modelling the dust and gas outflows from irc+10 216 -- i. ground-based and airborne observations

Modelling the dust and gas out¯ows from IRC+10 216 ± I. Ground-basedand airborne observations

C. J. Skinner,1*² K. Justtanont,2³ A. G. G. M. Tielens,2;3 A. L. Betz,4 R. T. Boreiko4

and F. Baas5

1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA2SRON, PO Box 800, 9700 AV Groningen, The Netherlands3NASA Ames Research Center, Mail Stop 245±3, Moffett Field, CA 94035±1000, USA4Center for Astrophysics & Space Astronomy, University of Colorado, Boulder, CO 80309, USA5Joint Astronomy Centre, 660 N. A`ohoÅkuÅ Place, University Park, Hilo, HI 96720, USA

Accepted 1998 September 7. Received 1998 September 7; in original form 1997 June 30

A B S T R A C T

We have developed a model for the dust and gas envelope of the C star IRC+10 216. Spherical

symmetry is assumed, and the model consistently solves the full radiative transfer problem for

the rotationally excited far-infrared and submillimetre wavelength CO lines and for the dust

continuum. New observations of the CO J � 9±8 and 12±11 lines, made with the Kuiper

Airborne Observatory, are presented. The model accounts for the ®rst 32 rotational states in the

lowest two vibrational levels of CO, and is shown to yield satisfactory ®ts to both line pro®les

and spatial maps of the CO J � 1±0, 2±1, 3±2, 4±3, 6±5, 7±6, 9±8 and 12±11 lines. The dust

model yields a good ®t to the spectral energy distribution from the near-IR to millimetre

wavelengths, assuming a distance to the star of 170 pc. From the CO model we are able to

con®rm previous ®ndings that the gas in the outer envelope is heated by the photoelectric

effect, and we also ®nd that the mass-loss rate must be of order 5´10ÿ5 M( yrÿ1, with a gas-to-

dust ratio of approximately 220, in order to ®t all the CO observations and the spectral energy

distribution simultaneously, and to predict accurately the observed wind terminal velocity via

radiative acceleration of the dust grains which are momentum-coupled to the gas. The gas

temperature distribution is found to be lower than predicted by a simple three-level molecule

approach which has been found to work for the envelopes of O-rich asymptotic giant branch

stars, but is in good agreement with some previously published models for this source. In

contrast with some previously published models, we ®nd no evidence for a recent change in

mass-loss rate.

Key words: stars: AGB and post-AGB ± stars: carbon ± circumstellar matter ± stars:

individual: IRC+10 216 ± stars: mass-loss ± radio lines: stars.

1 I N T R O D U C T I O N

During their ascent of the asymptotic giant branch (AGB), stars

undergo a dramatic series of changes. They switch from core

burning to burning H and He in concentric shells around a

degenerate C±O core. During this phase, the stellar envelope attains

giant proportions, and very low effective temperatures, while shell

burning continues to increase the core mass. However, while the

progenitor stars have masses in the range 1±8 M(, the planetary

nebula (PN) central stars which are their descendants have masses

of typically about 0.6 M( (e.g. Weidemann 1990; SchoÈnberner

1992). Therefore considerable mass loss must occur at some stage

between the beginning of the AGB and the commencement of the

PN phase.

Exactly when and how this mass loss occurs is not well estab-

lished, but observations and models are beginning to constrain the

problem. Many AGB stars are now known that are losing mass in

the range 10ÿ5 ±10ÿ4 M( yrÿ1, so that it is clear that suf®cient mass

can be lost in the AGB phase to enable the transition (e.g. Habing &

Mon. Not. R. Astron. Soc. 302, 293±304 (1999)

q 1999 RAS

*On assignment from the Space Sciences Department of the European Space

Agency.

²Chris Skinner died in his sleep on October 20, 1997. Chris had a long-

standing interest in various aspects of mass loss from late-type stars, and this

was one of the last papers that he submitted. Chris was a very talented

scientist who, despite his young age, had worked on a variety of problems in

observational, instrumental and theoretical astrophysics. Most of all, how-

ever, he was a good friend and a great guy to work with. We will miss him.

³Present address: Stockholm Observatory, 13336 Saltsjobaden, Sweden.

Blommaert 1992). Models and observations that accurately deter-

mine mass-loss rates and histories have been presented recently for

AGB stars and post-AGB stars by Justtanont & Tielens (1992),

Justtanont, Skinner & Tielens (1994), Justtanont et al. (1996),

Groenewegen (1994), Skinner et al. (1994, 1997) and Meixner et

al. (1997), amongst others. The picture which is developing from

various such studies is that most AGB stars lose mass relatively

sedately, at rates of order 10ÿ6 M( yrÿ1. However, towards the end

of their AGB lives, the mass loss rates can become very large, and

the star enters a `superwind' phase, which may last only a few

hundred years, and during which a signi®cant fraction of the star's

initial mass can be lost. The intense mass loss can be seen as

spectacular mid-infrared nebulae in ground-based images of stars in

transition between the AGB and PN phases. Almost all the post-

AGB stars that have been imaged reveal an axial, but not spherical,

symmetry, whereas many (but not all) AGB stars display spherical

symmetry in their mass loss (e.g. Olofsson 1993). In the emerging

overall picture, as the AGB wind accelerates into the superwind

phase, its morphology also evolves from spherical into a toroidal or

disc-like structure, which shapes the resulting planetary nebula.

The extreme C star IRC+10 216 is a key object in the study of

AGB star evolution. It was discovered in the IRC all-sky survey

(Neugebauer & Leighton 1969), and soon recognized to be highly

obscured in the visible but the second brightest object in the sky in

the infrared outside the Solar system (e.g. Becklin et al. 1969).

Further study rapidly revealed that it was a C star enveloped in a

massive envelope of dust and gas (Lockwood 1970; Miller 1970;

Herbig & Zappala 1970).

The envelope of IRC+10 216 is extremely rich in C-rich mole-

cules, and, because it is among the closest AGB stars to the Solar

system (at a distance of 170pc: e.g. Bagnulo, Doyle & Grif®n 1995),

it is extended to ground-based single-dish telescopes at the wave-

lengths of many molecular rotational lines in the millimetre and

submillimetre regions. Therefore it has been observed in a multi-

tude of molecules, including CO, HCN, C2H, HNC, SiC2, HC3N,

C3N and C4H (e.g. Bieging & Nguyen-Q-Rieu 1988; Takano, Saito

& Tsuji 1992; Dayal & Bieging 1993, 1995; Wooten, Nguyen-Q-

Rieu & Truong-Bach 1994; Groesbeck, Phillips & Blake 1994;

Lucas et al. 1995; Gensheimer, Likkel & Snyder 1995; Stanek et al.

1995). On a large scale, these observational studies imply that the

mass loss has been more or less spherically symmetric. Mass-loss

rates can be determined from some of these molecular line observa-

tions, and the results typically lie in the range 1±5 ´ 10ÿ5 M( yrÿ1

(e.g. Bieging, Chapman & Welch 1984; Sahai 1987; Truong-Bach,

Morris & Nguyen-Q-Rieu 1991).

Because it is so bright in the infrared, and consequently very

heavily observed at infrared wavelengths, IRC+10 216 is also one

of the prototype subjects for dust models. Dust is very important in

AGB star winds, as it has been suggested to be at least partly

responsible for the out¯ows, via radiation pressure driving the dust

grains outwards, dragging the gas along with them (e.g. Tielens

1983; Justtanont et al. 1994), and as it drags the gas with it viscously

it also heats the gas, and is thus one of the critical elements in the

determination of the gas temperature distribution in the wind

(Goldreich & Scoville 1976; Justtanont et al. 1994). Radiative

transfer modelling of the dust shells is able to determine the dust

mass-loss rate, and thence based on certain assumptions the total

mass-loss rate, in the warm inner region of the dust shell, which is

optically thick to all but the very high rotational levels of molecular

lines which arise in the inaccessible (from the ground) parts of the

far-infrared where the atmosphere is opaque. Such models have

been presented for AGB stars by Justtanont & Tielens (1992),

Groenewegen (1995) and Rowan-Robinson et al. (1986), and for

IRC+10 216 in particular by a number of workers including Grif®n

(1990) and Bagnulo et al. (1995).

Stars such as IRC+10 216 are thus very important in that they

represent a phase of stellar evolution during which the total mass of

the star and its internal structure are undergoing dramatic changes

which will profoundly affect its subsequent evolution and that of its

descendant, a PN. They are also the chief source of enrichment of

the interstellar medium (ISM), by their ejection of complex carbon-

based molecules in the gas phase, and of a large mass of dust. A

careful determination of the properties of stars like this is therefore

essential to understand the course of stellar evolution, to understand

the stellar populations of our own and other galaxies, and to

understand the chemical evolution of galaxies.

In this paper, we present some new observations of IRC+10 216

in the J � 9±8 and 12±11 rotational lines of the ground vibrational

state of CO, made with the Kuiper Airborne Observatory. We then

develop a full radiative transfer model for the dust and for the CO.

We show that this model can consistently ®t almost all the published

observations of CO transitions, including maps as well as single

pointings, as well as ®tting the overall spectral energy distribution

with the dust model. A small number of molecular line observations

are shown to be inconsistent with other published data, probably

indicating some calibration error. We show that, contrary to some

previous work, it does not appear necessary to invoke any variations

of the mass-loss rate of the star over time.

2 N E W O B S E RVAT I O N S

We observed IRC+10 216 at the wavelengths of the CO J � 9±8

and 12±11 lines, from the Kuiper Airborne Observatory (KAO)

during 1994 March. The observations were made during a New

Zealand deployment of the KAO, using a heterodyne spectrometer

(Betz & Boreiko 1993). The spectrometer has a spectral resolution

of 3.2 MHz, which at the frequencies of the J � 9±8 and 12±11

lines of CO corresponds to velocity resolutions of 0.9 and 0.7 km

sÿ1 respectively. The system temperature of the spectrometer is of

order 8000 K on the antenna temperature scale. Both spectra were

obtained using integration times of about 40 min. Calibration was

effected via observations of the Moon. The results are illustrated in

Figs 1 and 2, where they are compared with the model that is

described in Section 4. The data in these ®gures have been rebinned

from velocity resolutions of 0.9 and 0.7 to 3.6 and 1.4 km sÿ1 to

improve the signal-to-noise ratio. We report a de®nite detection of

the CO J � 12±11 line with a main beam temperature of

1.260.4 K, while the 9±8 line is barely detected at 1.060.5 K as

can be seen in both ®gures. We have plotted the expected line at the

local standard of rest (LSR) velocity of the star at ÿ26 km sÿ1. For

the latter line, the baseline is 060.5 K.

We also include in this paper observations of IRC+10 216 in the

J � 1±0 and 2±1 CO lines made using SEST (the Swedish±ESO

Submillimetre Telescope in La Silla) on 1990 May 15±16, and of

the J � 3±2 and 4±3 lines made using JCMT (the James Clerk

Maxwell Telescope on Mauna Kea, Hawaii) on 1994 August 21±

22. Our SEST data are consistent with previously published

observations using this telescope (e.g. Olofsson, Eriksson & Gus-

tafsson 1988; Olofsson et al. 1993), and are compared with our

model, described later, in Fig. 6. Our JCMT data are also consistent

with earlier observations in the JCMT library of standard spectra,

which are used for calibration and are publicly accessible, although

they are not entirely consistent with some previously published

JCMT observations (see Williams & White 1992; Avery et al.

294 C. J. Skinner et al.

q 1999 RAS, MNRAS 302, 293±304

1992). Again, they are presented in Fig. 6. The observing tech-

niques employed in our SEST and JCMT observations are entirely

consistent with those described by the various references quoted

above. For the SEST observations, the system temperatures are 500

and 720 K for the 1±0 and 2±1 transitions, respectively. The

velocity resolutions for the transitions are 0.043 and 0.7 MHz.

For both lines, the integration times are 10 min. For the JCMT, the

system temperatures for the 3±2 and 4±3 observations are 1450 and

3300 K (all on the antenna temperature scale) while the resolutions

are 0.938 and 0.313 MHz. The integration times are 10 and 20 min,

respectively.

3 C O M P I L AT I O N O F C O R OTAT I O N A L L I N E

O B S E RVAT I O N S O F I R C + 1 0 2 1 6

A wide variety of observations of IRC+10 216 have been made,

using the whole inventory of ground based millimetre-wave tele-

scopes, in a variety of low-lying rotational transitions of CO. In

constructing models, we have found that a few of the observations

appear to be incompatible with others. We list all the observations

that we have examined in Tables 1 and 2, where the ®rst lists single

pointings that are believed to be peaked up on the source, and the

second lists maps. These tables are not necessarily exhaustive, but

we believe they are close to a complete listing of observations with

useful calibration information, which can therefore in principle be

used in modelling. Note that the main beam temperatures listed for

the KAO observations are from the best Gaussian ®t to the observed

lines.

A little caution should be exercised regarding the line tempera-

tures quoted in these tables. Almost all studies of millimetre and

submillimetre wavelength molecular line emission report line

strengths as antenna temperatures. This is an inheritance from the

early days of radio astronomy, and the intention is to convert the

measured signal into the equivalent blackbody temperature of a

uniform extended source ®lling the beam. Unfortunately many

corrections have to be applied to the observations, including those

for atmospheric absorption, telescope beam ef®ciency and forward

scattering, in order to convert the observed antenna temperature into

a main beam temperature. The reporting of temperatures in the

literature is still very inconsistent: some papers report main beam

temperature but refer to it as antenna temperature, some refer to the

reported quantity as main beam temperature but appear to have

carried out a different set of corrections to the antenna temperature

than those that are required, and some refer to `temperature' without

stating whether it is an antenna temperature, a main beam tempera-

ture or an equivalent brightness temperature. We have attempted to

ensure consistency in the data reported above, by carrying out

corrections to the reported data where they appear necessary, but in

some cases insuf®cient information was presented in the paper to

establish with con®dence which quantity was being reported.

Some of the individual measurements reported in Table 1

probably should be regarded with some caution. The OSO observa-

tion reported by Olofsson et al. (1993) does not ®t the general trend

of the data, and we note that Huggins, Olofsson & Johansson (1988)

discuss dif®culties with the calibration of their 1±0 observations

with the OSO 20-m telescope, and that the latter authors declined to

report absolute calibrations of these observations. The IRAM 1±0

observations reported by Bujarrabal et al. (1986) appear incon-

sistent with latter observations with IRAM, and may re¯ect some

calibration and pointing errors early in the history of the IRAM 30-

m telescope. If we disregard these observations, most of the

remaining 1±0 observations appear to be roughly consistent.

Among the 2±1 observations, the NRAO 12-m observations

reported by Wannier et al. (1990) appear inconsistent with the

other observations from this telescope. The IRAM 2±1 observa-

tions reported by Truong-Bach et al. (1991) and by Olofsson et al.

(1993) are also inconsistent with one another. The 2±1 JCMT

observations are very consistent with one another, but very dif®cult

to reconcile with the mass of observations from other telescopes in

this line. We will show later that they are inconsistent with the

model also, and appear highly problematic. Finally the 3±2 obser-

vations are dif®cult to reconcile with one another. The JCMT 3±2

observations reported by Williams & White (1992) do not agree at

all well with those of Avery et al. (1992), or with those obtained

Modelling the dust and gas out¯ows from IRC+10 216 295

q 1999 RAS, MNRAS 302, 293±304

Figure 1. KAO observation of the J � 9±8 CO line in IRC+10 216

(histogram). The solid line represents the ®t to our best-®tting model (see

Section 4).

Figure 2. KAO observation of the J � 12±11 CO line in IRC+10 216

(histogram). The solid line represents the ®t to our best-®tting model (see

Section 4).

independently by ourselves and reported in the JCMT standard

spectra library. Williams & White mapped the sources in the 3±2

line, and derived a peak main beam temperature of order 39 K from

the map; it is this value which we list in Table 1. The 3±2

observations reported from the Caltech Submillimeter Observatory

(CSO) by Groesbeck et al. (1994) and Stanek et al. (1995) appear

very hard to reconcile with those reported elsewhere ± they imply

an antenna temperature larger than obtained with the NRAO 12-m

and comparable to that attained by the JCMT, both of which

telescopes have considerably larger collecting areas and smaller

beamwidths than does the CSO; this does not appear plausible.

However, more recent results from Wang et al. (1994), who


q 1999 RAS, MNRAS 302, 293±304

Table 1. Single-pointing CO observations of IRC+10 216.

Transition Telescope Diameter Beamsize 3 Tmb Reference

(m) (arcsec) (K)

1±0 NRAO 11.0 65 7.0 1

1±0 NRAO 11.0 66 6.7 2

1±0 BLT 7.0 100 5.1 3

1±0 NRAO 12.0 50 9.6 4

1±0 FCRAO 14.0 49 11.0 2

1±0 FCRAO 14.0 46 10.7 5

1±0 OVRO 10.4 60 8.0 6

1±0 IRAM 30.0 21 12.0 7

1±0 IRAM 30.0 22 16.2 8

1±0 IRAM 30.0 22 17.0 9

1±0 IRAM 30.0 21 16.2 25

1±0 OSO 20.0 33 12.5 10

1±0 SEST 15.0 45 12.4 11

1±0 SEST 15.0 40 10.4 12

1±0 SEST 15.0 45 10.7 10

2±1 OVRO 10.4 25 28.4 13

2±1 OVRO 10.4 26 18.0 14

2±1 NRAO 12.0 27 28.0 15

2±1 NRAO 12.0 25 21.2 16

2±1 NRAO 12.0 31 21.5 4

2±1 SEST 15.0 23 25.4 10

2±1 SEST 15.0 23 22.6 11

2±1 IRAM 30.0 12 45.5 10

2±1 IRAM 30.0 12 36.0 9

2±1 IRAM 30.0 12 38.7 25

2±1 JCMT 15.0 19 38 17,18

3±2 UKIRT 3.8 26 28.4 13

3±2 NRAO 12.0 20 35 6

3±2 CSO 10.4 20 44 19

3±2 CSO 10.4 20 42 20

3±2 CSO 10.4 20 32.5 26

3±2 JCMT 15.0 14 49 11,17

3±2 JCMT 15.0 14 59 18

3±2 JCMT 15.0 14 39 21

3±2 JCMT 15.0 14 41.6 25

4±3 JCMT 15.0 11 43 21

4±3 JCMT 15.0 10.4 58 11,17

6±5 IRTF 3.2 35 15 22

6±5 JCMT 15.0 7 45 23

7±6 IRTF 3.2 45 9 24

9±8 KAO 0.91 80 1.0 11

12±11 KAO 0.91 60 1.2 11

Note that, in some cases, different beamsizes are quoted for the same telescope. This re¯ects

information presented in the cited publications, and may re¯ect uncertainties in the measured

beamsizes, inccuracies in some publications, or real changes in beamsize owing to improvements

in telescope surface.

References: (1) Kuiper et al. (1976), (2) Kwan & Linke (1982), (3) Knapp & Morris (1985), (4)

Huggins et al. (1988), (5) Zuckerman, Dyck & Claussen (1986), (6) Sahai (1987), (7) Bujarrabal et

al. (1986), (8) Bujarrabal, Gomez-Gonzalez & Planesas (1989), (9) Truong-Bach et al. (1991),

(10) Olofsson et al. (1993), (11) recent work, (12) Olofsson et al. (1988), (13) Knapp et al. (1982),

(14) Wannier et al. (1979), (15) Wannier et al. (1990), (16) Wannier & Sahai (1986), (17) JCMT

standard spectra library, (18) Avery et al. (1992), (19) Groesbeck et al. (1994), (20) Stanek et al.

(1995), (21) Williams & White (1992), (22) Koepf et al. (1982), (23) Stutzki (1990), (24)

Wattenbach et al. (1988), (25) Groenewegen et al. (1996), (26) Wang et al. (1994).

recalibrated the CSO, seem more in line with the JCMT results (see

Table 1). Given the brightness of this source in CO lines (it is used as

a calibrator by many telescopes), it is somewhat disturbing how

inconsistent measurements made using different telescopes appear

at ®rst sight to be. We will discuss model ®ts to the various

observations later, and conclude that indeed there do appear to be

inconsistency problems.

4 R A D I AT I V E T R A N S F E R M O D E L S

4.1 Techniques

The modelling technique that we have adopted follows the outline

described by Justtanont et al. (1996). We have used a full radiative

transfer code for molecular rotational line emission which was

originally developed by SchoÈnberg (1988), and the current imple-

mentation of which has been described by Justtanont et al. (1994,

1996) and by Skinner (1996; this reference also describes how

copies of the code may be obtained). Expanding on the version of

the code used by Justtanont et al. (1996), we now solve the radiative

transfer for the ®rst 32 rotational levels of CO in the ®rst two

vibrational levels, including excitation of CO by both radiative and

collisional processes. We also now calculate the change in the

abundance of the CO in the outer regions of the envelope owing to

photodissociation by the interstellar UV ®eld, according to the

prescription given by Mamon, Glassgold & Huggins (1988). The

code assumes spherical symmetry for the envelope, which appears

to be consistent with the millimetre-wavelength interferometer

observations of IRC+10 216 by, for example, Dayal & Bieging

(1995) and Truong-Bach et al. (1991).

We seek a set of parameters with which we can simultaneously

solve the radiative transfer for CO, and ®t the line pro®les and

strengths, and also solve the radiative transfer in the dust shell and

thus ®t the continuum spectral energy distribution (see below). First

we require the dimensions of the star and envelope. We take the

stellar effective temperature from Winters, Dominik & Sedlmayr

(1994), then determine the stellar and envelope dimensions using

our dust radiative transfer code (see below). The CO code requires a

temperature distribution for the gas. In the case of OH 26.5+0.6

(Justtanont et al. 1996) and other O-rich AGB stars (Justtanont et al.

1994), we were able to determine the gas kinetic temperature

distribution in the wind by an approximate solution of the energy

balance equation for the wind. In that case we found that the thermal

balance of the wind was dominated by adiabatic cooling of the

expanding envelope, and line emission by CO and H2O. The

treatment must be somewhat modi®ed for the case of a C star

such as IRC+10 216, where there is no H2O present, but instead C-

bearing molecules, especially HCN. In the outer part of the

envelope we have also now added the heating owing to the photo-

electric effect, using the technique outlined by Tielens & Hollen-

bach (1985). With this modi®cation, our approximate energy

balance model can determine the gas kinetic temperature and

wind velocity distribution through the envelope. To calculate the

gas kinetic temperature, we solve the energy balance for the gas

including cooling by adiabatic expansion, heating by collisional

drag between dust and gas, photoelectric heating and rotational and

vibrational molecular cooling (or heating) by CO and HCN. For the

latter, we use the approach by Goldreich & Scoville (1976) in which

a molecule is approximated as three levels: two rotational levels in

the ground state and one in the ®rst vibrationally excited state.

These levels are populated collisionally and radiatively. The excita-

tion temperature of this three-level system is determined by solving

the detailed energy balance equation. This is a well-known form-

alism described in detail elsewhere (see Goldreich & Scoville 1976;

Groenewegen 1993; Justtanont et al. 1994). Finally, we require the

gas and dust density distributions in the envelope. The gas density

(and CO abundance) is obviously required in order to determine the

CO column and hence solve the radiative transfer. The dust density

distribution enters because the strong infrared radiation ®eld owing

to the dust acts to transfer CO molecules between vibrational states,

and as explained by SchoÈnberg & Hempe (1986) this can have a

profound effect on the overall population balance among the

rotational states. Thus attempting to solve the radiative transfer

accurately in CO without taking account of the effects of dust is

erroneous, and dangerous in the sense that it may generate accep-

table ®ts to the lines with inappropriate source parameters.

We have modelled the continuum spectral energy distribution of

IRC+10 216 using a full radiative transfer code from Haisch (1979).

Full details of the code and its application to AGB stars are given by

Grif®n (1990) and by Bagnulo et al. (1995), who also used the code

to model this source. The model assumes spherical symmetry: we

will discuss the validity of this assumption later, although we note


q 1999 RAS, MNRAS 302, 293±304

Table 2. Spectral maps of IRC+10 216 in CO lines.

Transition Telescope Diameter Beamsize Map radius Reference

(m) (arcsec) (arcsec)

1±0 BLT 7.0 106 120 1

1±0 FCRAO 14.0 49 135 1

1±0 OSO 20.0 33 210 2

1±0 NRAO 12.0 50 240 2

1±0 IRAM 30.0 21 54 3

2±1 OVRO 10.4 26 120 1

2±1 NRAO 12.0 31 240 2

2±1 IRAM 30.0 12 54 3

3±2 JCMT 15.0 14 40 4

3±2 CSO 10.4 20 50 5

6±5 JCMT 15.0 7 30 6

6±5 JCMT 15.0 7 16 7

References (1) Kwan & Linke (1982), (2) Huggins et al. (1988), (3) Truong-Bach et al. (1991), (4)

Williams & White (1992), (5) Stanek et al. (1995), (6) Stutzki (1990), (7) Crosas & Menten

(1995).

here that it is consistent with the CO model. We have modelled the

dust shell with three dust species ± amorphous carbon (adopting

dust optical constants from Rouleau & Martin 1991), silicon

carbide (adopting dust optical constants from PeÂgourieÂ 1988), and

MgS (adopting dust optical constants from Begemann et al. 1994).

We assume a stellar effective temperature of 2010 K (Winters et al.

1994), a terminal out¯ow velocity of 14.5 km sÿ1, a distance of

170 pc (Bagnulo et al. 1995) and a dust condensation temperature of

1500 K in order to calculate the inner radius of the dust shell. We

derive the luminosity, i.e. stellar radius, and a dust mass-loss rate by

®tting the energy distribution (Fig. 3). To obtain our model, we ®rst

run the dust code to determine the gross properties of the source,

such as the approximate mass-loss rate and luminosity. We then run

our energy balance code to determine the appropriate dust-to-gas

ratio to obtain the observed out¯ow velocity. Finally, we run the CO

code to determine the resulting line pro®les and strengths. The

process is iterated many times in order to re®ne the various

unknown parameters and obtain mutually consistent dust and gas

models. To solve the equations of motion and energy balance, we

assume a stellar mass of 1 M( and use the dust properties of

amorphous carbon which is the main dust constituent to drive the

gas to the terminal velocity. The momentum transfer ef®ciency is

derived for each grain size, assuming the Mathis, Rumpl &

Nordsieck (1977, hereafter MRN) size distribution. We obtain

heating and cooling rates which are used to determine the gas

kinetic temperature (Fig. 4), and the velocity as a function of radius

(Fig. 5). For the radiative transfer for CO lines, we assume all the

above stellar parameters as well as a stochastic velocity of 0.65 km

sÿ1 (SchoÈnberg 1988). The consistent results that are obtained for

the gas and dust models are summarized in Tables 3 and 4.

4.2 Results

We have found it impossible to obtain a ®t to the observed CO line

strengths using the temperature distribution predicted by our energy


q 1999 RAS, MNRAS 302, 293±304

Figure 3. Spectral energy distribution for IRC+10 216 predicted by our best

dust-plus-gas model (solid line), compared with a variety of observations

(for sources, see Bagnulo et al. 1995).

Figure 4. Kinetic temperature distribution derived from an approximate

energy balance model, as used successfully for O-rich AGB stars (dashed

line), and that determined to yield the best ®t by our CO model, where the

molecular cooling was increased (solid line).

Figure 5. Out¯ow velocity derived from our approximate energy balance

model, in which the out¯ow is driven by stellar radiation pressure on dust

grains in the wind. The out¯ow begins at the dust condensation temperature

of 3.4 stellar radii.

balance technique. The energy balance code predicts that for all

reasonable HCN abundances the envelope cooling is dominated by

CO, with HCN making only a small contribution to the cooling.

This is consistent with the cooling rate reported by Groenewegen

(1993), but quite contrary to the results obtained observationally

from the ISO-LWS far-infrared spectra by Cernicharo et al. (1996),

who estimated total cooling rates by CO and HCN of 0.28 and

0.44 L(, respectively including the millimetre and submillimetre

lines. This demonstrates unambiguously that the presence of HCN

has a major effect on the calculation of the energy balance and,

hence, on the ®nal temperature distribution. Our results support the

conclusion by Cernicharo et al (1996). The temperature distribution

obtained using our approximate energy balance code, when used as

input for our CO radiative transfer code, generates CO lines that are

far too bright. A full treatment of HCN cooling and analysis of the

observed line intensities is beyond the scope of this paper. Instead,

we have dealt with this problem semi-empirically, by adjusting the

parameters used for HCN in the energy balance code described in

Section 4.1, until the resulting temperature distribution yields, via

the radiative transfer code, CO line intensities that agree with the

observations. The best ®t is obtained for an HCN abundance of

4´10ÿ5, similar to that from Cernicharo et al. The two temperature

distributions are compared in Fig. 4. Our ®nal model temperature

distribution runs below the original temperature distribution for the

whole envelope, even though HCN is photodissociated in the outer

envelope. Essentially, the increased HCN cooling in the inner

envelope reduces the thermal energy of the expanding gas. (Note

that, anyway, in the outer envelope, cooling through adiabatic

expansion dominates over molecular line cooling.)

We show in Fig. 3 our model of the spectral energy distribution

compared with observations. The observations plotted are those

also adopted for the same purpose by Bagnulo et al. (1995). The

parameters adopted in this dust model are listed in Table 3. These

parameters are very similar to those determined by Bagnulo et al.,

except that we have adopted here a power-law grain size distribu-

tion as obtained by MRN, rather than the single grain size preferred

by Bagnulo et al. We prefer the power-law distribution because it is

consistent with ISM observations (MRN), and predicted theoreti-

cally for AGB winds (Biermann & Harwit 1980). This model gives

a good ®t to the overall spectral energy distribution, from the near-

infrared to the radio. The model falls somewhat below the observa-

tions at wavelengths of 1 mm and less. However, this will be shown

in a further publication (Skinner, Meixner & Bobrosky 1998) to be

due to the adoption of spherical symmetry in our model, whereas

the inner circumstellar envelope is actually toroidal, allowing

visible light to scatter out of the nebula along the lower density

polar directions. This effect is unlikely signi®cantly to affect the

overall results presented here, because the toroidal structure only

exists in the innermost part of the envelope. The stellar mass shown

in Table 3, 1 M(, may initially seem small for a C star. However, it

should be borne in mind that, by the time the star±envelope system

has evolved into a PN, the central white dwarf will probably have a

mass somewhat less than 1 M(: the star loses a considerable mass of

material in its stellar wind during the AGB phase. Thus we might

take the mass adopted here as an indication that IRC+10 216 has

almost completed its AGB evolution, having lost most of its stellar

envelope, and is preparing to enter the PN phase. Further evidence

in favour of this hypothesis is presented by Skinner et al. (1998).

The temperature distribution that we determine for the gas in our

®nal model is shown in Fig. 4. Both the temperature distribution

predicted by our energy balance model and that determined semi-

empirically from ®tting results of our CO model to observed lines

are shown. The radiative driving force on grains in this model

accelerates the wind to a terminal velocity of 14.5 km sÿ1, the

observed wind velocity (Fig. 5). From this velocity structure and the

constant mass-loss rate of 5´10ÿ5 M( yrÿ1, the density as a

function of the radius can be calculated. Terminal velocity is

reached at about 20 photospheric radii, so that the wind acceleration

is relevant in the region in which the higher rotational CO lines are

generated (e.g. the J � 9±8 and 12±11 lines in this study). It is only

marginally signi®cant in the dust code, however, because the optical

depth from the outside inwards to 20 stellar radii is already large in

the near-infrared and visible. All the input parameters used for our

CO model are listed in Table 4. It is interesting to note that our best-

®tting temperature is very similar in the outer envelope to that

derived by Crosas & Menten (1997), who calculated self-consis-

tently the molecular cooling (only by CO, however) from the level

populations derived by solving the full radiative transfer. This

similarity in the derived temperature distributions is perhaps not

too surprising since this is region where the low-lying CO levels

(J # 6±5) originate, and both models reasonably explain the

observations. We have also calculated the CO cooling using the

CO population obtained from the radiative transfer calculation. The

temperature structure is the same as in Fig. 4 out to 1017 cm. Beyond

this radius, the CO cooling obtained from the full radiative transfer

calculation is larger than that derived from the modi®ed three-level

approximation. This outermost part of the envelope, where the two

methods disagree, is precisely the region where the two lowest

rotational lines originate. In the inner part of the envelope, cooling

is dominated by H2, HCN and the adiabatic expansion. For r $ 1017

cm, CO cooling is comparable to the adiabatic cooling while HCN

is already photodissociated. Our temperature is about a factor of 2

lower than that derived by Kwan & Linke (1982) in the outer

(r $ 1016cm) part of the envelope. The calculated main beam

temperature is sensitive to the gas kinetic temperature, and that is


q 1999 RAS, MNRAS 302, 293±304

Table 3. Dust model parameters.

Stellar radius 7.6´1013 cm

Effective temperature 2010 K

Stellar mass 1.0 M(

Distance 170pc

Total dust mass-loss rate 2.3´10ÿ7 M( yrÿ1

Amorphous carbon dust mass fraction 0.89

SiC dust mass fraction 0.067

MgS dust mass fraction 0.044

Wind terminal velocity 14.5 km sÿ1

Dust shell inner radius 2.58´1014 cm

Dust shell outer radius 6´1017 cm

Table 4. CO model parameters.

Stellar radius 7.6´1013 cm

Effective temperature 2010 K

Distance 170 pc

Total dust mass-loss rate 2.3´10ÿ7 M( yrÿ1

Total dust gas-loss rate 5.0´10ÿ5 M( yrÿ1

Gas-to-dust ratio 220

CO/H2 6.0´10ÿ4

Wind terminal velocity 14.5 km sÿ1

Stochastic velocity 0.65 km sÿ1

Outer radius of CO envelope 7.2´1017 cm

Number of rotational levels 31

Number of vibrational levels 2

the origin of the differences between our results and those of Kwan

& Linke (1982).

In Fig. 6 we show the ®ts to the observed CO J � 1±0, 2±1, 3±2,

4±3, 9±8 and 12±11 lines obtained with our CO code. The 1±0 and

2±1 lines were observed by us at SEST on 1990 May 15 and 16

respectively, while the 3±2 and 4±3 lines were observed by us at the

JCMT on 1994 August 22 and 21 respectively. The model line

pro®les are shown as solid lines, while the model pro®les scaled by

a constant, in order to ®t the observed line brightness better, are

shown as dashed lines. It can be seen that our model generates 1±0

and 2±1 lines a little brighter than observed using SEST, while it

generates a 3±2 line slightly fainter than is observed with the JCMT.

The 9±8 and 12±11 model lines are of similar brightness to those

observed with the KAO. Given the signal-to-noise ratio, we can

probably regard the 9±8 line as just barely detected with the KAO.

We show in Table 5 the peak main beam temperatures predicted

by our models, compared with observations. At least one observa-

tion is shown for each of the telescopes listed in Table 1. The

observations described as doubtful in the previous section are not

included in this table. It is immediately clear that the majority of the

observations can be reasonably well ®tted by our model, implying

that the model provides a good representation of the temperature

structure of the envelope. Additionally, since the line pro®les are

also well ®tted, as seen in Fig. 6, the density structure must also be

reasonably well represented by our model. (The line pro®les are

very sensitive to the density: as the mass-loss rate is decreased, the


q 1999 RAS, MNRAS 302, 293±304

Figure 6. Observed CO line pro®les (histograms) compared with our model line pro®les, both exactly as predicted (solid lines) and scaled by a constant to yield

the best ®t to the observations (dashed lines). The telescopes and transitions are indicated in the upper part of each panel.

pro®les change from being inverted parabolae, to roughly ¯at-

topped, to double-peaked pro®les with a minimum at the central

velocity. In the case of IRC+10 216, where the pro®les are

parabolic, a change in mass-loss rate by a factor of 2 increases

the FWHM of the parabolae by of order 2 km sÿ1, appreciably

degrading the ®t to the observed lines.)

A number of maps of IRC+10 216 have been presented in CO

transitions, and we also now compare our model with those. The

most extensive maps were those made in the 1±0 and 2±1 transi-

tions with the NRAO 12-m telescope by Huggins et al. (1988). We

display our model ®ts to these maps in Fig. 7. The model ®ts are

reasonable out as far as 2 arcmin from the star. At greater distances

the model somewhat underestimates the 2±1 emission and over-

estimates the 1±0 emission. This is in the part of the envelope that is

primarily heated by the photoelectric effect, and is very sensitive

both to the CO abundance (which is rapidly changing in this region

owing to photodissociation) and to the grain size and abundance.

Maps have also been made in both the 1±0 and 2±1 transitions using

the IRAM telescope, by Truong-Bach et al. (1991), and we display

the ®t of our model to these maps, which have smaller extent but

much higher spatial resolution, in Fig. 8. Using the JCMT, maps

have been made in the 3±2 (Williams & White 1992) and 6±5

(Stutzki 1990) transitions, and we show the comparison of our

model with these maps in Fig. 9.

The ®t to the JCMT 6±5 observations by Stutzki (1990) requires

some explanation. The map presented by Stutzki shows 6±5

emission only to the south-west of the nominal source position. In

fact the emission 11 arcsec from the nominal source position is

more than twice as bright as that from the source position. Stutzki

does not, however, quote the assumed source position. It appears

improbable that the 6±5 emission can be brightest 11 arcsec

(3 ´ 1016 cm) from the star, and arise only in an isolated blob to

the south-west, especially given the fairly symmetric distribution

seen in other transitions and in other molecules (e.g. Truong-Bach

et al. 1991). It is much more likely that the nominal source position

was in fact incorrect, and that the map centre is somewhat offset

from the star. We have assumed that our spherical model 6±5

emission as plotted in Fig. 9 is correct, and we have used the main

beam temperature measured by Stutzki to estimate from our model

how far from the star the JCMT should have been pointed in order to

obtain this temperature. By forcing the four detections in the map of

Stutzki to lie on a uniformly spaced grid, we are then able to

determine whereabouts in the grid the star actually was. By this

technique we estimate that the star was in fact about 5 arcsec west

and 6 arcsec south of the map centre. Given the possible pointing

uncertainties of the JCMT, and the possible uncertainty in target


q 1999 RAS, MNRAS 302, 293±304

Table 5. Observed versus model line brightness.

Observed Model

Telescope Transition (K) (K)

NRAO 11-m 1±0 7.0 11

BLT 1±0 5.1 7.4

NRAO 12-m 1±0 9.6 10

FCRAO 1±0 11 13

OVRO 1±0 8.0 10

IRAM 1±0 17 25

OSO 1±0 13 18

SEST 1±0 12 14

NRAO 12-m 2±1 22 23

SEST 2±1 23 27

IRAM 2±1 46 62

JCMT 2±1 38 24

UKIRT 3±2 7.5 7.0

NRAO 12-m 3±2 35 33

CSO 3±2 32.5 25

JCMT 3±2 49 40

JCMT 4±3 58 55

IRTF 6±5 15 7.7

JCMT 6±5 see text 89

IRTF 7±6 8.7 8.7

KAO 9±8 0.85 0.85

KAO 12±11 1.2 1.1

Figure 7. Peak main beam temperature as a function of offset from the star,

for NRAO 12-m observations by Huggins et al. (1988) in the 1±0 (squares)

and 2±1 (circles) transitions, versus models in the 1±0 (solid line) and 2±1

(dashed line) transitions.


for IRAM 30-m observations by Truong-Bach et al. (1991) in the 1±0

(squares) and 2±1 (circles) transitions, versus models in the 1±0 (solid line)

and 2±1 (dashed line) transitions.

coordinates for an extremely red source like IRC+10 216, such an

error does not appear improbable. Given the large uncertainties in

the observational data of Stutzki, the ®t of our model to the four

offset observations as presented in Fig. 9 then appears quite

satisfactory, and we conclude that our model may be entirely

consistent with these observations.

5 D I S C U S S I O N

The great profusion of observations of IRC+10 216 in molecular

rotational lines is at the same time a blessing and a curse. The large

number of lines observed allows a model such as ours to be tested

and re®ned in very great detail, eventually bestowing considerable

plausibility on it (assuming a successful outcome of the com-

parison). However, in some of the CO lines this object has been

observed by many different observers at many different telescopes,

and the comparison of these different observations does not always

yield very comforting results.

Table 5 summarizes the comparison between our model and what

should be the most reliable single pointed observations. Among the

1±0 and 2±1 line observations, those made using the NRAO 12-m

telescope and SEST are ®tted rather well by our model. The oldest

observations, made with the NRAO 11-m and BLT 7-m telescopes,

are ®tted rather less well. Most surprising perhaps are the JCMTand

IRAM results. The JCMT 2±1 line temperature is not at all

consistent with that determined by a variety of observers (including

ourselves) at SEST, which has the same diameter and a similar

beamsize and ef®ciency. Our model predicts a much brighter and

more sharply peaked core than is observed with IRAM: we will

return to this later, and merely point out here that it is very dif®cult

to explain.

In the higher transitions, things appear in general quite favour-

able. For the 3±2 line our model predictions agree well with

observations using the United Kingdom Infrared Telescope

(UKIRT) and the NRAO 12-m telescope. The model agrees

extremely well with the JCMT observations by Williams & White

(1992), but rather less well with those by ourselves and obtained

from the JCMT standard spectra library. The model greatly under-

estimates the 3±2 observations by Groesbeck et al. (1994) using the

CSO. However, these CSO observations appear rather hard to

reconcile with the JCMT observations, which in general yield

main beam temperatures that are very similar, despite the much

greater collecting area of the JCMT. In order for the quoted CSO

main beam temperature to be consistent with the JCMT data, the 3±

2 emitting gas would have to be more or less isothermal across the

20-arcsec CSO beam. The maps of Williams & White (see Fig. 9)

demonstrate that this is certainly not the case. Newly calibrated

CSO observations by Wang et al. (1994) brought the main beam

temperature closer to what is predicted by our model. The model

agrees rather well with the 4±3 observations at JCMT by ourselves,

and with the IRTF 7±6 observations by Wattenbach et al. (1988).

However, it underestimates the IRTF 6±5 line temperature observed

by Koepf et al. (1982), but greatly overestimates the JCMT 6±5 line

temperature observed by Stutzki (1990). We will return to this latter

observation later. Finally, we obtain a reasonably good ®t to our

KAO 9±8 and 12±11 line observations.

One-dimensional maps across the IRC+10 216 envelope in

various CO lines are in general quite well ®tted by our model.

Fig. 7 shows the ®t to the maps presented by Huggins et al. (1988)

using the NRAO 12-m telescope. The ®t to the observations is

reasonable out to about 100 arcsec. At 180 arcsec, although the ®t to

the 2±1 observations is reasonable, our model overestimates the 1±

0 temperature by a factor of 2. At such large radii, the gas

temperature is largely determined by photoelectric heating, and

so is somewhat uncertain. However, if we reduce the temperature,

although this will improve the ®t to the 1±0 data it will degrade the

®t to the 2±1 data. Our ®t to the IRAM 1±0 and 2±1 maps presented

by Truong-Bach et al. (1991) is shown in Fig. 8. In both lines we

overestimate the temperature in the core of the envelope, within 10

arcsec or so of the star, by about 50 per cent. Further from the star,

our ®t to the data is rather good, except that we somewhat over-

estimate the temperature in the 1±0 line 50 arcsec from the star. In

complete contrast, the ®t to the NRAO data over the whole of the

inner region is quite good. The IRAM maps and the NRAO maps are

thus hard to reconcile with one another. We obtain a very good ®t to

the map of Williams & White (1992) using the JCMT in the 3±2 line

(Fig. 9), across the entire inner envelope. As described earlier, our

®t to the 6±5 map of Stutzki (1990) may also be quite good, but only

if we assume that the whole map was somewhat offset with respect

to the star, which is entirely possible. New maps of this source in the

6±5 line would be highly desirable in order to test this suggestion.

All in all, our model provides a satisfactory ®t to the majority of

observations, both single pointings and maps, from the 12±11

transition down to 1±0. Observations that appear, on the basis of

both our model and other, independent, observations, to be dis-

crepant include the 1±0 and 2±1 observations using IRAM, the

JCMT 2±1 (Avery et al. 1992) observations, and the CSO 3±2

observations (Groesbeck et al. 1994). While the JCMT line tem-

perature discrepancy may be attributed to pointing errors, it appears

hard to invoke pointing errors in the other cases.

The IRAM maps (Truong-Bach et al. 1991) are a particularly

distressing case. Our model predicts roughly the right shape for a

one-dimensional scan across the central region of the source using

IRAM, but the line temperature is overestimated by about 50 per

cent for both the 1±0 and 2±1 transitions. We have investigated the

possibility of a very dense shell of gas, generated by some intense

burst of mass loss in the past, which might greatly increase the

optical depth to the central region and thus reduce the line


q 1999 RAS, MNRAS 302, 293±304


for JCMTobservations in the 3±2 (squares: Williams & White 1992) and 6±

5 (circles: Stutzki 1990) transitions, versus models in the 3±2 (solid line) and

6±5 (dashed line) transitions.

temperature, but even increases in mass loss by as much as an order

of magnitude are able to reduce the line temperature by only a small

margin. The line temperature in this central region can only

effectively be reduced by reducing the gas kinetic temperature in

this region. However, this will also greatly reduce the line tempera-

tures for all other transitions, decreasing the quality of the ®t to the

NRAO maps, and the many observations with which we are able to

achieve a good agreement with the current model.

The gas turbulent velocity that we have adopted in our model is

0.65 km sÿ1. As shown by SchoÈnberg (1988), this value gives a good

®t to the shape of optically thin 13CO lines for this source, and it was

the ®rst value that we tried for this parameter. Varying the value of

the turbulent velocity has a number of observable effects. In the

outer part of the envelope, the amount of gas that is able to interact

along a given column in a given velocity bin is critically dependent

on the turbulent velocity. Along the line of sight to the star, on the

other hand, most of the gas is in the extreme velocity bins, and thus

rather large changes to the turbulent velocity are needed to change

the emerging line intensity and pro®le substantially. We ®nd that if

we increase the turbulent velocity to 1.0 km sÿ1, the model 2±1 line

as observed by IRAM is reduced from 62 to 55 K peak main beam

temperature, bringing the model substantially closer to the observa-

tions. Reductions in model main beam temperature are also then

seen for the other telescopes. The same increase in turbulent

velocity reduces the model 1±0 main beam temperature at 240-

arcsec offset, as seen by the NRAO 12-m telescope, to approxi-

mately the level observed by Huggins et al. (1988), but also reduces

the 2±1 main beam temperature at all offsets greater than 100 arcsec

to a value as small as one-tenth that observed. The NRAO 12-m

maps appear to limit the allowed values of turbulent velocity to

about 0.5±0.8 km sÿ1 in the outer part of the envelope. Keady, Hall

& Ridgeway (1988) estimated a turbulent velocity of about 1.0 km

sÿ1 at a distance of a few stellar radii from the star, from near-

infrared Fourier transform spectra. They also speculated that the

turbulent velocity could well be higher still closer to the star. We

could speculate, therefore, that the turbulent velocity decreases

somewhat with increasing distance from the star, from a value of a

few km sÿ1 close to the stellar surface to 0.6±0.7 km sÿ1 at hundreds

of stellar radii. We have not investigated this possibility in detail,

but note instead that it probably offers the best means available to us

to bring our model closer to agreement with the IRAM maps of

IRC+10 216 without destroying the relatively good agreement that

we have with many other data. The signi®cant effect of changing the

turbulent velocity noted here is a good illustration of why a large

velocity gradient (LVG) type radiative transfer solution ought not to

be used for AGB star envelopes.

The higher CO transitions (J � 6±5 and above) all lie in

wavelength regions that are dif®cult to observe. The 6±5 and 7±6

lines have been observed from the JCMT and the IRTF, but the

atmosphere has rather low transmission at these wavelengths, and

calibrations are often uncertain. The only higher transitions

observed that are spectrally resolved are the 9±8 and 12±11

observations with the KAO which we include here, and these

were detected at fairly low signal-to-noise ratio. Therefore the

properties of the very warm gas close to the star, which emits in

these higher transitions, are not very strongly constrained observa-

tionally. Our model appears to ®t all the high-lying lines listed in

Tables 1 and 2 quite well, suggesting that our model represents the

warm gas reasonably well, but its failure to ®t well the IRAM maps

in the core of the envelope is in contradiction to this. A large number

of high CO transitions were detected in the ISO Long Wavelength

Spectrometer spectrum of IRC+10 216 presented by Cernicharo et

al. (1996), and these data will be used in a future paper concentrat-

ing on the gas in the inner 10 to 20 stellar radii only, where ISO lines

arise.

Some previous workers (Sahai 1987; Truong-Bach et al. 1991),

using Sobolev approximation models, have adopted a hot, low

mass-loss rate inner region for the IRC+10 216 envelope. We ®nd

that such a model cannot ®t the observations in two important ways.

First, quite apart from any differences in the way that we model the

CO, we require a high dust mass-loss rate in the neighbourhood of

the star in order to ®t the spectral energy distribution. The high

optical depth of the circumstellar dust shell around this source is

contributed almost entirely by the dust within a few tens of stellar

radii of the star. The mass-loss rate that we require in this region,

adopting a gas-to-dust ratio which (i) provides the correct wind

terminal velocity in our energy balance code, and (ii) is consistent

with that derived by other workers for many C stars, is entirely

consistent with the mass-loss rate required by our CO code to yield

good ®ts to the line pro®les of the lower lying rotational lines

(J � 4±3 and lower). If the mass-loss rate were to be lower by a

factor of 4 close to the star, as suggested by Sahai (1987), we would

require a dust-to-gas ratio in this region of about 0.02, which is

about a factor of 4 higher than typical values found for C stars.

Secondly, we ®nd that adopting a hot, low mass-loss rate wind in the

inner region does not in fact reduce the 2±1 and 1±0 line strengths,

but increases them somewhat, as one would expect for an optically

thick line. We in fact rely on this increase in brightness to explain

the very bright high-J lines, using the gas heating which results from

grain±gas collisions in the inner part of the envelope. Decreasing

the mass-loss rate has little effect on the line strength, again as

would be expected for an optically thick line: it is the kinetic

temperature, not the density, that determines the line strengths.

What is the precision of the determinations of the various

parameters by our model? In the outer region of the envelope,

from a 100 stellar radii outwards, the temperature is rather accu-

rately determined from the ®t to the various CO maps. The envelope

appears roughly spherical in this region, and the model line pro®les

are sensitive to changes in temperature of only a few degrees

throughout this region. The density is somewhat less well con-

strained, since its principal effect is to alter the line pro®les. As

mentioned earlier in this paper, changes in the mass-loss rate (and

thus density) by a factor of 2 change the FWHM of the model lines

by about 2 km sÿ1, which is easily noticeable. Changes in mass-loss

rate by a factor of 1.5 or so have an effect which is marginally

noticeable. In the inner envelope, the model is not quite so well

constrained. For the lower lying lines, the effects of changing the

temperature within the inner 100 stellar radii or so of the envelope

are fairly small, because of the large optical depth to this region. In

the higher lying lines (6±5 and higher) the effect on the model line

becomes increasingly large with increasing rotational quantum

number, but unfortunately the uncertainties in the observations

also increase greatly. Line pro®le information in these higher

lying lines is also rather poor, and so the mass-loss rate can only

be determined to within a factor of a few. It is this inner region that is

currently most enigmatic. Skinner et al. (1998) have presented a

Hubble Space Telescope image revealing the structure of this inner

region, and Cernicharo et al. (1996) have presented ISO spectra

including the high-lying CO lines which arise entirely within a few

tens of stellar radii of the star, so that the curtain is beginning to be

lifted from in front of this region. In our next publication on this

remarkable source, we will show how our model can be applied to

this innermost region, without signi®cantly affecting the conclu-

sions reached in this paper.


q 1999 RAS, MNRAS 302, 293±304

6 C O N C L U S I O N S

We have presented the ®rst attempt to ®t the complete spectral

energy distribution of IRC+10 216, using a full radiative transfer

code for dust and all the known ground-based and airborne

observations of CO from this source, using consistent model

parameters. We ®nd that it is possible to do so, and we obtain

satisfactory ®ts to almost all the published CO observations. The

mass-loss rate that we deduce is 5 ´ 10ÿ5 M( yrÿ1 for a CO

abundance relative to H2 of 6 ´ 10ÿ4, and a gas stochastic velocity

of 0.65 km sÿ1. We suggest that the gas stochastic velocity may

decrease somewhat from a value of 1.0 km sÿ1 or higher very close

to the star, to a value of only 0.65 km sÿ1 in the outer part of the

envelope. These results are basically consistent with earlier studies

of this source. However, we ®nd no evidence for a lower mass-loss

rate in the inner region of the envelope as found by some other

studies. We ®nd that a few telescopes are yielding antenna tem-

peratures for certain CO transitions that do not appear consistent

with observations made using other telescopes or with our

model. This is consistently the case for the IRAM 30-m telescope

in the 1±0 and 2±1 transitions, and for the CSO 10.4-m in the 3±2

transition.

AC K N OW L E D G M E N T S

This paper is based on observations collected at the European

Southern Observatory, La Silla, Chile. The JCMT is operated by

the Joint Astronomy Centre on behalf of the Particle Physics and

Astronomy Research Council of the United Kingdom, the Nether-

lands Organization for Scienti®c Research, and the National

Research Council of Canada.

REFERENCES

Avery L. W. et al., 1992, ApJS, 83, 363

Bagnulo S., Doyle J. G., Grif®n I., 1995, A&A, 301, 501

Becklin E. E., Frogel J. A., Hyland A. R., Kristian J., Neugebauer G., 1969,

ApJ, 162, L19

Begemann B., Dorschner J., Henning T., Mutschke H., Thamm E., 1994,

ApJ, 423, L71

Betz A., Boreiko R. T., 1993, in Kwok S., ed., ASP Conf. Ser. Vol. 41,

Astronomical Infrared Spectroscopy. Astron. Soc. Pac., San Francisco

p.349

Bieging J. H., Nguyen-Q-Rieu, 1988, ApJ, 329, L127

Bieging J. H., Chapman B., Welch W. J., 1984, ApJ, 285, 656

Biermann P., Harwit M., 1980, ApJ, 241, L105

Bujarrabal V., Planesas P., Gomez-Gonzalez J., Martin-Pintado J., del

Romero A., 1986, A&A, 192, 157

Bujarrabal V., Gomez-Gonzalez J., Planesas P., 1989, A&A, 219, 256

Cernicharo J. et al., 1996, A&A 315, L201

Crosas M., Menten K., 1995, in Taylor A. R., Paredes J., eds, ASP Conf. Ser.,

Vol. 93, Radio Emission from the Stars and the Sun. Astron. Soc. Pac.,

San Francisco, p. 98

Crosas M., Menten K., 1997, ApJ, 483, 913

Dayal A., Bieging J. H., 1993, ApJ, 407, L37

Dayal A., Bieging J. H., 1995, ApJ, 439, 996

Gensheimer P. D., Likkel L., Snyder L. E., 1995, ApJ, 439, 445

Goldreich P., Scoville N., 1976, ApJ, 205, 144

Grif®n I. P., 1990, MNRAS, 247, 591

Groenewegen M. A. T., 1993, PhD thesis, Sterrenkundig Institut, Amster-

dam

Groenewegen M. A. T., 1994, A&A, 290, 531

Groenewegen M. A. T., 1995, A&A, 293, 463

Groenewegen M. A. T., Baas F., de Jong T., Loup C., 1996, A&A, 306, 241

Groesbeck T. D., Phillips T. G., Blake G. A., 1994, ApJS, 94, 147

Habing H. J., Blommaert J. A. D. L., 1992, in Weinberger R., Acker A., eds,

Proc. IAU Symp. 155, Planetary Nebulae. Kluwer, Dordrecht p. 243

Haisch B. M., 1979, A&A, 72, 161

Herbig G. H., Zappala R. R., 1970, ApJ, 162, L15

Huggins P. J., Olofsson H., Johansson L. E. B., 1988, ApJ, 332, 1009

Justtanont K., Tielens A. G. G. M., 1992, ApJ, 389, 400

Justtanont K., Skinner C. J., Tielens A. G. G. M., 1994, ApJ, 435, 852

Justtanont K., Skinner C. J., Tielens A. G. G. M., Meixner M., Baas F., 1996,

ApJ, 456, 337

Keady J. J., Hall D. N. B., Ridgeway S. T., 1988, ApJ, 326, 832

Knapp G. R., Morris M., 1985, ApJ, 292, 640

Knapp G. R., Phillips T. G., Leighton R. B., Lo K. Y., Wannier P. G., Wooten

H. A., Huggins P. J., 1982, ApJ, 252, 616

Koepf G. A., Buhl D., Chin G., Peck D. D., Fetterman H. R., Clifton B. J.,

Tannenwald P. E., 1982, ApJ, 260, 584

Kuiper T. B. H., Knapp G. R., Knapp S. L., Brown R. L., 1976, ApJ, 204, 408

Kwan J., Linke R., 1982, ApJ, 254, 587

Lockwood G. W., 1970, ApJ, 160, L47

Lucas R., GueÂlin M., Kahane C., Audinos P., Cernicharo J., 1995, Ap&SS,

224, 293

Mamon G. A., Glassgold A. E., Huggins P. J., 1988, ApJ, 328, 797

Mathis J. S., Rumpl W., Nordsieck K. H., 1977, ApJ, 217, 425 (MRN)

Meixner M., Skinner C. J., Grahams J. R., Keto E., Arens J. F., Jernigan J. G.,

1997, ApJ, 482, 897

Miller J. S., 1970, ApJ, 161, L95

Neugebauer G., Leighton R. B., 1969, Two Micron Sky Survey, NASA AP-

3047

Olofsson H., 1993, in Schwartz H. E., ed., 2nd ESO/CTIO Workshop, Mass

Loss on the AGB and Beyond. ESO, Garching-bei-MuÈnchen p. 330

Olofsson H., Eriksson K., Gustafsson B., 1988, A&A, 196, L1

Olofsson H., Eriksson K., Gustafsson B., CarlstroÈm U., 1993, ApJS, 87, 267

PeÂgourieÂ B., 1988, A&A, 194, 335

Rouleau F., Martin P. G., 1991, ApJ, 377, 526

Rowan-Robinson M., Lock T. D., Walker D. W., Harris S., 1986, MNRAS,

222, 273

Sahai R., 1987, ApJ, 318, 809

SchoÈnberg K., 1988, A&A, 195, 198

SchoÈnberg K., Hempe K., 1986, A&A, 163, 151

SchoÈnberner D., 1992, in Weinberger R., Acker A., eds, Proc. IAU Symp.

155, Planetary Nebulae. Kluwer, Dordrecht p. 415

Skinner C. J., 1996, in Jeffery C. S., ed., CCP7 Newsletter No. 24. Daresbury

Laboratory p. 4

Skinner C. J., Meixner M., Hawkins G., Keto E., Jernigan J. G., Arens J. F.,

1994, ApJ, 423, L135

Skinner C. J. et al., 1998, A&A, 328, 290

Skinner C. J., Meixner M., Bobrosky M., 1998, MNRAS, in press

Stanek K. Z., Knapp G. R., Young K., Phillips T. G., 1995, ApJS, 100, 169

Stutzki J., 1990, JCMT Newsletter, 9, 9

Takano S., Saito S., Tsuji T., 1992, PASJ, 44, 469

Tielens A. G. G. M., 1983, ApJ, 271, 702

Tielens A. G. G. M., Hollenbach D. J., 1985, ApJ, 291, 722

Truong-Bach, Morris D., Nguyen-Q-Rieu, 1991, A&A, 249, 435

Wang Y., Jaff D. T., Graf U. U., Evans N. J., II, 1994, ApJS, 95, 503

Wannier P. G., Sahai R., 1986, ApJ, 311, 335

Wannier P. G., Leighton R. B., Knapp G. R., Redman R. O., Phillips T. G.,

Huggins P. J., 1979, ApJ, 230, 149

Wannier P. G., Sahai R., Andersson B-G., Johnson H. R., 1990, ApJ, 358,

251

Wattenbach R., Krugel E., Roser H. P., Nett H., Schwaab G., Densing R.,

1988, A&A, 202, 133

Wiedemann V., 1990, ARA&A, 28, 103

Williams P. G., White G. J., 1992, A&A, 266, 365

Winters J. M., Dominik C., Sedlmayr E., 1994, A&A, 288, 255

Wooten A. L., Nguyen-Q-Rieu, Truong-Bach, 1994, A&A, 290, 198

Zuckerman B., Dyck H. M., Claussen M. J., 1986, ApJ, 304, 401

This paper has been typeset from a TEX=LATEX ®le prepared by the author.


q 1999 RAS, MNRAS 302, 293±304

modelling the dust and gas outflows from irc+10 216 -- i. ground-based and airborne observations

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