Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/UU_Aur.ps Äàòà èçìåíåíèÿ: Tue Nov 19 18:25:09 1996 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:11:23 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 8

A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
08(08.03.1; 08.03.4; 08.09.2)
ASTRONOMY
AND
ASTROPHYSICS
18.11.1996
Carbon stars with detached dust shells:
the circumstellar envelope of UU Aurigae
S. Bagnulo 1 , C.J. Skinner 2 , J.G. Doyle 1 , and M. Camphens 3
1 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland. E­mail: sba@star.arm.ac.uk & jgd@star.arm.ac.uk
2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore MD 21218, USA. E­mail: skinner@stsci.edu
3 Sterrekundig Instituut, Postbus 8000, 3508 TA Utrecht, The Netherlands. E­mail: M.Camphens@fys.ruu.nl
Abstract. We have modelled the spectral energy distri­
bution of the carbon­rich star UU Aurigae, which shows
an excess flux in the far infrared and sub­millimeter re­
gions, in terms of a detached shell generated by an episode
of higher (than the current) mass loss rate. Two different
compositions for the detached shell were used: oxygen­rich
and carbon­rich dust grains. By assuming that at longer
wavelengths the extinction coefficients of the oxygen­rich
grains follow a – \Gamma2 law, and those of the amorphous car­
bon follow a – \Gamma1:3 law, we show that the model including
a detached carbon­rich shell produces a more satisfactory
fit to the observational data compared to the model with
a detached oxygen­rich shell. Moreover, we derived a rel­
atively small value for the distance of the detached shell
from the central star, which implies that the episode of
high mass loss rate ended only few hundred years ago.
The results of our analysis are consistent with the scenario
for the stellar evolution on the asymptotic giant branch
which predicts a short time­scale modulation of the mass
loss rate induced by repeated Helium shell­flashes.
Key words: Stars: carbon -- circumstellar matter -- Stars:
individual: UU Aur
1. Introduction
Asymptotic giant branch (AGB) stars are evolved low or
intermediate mass objects which show copious mass loss.
Dust grains form in the cool expanding circumstellar en­
vironment, absorb the optical radiation of the parent star,
and re­emit in the infrared (IR). The chemical nature of
the dust grains in a stellar wind depends on the compo­
sition of the stellar photosphere. Grains of carbon com­
pounds such as amorphous carbon (AC) and silicon car­
bide (SiC) surround C­rich stars, while silicate constitutes
Send offprint requests to: S. Bagnulo [sba@star.arm.ac.uk]
the main component of the dust around O­rich stars (Sav­
age & Mathis 1979).
In the last decade it has been well established that
many carbon stars -- especially those optically visible --
show excess flux in the far­IR (e.g., Thronson et al. 1987,
Chan & Kwok 1988, Willems & de Jong 1988). Based
on the present knowledge of the optical properties of the
dust grains in the far­IR, and assuming that the mass loss
rate is constant with time, in many cases one is not able
to explain the flux at 60 and 100 ¯m measured by the
Infrared Astronomical Satellite (IRAS).
Recently, Van der Veen et al. (1995) found that 4
AGB stars (among a sample of 11 detected in the sub­
mm range), have fluxes greater by a factor 3--5 than what
can be explained with a constant mass loss model. Three
out of the 4 stars with far­IR flux excess have an optically
thin shell at shorter wavelengths.
Several reasons can be invoked to explain the observed
sub­mm excess: contribution of molecular lines, free­free
emission, or mass loss variability. Here we follow the ap­
proach of reproducing the large excess flux observed at
the longer wavelengths (from 60 ¯m to the millimeter), by
attributing it to the presence of a large dust shell emitting
at these wavelengths, produced by past episodes of mass
loss.
Indeed, the idea that sudden mass loss changes may
occur in C­rich stars is not new. In particular, two kinds
of scenarios were suggested in recent years, both of them
based on the assumption that the excess flux is emitted
by a detached remnant shell ejected in a previous episode
of high mass loss rate. However, these scenarios disagree
on the typical size and chemical composition of the de­
tached shell, and on the physical processes which cause
its formation.
Willems & de Jong (1988) hypothesized that most of
the detached shells are O­rich. During the AGB evolution,
an M Mira variable star produces a silicate shell. Trig­
gered by a thermal pulse, carbon becomes more abundant
than oxygen in the stellar photosphere, and the mass loss

2 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
drops suddenly. The silicate shell expands far away from
the star, while an inner C­rich shell is generated via a low
mass loss rate. Eventually the mass loss rate increases and
-- on a time­scale of 10 4 years -- the circumstellar C­rich en­
vironment obscures the parent star. Optical carbon stars
-- including those few which show a silicate feature in their
mid­IR spectrum (Willems & de Jong 1986) -- would be
objects at an intermediate evolutionary phase, i.e., after
the O­rich phase and before they form a thick C­rich dust
shell. Based on a statistical approach, there have been sev­
eral studies supporting this theory. For example, Egan &
Leung (1991) considered a sample of 125 C­rich stars taken
from the IRAS Low Resolution Spectrometer (LRS) cata­
logue, performed radiative transfer calculations, and com­
pared their results to the IRAS colour­colour diagrams.
Their picture of the circumstellar envelopes around C­rich
stars is a two­shell structure, where the outer shell has an
inner radius of 0.1 pc and an outer radius of 1 pc. Based
on considerations about the time­scale required by their
models, their conclusions were in favour of the Willems &
de Jong (1988) theory.
An alternative scenario is supported by Zuckerman
(1993), along with other researchers (e.g., van der Veen
& Habing 1988, Olofsson et al. 1990) who suggest that
most detached envelopes are C­rich, (some with multiple
structure), and are due to thermal pulses which suppress
for some time the dynamical pulsation and also the mass
loss. Apart from the different origin and chemical com­
position of the outer shell, a notable disagreement with
the previous scenario concerns the size of the dust shells.
Modelling of CO emission by Olofsson et al. (1990, 1992),
and spectral and spatial distribution of the IRAS broad­
band photometry by Hawkins (1990, quoted by Zucker­
man 1993), yield for the outer radius of the C­rich cir­
cumstellar envelopes values about ten times smaller than
those estimated by Egan & Leung (1991).
C­rich stars with a hollow circumstellar shell (or even
multiple shells) are also predicted by Vassiliadis & Wood
(1993), who suggest that in low mass AGB stars (M ! ¸
2:5M fi ), the mass loss rate is negligible except during the
last few shell flash cycles. Some AGB stars would undergo
a period of high mass loss rate, preceded and followed by
longer periods of low mass loss rate.
We decided to approach the problem concerning the
nature of the outer shell (or shells) by focusing our atten­
tion on one star, and showing how different models (con­
sistent with the scenarios quoted above) compare to the
observed spectral energy distribution (SED). The target
selected was UU Aurigae, an optically identified carbon
star with a large far­IR excess. We obtained a mid­IR low
resolution spectrum at the United Kingdom Infrared Tele­
scope, and a photometric measurement in the sub­mm at
the James Clerk Maxwell Telescope. Our data, together
with optical and near­IR photometry taken from the lit­
erature and the IRAS broadband photometry, provide a
coverage of the observable SED spanning from 0:44 ¯m to
0:8 mm.
We consider a number of different hypotheses concern­
ing the nature of the dust shell, that is, we assume differ­
ent dust components (SiC, AC and silicate) and different
kinds of spatial distributions for the dust grains, then we
compare and discuss the resulting best­fits.
2. Method
2.1. Radiative transfer code
The analysis carried out in this paper is based on the
modelling technique described in Bagnulo et al. (1995).
A FORTRAN code originally developed by Haisch
(1979) -- with several upgrades -- solves the radiative trans­
fer equation in a spherically symmetric medium, taking
into account the absorption and scattering properties for
a multiple dust grain composition, and multiple size dis­
tribution. The zero, first and second order moments of the
transfer equation are numerically solved under a general­
ized two­stream Eddington approximation due to Unno &
Kondo (1976).
The model SED is then compared to the observed
broadband photometry (from the optical to mm wave­
lengths), and to low resolution mid­IR spectrum.
2.2. Inputs
The inputs to this code are as follows.
i) The radius R \Lambda , the effective temperature T \Lambda , and the
distance d \Lambda of the central star, the radiation field of which
is approximated by that of a blackbody. Obviously, these
three parameters are not independent, since combined
they have to account for the apparent stellar luminosity.
ii) The inner and outer radii of each dust component.
iii) The absorption and scattering cross­sections for each
dust component.
iv) The size distribution of the dust grains.
v) The spatial density distribution of the dust grains.
2.3. Outputs
The most significant output is the emerging flux, which
is compared to the broadband photometric and spectro­
photometric measurements. Grain temperature distribu­
tions and surface brightness profiles are also provided by
the code.
2.4. Comparing theoretical models and observational data
When we attempt to reproduce both the spectral features
observed in the mid­IR and the general shape of the whole
SED, the definition of the ``best­fit'' to the observational
data is not obvious. This is because we usually cannot
find a unique model reproducing all the observational data
ranging from the optical to the sub­mm. Often, a model

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 3
which produces the best­fit to the spectro­photometric
data, cannot account for the overall SED, or, vice versa,
a model which reproduces the general shape of the spec­
tral distribution does not fit the low­resolution spectral
features. Therefore we are forced to seek a model which
represents a ``reasonable compromise'' between the two.
The best­fit parameters however, can differ depending on
what we consider as ``reasonable compromise''. The strat­
egy adopted is described below.
We assign a priori an error of 25 % to the ground­based
photometric data. Of course, at shorter wavelengths, mag­
nitudes are determined with much more precision; the
large value for the error that we estimate is due to the un­
certainty of deriving the flux at the effective wavelengths
from the broadband photometric measurements (see. e.g.,
Bergeat et al. 1976).
Broadband photometry at 12, 25, 60 and 100 ¯m taken
by IRAS is considered with the original error declared in
the IRAS Point Source Catalog (1986) (in the present case,
4 %, 4 %, 10 % and 11 %, respectively). Such measurements
were colour corrected by convolving the model spectra
with the filter responses tabulated in the Explanatory Sup­
plement (Joint IRAS Science Working Group 1986).
We calculate a number of theoretical models, consid­
ering different numerical values as input parameters. For
each model we calculate three contributions to the total
ü 2 defined by the three spectral regions, namely:
-- the contribution ü 2
NIR due to the broadband photometric
measurements with – Ÿ 10 ¯m;
-- the contribution ü 2
SPECT due to the spectro­photometric
measurements;
-- the contribution ü 2
FIR due to the broadband photometric
measurements with – ? 10 ¯m.
In fact, we do not take into account the broadband
photometric measurements at the wavelengths covered by
the mid­IR spectrum, in the present case, those from 7 to
24 ¯m.
In the millimeter regions beam­size effects may become
important since the beam used to observe the source could
be smaller than the angular extent of the object. There­
fore the measurement in the sub­mm was compared to
the model spectra convolved with a Gaussian of FWHM
= 18.5 arcsec (see Sect. 4.3).
The absolute calibration of the spectro­photometric
measurements is made consistent with the particular SED
model by multiplying the measured flux by a scaling­factor
f which minimises the value of ü 2
SPECT , but we reject the
models for which the condition 0:9 ! f ! 1:1 is not satis­
fied. This approach is consistent with taking for the mid­
IR spectrum an absolute calibration uncertainty of 10 %.
We mention here that for all the models presented in this
paper, this factor was about 1.1. After this correction, the
absolute mid­IR spectrum was always fully consistent with
the colour­corrected 12 ¯m IRAS broadband photometry.
We deem as ``a reasonable model'' one which produces
a fit with all the above defined ü 2 -- divided by the number
of relevant measurements, about 1.
Let us consider a shell composed of dust grains hav­
ing radius a, with a number density / r \Gamma2 , r being the
distance from the central star. The absorption and scat­
tering coefficients, k – (a; r) and oe – (a; r), respectively, are
function of the dust mass loss rate, —
M d , of the density of
the grain material ae d , of the velocity of the out­flowing
dust, v d , and of the absorption and scattering efficiency
factors, Q abs (a; –) and Q sca (a; –), respectively. They can
be written as
k– (a; r) = A
Q abs (a; –)
a
1
r 2
oe – (a; r) = A
Q sca (a; –)
a
1
r 2
;
where
A = 3
16ú
1
ae d v d
—
M d : (1)
Once the stellar parameters and the optical constants of
the dust grains have been fixed, it is possible to derive
A by comparing the model SED with the observations.
Then, from Eq. (1), one can derive the dust mass loss rate
if ae d and v d are known, and estimate the dust­to­gas ratio
if the gas mass loss rate, —
M g , is also known.
It should be noted that, in most cases, stellar parame­
ters are not well determined. In the present case, the angu­
lar diameter of UU Aur is known via direct measurements
(see Sect. 5.2), thus, from the broadband photometry, we
can obtain the stellar effective temperature. Instead, the
distance is only estimated by a priori setting a value for
the absolute luminosity of the star.
Let us consider a star of radius R 0
\Lambda to a distance
d 0
\Lambda , surrounded by a dust shell with an inner radius of
R inn = R 0
inn , outer radius R out = R 0
out , and characterised
by a value A = A 0 . Let us consider a second star with the
same effective temperature as the previous one, having ra­
dius R 00
\Lambda , to a distance d 00
\Lambda , and surrounded by a shell com­
posed of the same kind of dust grains, and characterised
by R inn = R 00
inn , R out = R 00
out , and A = A 00 . The rele­
vant SEDs predicted for these two systems are identical if
the parameters quoted above differ by the same scaling­
factor ff, that is, if R 00
\Lambda = ffR 0
\Lambda , d 00
\Lambda = ffd 0
\Lambda , R 00
inn = ffR 0
inn ,
R 00
out = ffR 0
out , A 00 = ffA 0 . Therefore, once the effective
temperature and the angular diameter of a star are fixed,
the quantity actually derived via spectral analysis is the
ratio A=d \Lambda (or A=R \Lambda ).
3. Optical constants of the dust grains
Amorphous carbon, SiC and silicate were considered as
possible components of the dust shell. Absorption and
scattering cross­sections were derived via Mie­Theory

4 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
adopting suitable runs of optical constants which are pre­
sented in the following.
We assumed the density of the dust grains to be 1.8,
3.2 and 3:0 gcm \Gamma3 for AC, SiC and silicate, respectively.
Fig. 1. Absorption coefficients per unit of grain radii vs. wave­
length, for various dust species. The grain radius is set to
5 10 \Gamma3 ¯m. Long­dashed line: ``BE'' sample of AC, optical con­
stants calculated by Preibisch et al. (1993). Solid line: ``AC1''
sample, optical constants calculated by Rouleau & Martin
(1991). Dot­dashed line: MgFeSiO4 , optical constants given by
Dorschner et al. (1995). Dotted line: ``astronomical silicate'',
optical constants given by Draine (1985). At longer wave­
lengths, the absorption coefficients are derived basing on an
extrapolation on the last data points tabulated by the authors
(see text)
3.1. Amorphous carbon
Optical properties of AC have been extensively investi­
gated in the laboratory by several authors (e.g. Koike et
al. 1980, 1994; Bussoletti et al. 1987; Blanco et al. 1991;
Colangeli et al. 1995).
Rouleau & Martin (1991) derived four sets of optical
constants from the extinction data of the AC samples pro­
duced in the laboratory by Bussoletti et al. (1987). In this
work we consider those labeled with ``AC1'' in their Ta­
ble 1. At wavelengths shorter than 100 ¯m, the absorption
coefficients follow a power law in – \Gammafi with spectral index
fi ' 1, which rises up to ' 1:8 at the two last data points
tabulated by the authors (– = 283 and 300 ¯m). In order
to calculate the absorption cross­sections at wavelengths
longer than those considered by the authors, we decided
though to base an extrapolation on all data points tabu­
lated from – = 250 ¯m to – = 300 ¯m. The spectral index
so derived is fi ' 1:3.
Preibisch et al. (1993) published a set of optical con­
stants derived from the laboratory measurements by Bus­
soletti et al. (1987) and by Blanco et al. (1991), which
extend up to 800 ¯m, and, at longer wavelengths, the spec­
tral index is fi ' 1:9.
In Fig. 1 we compare the absorption coefficients de­
rived from the optical constants given by Rouleau & Mar­
tin (sample AC1, solid line) with those derived from the
optical constants calculated by Preibisch et al. (1993)
(sample ``BE'', long­dashed line). At 1 ¯m, the absorption
coefficients of the sample AC1 are smaller by a factor 2
than those of the BE sample.
It should be noted that the extinction curve derived
from the laboratory measurements carried out in other
works exhibit a smaller spectral index at longer wave­
lengths. Tanab'e et al. (1983) report for hydrogenated AC
grains a spectral index fi = 0:6 in the far­IR, a value con­
sistent with that derived by Colangeli et al. (1995), who
give fi ' 0:5 in the range – = 30 \Gamma 180 ¯m, and fi ' 1:1 in
the range 340 \Gamma 1100 ¯m. Extinction cross­sections are ac­
tually dependent on the laboratory conditions of produc­
tion of the sample of dust grains. Modelling of observed
SEDs of a large number of objects is required in order to
establish which particular form of AC (or hydrogenated
AC) is more likely produced in the circumstellar environ­
ments of C­rich stars.
In this work we adopted the absorption and scattering
coefficients derived from the optical constants given by
Rouleau & Martin (1991).
3.2. Silicon carbide
Silicon carbide exists in two crystallographic forms, re­
ferred to as ff­SiC (hexagonal/rhomboedric), and fi­SiC
(cubic). Baron et al. (1987) and Papoular (1988) favoured
ff­SiC to explain the shape of the feature seen in the low­
resolution spectra of C­rich stars. Groenewegen (1995)
also found that mid­IR spectra of 19 out of 21 C­rich stars
he modelled were fitted with ff­SiC.
Here we adopted the optical constants for ff­SiC given
by P'egouri'e (1988), which were synthesized on the basis
of laboratory measurements carried out by Phillip & Taft
(1969) and by Borghesi et al. (1985, 1986). At wavelengths
longer than ' 170 ¯m, the slope of the extinction curve

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 5
is constant, with a spectral index fi ' 2. The data points
beyond 244 ¯m were extrapolated by adopting this value
for the spectral index.
3.3. Silicate
A large number of laboratory measurements and theo­
retical calculations have been made on O­rich grains. A
comprehensive collection of optical constants for silicate
grains has been presented by Draine & Lee (1984) and
Draine (1985) (see also Laor & Draine 1993). This set of
optical constants was synthesized by requiring that the
grain optical properties were consistent with a number of
constraints obtained from both astronomical observations
and laboratory measurements. The absorption coefficients
follow a – \Gammafi law, with fi = 2, for – ? ¸ 20 ¯m. Such a be­
haviour at longer wavelengths is consistent with that of
the absorption cross­sections of several kinds of silicate
obtained from laboratory measurements. Magnesium­iron
silicates studied by Day (1981) follow a power law with
fi = 1:8 from – = 100 ¯m to – = 300 ¯m. Magnesium­iron
silicates studied by Dorschner et al. (1995) have fi = 2 for
– ? ¸ 70 ¯m. Figure 1 shows the absorption coefficients per
unit of grain radii derived from the optical constants for
astronomical silicate given by Draine (1985) (dotted line)
and for the olivine MgFeSiO 4 presented by Dorschner et
al. (1995) (dot­dashed line).
In the present work we adopted the set of optical con­
stant given by Draine (1985).
4. Size of the dust grains
Since the dust ejected by evolved late­type stars is a major
component of the interstellar matter, the size distribution
of circumstellar dust grains must be related to that of the
interstellar dust grains. The standard model of Mathis et
al. (1977) for the interstellar medium predicts that dust
grains have a radius a ranging approximately from 5 10 \Gamma3
to 0:25 ¯m, following a distribution / a \Gamma3:5 . The existence
of a few larger grains is not excluded by other authors
(see e.g. Kim et al. 1994), but it is widely accepted that
most of the interstellar grains have a relatively small size
(e.g., the mean radius predicted by the size distribution
proposed by Mathis et al. 1977 is ' 8 10 \Gamma3 ¯m). By con­
trast, it is unclear whether such small grains are formed
in circumstellar environments, or if they are produced in
interstellar space by shock fragmentation. Seab & Snow
(1989) modelled the observed ultraviolet extinction curve
for the circumstellar dust of the red supergiant ff Scorpii
concluding that no silicate grains smaller than 8 10 \Gamma2 ¯m
are present.
Sorrel et al. (1990) suggested that AC grains with
radius larger than 0:05 ¯m will be destroyed by hydro­
genation and chemical sputtering in dense clouds. Groe­
newegen (1996) fitted the visibility data of IRC +10 216
by adopting AC grains with a radius of 0:16 ¯m. There­
fore, we assumed that the mean radius of AC grains was
definitely not larger than few 0:1 ¯m. However we were
not able, with the available photometry at shorter wave­
lengths, to determine the best size distribution for the
dust grains. In fact, in the present analysis we considered
all the grains having the same radius, which was set to
5 10 \Gamma3 ¯m. For grains so small, even at the shortest ob­
served wavelengths, the scattering is negligible, and the
absorption coefficients (in units of grain radii) are inde­
pendent of the grain radius. In Sect. 7 we will also discuss
the cases of dust shells composed of grains having radii of
0:25 ¯m, and having a size distribution like the one sug­
gested by Mathis et al. (1977). Since the present work is
focussed on the analysis of the large far­IR and sub­mm
excess observed in the SED of UU Aur, the main results
will not be affected by the choice of grain size, provided
that most of the grains composing the circumstellar en­
velope have a radius not much larger than 1 ¯m. This is
because the wavelengths at which the (cool) dust grains
of the outer shell emit are much larger than the grain ra­
dius. With this condition satisfied, transport coefficients
and the calculated emerging flux are independent of the
grain size.
5. Parameters of UU Aurigae
5.1. Spectral type
UU Aurigae is a carbon star of spectral type C 6,4, ac­
cording to the classification by Yamashita (1972).
5.2. Effective temperature
Quirrenbach et al. (1994) measured the angular diameter
of this star, giving the value (corrected for limb­darkening)
of ` = 12:07 \Sigma 0:22 mas. Then they inferred -- based on
the bolometric flux -- an effective temperature T \Lambda = 2767 \Sigma
25 K, which is in good agreement with the value of 2825 K
obtained by Tsuji (1981) via the infrared flux method.
5.3. Distance
Two parallax estimates are given by the Simbad database,
0:002 \Sigma 0:001 and 0:003 \Sigma 0:001, from which we obtain that
the distance of UU Aur is ranging from 250 to 1000pc.
Frogel et al. (1980) found that N type C­rich stars in
the Magellanic Cloud clusters have an absolute J mag­
nitude of ' \Gamma8:1. By adopting the same absolute magni­
tude for UU Aur, Olofsson et al. (1987) derived a value for
the distance of 290pc, which is in agreement with both
the value of 270pc given by Groenewegen et al. (1992)
(derived by assuming for UU Aur an absolute luminosity
of 7050 L fi ), and the value of 320pc adopted by Knapp
(1986).
Loup et al. (1993) quote the value of 1200pc which
is not consistent with the adopted photometric data (see
Sect. 6). This would result in a star with a luminosity of

6 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
140; 000 L fi , which is almost an order of magnitude above
the theoretical AGB limit.
5.4. Mass loss rate
To estimate the dust­to­gas ratio of the different dust com­
ponents requires knowledge of the gas mass loss rate.
Based on a CO J = 1 \Gamma 0 line detection, Knapp (1986)
derived a gas mass loss rate of 2:9 10 \Gamma7 M fi yr \Gamma1 , consis­
tent with the value of 2:8 10 \Gamma7 M fi yr \Gamma1 , obtained by Olof­
sson et al. (1987). More recently though, Olofsson et al.
(1993) derived the value of 1:3 10 \Gamma7 M fi yr \Gamma1 . Olofsson et
al. (1993) show also CO line profiles, which do not appear
double peaked (see discussion in Sect. 9).
Groenewegen et al. (1992) found that the general for­
mula used to derive the mass loss rate from CO line
detection (see e.g. Eq. (10) of Groenewegen et al. 1992)
yields systematically higher values for non resolved en­
velopes (as that of UU Aur), and, after analysing fur­
ther the previous measurements, they propose the value
of 8:0 10 \Gamma8 M fi yr \Gamma1 . On the other hand, Olofsson et al.
(1993) suggest that the same formula underestimates the
gas mass loss rate, especially for small values of —
M g , and
more detailed models of circumstellar CO by Kastner
(1992) provide mass loss rate for low­ —
M g objects higher
by a factor 2 than those obtained by using the general
formula quoted above. We note that the discrepancies be­
tween the values of —
M g quoted above can be partially
reduced by scaling them like d 2
\Lambda . However, the value for
the ratio —
M g =d 2
\Lambda as derived by Groenewegen et al. (1992)
(namely, 1:1 10 \Gamma12 M fi yr \Gamma1 pc \Gamma2 ) is 2/3 of the value de­
rived by Olofsson et al. (1993) and 2/5 of the value derived
by Knapp (1986).
5.5. Out­flowing dust velocity
In order to derive the mass loss rate for the dust, we need
to know the value of the velocity v d of the out­flowing
dust.
The velocity of the out­flowing gas, v g , as given by
Knapp (1986), is 13:4 km s \Gamma1 , while both Groenewegen et
al. (1992) and Olofsson et al. (1993) derived a value around
11km s \Gamma1 .
In general, we cannot assume that the dust velocity
is equal to the gas velocity, since it is known that dust
grains move with a drift velocity relative to the gas. Such a
drift velocity is definitely negligible with respect to the gas
velocity only in optically thick shells with mass loss rates
of ¸ 10 \Gamma5 M fi yr \Gamma1 or higher. On the contrary, UU Aur is
surrounded by an optically thin shell, with a rather small
gas mass loss rate.
Detailed calculations of two­fluid models for station­
ary dust­driven winds carried out by Kr¨uger et al. (1994)
show that, for a star of 10 4 L fi and gas mass loss rate of
¸ 4:4 10 \Gamma6 M fi yr \Gamma1 , the drift velocity is less 1km s \Gamma1 for
grains of radius a = 0:012 ¯m, and less than 10km s \Gamma1 for
grains of radius 0.25 ¯m. Assuming that the grain drift
velocity depends on (L= —
M g ) 1=2 , for grains with radius
5 10 \Gamma3 ¯m as adopted in this work, the grain drift veloc­
ity is probably negligible, compared to the gas velocity. If
the grain drift velocity is non­negligible, then the dust­to­
gas ratios determined later in this work will be underesti­
mated.
5.6. Adopted parameters for UU Aurigae
We adopted for UU Aur the effective temperature and the
stellar angular diameter as given by Quirrenbach et al.
(1994), which are fully consistent with the set of photo­
metric data that we have considered (see Sect. 6).
For the sake of clarity, in the following we will describe
our results by quoting the mass loss rates and dust­to­gas
ratios as derived by setting v d = v g , and by adopting the
set of parameters v g , —
M g , d \Lambda and R \Lambda given by Olofsson et
al. (1993) (the stellar radius R = 370 R fi is derived from
the observed SED).
The dust mass loss rates and dust­to­gas ratios that
would be obtained by adopting different parameters for
v d , —
M g , d \Lambda and R \Lambda can be obtained simply by multiplying
the values that we are going to quote by suitable scaling­
factors. Namely, from the mass loss rate —
M d as derived by
adopting the parameters given by Olofsson et al. (1993),
one can derive the mass loss rate for the parameters given
by Groenewegen et al. (1992) or by Knapp (1986), by mul­
tiplying —
M d by g 1 = 0:96, or g 1 = 1:36, respectively. Simi­
larly, the dust­to­gas ratios as calculated by adopting the
parameters given by the other authors can be obtained by
multiplying the dust­to­gas ratio derived from the param­
eters of Olofsson et al. (1993) by g 2 = 1:55, (for the data
of Groenewegen et al. 1992) or g 2 = 0:60 (for the data of
Knapp 1986) (see Table 1).
Table 1. Parameters for UU Aur as given by different authors.
The stellar radius is consistent with the distance, the adopted
value for the effective temperature of 2767 K, and the photome­
try. The meaning of the scaling­factors g1 and g2 are explained
in the text (Sect. 5.6)
distance —
Mg vg R \Lambda
(pc) (M fi yr \Gamma1 ) km s \Gamma1 (R fi ) g1 g2 Ref.
290 1:3 10 \Gamma7 10.9 370 1.00 1.00 1
270 8:0 10 \Gamma8 11.4 340 0.95 1.55 2
320 2:9 10 \Gamma7 13.4 410 1.35 0.60 3
Key to references. 1: Olofsson et al. (1993); 2: Groenewe­
gen et al. (1992); 3: Knapp (1986)

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 7
6. Observations of UU Aurigae
6.1. Selection of the ground­based broadband photometric
measurements
Among the ground­based photometric measurements pub­
lished in the literature, we used those gathered in Ta­
ble 4 of Bergeat et al. (1976) spanning from 0:44 ¯m to
20:0 ¯m. Measurements given by Fernie et al. (1983) and
by Noguchi et al. (1981) are not in agreement with Bergeat
et al.'s set of measurements, possibly due to the variability
of the star.
6.2. Mid­IR Spectra
A low­resolution mid­IR spectrum (R = –=\Delta– = 60) of
UU Aur was obtained at the 3:8 m United Kingdom In­
frared Telescope (UKIRT) on 30 October 1993 using the
common­user mid­IR spectrometer CGS3. An 8 \Gamma 13 ¯m
spectrum was taken in the usual manner, chopping the
secondary 15'' E--W at 5 Hz and nodding E--W at 10 sec­
ond intervals in order to remove thermal background emis­
sion. Atmospheric features were removed using spectra of
the standard star ff Tau. It was not possible to obtain
a 16 \Gamma 24 ¯m spectrum due to inadequate sky conditions.
With a similar technique, we observed UU Aur once again
on 21 and 22 August 1995. This time we managed to take
both a 8 \Gamma 13 ¯m and a 16 \Gamma 24 ¯m spectrum of good
quality. The spectra of UU Aur were obtained as part of
a survey of mid­IR spectra of C­rich stars, the results of
which will be presented in a forthcoming paper.
Figure 2 shows both our CGS3 spectra compared to
that of the IRAS LRS catalogue, and the IRAS broadband
photometry at 12 and 25 ¯m colour corrected according to
the model shown in Fig. 2. The absolute calibration of the
more recent spectrum taken at the UKIRT (solid line) is
fully consistent with that of the spectrum taken in 1993,
while the absolute flux measured by the IRAS LRS (Joint
IRAS Science Working Group 1986) is about 15 % higher.
Since the IRAS flag for the mid­IR variability of UU Aur
is 0/10, these small discrepancies can probably be ascribed
to uncertainty in the absolute calibration.
In our analysis we used the more recent CGS3 spec­
trum.
6.3. A sub­millimeter measurement
A measurement at – = 0:8 mm was obtained on 9 Decem­
ber 1994 using the common­user instrument UKT14 at
the Nasmyth focus of the James Clerk Maxwell Telescope
(JCMT) on Mauna Kea, Hawaii. UKT14 is a 3 He­cooled,
single­channel bolometer with filters that cover all major
sub­millimeter windows. Using an aperture of 65 mm gives
a beam width of ¸ 18:5 arcsec in all filters. Sky subtrac­
tion was achieved via a chopping secondary, using a chop
of 60 arcsec in azimuth with a frequency of 7.8Hz. For flux
calibration we used Saturn as a primary calibrator and
Fig. 2. Mid­IR low resolution spectra of UU Aur. The solid
line shows the CGS3 spectrum taken at the UKIRT on 21 and
22 August 1995, the dotted line that taken on 30 October 1993,
the long dashed line is the spectrum taken by the IRAS LRS.
The empty circles represent the IRAS broadband photome­
try at 12 and 25 ¯m (colour corrected according the model of
Fig. 2). Filled circles represent the ground­based broadband
photometry (see Sect.6.1)
CRL 618 as the secondary, The flux for Saturn was de­
rived using the JCMT utility program FLUXES. UU Aur
was observed at – = 0:8 mm, and a flux of 78 \Sigma 20 mJy
was measured.
7. The flux excess of UU Aurigae
A common modelling technique pictures carbon stars as
blackbodies surrounded by dust shells with an inner radius
of a few stellar radii (e.g. Lorenz­Martins & Lef`evre 1993,
1994), composed of SiC and/or AC grains (or graphite
instead of AC), with a r \Gamma2 number density, implying a
constant mass loss rate.
The hypothesis that C­rich stars are surrounded by
dust shells composed of only SiC, as suggested by Le
Bertre (1988a, 1988b), probably represents the simplest
one in order to explain both the general shape of the SED
and the mid­IR spectrum. Chan & Kwok (1990) modelled
a large sample of C­rich stars assuming SiC as the sole
source of opacity in the circumstellar envelopes. In the
case of UU Aur, we were unable to reproduce satisfac­
torily both the near­IR broadband photometry and the
mid­IR spectrum by assuming a dust shell composed ex­
clusively of SiC. On the other hand, we found that the

8 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
feature around 11 ¯m could not be reproduced without
including SiC. Therefore we tackled the problem of repro­
ducing the SED of UU Aur by adopting a two­component
model including both AC and SiC.
Fig. 3. A model for UU Aur, obtained assuming a shell com­
posed of SiC and AC, produced with a constant mass loss rate.
Inner radius for SiC shell is 3 R \Lambda , inner radius for AC shell is
9 R \Lambda , the other parameters are given in the text; note that
the SED at longer wavelengths is not accounted for. Filled cir­
cles: ground­based photometric measurements (see Sects. 6.1
and 6.3). Empty circles: IRAS broadband photometric mea­
surements at 12, 25, 60, 100 ¯m, colour­corrected. Crosses:
the original IRAS photometry not colour­corrected. Empty
squares: UKIRT CGS3 low­resolution spectrum (see Sect. 6.2).
The dashed line is the SED of a blackbody of T = 2767 K,
which approximates the radiation field of the central star
Figure 3 shows one of the best­fits to the near and
mid­IR that we obtained. The relevant parameters are as
follows. For the SiC shell, inner radius 3 R \Lambda and dust mass
loss rate of 6:4 10 \Gamma11 M fi yr \Gamma1 ; for the AC shell, inner ra­
dius 9 R \Lambda and dust mass loss rate 2:0 10 \Gamma10 M fi yr \Gamma1 . The
temperature at the inner radius for SiC and AC shells
are 1300K and 900K, respectively. The outer radius is
10; 000 R \Lambda . The value of the SiC/AC ratio, 1/3, is consis­
tent with the hypothesis that this quantity may be higher
for stars with low mass loss rate than for stars with high
mass loss rate (Skinner & Whitmore 1988). The value for
ü 2
NIR is 1, ruling out the measurement at 0:44 ¯m, where
the calculated flux is higher by a factor 2.5 than the ob­
served one. The fit to the optical and near­IR broadband
photometry could be improved by adopting a lower effec­
tive temperature for the star, e.g. setting T \Lambda = 2500K,
which is in disagreement with the direct measurements of
T \Lambda presented in Sect. 5.2. Note that we were not able to
reproduce the feature seen at 7:8 ¯m. A similar feature,
which may be due to molecular bands in the stellar atmo­
sphere, was also observed in the mid­IR of other visible
carbon stars, i.e., EL Aur, RT Cap and R Scl.
The search for the best­fit was repeated by assuming
that the dust grains have a radius of 0:25 ¯m, and keeping
the same values of the inner and outer radii as for the
model shown in Fig. 3. We found that the dust mass loss
rate for both components is reduced to 50% of the values
quoted above. By adopting a size distribution / a \Gamma3:5 ,
having lower limit a = 5 10 \Gamma3 ¯m and upper limit a =
0:25 ¯m, we obtained a best­fit for values of the dust mass
loss rate intermediate between those obtained assuming
that all the grains have a radius a = 5 10 \Gamma3 ¯m and those
obtained under the assumption that all the grains have
a radius a = 0:25 ¯m, i.e., for SiC a dust mass loss of
4:8 10 \Gamma11 M fi yr \Gamma1 , and for AC a dust mass loss rate of
1:6 10 \Gamma10 M fi yr \Gamma1 . We were not able to distinguish the
best­fit among those obtained with different grain sizes.
It should be noted that, for grains of radius 0:25 ¯m, the
absolute velocity of the out­flowing dust may be almost
twice the gas velocity, thus the actual values of the dust
mass loss rate for large grains are probably close to those
derived for smaller grains.
It was not possible to determine a precise value for the
inner radius of the dust shell. Setting the inner radius of
the SiC shell to 1:2 R \Lambda , and the inner radius of the AC
shell to 6 R \Lambda , we obtained a reasonable fit with a dust
mass loss rate of 6:0 10 \Gamma11 M fi yr \Gamma1 for the SiC shell, and
of 1:6 10 \Gamma10 M fi yr \Gamma1 for the AC shell. The correspond­
ing condensation temperatures are ' 2000K for the SiC
grains and ' 1000K for the AC grains. This model pro­
duces a slightly better fit to the near­IR photometry, and a
slightly worse fit to the mid­IR spectrum than that shown
in Fig. 3, but it is not really possible to decide which is
the best one. On the other hand, by setting the value of
the inner radius for both components to 100 R \Lambda , we found
that, with a dust mass loss rate of ' 6:5 10 \Gamma10 M fi yr \Gamma1
for both AC and SiC, we were still able to reproduce the
near­IR photometry and the mid­IR spectrum, although
the fit to the feature around 11 ¯m is poorer than that

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 9
Fig. 4. Twelve models reproducing the broadband photometry at 800 ¯m. The inner shell is the same as in Fig. 3. The outer
shell is composed of silicate, and its inner radius is set to 300 R \Lambda (solid line), 1000 R \Lambda (dotted line), 2000 R \Lambda (long dashed line),
4000 R \Lambda (dot­dashed line). All these models account for the measurement at 0.8 mm after the correction for the finite beam­size
effect. IRAS broadband photometry is plotted non colour­corrected, and the measurement at 800 ¯m is plotted uncorrected for
the finite beam­size effects. In the figure we also quote the dust­to­gas ratios of the detached shell for the different models,
calculated by assuming that the rate measured via CO lines reflects the mass loss in the outer regions of the envelope
shown in Fig 3. By further increasing the value of the in­
ner radius to values as large as 200 R \Lambda it was still possible
to roughly reproduce the shape of feature seen at 11 ¯m,
but with lack of consistency in the absolute calibration
of the mid­IR spectrum and broadband photometry (the
factor f required to fit the mid­IR spectrum is about 0.85,
and the model predicts about 75% of the flux at 12 ¯m
measured by IRAS).
In conclusion, our results are consistent with the hy­
pothesis that the inner radius of the dust shells is a few
stellar radii, that is, UU Aur is currently undergoing an
episode of (low) mass loss. We were unable to reproduce
the observed SED at longer wavelengths. The fit of Fig. 3
predicts at – = 60 ¯m, 100 ¯m and 0.8 mm a flux which is
respectively about 50%, 30 % and 40% of that observed.
It could be argued whether the observed far­IR excess
is really due to the dust emission from the circumstellar
environment of UU Aur.
Avery et al. (1992) found that 65% of the flux from
IRC +10 216 in the range – ' 0:82 \Gamma 0:88 mm is to be
ascribed to molecular emission lines.
Confusion flags for cirrus contamination declared in
the IRAS Point Source Catalog are CIRR1 = 6 and CIRR2
= 3. The value of CIRR1 might indicate contamination
by cirrus with structure on the point source size scale,
but the value of CIRR2 estimates the contribution of
the cirrus flux less than ¸ 6% of the flux due to the
source at 100¯m. Furthermore, the small value of the ra­
tio CIRR3/F 60 (= 1:3), where F 60 is the flux expressed
in Jy at 60 ¯m, indicates a negligible contribution from
interstellar contamination, according to Ivezi'c & Elitzur
(1994). Therefore the presence of a detached shell is defi­
nitely required in order to explain the far­IR excess.
In the following sections we will approach the problem
of reproducing the observed SED of UU Aur by assuming
that a large amount of cool dust in the outer part of the
shell is actually responsible for the observed flux excess at
the longer wavelengths.
8. Detached shell models for UU Aurigae
As a first approach to deal with the phenomena of non­
constant mass loss, we kept the common assumption that
the number density of the dust grains follows a r \Gamma2 law,
allowing the value of the inner radius of one dust compo­
nent to vary. We considered an inner shell with the same
features as those of the model shown in Fig. 3, that is,
composed of AC and SiC. To mimic the presence of a de­
tached shell we added a third component, and we searched
for the best­fit varying the values of the inner radius from

10 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
Fig. 5. Left. Top and middle panels: the solid line shows a model with a silicate detached shell, with inner radius of 1500 R \Lambda , outer
radius of 100; 000 R \Lambda , and dust mass loss rate of 5:2 10 \Gamma8 M fi yr \Gamma1 . Bottom panel: the surface brightness profiles corresponding
to the model represented above. Right. Top and middle panels: the solid line shows a model with a silicate detached shell which
accounts for the 65 % of the flux at 0.8 mm. The inner radius of the detached shell is 500 R \Lambda , the outer radius is 100; 000 R \Lambda , and
the dust mass loss rate is 1:4 10 \Gamma8 M fi yr \Gamma1 . Bottom panel: the normalised surface brightness profiles, at various wavelengths,
for the model represented above

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 11
100 to 4000 R \Lambda . The outer radius of the inner shell was set
equal to the inner radius of the outer shell.
8.1. A detached shell of silicate grains
Due to the the emissivity law in – \Gamma2 of the silicate grains,
we found it difficult to reproduce both the far­IR and the
sub­mm broadband photometry. Models which fit the sub­
mm broadband photometric measurement do not repro­
duce the IRAS broadband photometry satisfactorily.
Figure 4 shows 12 models including a silicate detached
shell which fully accounts for the observed flux at 0.8 mm.
These models were obtained by fixing a value for the in­
ner and outer radius, and then looking for a model which
reproduces the 0.8 mm measurement. The outer radius for
these models is fixed to 10; 000 R \Lambda (' 0:1 pc, left panel),
100; 000 R \Lambda (' 1 pc, middle panel), 1; 000; 000 R \Lambda (' 10 pc,
right panel). Inner radii of 500 R \Lambda (solid line) 1000 R \Lambda (dot­
ted line), 2000 R \Lambda (long dashed line) and 4000 R \Lambda (dot­
dashed line) were considered. Each of these models fully
explain the measurement at 800 ¯m after the correction
for the beam­size effect, but since this correction is de­
pendent on the model, only the uncorrected measurement
is plotted. The IRAS broadband photometry is also plot­
ted non colour­corrected. Figure 4 helps us to understand
that, in order to reproduce the SED at longer wavelengths,
it is required to assume a (relatively) small value for the
inner radius (R inn ¸ 1000 R \Lambda ), a large value for the outer
radius (R out ? ¸ 1 pc) and a very large amount of dust (a
few units in 10 \Gamma8 M fi yr \Gamma1 ).
The fits of Fig. 4 can clearly be improved by changing
the values for the inner radius of the detached shell, and
the value of the outer radius. The solid line on the left
of Fig. 5 (top and middle panels) shows the best­fit to
the observed SED of UU Aur, obtained by setting R inn =
1500 R \Lambda , R out = 100; 000 R \Lambda ; the dust mass loss rate is
5:2 10 \Gamma8 M fi yr \Gamma1 . Since the (cool) detached shell emits at
longer wavelengths, all these values are independent of the
grain size (except for the fact that for large grains the drift
velocity becomes important, see also Sect. 9). The dust
grain temperature at the inner edge of the silicate shell
is ¸ 50K. At 25, 60, 100 and 800 ¯m the ratio between
observed and predicted flux is 0.75, 0.80, 0.95 and 1.0,
respectively.
The situation would be slightly different if we assumed
that a substantial fraction of the flux measured at 0.8 mm
is to be ascribed to molecular emission lines. The solid line
in the top and middle right panels of Fig. 5 shows the best­
fit obtained by requiring to explain at least 50% of the
flux observed at 0.8 mm, and by setting the outer radius
to 100; 000 R \Lambda . The inner radius is 500 R \Lambda and the dust
mass loss rate is 1:4 10 \Gamma8 M fi yr \Gamma1 . This model accounts
for 65% of the observed sub­mm flux. At 25, 60, and
100 ¯m, this fit is relatively poor: at these wavelengths,
the ratio between predicted and observed flux is 0.85, 1.25,
0.90, respectively.
8.2. A detached shell of amorphous carbon grains
Figure 6 shows a fit obtained by considering an inner shell
composed of AC and SiC, and an outer shell composed
only of AC. The parameters of the inner shell are the same
as those of the model presented in Sect. 7, while the outer
shell of AC has an inner radius of 300 R \Lambda , and dust mass
loss rate of 7:2 10 \Gamma9 M fi yr \Gamma1 . The dust grain temperature
at the inner radius is 170K. At 0.25, 0.60, 100, and 800 ¯m
the ratio between predicted and observed flux is 0.95, 0.95,
1.15 and 0.95, respectively.
The value of the outer radius was set to 10; 000 R \Lambda .
By reducing it to 3; 000 R \Lambda , we found that the best­model
parameters (inner radius and dust mass loss rate) are the
same as in the previous case, and the predicted flux at
100 and 800 ¯m is 90 % and 70% of that observed. Setting
the outer radius to 50; 000 R \Lambda , the model predicts a flux
which is 130% of that observed at 800 ¯m. At the other
wavelengths these two models are almost identical to that
shown in Fig. 6. The value of the outer radius for a C­
rich detached shell is therefore quite undetermined, but is
likely ranging from few thousands to few tens of thousand
stellar radii.
9. Discussion
The models including a detached shell composed of silicate
dust grains, with opacity law / – \Gamma2 , do not allow one to
reproduce the SED of UU Aur at longer wavelengths as
well as the model with a C­rich detached shell. In fact,
the models with a detached O­rich shell could be improved
upon by forcing the absorption cross­sections for silicate
to behave as – \Gamma1 , instead of – \Gamma2 . This has been previ­
ously tried by several authors (e.g., Willems & de Jong
1988, Chan & Kwok 1988, Justtanont & Tielens 1992,
Griffin 1993). We ruled out this approach though, since
we would get a set of optical constants which do not re­
spect the Kramer­Kroenig relationships. Furthermore, the
numerical results of the analysis (basically the dust mass
loss rate for silicate) would be meaningless, since they are
strongly dependent on the (arbitrary) starting wavelength
from which one decides to force the extinction coefficients
to follow a pre­defined power law in –.
Strictly speaking, the only model which produces a fit
with ü 2
FIR ! 1 is the one obtained with the outer shell
composed of AC. It might be argued though whether this
can demonstrate that UU Aur is surrounded by a C­rich
detached shell rather than an O­rich one. Indeed, the small
number of observational data compared to the number of
free parameters prevent us from rigorously applying the
statistical test of ü 2 . There are more free parameters than
observational data.
The predicted surface brightness profiles (see bottom
of Figs. 5 and 6) show that IR imaging techniques could
not help to distinguish between the models. At longer
wavelengths, using, e.g., the Plateau de Bure interferom­

12 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
Fig. 6. A double shell model for UU Aur. The inner shell is
composed of AC and SiC grains; the outer shell is composed of
AC and its inner radius is 300 R \Lambda . Top and middle panels show
the fit to the observed SED. Keys to the symbols are the same
as Fig. 3; the cross (filled circle) at 0.8 mm is the photometric
measurement uncorrected (corrected) for the beam­size effect.
Bottom: the corresponding surface brightness profiles
eter (France) -- which achieves an angular resolution of
0.6 arcsec at 1.3 mm -- one might be able to observe the
inner radius of the outer shell composed of AC, but the
radiation emitted at the inner radius of an outer silicate
shell would be too faint to be detected.
It could be possible to discriminate between the mod­
els by comparing the dust­to­gas ratios derived for the
outer shells to the cosmic abundances of the elements
which compose the dust grains. However, it should be dis­
cussed first whether the gas mass loss rate measured via
CO molecular line is to be related to the inner regions of
the envelope or to the detached shell.
By assuming that for UU Aur the CO line measure­
ments probe the inner regions of the shell, the dust mass
loss rates of the inner shell correspond to a dust­to­gas
ratio of 0.05% for the SiC, and of 0.15 % for AC. These
values -- which were derived by adopting the distance and
gas mass loss rate given by Olofsson et al. (1993) -- could
be under or over estimated by 50%, depending on the
choice of distance and gas mass loss rate (see Table 1). If
the mass loss rate measured via CO line detection reflects
that of the inner regions of the shell, then the value of the
dust­to­gas ratio is unusually low, compared to the cosmic
abundance of Si and C. Since CO line profiles of UU Aur
presented by Olofsson et al. (1993) are not double peaked,
the outer shell should be so far away from the central star
that CO molecules are either photo dissociated or too rar­
efied to be detected.
By assuming that the CO traces the outer regions of
the envelope of UU Aur, the dust­to­gas ratio of the outer
shell would be 40% and 11% for the models with an O­
rich detached shell shown in Fig. 5 (left and right panels,
respectively) and 5.5 % for the model with a detached shell
formed of AC, shown in Fig. 6. As for the inner shell,
these values could be under or over estimated by 50%,
depending on distance and gas mass loss rate. Moreover,
if we adopt a grain size of 0:25 ¯m, the resulting dust mass
loss rate in the outer shell (and the dust­to­gas ratio as
well) may be further underestimated by a factor 2 because
of the drift velocity of the dust grains. Table 2 summarises
our estimates of all the parameters for the various cases.
If the measured gas mass loss rate corresponds to the
outer shell, it clearly turns out that the value of the dust­
to­gas ratio of the models including a silicate detached
shell is too high, compared to the cosmic abundance of
the elements which are expected to form the silicate grains
in the circumstellar environments (Mg, Fe, Si, O), there­
fore the model including an O­rich detached shell has to be
ruled out. The inconsistency of the derived dust­to­gas ra­
tio could be slightly reduced by adopting a smaller stellar
distance. Indeed, the quantity derived via spectral analysis
is —
M d =d \Lambda (see Sect. 2.4), and the one derived via CO line
detection is —
M g =d 2
\Lambda . Therefore, the dust­to­gas ratio can
be scaled like 1=d \Lambda . By adopting a distance of 250pc (the
lower limit from the parallax measurements), the stellar

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 13
Table 2. A summary of the parameters of the models discussed in Sect. 8. Column 2 gives the value of the inner radius of the
dust component specified in Column 1. Column 3 gives the dust mass loss rate and column 4 the dust­to­gas ratio. Columns 5--8
give the ratio between the flux predicted by the model and the observed flux. Column 9 quotes the figure numbers of the relevant
models
R inn
—
M d dust­to­gas F model
– =F obs
–
Dust Component (R \Lambda ) (10 \Gamma10 M fi yr \Gamma1 ) ratio (%) 25 ¯m 60 ¯m 100 ¯m 800 ¯m Fig.
inner shell: SiC 3 0.6 -- 0.9 0.03 -- 0.07 \Lambda
inner shell: AC 9 1.9 -- 2.7 0.09 -- 0.20 \Lambda
O­rich detached shell 1500 500 -- 1400 24 -- 125 \Lambda\Lambda 0.75 0.80 0.95 1.0 5 Left
O­rich detached shell 500 130 -- 380 6 -- 30 \Lambda\Lambda 0.85 1.25 0.95 0.65 5 Right
C­rich detached shell 300 70 -- 200 3 -- 17 \Lambda\Lambda 0.95 1.15 0.95 0.95 6
\Lambda Derived by assuming that CO line observations probe the inner shell, that is, they measure the present­day gas mass
loss rate.
\Lambda\Lambda Derived by assuming that CO line observations probe the detached shell, that is, they measure a previous episode
of mass loss.
luminosity would be ¸ 5250 L fi and the dust­to­gas ratios
would be reduced by 20 % only.
The dust­to­gas ratio for the model including a C­rich
detached shell is also rather high. The lower limit of 3%
derived for this quantity is indeed larger than what is ex­
pected from the cosmic abundance of C, but it could be
reduced further if the adopted values of the adopted ex­
tinction coefficients were underestimated (see Sect. 3.1).
Justtanont et al. (1994) developed a theoretical model
for gas kinetic temperature of circumstellar envelopes, and
they applied it to three O­rich stars. They concluded that
the CO mass loss rate derived from J = 2 \Gamma 1 and J =
1 \Gamma 0 transitions measures the gas mass loss rate in the
outer parts of the envelopes. By assuming that also for
UU Aur the rate measured via CO emission lines reflects
the (high) mass loss of the outer shell, rather than the
(low) mass loss in the inner shell, the lack of a clear double
peaked CO line profile could be explained by the fact that
the outer shell is too near to the star to allow one to
see a double peaked profile. Under this assumption, the
comparison of the dust­to­gas ratios derived for the O­
rich and C­rich detached shells seems in favour of this
latter case. Moreover, it should be noted that a value of
the order of 1000 R \Lambda (that is, ¸ 0:01 pc) for the inner
radius of the outer shell does not match the typical value
of 0.1 pc expected from the scenario of stellar evolution
describing the detached shells as O­rich (Egan & Leung
1991). Instead, the value of 300 R \Lambda -- derived from the best­
fit with a C­rich detached shell -- is consistent with the
hypothesis of a short­time scale modulation in the mass
loss rate.
The results of our analysis suggest us the follow­
ing picture of UU Aur: we are looking at a C­rich star
presently undergoing an episode of very low mass loss rate
(! 10 \Gamma8 M fi yr \Gamma1 ), with a C­rich detached circumstellar
envelope produced by a previous episode of higher mass
loss rate (¸ 10 \Gamma7 M fi yr \Gamma1 ), which lasted for 10 3 \Gamma 10 4
years, and ended a few hundred years ago. The total
amount of mass ejected during this period is less that
0:01 M fi .
10. Conclusions
We carried out a detailed analysis of the observed spectral
energy distribution of the carbon­rich star UU Aurigae, in
order to obtain an insight on the nature of its circumstellar
envelope.
A two­component model including a dust shell com­
posed of amorphous carbon and silicon carbide, and pro­
duced by constant mass loss rate, allows us to reproduce
the near­IR photometry as well as the mid­IR spectrum,
but it does not explain the observed SED at far­IR and
sub­mm. We assumed that a discontinuity in the dust
grain spatial density distribution is responsible for the
large far­IR excess observed in the SED, and we modelled
the circumstellar environment of UU Aur as composed of
two shells, each of them following a r \Gamma2 spatial density
distribution.
Amorphous carbon and silicate were considered as (al­
ternative) candidate components of the outer shell.
Assuming that the extinction coefficients of silicate at
longer wavelengths follow a – \Gamma2 law, and that of amor­
phous carbon follow a – \Gamma1:3 law, the model including a
C­rich outer shell provides a better fit to the far­IR and
sub­mm data than the one including an O­rich outer shell.
Assuming that the CO line measurements probe the
inner regions of the shell, then the dust­to­gas ratio of the
material ejected from the star is unusually low.
Assuming that the measured gas mass loss rate corre­
sponds to the outer regions, we found that both models
require a high dust­to­gas ratio in the detached shell. The
model with silicate grains, in order to fully account for
the sub­mm photometry, would require a dust­to­gas ratio

14 S. Bagnulo et al.: The circumstellar envelope of UU Aurigae
larger than 20%. This value could be reduced to 6%, if we
assume that a substantial fraction of the observed flux is
to be ascribed to molecular line emission. The lower limit
of the dust­to­gas ratio for the best­fit obtained with a
C­rich detached shell is 3 %. The inconsistency with the
value expected from the cosmic abundance of C might be
ascribed to uncertain model calculations of CO emission,
and to uncertain values of the extinction coefficients of
AC.
For both models, the value derived for the inner radius
of the outer shell is a few hundred stellar radii. Hence, the
mass loss rate dropped a few hundred years ago. This is
more consistent with a short time­scale modulation in the
mass loss rate, than with an interruption of the mass loss
for ¸ 10 4 years corresponding to the one­time transition
from the O­rich to the C­rich phase (see Sect. 1).
We propose that the outer dust shell of UU Aurigae,
rather than representing a remnant of the star's former
O­rich phase, instead represents a past episode of higher
mass loss rate as a C­star.
Acknowledgements. Research at Armagh Observatory is grant­
aided by the Dept. of Education for N. Ireland, while par­
tial support is provided in terms of both software and hard­
ware by the STARLINK Project which is funded by the UK
PPARC. S.B. thanks STScI for a grant under the Visitor Pro­
gram, which greatly facilitated this work; M.C. thanks the EU
for funding via the COMETT programme. The JCMT and
UKIRT are operated by the Royal Observatory Edinburgh on
behalf of PPARC. The authors thank M. Barlow, I.P. Griffin
and K. Mitrou for many useful comments and suggestions, and
Tom Geballe and Goeran Sandell for excellent support during
the observations on Mauna Kea. This research has made use
of the Simbad database, operated at CDS, Strasbourg, France.
References
Avery L.W., Amano T., Bell M.B., et al., 1992, ApJS 83, 363
Bagnulo S., Doyle J.G., Griffin I.P., 1995, A&A 301, 501
Bergeat J., Sibille F., Lunel M., Lef`evre J., 1976, A&A 52, 227
Baron Y., de Muizon M., Papoular R., P'egouri'e B., 1987,
A&A 186, 271
Blanco A., Fonti S., Rizzo F., 1991, Infrared Phys. 31, 167
Borghesi A., Bussoletti E., Colangeli L., De Blasi C., 1985,
A&A 153, 1
Borghesi A., Bussoletti E., Colangeli L., et al., 1986, Infrared
Phys. 26, 37
Bussoletti E., Colangeli L., Borghesi A., Orofino V., 1987,
A&AS 70, 257
Chan S.J., Kwok S., 1988, ApJ 334, 362
Chan S.J., Kwok S., 1990, A&A 237, 354
Colangeli L., Mennella V., Palumbo P., Rotundi A., Busso­
letti E., 1995, A&AS 113, 561
Day K.L., 1981, ApJ 246, 110
Dorschner J., Begemann B., Henning Th., Jager C., Mut­
schke H., 1995, A&A 300, 503
Draine B.T., 1985, ApJS 57, 587
Draine B.T., Lee H.M., 1984, ApJ 285, 89
Egan M.P., Leung C.M., 1991, ApJ 383, 314
Fernie J.D., 1983, ApJS 52, 7
Frogel J.A., Persson S.E., Cohen J., 1980, ApJ 239, 495
Griffin I.P., 1993, MNRAS 260, 831
Groenewegen M.A.T., 1995, A&A 293, 463
Groenewegen M.A.T., 1996, A&A (in press)
Groenewegen M.A.T., de Jong T., van der Bliek N.S., Sli­
jkhuis S., Willems F.J., 1992, A&A 253, 150
Haisch B.M., 1979, A&A 72, 161
Hawkins G.W., 1990, PhD Thesis, University of California, Los
Angeles
Ivezi'c Ÿ
Z., Elitzur M., 1994, ApJ 445, 415
Joint IRAS Working Group, 1986, IRAS catalogues and at­
lases, Low Resolution Spectrograph (LRS), A&AS 65, 607
Joint IRAS Working Group, 1986, IRAS catalogues and at­
lases, IRAS Point Source Catalog, US Governement Print­
ing Office, Washington
Joint IRAS Working Group, 1986, IRAS catalogues and at­
lases, Explanatory Supplement, US Governement Printing
Office, Washington
Justtanont K., Tielens G.G.M., 1992, ApJ 389, 400
Justtanont K., Skinner C.J., Tielens G.G.M., 1994, ApJ 435,
852
Kastner J.H., 1992, ApJ 401, 337
Kim S.­H., Martin P.G., Hendry P.D., 1994, ApJ 422, 164
Knapp G.R., 1986, ApJ 311, 731
Koike C., Hasegawa H., Manabe A., 1980, Ap&SS 67, 495
Koike C., Kaito C., Shibai H., 1994, MNRAS 268, 321
Kr¨uger D., Gauger A., Sedlmayr E., 1994, A&A 290, 573
Laor A., Draine B.T., 1993, ApJ 402, 441
Le Bertre T., 1988a, A&A 190, 79
Le Bertre T., 1988b, A&A 203, 85
Lorenz­Martins S., Lef`evre J., 1993, A&A 280, 567
Lorenz­Martins S., Lef`evre J., 1994, A&A 291, 831
Loup C., Forveille T., Omont A., Paul J.F., 1993, A&AS 99,
291
Mathis J.S., Rumpl W., Nordsieck K.H., 1977, ApJ 217, 425
Noguchi K., Kawara K., Kobayashi Y., Okuda H., Sato S.,
1981, PASJ 33, 373
Olofsson H., Eriksson K., Gustafsson B., 1987, A&A 183, L13
Olofsson H., Carlstr¨om U., Eriksson K., Gustafsson B., Will­
son L.A., 1990, A&A 230, L13
Olofsson H., Carlstr¨om U., Eriksson K., Gustafsson B., 1992,
A&A 253, L17
Olofsson H., Eriksson K., Gustafsson B., Carlstr¨om U., 1993,
ApJS 87, 267
Papoular R., 1988, A&A 204, 138
P'egouri'e B., 1988, A&A 194, 335
Preibisch T., Ossenkopf V., Yorke H.W., Henning T., 1993,
A&A 279, 577
Phillip H.R. and Taft, E. A., 1969, Proc. Conference on Sili­
con Carbide, O'Connor J. and Smiltens S. (eds.), Pergamon
Press
Quirrenbach A., Mozurkewich D., Hummel C.A., Busher D.F.,
Armstrong J.T., 1994, A&A 285, 541
Rouleau F., Martin P.G., 1991, ApJ 377, 526
Savage B.D., Mathis J.S., 1979, ARA&A 17, 73
Seab C.G., Snow T.P., 1989, ApJ 347, 479
Skinner C.J., Whitmore B., 1988, MNRAS 235, 603
Sorrel W.H., 1990, MNRAS 243, 570
Tanabe T., Nakada Y., Kamijo F.,Sakata A., 1983, PASJ 35,
397

S. Bagnulo et al.: The circumstellar envelope of UU Aurigae 15
Thronson H.A. Jr, Latter W.B., Black J.H., Bally J., Hack­
ing P., 1987, ApJ 322, 770
Tsuji T., 1981, J. Astrophys. Astr. 2, 95
Unno W., Kondo M., 1976, PASJ 28, 347
van der Veen W.E.C.J., Habing H.J., 1988, A&A 194, 125
van der Veen W.E.C.J., Omont A., Habing H.J., Matth­
ews H.E., 1995, A&A 295, 445
Vassiliadis E., Wood P.R., 1993, ApJ 413, 641
Willems F.J., de Jong T., 1986, ApJ 309, L39
Willems F.J., de Jong T., 1988, A&A 196, 173
Yamashita Y., 1972, Tokyo Astron. Obs. Ann. 13, 169
Zuckerman B. 1993, A&A 276, 367
This article was processed by the author using Springer­Verlag
L A T E X A&A style file L­AA version 3.