfer calculations have been performed
to model both the SED and the 2.13 m visibility.

2 B. Yudin et al.: Speckle interferometry and radiative transfer modelling of WR 118
2. Observations and data reduction
The WR 118 speckle interferograms were obtained with the
Russian 6 m telescope at the Special Astrophysical Observatory
on September 27, 1999. The speckle data were recorded with
HAWAII speckle camera (HgCdTe array, 256 2 pixels, sensitiv­
ity from 1 to 2.5 m, frame rate 2 frames/s) through an inter­
ference filter with a central wavelength of 2.13 m and a band­
width of 0.21 m. Speckle interferograms of the unresolved
star HIP 87540 were taken for the determination of the atmo­
spheric speckle transfer function. The observational parame­
ters were as follows: exposure time/frame 20 ms; number of
frames 210 (130 of WR 118 and 80 of HIP 87540; 2.13 m
seeing (FWHM) 1: 00 4; field of view 5: 00 1 x 5: 00 1; pixel size 26.4
mas. The resolution was 73 mas. The visibility function (mod­
ulus of the Fourier transform of the object intensity) was de­
termined with the speckle interferometry method (Labeyrie
1970). Figure 1 shows the two­dimensional 2.13 m visibility
and the azimuthally averaged 2.13 m visibility of WR 118 up
to the diffraction cut­off frequency. There is no evidence for
deviation from circular symmetry. The visibility curve can be
approximated by a linear function and dropped to 0.66 at the
diffraction cut­off frequency.
3. The dust shell model
Using the quasi­diffusion method of Leung (1975), as imple­
mented in the CSDUST3 code (Egan et al. 1988), we have
constructed spherically symmetric radiative transfer models to
match both the observed SED and the 2.13 m visibility. The
input parameters of the model are: (i) the spectral shape and
bolometric luminosity of the star (f()L bol ), after passing the
shell, f() L bol transforms to f 0 ()L bol ; (ii) the inner shell ra­
dius (r in ); (iii) the relative thickness of the shell, i.e. the ratio
of outer to inner shell radius (Y out = r out =r in ); (iv) the den­
sity distribution (r); (v) the chemical composition and grain­
size distribution; (vi) the total optical depth at a given reference
wavelength.
The input parameter of the radiative transfer model, which
relates the stellar bolometric luminosity and the inner shell
radius, is the incident flux at the inner boundary of the dust
shell: F in = L bol =(4r 2
in ). It is based on the assumption that
the temperature of the dust grains is controlled by the radia­
tion field only. This means that if we change L bol but keep
F in = const (i.e. change r in /
p
L bol , resp.) we obtain (i)
the same SED; (ii) the same normalized surface brightness dis­
tribution as a function of b=r in (b=r in : impact parameter); and
(iii) the same visibility curve as function of q in (q: spatial fre­
quency;  in : angular diameter of the dust shell's inner bound­
ary, b=2r in = = in ). For more details of self­similarity and
scaling behaviour of infrared emission from radiatively heated
dust, see also Ivezic & Elitzur (1997) and references therein.
For the sake of clarity, we have incorporated L bol and r in sepa­
rately in the CSDUST3 code instead of using F in only. During
the SED fitting procedure, we kept L bol constant., i.e. changed
only r in .
Keeping in mind that the distance is defined by the relation
d =
p
f 0 ()L bol =4F obs () (F obs (): observed (dereddened)
­12 ­8 ­4 0 4 8 12
Cycles per arcsec
­12
­8
­4
0
4
8
12
0.0
0.2
0.4
0.6
0.8
1.0
0 2 4 6 8 10 12
Visibility
Cycles per arcsec
Fig. 1. Two­dimensional 2.13 m visibility (top) and azimuthally av­
eraged 2.13 m visibility of WR 118 (bottom) shown up to the diffrac­
tion limit.
spectral energy flux), i.e. d /
p
L bol , it can be shown that the
angular surface brightness distribution of the model, in particu­
lar  in = 2r in =d, does not depend on L bol . In our calculations
 in is determined by comparing the modelled and observed K­
band ( = 2:2 m) flux. We note that, if the observed SED is
properly fitted, we get the same value of  in conducting the
flux normalization at any other wavelength. In principle, the
bolometric flux can be used as well, but for WR 118 this ap­
pears to be unfavorable due to the lack of optical and UV data.
In our model calculations, we firstly assumed a bolomet­
ric luminosity of L bol = 4
10 4 L . Luminosity­independent
model parameters are given in Tab. 1. Removing the redden­
ing from the observed J magnitude of WR 118 and taking the
model V J color, we obtain the (unreddened) model V 0 mag­
nitude of WR 118.

B. Yudin et al.: Speckle interferometry and radiative transfer modelling of WR 118 3
Table 2. Predicted WR 118 parameters: color V J ; dereddened and reddenend visual magnitudes V0 and V ; distance d, bolometric luminosity
Lbol ; radius r in and density  in at inner dust shell rim; and dust mass­loss rate _
M dust .
model V J V0 V d Lbol r in  in _
M dust
(mag) (mag) (kpc) (10 4 L ) (10 3 R ) (10 19 g/cm 3 ) (10 7 M /yr)
M 1 2.22 6.87 19.7 2.3 6.7 4.2 0.9 1.8
M 2 1.68 6.33 19.1 1.8 5.6 3.0 1.2 1.3
M 3 1.67 6.32 19.1 1.8 5.6 3.2 0.8 1.0
M 1.1 2.15 6.46 20.5 1.9 5.5 3.4 0.9 1.2
M 2.1 1.62 5.93 19.9 1.5 4.7 2.4 1.2 0.8
Table 1. Model dust­shell parameters. The models M 1, M 2, M 1.1
and M 2.1 refer to double­sized grains with a = 0:05 m and a =
0:38 m, the model M 3 to a grain size distribution of n(a) / a 3
with 0:005 m a  0:6 m. V is the optical depth at 0.55 m; r in ,
T in and  in are the radius, the temperature (refering to the smallest
grains) and the angular diameter of the inner dust shell rim, n0:05 and
m0:05 are the abundances of 0.05 m grains by number and mass,
resp., and AK is the 2.2 m dust­shell albedo.
model V r in T in n0:05 m0:05 AK  in
(R ) (K) (%) (%) (mas)
M 1 0.88 179 1670 99.55 34 0.36 17.8
M 2 0.70 140 1820 98.83 17 0.40 16.3
M 3 0.70 152 1760 0.36 17.5
M 1.1 0.73 159 1740 99.55 34 0.36 17.4
M 2.1 0.58 125 1900 98.83 17 0.40 16.0
Adopting a WC9­10 absolute magnitude of M V = 4:9
(Williams et al. 1987), d and L bol can be estimated. Taking this
new value of L bol (see Tab. 2) we recalculated the luminosity­
dependent model parameters such as r in , the rate of dust for­
mation at the inner boundary of the dust shell ( _
M dust ), and the
density of the dust shell at the inner boundary ( in ) using the
relations r in /
p
L bol , _
M dust /
p
L bol , and  in / 1=
p
L bol .
Concerning the dust formation rate, an outflow velocity of
V wind = 1200km/s was adopted (Williams et al. 1987). The
model predictions for all these luminosity dependent parame­
ters of WR 118 are given in Tab. 2.
For the SED of the star, f(), we took basically a black
body of 19000 K (van der Hucht et al. 1986). We corrected it
in the region of 0.5­1.25 m to have f() /  3:0 (Williams
et al. 1998) corresponding to (V J)  0:0. In the infrared,
corrections for the continuum radiation of the ionized gas shell
have been made to obtain (J K)  0:25 and f() /  2:7
longwards of 10 m (Williams et al. 1987). It should be noted
that these corrections have only minor effects on the model
SED due to a very strong IR excess caused by the emission
of dust grains.
The density distribution of the dust shell is given by  /
r 2 , i.e by a uniform outflow model. The outer shell bound­
ary was chosen to be Y out = 10 3 . Larger values of Y out af­
fect the SED only in the far­infrared, i.e. far beyond the IRAS
25 m photometric band, which defines the long­wavelength
tail in this study. Concerning the optical dust­grain constants,
we considered the amorphous carbon grains (cel1000) of J˜ager
et al. (1998). The reference wavelength of the optical depth was
chosen to be 0.55 m, and the model SED is normalized to the
observed one in the J band.
Figure 2 shows the 2.13 m model visibility for differ­
ent optical depths (0.6 and 4) and grain sizes (single­sized
grains with 0.01 m, 0.1 m and 0.38 m) for a dust shell with
r in =R  = 200 in comparison with the observed visibility. Only
for the model with the largest grains, the visibility curve ap­
proaches to a linear function, i.e. its shape approaches the one
of the observed visibility of WR 118.
Fig. 2. 2.13 m model visibility function of WR 118 for different opti­
cal depths and grain sizes for a dust­shell with r in = 200R together
the observed visibility. The dotted, short­dashed, dot­dashed, solid
and long­dashed lines refer to V = 0:6, a = 0:01m; V = 0:6,
a = 0:10m; V = 4:0, a = 0:10m; V = 4:0, a = 0:38m; and
V = 0:6, a = 0:38m, resp.
The transformation of the shape of the 2.13 m visibil­
ity curve from parabolic to rectilinear is connected with the
transformation of a mostly thermally emitting dust shell to a
highly scattering one when the albedo of dust grains is get­
ting large. The 2.13 m albedo of the J˜ager et al. (1998) carbon
grains with a=0.1 m is 0.04, i.e. the dust shell's radiation is
dominated by direct thermal emission at this wavelength. The
albedo of the corresponding 0.38 m grains is 0.4, i.e. the dust

4 B. Yudin et al.: Speckle interferometry and radiative transfer modelling of WR 118
shell scatters the IR light very efficiently. Increasing the opti­
cal depth of an ``emitting'' and a ``scattering'' dust shell results
into a slight increase and decrease of the visibility's curvature,
respectively (Fig. 2).
Keeping in mind the very hostile environment for dust con­
densation in the shells of WR stars, it appears to be obvious
to assume that the dust grains are rather small (Williams et al.
1987). However, such models will not be able to reproduce the
shape of the visibility curve of WR 118. On the other hand, it is
clear that the dust shell cannot consist entirely of large grains,
which grow up from their small progenitors. In our double­
sized grains models, we considered the combination of small
grains (a = 0:05 m) and large grains (a = 0:38 m).
The temperature of the large grains is  1:5 times lower
than that of the small ones. Thus, if one increases the abun­
dance of the large grains, r in has to be decreased to preserve the
SED fits in the near­infrared domain. Although this even wors­
ens the condition of dust­grain condensation in the correspond­
ing models, the observed shape of the visibility curve clearly
requires to include large grains in the dust shell of WR 118.
The decrease of the small grains' size does not affect the
SED nor the visibility substantially, i.e. the grains with a 
0:05 m behave similarly, in this respect, in the optical and IR
domain. The increase of the relative abundance of the small
grains mainly reflects in an increase of the emergent radia­
tion's reddening in the optical region, and a decrease of the
dust shell's albedo in the infrared. The latter leads to an es­
sential change of the visibility's curvature in the ``wrong'' di­
rection. Both these points define the abundance of small grains
in the dust shell. However, in the case of WR 118, we have
no accurate estimations of its brightness in the optical wave­
length range, and thus cannot determine how much reddening
we need. Calculations were performed adopting A V = 12:8
and 14, which leads to J 0  4:65 and 4.31 (Allen et al. 1977,
Williams et al. 1987), resp.
The increase of the large grains' size does not affect the
SED and the 2.13 m visibility very much, either. However,
the size of the large grains cannot be decreased significantly
because the 2.13 m albedo of the J˜ager et al. (1998) grains
with a = 0:25 m is  0:27 being already too low to allow a
proper fit of the visibility. Besides double­sized grains models,
we also calculated models with a power­law grain­size distri­
bution of n(a) / a (0:005 m a  0:6 m) to investigate
which exponent is most appropriate. For all these models, T in
is calculated for the smallest dust grains with a = 0:005 m.
This temperature exceeded that of the a = 0:05 m grains by
 5%.
4. Results of calculations and discussion
Figures 3­4 show the observed 2.13 m visibility of WR 118
and its SED corrected for interstellar extinction of A V = 12:8
and 14, respectively. The latter includes the data of Massey
& Conti (1983) (V band), Cohen & Vogel (1978) (V band),
Allen et al. (1977) (JHKL bands), Williams et al. (1987)
JHKL0M [8.4], [11.6], [12.5], [12.9], and [19] bands) and
color­corrected IRAS photometry (IRAS Science Team 1988)
([12] and [25] bands). Figures 3 and 4 also show the 2.13 m
Fig. 3. Model SED corrected for interstellar extinction of AV = 12:8
and 2.13 m visibility function of WR 118 for the models M1 (solid
lines), M2 (short­dashed lines), and M3 (long­dashed lines) as given
in Tabs. 1­2. The squares refer to the observations (see text).
visibility and SED of those 5 models, which proved to be best
suited for the dust shell of WR 118 in the framework of spher­
ical symmetry. Their parameters are given in Tab. 1 and 2. For
comparison, Williams et al. (1987) have found that the dust
shell of WR 118 have the following parameters: r in = 260R  ,
Y out = 30, T in = 1410K,  in = 4:9
10 19 g/cm­3 and
_
M dust = 8:2
10 7 M /yr.
The models M1, M2, and M3 refer to an interstellar ex­
tinction of A V = 12:8, and the models M1.1 and M2.1 to
A V = 14:0. M3 is the model with a power law grain­size dis­
tribution with = 3. The other models refer to double­sized
grains. In the latter case the relative abundance of 0.05 m
grains in number (n 0:05 ) and mass (m 0:05 ) are given in Tab. 1,
which also contains the optical depth of the dust envelope  V
and its albedo at 2.13 m (AK ).
Regarding the models with the double­sized grains (a =
0:05 m and a = 0:38 m), the relative concentration of the
0.05 m grains is subject to some uncertainty, since the small
grains determine the reddening, which is not precisely known.
A more accurate determination of this parameter demands a
more precise estimation of the optical brightness of WR 118
at several wavelengths. However, the grain density at the inner

B. Yudin et al.: Speckle interferometry and radiative transfer modelling of WR 118 5
Fig. 4. Model SED corrected for interstellar extinction of AV = 14:0
and 2.13 m visibility function of WR 118 for the models M1 (solid
lines), M2 (short­dashed lines), and M3 (long­dashed lines) as given
in Tabs. 1­2. The squares refer to the observations (see text).
boundary of the dust shell and the dust formation rate do not
depend strongly on the adopted AV and relative grain concen­
tration. Thus, the estimations given in Tab. 2 can be considered
as reliable in the framework of a spherically symmetric dust
shell model.
Furthermore, it turned out that a match of the SED at the
region of 25m can be improved if the exponent in the power
law of the dust density distribution is  = 2:1 instead of 2. It
remains open if this deviation from the uniform outflow is sig­
nificant with respect to the observational and theoretical uncer­
tainties. The same effect as increasing  can be reached by de­
creasing Y out to 300. This is the lower limit for the dust thick­
ness above which the 25m flux is not affected any longer.
However, such a sharp truncation of the outer parts of the dust
shell looks less natural than, e.g., a gradual change of the mass­
loss rate.
The M1 and M3 models have almost the same albedo AK ,
and the M2 and M3 models have almost the same circumstel­
lar (cst) reddening (A V A J )/A V j cst . It defines the similarity
of the M1 and M3 visibility curves and the similarity of corre­
sponding SEDs (Fig. 1). The mass fraction of the grains with
a  0:3m in model M3 is  50%.
Table 3. Model dust­shell parameters for grain­size distributions with
n(a) / a and 0:005 m a  0:6 m. V is the optical depth at
0.55 m; r in , T in and  in are the radius, the temperature (refering to
the smallest grains) and the angular diameter of the inner dust­shell
rim, and AK is the 2.2 m dust­shell albedo.
model V r in T in AK  in
(R ) (K) (mas)
M 4 0.87 197 1610 3.5 0.29 19.2
M 3 0.70 152 1760 3.0 0.36 17.5
M 5 0.56 124 1900 2.5 0.38 17.1
Increasing the exponent in the power­law grain­size dis­
tribution from 3.0 (M3) to 3.5 (M4) leads to a decrease of
the albedo AK from 0.36 (Tab. 3) to 0.29, and to a signifi­
cant increase of the visibility curvature, and thus to a worse
match of the observations. The strong dependence of the visi­
bility curve's shape on the albedo is confirmed by model cal­
culations with double­sized grains. On the other hand, the de­
crease of to 2.5 does not change the albedo AK much (to only
 0:38) and correspondingly the visibility curve either (model
M5). However, then the model V J color decreases to 1.20
(1.67 for M3) in contradiction to the observations. Moreover,
the increase of the relative concentration of large grains en­
forces a decrease of r in to keep a good match of the SED in the
near­infrared. This, in turn, leads to a corresponding increase
of temperature at the inner rim, T in , which is already very high
(Tab.3). Thus, from the models with power­law grain­size dis­
tributions the best one is that with = 3.
If the wind of WR 118 is flattened due to some reason (due
to stellar rotation, binarity), one can conclude from the circu­
lar symmetric shape of the two­dimensional visibility function,
that one looks face­on at the flattened shell (``disk''). Williams
et al. (1987) estimated the fraction of WR 118's luminosity ab­
sorbed by dust and re­radiated in the IR to be  71%. If the
star is not obscured by its dust disk, we estimate that this frac­
tion should not be less than 50%. This means that the dust disk
should be optically thick and cover more than one half of the
sphere. Such a dust shell would not look like a geometrically
thin disk, but rather as a sphere with a hole in the light of sight,
i.e. as a torus with a large opening angle. However, first we
should have clear indications of such asphericities, before we
introduce a more complex geometry to the dust shell model of
WR 118. We note that van der Hucht (2001) suggested that all
apparently single and persistently dust­making WC9 stars may
possibly owe their heated circumstellar dust signatures to col­
liding WC+OB wind effects.
Recently, Veen et al. (1998) have attributed eclipse­like
variations of the optical brightness of the dusty Wolf­Rayet
stars WR 103, WR 121 and WR 113 to the obscuration of
starlight by dust clouds in the light­of­sight very close to the
star, i.e. between the stellar surface and the permanent dust
shell that is inferred from the IR excess. Moreover, they have
estimated the sizes of the particles in the clouds to be of the
order 0.1 m. Crowther (1997) has discovered the visual fad­
ing of WR 104, accompanied by the disappearance of high­
ionization spectral lines, and placed the dust clouds inside the

6 B. Yudin et al.: Speckle interferometry and radiative transfer modelling of WR 118
permanent dust shell. Thus, the decrease of the dust shell's in­
ner boundary proposed by our modelling does not look as ex­
traordinary as it appears with respect to the even more hostile
conditions for grain condensation.
5. Conclusions
We presented the first diffraction­limited 2.13 m speckle
interferometric observations of the dusty Wolf­Rayet star
WR 118 with 73 mas resolution. No evidence was found for
any significant deviation of the dust shell from circular sym­
metry. Radiative transfer calculations were carried out to model
the spectral energy distribution and our 2.13 m visibility func­
tion. The main conclusion of these calculations is that the
grains in the permanent dust shell of the persistently dust­
making Wolf­Rayet star WR 118 grow to the relatively large
sizes (a  0:3 m). They contribute more than 50% in to­
tal mass of the dust shell and rises its 2.13 m albedo up to
 0:35. The observations can be fitted either with a model
containing double­sized grains with radii of a = 0.05 m and
0.38m or, alternatively, by a model with a grain size distribu­
tion function n(a)  a 3 , with a ranging between 0.005m
and 0.6m. At the inner boundary of the dust shell, which
has an angular diameter of  in = (17  1) mas and is lo­
cated at r in = (150  30)R  , the temperature of the small­
est grains amounts to 1750K  100 K and the dust­shell den­
sity to (1  0:2)
10 19 g/cm 3 . Adopting a wind velocity of
V wind = 1200 km/s, the dust formation rate is found to be
(1:3  0:5)
10 7 M /yr.
The existence of large grains in the dust shell leads to a
revision of the previously assumed size of the inner dust­shell
boundary. The inner dust­shell boundary is then located even
closer to the star leading to higher grain temperatures. This,
in turn, further worsens the conditions of grain condensation
which are already extremely harsh in any case. The question
how dust grains permanently condense under such conditions is
still yet open (see Cherchneff et al. 2000 and references therein)
but the existence of dust shells around Wolf­Rayet stars as in
the case of WR 118 clearly shows its warrant urgency.
Acknowledgements. The observations were made with the SAO 6 m
telescope, operated by the Special Astrophysical Observatory, Russia.
References
Allen D.A., Hyland A.R., Longmore A.J., Caswell J.L., Goss W.M.,
Haynes R.F., 1977, ApJ 217, 108
Cherchneff I., Le Teuff Y.H., Williams P.M., Tielens A.G.G.M., 2000,
A&A 357, 572
Cohen M., Vogel S.T., 1978, MNRAS 185, 47
Crowther P.A., 1997, MNRAS 290, L59
Draine B.T., 1985, ApJS 57, 587
Egan M.P., Leung C.M., Spagna G.F., 1988, Comput. Phys. Comm.
48, 271
IRAS Science Team, 1988, Explanatory Supplement to the IRAS
Point Source Catalogue, NASA
Ivezic Z., Elitzur M., 1997, MNRAS 287, 1997
J˜ager C., Mutschke H., Henning T., 1998, A&A 332, 291
Labeyrie A., 1970, A&A 6, 85
Leung C.M., 1976, ApJ 209, 75
Massey P., Conti P.S., 1983, PASP 95, 440.
Roche P.F., Aitken D.A., 1984, MNRAS 208, 481
Schutte W.A., van der Hucht K.A., Whittet D.C.B., et al., 1998, A&A
337, 261
van der Hucht K.A., 2001, New Astronomy Reviews 45, 135
van der Hucht K.A., Cassinelli J.P., Williams P.M., 1986, A&A 168,
111
van der Hucht K., Williams P.M., Morris P.W., et al., 1996, A&A 315,
L193
Veen P.M., van Genderen A.M., van der Hucht K.A., Li A., Sterken
A., Dominik C., 1998, A&A 329, 199
Williams P.M., van der Hucht K.A., The P.S., 1987, A&A 182, 91
Williams P.M., van der Hucht K.A., Morris P.W., 1998, Ap&SS 255,
169
Williams P.M., van der Hucht K.A., 2000, MNRAS 314, 23