A&A 376, 997-1010 (2001)
DOI: 10.1051/0004-6361:20011033
T. Le Bertre1 - M. Matsuura2,3,4 - J. M. Winters1,5 -
H. Murakami2 - I. Yamamura2 -
M. Freund2,6 -
M. Tanaka2,7
1 - DEMIRM, UMR8540, Observatoire de Paris, 61 Av. de l'Observatoire,
75014 Paris, France
2 -
Institute of Space and Astronautical Science, 3-1-1 Yoshinodai,
Sagamihara, Kanagawa 229-8510, Japan
3 -
Department of Astronomy, University of Tokyo, 7-3-1 Hongo,
Bunkyo, Tokyo 113-0033, Japan
4 -
UMIST, Department of Physics, PO Box 88, Manchester M60 1QD, UK
5 -
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69,
53121 Bonn, Germany
6 -
Infrared Astrophysics Branch, Code 685,
Goddard Space Flight Center, Greenbelt, MD 20771, USA
7 -
Department of Physics, Catholic University of America,
Washington, DC 20064, USA
Received 25 April 2001 / Accepted 12 July 2001
Abstract
AGB mass-losing sources are easy to identify and to characterize
in the near-infrared range (1-5
m). We make use of the near-infrared
data acquired by the Japanese space experiment IRTS to study a sample of
sources detected in the 2 celestial strips surveyed by the IRTS. Mass-loss
rates and distances are estimated for 40 carbon-rich sources and
86 oxygen-rich sources of which 8 are probably of S-type. Although the sample
is small, one sees a dependence of the relative contribution of the two kinds
of sources to the replenishment of the interstellar medium (ISM) on
the galactocentric distance. E.g. from 6 to 8 kpc, oxygen-rich sources
in our sample
contribute 10-12 times as much as carbon rich sources, whereas from 10
to 12 kpc, the latters contribute 3-4 times as much as the formers.
Therefore, one would expect a gradient in the composition of the ISM
between 6 and 12 kpc from the Galactic Centre, especially in its dust
component. Most of the replenishment (>50%) by AGB stars is due to
sources with mass-loss rate larger than 10
yr-1.
Key words: stars: carbon - stars: mass-loss - stars: AGB and post-AGB - ISM: evolution - galaxy: solar neighbourhood - infrared: stars
Red giants at some epochs during their evolution along the Asymptotic Giant Branch (AGB) lose matter at a large rate. By this process, these stars contribute to more than 50% of the replenishment of the Interstellar Medium (ISM). In the Solar Neighborhood this proportion might even be higher (Sedlmayr 1994). Furthermore, due to convective mixing, their external layers are enriched in material nuclearly processed in the interiors. Therefore during these epochs of intense mass loss they also participate in the chemical evolution of stellar systems. In particular, it is considered that AGB stars are responsible for the carbon enrichment of the ISM and are the major source for the injection of dust grains (Gehrz 1989).
There are basically 2 kinds of mass-losing AGB stars, those with an
oxygen-rich composition (C/O<1) and those with a carbon-rich one
(C/O>1).
These 2 kinds correspond to a different level of chemical enrichment in the
atmosphere. The difference appears clearly in the molecular bands and in the
dust features that they display in their spectra, particularly in the infrared
range. Our objective is to quantify the contribution of both types of mass
losing AGB sources to the cosmic cycle of matter. The spectral range from 1
to 10
m is crucial to perform this work (Epchtein 1999).
With such objective in mind, we want to exploit the data obtained in the
near-infrared range (1-4
m) by the
space experiment IRTS. In this first paper
we examine in detail a subset of recently released data which covers a small
sample (
120) of mass-losing AGB sources. We will concentrate on the
description of the method that we apply to the IRTS data in order
to derive mass-loss rates. An important feature of our method
is to be sensitive to the present mass loss of AGB stars. In a second
paper (II), when the full data set is made available, we will apply the same
approach to a larger sample (
1000) with the objective of estimating
the mass injection rate from the 2 kinds of
AGB stars in the Solar Neighborhood.
The IRTS (Infrared Telescope in Space) is a 15 cm He-cooled telescope
which has been operated in space during 38 days in March and April 1995
(Murakami et al. 1996). It surveyed in a scanning mode
two strips in the sky amounting to a
total of 2700 square degrees (or 7% of the sky). The first one (or North-scan) was inclined at 15
over the Galactic Plane (GP) and
crossed it at
and 180
;
it covered
2% of the sky. The second one
(or South-scan) was inclined at 50
over the GP
and crossed it at
and 229
;
it covered
5% of the sky. The main purpose of
the IRTS mission was to perform a survey of the infrared (1-1000
m)
diffuse emission with moderate spatial resolution (Okuda et al. 1997).
The telescope was equipped
with four focal instruments of which two are of relevance also for the study
of point sources: the NIRS (Near-Infrared Spectrometer) and the MIRS
(Mid-Infrared Spectrometer). Both are grating spectrometers with
entrance apertures. The NIRS was fitted
with two linear arrays of 12 InSb detectors covering the wavelength ranges
1.38-2.51
m and 2.85-3.96
m. The spectral resolution is
0.1
m for point sources (and 0.13
m for diffuse sources)
and allows to see clearly molecular bands in late-type stars such as those
of CO, at 1.5 and 2.3
m, H2O, at 1.4, 1.9 and 2.7
m
and C2H2-HCN, at 3.1
m, (Yamamura et al. 1997;
Matsuura et al. 1999).
The MIRS covers the wavelength range 4.5-11.7
m with spectral
resolution
0.3
m. It mainly detected the Unidentified
Infrared Bands (UIB) at 6.2, 7.7, 8.6 and 11.3
m in the
diffuse interstellar medium (Onaka et al. 1996), and silicate and
silicon-carbide dust features in late-type stars, as well as molecular bands.
In January 1996, the satellite was recovered from space by the Space Shuttle allowing for post-flight inspection and re-calibration (Murakami et al. 2001; Onaka et al. 2001).
The basis of the NIRS data processing is described in Noda et al. (1996).
Events (i.e. blocks of data where the signals from the detectors
are significantly higher than the background) are extracted from each scan
after identification and removal of glitches, and background subtraction.
The final version of the data processing pipeline
is still under development. The pointing was reconstructed
at IPAC using records by a focal-plane star sensor operating at 1.25
m and by gyros
(Moshir et al. 1997). In general, the accuracy
of the source coordinates is
1
for in-scan direction
and
2
for cross-scan direction. However some scans are
found to be
affected by systematic effects which are larger. Also for some individual
events the position could be uncertain by as much as the aperture size (
8
)
along the cross-scan direction. On the basis
of positions
the events are cross-identified, and eventually recombined into sources.
Spectra are measured for each event.
The data were corrected using post-flight measurements and
a ray-tracing simulation of the instrument (Murakami et al. 2001).
The absolute wavelength calibration of the instrument is excellent.
However, for point sources, depending on the centering in the aperture,
the spectra moved over the array by
0.05
m. The photometric
calibration was derived from the infrared calibration of four non-variable
late-type giants (
Her,
Cnc,
Gru, IRC+60231),
which have been well observed by the NIRS (Cohen et al. 1999).
The photometric stability of
the NIRS system has been checked to be better than 5% over the whole
mission (including the orbits crossing the South Atlantic Anomaly, SAA,
where the instruments were exposed to showers of high-energy protons).
The comparison of the magnitude scale of the IRTS with ground-based
photometry is not straightforward because many detected sources
are variable and because the data set presently available is small.
Also the fluxes measured for a point source depend on its exact positioning
in the aperture and therefore also on its spectral shape.
However one finds good one-to-one correlations between the NIRS fluxes
and the fluxes obtained from the ground in K and
although with some scatter (
0.3 mag).
Color indices are less sensitive to variability than magnitudes.
In Fig. 1, we compare the [2.20-3.77] index from the IRTS to
for sources belonging to the sample described in the next section,
and also observed by us at ESO (Fouqué et al. 1992; Le Bertre 1992, 1993).
This plot is consistent with a one-to-one relation between the 2 color
indices.
![]() |
Figure 1:
[2.20-3.77]
|
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For some scans the telemetry was operated at a rate of 3 kbps
(kilo-bit per second) instead of
6 kbps. In these situations (which affected about 12% of the sources,
the majority of which belongs to the North-scan)
only the fluxes from every alternate
(odd-numbered) channels were transmitted, which means that the 2.20
m
fluxes (channel 16) are not available. In Fig. 2 we present the
[2.20-2.30] color (obtained from channels 16 and 15) versus the
[2.30-3.77] color (obtained from channels 15 and 3) for sources which
have been observed at 6 kbps. The dispersion is large, but one notes first
a negative trend, then from
(0.4, -0.1) a positive one. This
dependence can be understood as the effect of an increasing 2.3
m CO absorption band for stars of late spectral type which tends to be filled in
by dust emission for those which undergo mass loss.
A color-color relation can be derived empirically:
![]() |
(1) |
![]() |
Figure 2: [2.20-2.30] versus [2.30-3.77] for 531 NIRS sources. S Cas is an S star with a deep CO absorption band and R Cap, a carbon star (see text). |
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Carbon stars tend to fall above the line and oxygen-rich stars, below.
This effect could be due to the contribution of H2O absorption at 2.3
m in oxygen-rich stars. However, the 2 populations overlap widely;
also S Cas, an S star, shows the largest absorption at 2.3
m. Another
source of intrinsic scatter might be the variability. Indeed Miras are
known to show deeper molecular absorption bands than Semi-Regular variables
and non-variable giants of the same effective temperature,
because of the pulsation-induced extension of their outer
atmospheric layers. Also, the depths of their molecular bands are strongly
variable with phase (Yamamura & de Jong 2000; Matsuura et al. 2001).
About 1000 sources have been detected by the MIRS and an estimated 10000,
by the NIRS. The MIRS processing is almost completed and a first catalogue
containing
700 spectra is in preparation (Yamamura et al.
2001). For many sources, the MIRS spectra were affected by a varying
response of the detectors developing after the satellite crossed the South
Atlantic Anomaly (SAA). The current MIRS process rejects about 5%
of the MIRS events due to the SAA. The remaining events show drops of
the responsivity up to
10% (Onaka et al. 2001). Fortunately,
this effect was always much smaller for the NIRS detectors (
5%)
so that in general we could ignore the effect of the SAA on the
NIRS events. On the other hand,
the NIRS data are more affected by confusion and by the dependence of
the wavelength calibration on the source position in the aperture.
From this set of 1000 sources detected by the MIRS we have first
removed about 200 items which are Solar System objects (asteroid Ceres and
space debris), extended sources or compact (as compared to the 8
beamsize) H II regions. The latters are easily identified by their
UIBs which stand out in the 6-11
m range.
Counterparts have been searched for the remaining 800 sources, which
therefore are expected to be stellar, in the NIRS database.
Plausible identifications have been obtained for 598 sources.
The stellar MIRS sources which have no NIRS counterpart are extremely
red sources, which were too faint in the near-infrared range to be detected,
or sources which have been lost. Two kinds of sources have been lost,
(i) sources which saturated the NIRS detectors, because they are too bright
in the near-infrared, (ii) sources which could not be properly extracted
due to confusion (e.g. close to the Galactic Plane).
We base our present analysis on this sub-set of 598 sources of which 531
were observed at 6 kbps and the remaining 67, at 3 kbps.
The processing of the complete NIRS data is under progress and the catalogue
with all NIRS point sources will be released in the future. It is expected
to contain 10-15 times as many sources as the current sub-set.
The latter should be on average
fainter and/or bluer than those of the present sample.
The limiting magnitudes for the detection of a NIRS point source are
8.0 at [2.20], and
7.0 at [3.77], but with some
degradation close to the Galactic Plane due to confusion.
For most of the sources we could identify an IRAS counterpart.
In Fig. 3 we present
the color diagram IRAS [12-25] versus IRTS [2.20-3.77]
for the corresponding 554 sources.
Again some sources (44) have been lost, mainly because of astrometric
inaccuracies which prevented an unambiguous identification with IRAS.
On the other hand, due to the large entrance aperture used for
the observations (
), some sources
might have been incorrectly identified to an IRAS source especially
close to the Galactic Plane.
For the sources observed with 3 kbps the 2.20
m flux was estimated
from the 2.30
m one using relation 1. As this approach presents
some uncertainties, in the following we will keep these sources separated
from the others. This diagram
resembles similar ones (i.e. [12-25] versus
)
already published
(see e.g. Epchtein et al. 1987, Fig. 5). Two clumps are noted: the first
one around [2.20-3.77]
0.2,
[12-25]
0.1, and a second one around [2.20-3.77]
0.3,
[12-25]
0.8.
![]() |
Figure 3:
IRAS [12-25] versus [2.20-3.77] for the 554 NIRS sources
cross-identified with IRAS; ( |
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The first clump (
Valinhos "a'' in Epchtein et al. 1987)
corresponds to sources, mainly late-type giants,
with photospheric colors. The second clump (Valinhos "b'') corresponds
to red-giant stars with weak circumstellar dust shell emission. Sources
with mass-loss rate
10
yr-1 are expected
to be found in this area. Le Bertre et al. (1994) note that this group
contains also stars with cool shells (i.e. sources which have recently
undergone a drastic reduction in their rate of mass loss). These stars may
still show up with a large value of the index [12-25]. In general,
in an IRAS colors diagram (van der Veen & Habing 1988) they would be
found in the regions VIa and VIb. To the right
of [2.20-3.77]=0.7, one finds stars which are presently
undergoing mass loss at a large rate (Valinhos "o2'', "o3'' and "c'').
Most of those are red giants, but a few supergiants can be found
here and also possibly some young stars. Furthermore, beyond this limit
the data points split into 2 bands which are discussed below
(Sect. 3.3).
Finally one notes a few sources with peculiar colors. Sources with
[2.20-3.70]
0.0 and a large [12-25] (
0.25)
index can be the products of the merging of two closeby
but unrelated objects. The same applies
to sources above the line
.
However it should be noted that some real objects (e.g. post-AGB sources)
can also be found in these regions. The source labelled 621(
IRAS05198+3325) has been associated to a young stellar object and the source
404(
IRAS06245-1013), to a T Tauri star.
The proportions of the different classes of sources in
the Epchtein et al. (1987) sample and in the present one are expected to be
different because the former were extracted from a survey at 2
m
and the latter from the MIRS survey (i.e. at
8
m).
We will restrict our analysis of the mass-losing AGB stars to the sources
with [2.20-3.77]
0.7 and
.
Therefore, in our final sample we keep all objects presently undergoing mass
loss at a large rate (
yr-1). The
sources with a lower mass-loss rate are excluded and their contribution will
have to be evaluated separately. We also exclude the stars which in the past
had a large
,
but since have experienced an important reduction of this
rate.
We determine the bolometric magnitude,
,
for each source by
applying a bolometric correction,
,
to the
[2.20] magnitude:
The average luminosity of a mass-losing AGB star is expected to be
8000
.
We adopt an absolute bolometric magnitude
.
Then, the distance of each source is estimated
consistently after correction of [2.20] and [2.20-3.77] for interstellar
extinction.
These estimates should be handled with care. The sources are variable and
may change by 1 mag between minimum and maximum. Also, the true
average luminosity may differ from 8000
by a factor up to 2.
Therefore the estimates of the distances to individual sources are
uncertain by a factor 1.8.
The interstellar extinction along a line of sight is determined from an
analytical description of the distribution of dust in the Solar Neighborhood
(Jones et al. 1981). In this approach the local absorption is an exponential
function of r, the distance to the Galactic Centre, and z, the distance to
the Galactic Plane. At the Sun position, the local absorption at 2.20
m,
,
is taken to be 0.07 magkpc-1, and at 3.77
m,
,
0.02 magkpc-1. The scale height, in the Z
direction, is taken to be 0.1 kpc, and the scale length, in the R
direction, 4 kpc. Finally we adopt a distance of the Sun to the Galactic
Centre of 8.5 kpc and assume that the Sun is in the Galactic Plane.
We do not consider the effects of the spiral arms and of the Molecular Ring.
This description of the interstellar extinction in the Solar Neighborhood
is consistent with the more recent one of Wainscoat et al. (1992),
except that we do not apply truncation.
In general the corrections for interstellar extinction are small (<0.15 mag at 2.20
m). The effect on the estimated distance is at most 7%, which is negligible considering the other sources of uncertainty.
This is not only because the extinction in the IR is small but also because
the corrections on [2.20] and [2.20-3.77] have opposite effects on
which tend to cancel for the reddest sources
([2.20-3.77]>2.1).
The main effect is to move a few sources (10) from just above
[2.20-3.77]=0.7 to just below. For consistency, these sources have
been removed from the final sample. However, as the distances are uncertain by
a factor 1.8, the interstellar extinction might have been overestimated for
some of them. It means that individually they could meet the criterion
[2.20-3.77]
![]()
0.7. Their names and properties
are reported in Table 1.
We find that in our sample most of the sources should be within
3.5 kpc from the Sun, but some sources are found up to 6.5 kpc.
In the Z direction, we get sources up to
1.5 kpc from the GP.
| Index | [2.20] | [2.20-3.77] | [12-25] | IRAS name |
| 82 | 3.53 | 0.70 | 1.11 | 15455-6108 |
| 180 | 4.15 | 0.79 | 0.82 | 16538-4633 |
| 192 | 3.27 | 0.74 | 1.21 | 16575-4344 |
| 213 | 3.30 | 0.74 | 1.18 | 17116-4036 |
| 289 | 3.29 | 0.73 | 0.73 | 17372-2632 |
| 469 | 3.50 | 0.70 | 0.48 | 18141+0340 |
| 551 | 3.63 | 0.75 | 0.23 | 19122+1830 |
| 499 | 3.23 | 0.72 | 0.21 | 19155+0847 |
| 524 | 3.44 | 0.76 | 1.10 | 19271+1354 |
| 510 | 2.31 | 0.72 | 1.01 | 19248+1122 |
The NIRS data covers the wavelength range 1.4-4.0
m which contains
various molecular bands such as those of H2O (1.9
m) or
C2H2+HCN (3.1
m). These features in principle allow us
to separate O-rich from C-rich sources (Fig. 4). However, in the
case of very red sources these bands are partially filled in by dust emission.
![]() |
Figure 4:
Typical NIRS/IRTS spectra of mass-losing AGB sources. From bottom
to top: WPic, a carbon star; SCas, an S-type star and RRAql, an M-type
star. Note the deep H2O band at 1.9 |
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A method based on the color indices,
and IRAS [12-25],
has been developped by Epchtein et al. (1987). In the corresponding
color-color diagram, C-rich and O-rich sources surrounded by circumstellar
shells separate clearly. The reason for this separation lies in
the very different optical properties of the carbon-rich
and oxygen-rich dust grains in the infrared range. In Fig. 5
we present the [12-25] versus [2.20-3.77] colors diagram
for the NIRS sources of our sample which satisfy the criteria
[2.20-3.77]
0.7 and
.
O-rich and C-rich sources separate clearly.
We adopt the same dividing line as in Epchtein et al.:
[12 - 25] = 0.42
[2.20 - 3.77]+0.10,
for [2.20-3.77]
0.7.
Each of the 130 NIRS spectra has been checked individually. In general
this inspection confirms the validity of the Epchtein et al. (1987)
classification criterion: the H2O band at 1.9
m is found in sources
belonging to the "O-rich'' region (Fig. 4; RRAql)
and the band at 3.1
m, in sources
belonging to the "C-rich'' region (Fig. 4; WPic).
For 8 sources (Table 2)
belonging to the "O-rich'' region, none of these bands can be seen.
However, they show clearly a deep CO absorption at 2.3
m
(Fig. 4; SCas). When available the IRAS Low
Resolution Spectrum confirms the O-rich composition of the circumstellar
shell and 3 sources are known to be of S-type (Nos. 793, 207, and 686).
We consider that the 5 other sources which have similar NIRS spectra are
likely to be also of S-type.
We note however that some stars which are identified to be of S-type
(e.g. TTCMa) do show the H2O absorption band at 1.9
m.
It is known that S stars exhibit a range of spectroscopic properties
intermediate between those of M stars and those of pure S stars.
Piccirillo (1980) shows that H2O tends to disappear from the photospheric
layers of S-type stars when the C/O abundance ratio becomes greater than 0.9. The absence of the 1.9
m H2O band in our spectra would then
point to S stars with a rather large C/O ratio. Finally, H2O is found
to be weak or even absent in red supergiants spectra (Alvarez et al. 2000),
a combined effect of their low surface gravity and higher effective
temperature. In this context we note that the source No. 251
might in fact be associated to an M0Ia star (Massey et al. 2001).
Three sources (Nos. 316, 252 and 339) are obviously mis-classified.
The 316 NIRS spectrum shows clearly the absorption feature at 3.1
m
and the source is associated to GM CMa, a carbon star. Finally 3 sources
are unrelated to the AGB (Nos. 709, 714 and 385). Their NIRS spectra
are featureless. The sources 709 and 385 are associated to emission line
stars of spectral type B and 714, to an RV Tauri type star. Therefore we have
removed the sources 709, 714, 385 and 316 from the sample and corrected the
spectral classification of the sources 252 and 339. We thus get a sample of
126 AGB stars of which 40 are carbon-rich and 86, oxygen-rich.
![]() |
Figure 5:
IRAS [12-25] versus [2.20-3.77] for the selection
of 130 mass-losing AGB candidates. The [2.20-3.77] index is corrected
for interstellar extinction assuming that each candidate has a luminosity
of 8000 |
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| Index | IRAS name | optical id. | IRAS LRS |
| 793 | 01159+7220 | S Cas | 22 |
| 484 | 05591+0638 | ||
| 168 | 16538-4652 | 14 | |
| 207 | 16598-4117 | CSS952 | 24 |
| 234 | 17187-3750 | 26 | |
| 230 | 17244-3827 | 14 | |
| 251 | 17328-3327 | 29 | |
| 686 | 19354+5005 | R Cyg | 22 |
| Index | IRAS name | optical id. | IRAS LRS |
| 709 | 04156+5552 | CI Cam | |
| 714 | 04166+5719 | TW Cam | |
| 385 | 06259-1301 | HD 45677 | 24 |
| 316 | 06391-2213 | GM CMa | 23 |
| 252 | 17209-3318 | 43 | |
| 339 | 17540-1919 | VVSgr | 28 |
Several methods are used to derive the mass-loss rates of AGB stars
from observations. An introduction to this topic
can be found in Lafon & Berruyer (1991). Up to now, mainly 2 methods
have been applied. The first one is based on the modelling
of CO rotational lines (Knapp & Morris 1985) and the second one, on the
modelling of the continuum emission observed in the infrared (Jones & Merrill
1976). In both cases, the modelling assumes that the mass-loss rate
has been constant over time,
a few thousand years in the first
case,
a few hundred years in the second.
Both methods assume a conversion ratio, from a minor species (CO or
dust) to the total mass, which might not be constant. Nevertheless,
in general, the two methods agree to within a factor 3.
However, the mass-loss phenomenon is known to exhibit variations on several
timescales. This effect explains that, in fact, different methods may give
very different results. For instance, using CO rotational line data
Loup et al. (1993) find
10
yr-1
for RScl, whereas LeBertre (1997),
using IR continuum data, finds
10
yr-1, a
factor about one hundred less. The explanation lies in a drastic reduction
of the RScl mass loss about 100 years ago, an effect discovered by
Rowan-Robinson et al. (1986) and which can be inferred from the IRAS data
which shows an excess at
m.
The situation is even more complex if one considers
the multiple molecular winds recently brought to evidence from composite
CO line profiles (Kahane & Jura 1996; Knapp et al. 1998). In these cases,
the mass-loss rate variations can be uncovered because the properties
of the winds, in particular the outflow velocities, are very different.
One may suspect that, in other situations where the
changes are less radical, such effects would not be detected,
but still affect the determination of
.
This is particularly true for the
CO method which probes a shell of typically 1017 cm in size, which
is filled in on a timescale of 1 to a few 103 years. The
IR method is less sensitive to this problem because it is the most internal
parts of the circumstellar dust shells which dominate the IR continuum
emission. The near-infrared (1-5
m) continuum emission
originates in a shell of
1015 cm,
whereas the far-infrared emission (
m)
comes from a larger region of
1016 cm (e.g. Rowan-Robinson
et al. 1986). The IR method is thus expected to give an estimate of
which fits more closely the present characteristics of the central star
than the CO method.
Both methods can be used to derive mass-loss rates only for well observed
sources at known distances from the Sun. To handle large samples, relations
allowing to estimate easily
have been proposed. For instance Jura (1987)
has proposed to estimate
from the 60
m IRAS fluxes. This approach
works well for sources which have not undergone a recent variation of their
mass-loss rate like R Scl. Here also the distances must be known. More
recently, Le Bertre (1997) and Le Bertre & Winters (1998) have shown that the mass-loss rates of AGB stars are correlated with the
color index.
Their empirical relations are derived from a sample of well studied sources
in the Solar Neighborhood for which
has been determined through
the IR method.
On the basis of these works, we adopt:
log
= -9.0/([2.20-3.77]+1.4) + 2.75,
for C-rich sources, and
log
= -2.75/[2.20-3.77] + 2.25,
for O-rich sources,
where
is in 10
yr-1 and [2.20-3.77]
has been corrected for interstellar extinction.
In a systematic study, Winters et al. (2000) showed that self-consistent
hydrodynamical models which produce winds with
yr-1 follow such kind of
relations.
They show that these relations hold for various dust-to-gas ratios
due to the interplay between mass-loss rate, dust-to-gas ratio and expansion
velocity.
In these models, the flux of matter is variable over a timescale of
one stellar pulsation period,
or a few in the cases of multiperiodic models (Fleischer
et al. 1995). Winters et al. define the mass-loss rate as a flux average
over 20 stellar periods, or
20-50 years. On the basis of their
study it does not seem meaningful to define a mass-loss rate over a shorter
timescale; it is only on such a timescale that AGB sources can be considered
as stationary systems. Furthermore, there are evidences that on longer
timescales (>40 years) some AGB sources might undergo large variations
of the mass loss (Mauron & Huggins 2000; see also the previous discussion on
RScl and on mutiple winds). Therefore, by "present'' mass-loss rate
we refer to an average over the last
20-50 years.
The use of a near-infrared index, [2.20-3.77], ensures that our estimates
are relevant to the present mass-loss rates
as defined above (Winters et al. 2000).
In the context of the evaluation of the replenishment of the ISM it is
important to use an estimate corresponding to a stage of the star for which
it can be considered as stationary. Another
advantage of this approach is that these relations are distance independent,
so that an error on the distance estimation would not translate into an error
on
(apart for the small interstellar correction on the color). On the
other hand the correlations which have been found apply to mean color indices
averaged over several periods. From Le Bertre (1997) we evaluate to a factor 2
the error made by using indices based on single epoch measurements
such as those acquired by the IRTS. Therefore
the individual estimates of
should be handled with care.
| Index | IRAS name | [2.20] | [2.20-3.77] |
|
z |
|
log
|
composition |
| pc | pc | kpc | 10
|
|||||
| 793 | 01159+7220 | 1.60 | 1.19 | 729. | 125. | 8.93 | -0.063 | O |
| 790 | 01411+7104 | 4.03 | 1.16 | 2223. | 345. | 9.98 | -0.760 | C |
| 775 | 02596+6639 | 4.36 | 2.13 | 2529. | 321. | 10.44 | 0.199 | C |
| 749 | 03374+6229 | 0.43 | 0.79 | 424. | 44. | 8.83 | -1.366 | C |
| 721 | 03575+5922 | 4.03 | 1.27 | 2222. | 197. | 10.39 | -0.616 | C |
| 708 | 04207+5548 | 3.84 | 0.88 | 2038. | 162. | 10.31 | -1.206 | C |
| 684 | 04449+4951 | 4.49 | 2.57 | 1939. | 111. | 10.31 | 0.483 | C |
| 683 | 04504+4949 | 2.70 | 1.03 | 1205. | 82. | 9.62 | -0.946 | C |
| 159 | 05096-4834 | 0.18 | 0.73 | 379. | -224. | 8.59 | -1.538 | O |
| 664 | 05106+4520 | 5.95 | 2.65 | 3587. | 244. | 11.97 | 0.526 | C |
| 627 | 05149+3511 | 3.77 | 1.84 | 1974. | -50. | 10.46 | -0.028 | C |
| 616 | 05185+3227 | 1.89 | 0.95 | 829. | -34. | 9.32 | -1.076 | C |
| 617 | 05204+3227 | 5.28 | 1.54 | 3959. | -141. | 12.44 | 0.467 | O |
| 648 | 05214+4001 | 4.00 | 1.26 | 2199. | 93. | 10.66 | -0.639 | C |
| 623 | 05238+3406 | 1.35 | 1.51 | 647. | -6. | 9.14 | -0.345 | C |
| 577 | 05325+2351 | 2.76 | 0.89 | 1243. | -100. | 9.74 | -0.825 | O |
| 606 | 05345+3002 | 3.20 | 0.95 | 1522. | -23. | 10.02 | -1.081 | C |
| 190 | 05345-4406 | 2.46 | 0.74 | 1082. | -566. | 8.86 | -1.493 | O |
| 573 | 05352+2247 | 3.00 | 0.92 | 1384. | -112. | 9.88 | -1.138 | C |
| 175 | 05418-4628 | 1.02 | 0.85 | 557. | -284. | 8.65 | -1.254 | C |
| 583 | 05421+2424 | 1.50 | 0.82 | 694. | -29. | 9.19 | -1.305 | C |
| 562 | 05426+2040 | 0.32 | 0.78 | 403. | -30. | 8.90 | -1.375 | C |
| 575 | 05465+2321 | 4.24 | 0.96 | 2449. | -89. | 10.94 | -1.055 | C |
| 184 | 05510-4522 | 3.33 | 0.79 | 1615. | -781. | 9.04 | -1.244 | O |
| 484 | 05591+0638 | 4.26 | 1.03 | 2479. | -342. | 10.82 | -0.428 | O |
| 463 | 06026+0322 | 6.38 | 2.11 | 6506. | -992. | 14.59 | 0.188 | C |
| 397 | 06266-1148 | 3.40 | 0.96 | 1663. | -297. | 9.79 | -0.618 | O |
| 341 | 06496-1858 | 1.76 | 0.85 | 781. | -115. | 9.02 | -1.004 | O |
| 340 | 06550-1915 | 3.87 | 0.88 | 2070. | -270. | 9.92 | -0.879 | O |
| 320 | 06588-2138 | 5.41 | 1.89 | 4196. | -569. | 11.48 | 0.011 | C |
| 354 | 07019-1631 | 3.03 | 0.76 | 1407. | -117. | 9.48 | -1.344 | O |
| 368 | 07028-1456 | 4.29 | 2.46 | 1921. | -129. | 9.89 | 0.417 | C |
| 359 | 07031-1604 | 4.91 | 1.29 | 3336. | -252. | 10.98 | -0.595 | C |
| 405 | 07118-1022 | 4.96 | 1.89 | 3412. | 12. | 11.18 | 0.012 | C |
| 371 | 07145-1428 | 4.26 | 1.64 | 2470. | -49. | 10.30 | -0.208 | C |
| 383 | 07180-1314 | 3.53 | 1.41 | 1766. | 7. | 9.77 | 0.297 | O |
| 370 | 07197-1451 | 2.54 | 0.72 | 1122. | -3. | 9.27 | -1.553 | O |
| 375 | 07208-1410 | 3.58 | 0.85 | 1808. | 11. | 9.78 | -1.243 | C |
| 431 | 07227-0537 | 5.45 | 1.62 | 4290. | 361. | 12.03 | -0.232 | C |
| 429 | 07232-0544 | 1.73 | 0.70 | 772. | 66. | 9.09 | -1.656 | O |
| 445 | 07487-0229 | 2.95 | 1.68 | 1355. | 282. | 9.52 | -0.171 | C |
| 517 | 08138+1152 | -0.67 | 0.74 | 256. | 104. | 8.70 | -1.478 | O |
| 526 | 08186+1409 | 3.18 | 0.72 | 1504. | 663. | 9.69 | -1.583 | O |
| 9 | 11318-7256 | 1.17 | 1.83 | 596. | -116. | 8.25 | -0.035 | C |
| 773 | 12544+6615 | 0.15 | 0.85 | 374. | 291. | 8.63 | -1.254 | C |
| 12 | 13350-7221 | 2.86 | 0.87 | 1297. | -228. | 7.81 | -0.908 | O |
| 13 | 13417-7221 | 4.08 | 0.80 | 2278. | -404. | 7.37 | -1.179 | O |
| 29 | 14188-6943 | 2.69 | 0.71 | 1202. | -179. | 7.78 | -1.642 | O |
| 36 | 14473-6842 | 3.80 | 0.79 | 1999. | -300. | 7.28 | -1.236 | O |
| 54 | 15155-6531 | 3.34 | 1.16 | 1622. | -201. | 7.39 | -0.130 | O |
| 60 | 15332-6430 | 1.96 | 1.18 | 859. | -110. | 7.87 | -0.078 | O |
| 55 | 15389-6517 | 3.09 | 0.71 | 1442. | -209. | 7.47 | -1.627 | O |
| 116 | 16156-5613 | 2.99 | 1.12 | 1379. | -106. | 7.36 | -0.213 | O |
| 146 | 16376-5040 | 2.92 | 0.74 | 1335. | -67. | 7.31 | -1.473 | O |
| 132 | 16410-5240 | 3.22 | 0.87 | 1531. | -124. | 7.16 | -0.912 | O |
| Index | IRAS name | [2.20] | [2.20-3.77] |
|
z |
|
log
|
composition |
| pc | pc | kpc | 10
|
|||||
| 142 | 16455-5124 | 3.71 | 0.74 | 1924. | -147. | 6.80 | -1.449 | O |
| 178 | 16507-4644 | 4.07 | 0.99 | 2269. | -80. | 6.42 | -0.523 | O |
| 168 | 16538-4652 | 2.36 | 0.81 | 1034. | -45. | 7.54 | -1.137 | O |
| 182 | 16558-4526 | 2.42 | 0.76 | 1061. | -34. | 7.50 | -1.350 | O |
| 207 | 16598-4117 | 2.05 | 1.06 | 896. | 1. | 7.64 | -0.345 | O |
| 195 | 17054-4342 | 3.02 | 1.02 | 1397. | -53. | 7.17 | -0.966 | C |
| 227 | 17163-3835 | 0.90 | 0.86 | 527. | -7. | 7.98 | -0.931 | O |
| 234 | 17187-3750 | 1.33 | 0.94 | 641. | -8. | 7.87 | -0.684 | O |
| 252 | 17209-3318 | 4.15 | 2.52 | 1720. | 43. | 6.79 | 0.452 | C |
| 263 | 17209-3126 | 3.52 | 1.45 | 1762. | 75. | 6.75 | 0.349 | O |
| 230 | 17244-3827 | 3.16 | 0.73 | 1490. | -55. | 7.04 | -1.541 | O |
| 251 | 17328-3327 | 0.60 | 0.92 | 458. | -6. | 8.04 | -0.729 | O |
| 308 | 17346-2312 | 3.36 | 0.94 | 1635. | 128. | 6.88 | -0.682 | O |
| 292 | 17346-2612 | 4.34 | 0.85 | 2571. | 128. | 5.93 | -0.990 | O |
| 307 | 17367-2319 | 2.62 | 1.12 | 1162. | 82. | 7.34 | -0.213 | O |
| 326 | 17389-2045 | 2.26 | 1.02 | 987. | 86. | 7.52 | -0.440 | O |
| 366 | 17462-1511 | 3.69 | 0.97 | 1905. | 211. | 6.66 | -0.596 | O |
| 365 | 17468-1503 | 4.53 | 1.01 | 2801. | 306. | 5.81 | -0.460 | O |
| 362 | 17482-1529 | 2.93 | 0.82 | 1339. | 134. | 7.20 | -1.111 | O |
| 376 | 17541-1404 | 2.79 | 0.76 | 1260. | 117. | 7.29 | -1.361 | O |
| 425 | 17573-0807 | 2.75 | 0.99 | 1233. | 161. | 7.36 | -0.524 | O |
| 426 | 18039-0813 | 1.63 | 1.02 | 738. | 78. | 7.82 | -0.458 | O |
| 427 | 18054-0649 | 3.80 | 0.80 | 2001. | 222. | 6.70 | -1.169 | O |
| 626 | 18076+3445 | 3.81 | 1.55 | 2008. | 789. | 7.79 | 0.477 | O |
| 485 | 18202+0636 | 4.17 | 0.86 | 2375. | 385. | 6.74 | -0.962 | O |
| 504 | 18209+0928 | 4.09 | 0.98 | 2290. | 418. | 6.88 | -0.552 | O |
| 637 | 18306+3657 | 0.21 | 0.84 | 383. | 128. | 8.36 | -1.265 | C |
| 568 | 18444+2143 | 3.44 | 0.71 | 1700. | 316. | 7.59 | -1.609 | O |
| 559 | 18512+2029 | 4.49 | 1.59 | 2754. | 422. | 7.14 | 0.520 | O |
| 538 | 18561+1642 | 2.57 | 0.81 | 1137. | 119. | 7.80 | -1.162 | O |
| 574 | 19029+2305 | 4.35 | 0.96 | 2583. | 337. | 7.34 | -0.620 | O |
| 545 | 19090+1746 | 3.23 | 1.00 | 1540. | 103. | 7.63 | -0.513 | O |
| 528 | 19111+1404 | 2.86 | 0.89 | 1296. | 38. | 7.69 | -0.846 | O |
| 654 | 19158+4243 | 3.45 | 0.74 | 1702. | 401. | 8.21 | -1.471 | O |
| 541 | 19172+1706 | 2.28 | 0.73 | 996. | 31. | 7.92 | -1.536 | O |
| 503 | 19192+0922 | 3.42 | 2.36 | 1389. | -57. | 7.58 | 1.082 | O |
| 496 | 19224+0732 | 3.61 | 1.11 | 1834. | -124. | 7.28 | -0.234 | O |
| 491 | 19248+0658 | 2.97 | 1.95 | 1368. | -111. | 7.57 | 0.061 | C |
| 514 | 19264+1132 | 3.56 | 0.99 | 1790. | -90. | 7.41 | -0.523 | O |
| 686 | 19354+5005 | 0.47 | 0.75 | 433. | 103. | 8.46 | -1.399 | O |
| 482 | 19354+0636 | 3.30 | 0.94 | 1593. | -198. | 7.45 | -1.100 | C |
| 465 | 19412+0337 | 2.76 | 1.51 | 1241. | -213. | 7.64 | 0.425 | O |
| 448 | 19433-0158 | 4.93 | 1.63 | 3367. | -754. | 6.23 | 0.563 | O |
| 466 | 19454+0355 | 3.06 | 1.15 | 1427. | -264. | 7.54 | -0.138 | O |
| 446 | 19550-0201 | -0.01 | 0.91 | 347. | -93. | 8.24 | -0.780 | O |
| 428 | 20077-0625 | 2.34 | 2.31 | 876. | -306. | 7.85 | 1.057 | O |
| 372 | 20084-1425 | 2.91 | 1.30 | 1326. | -541. | 7.46 | -0.588 | C |
| 750 | 20215+6243 | 2.08 | 0.76 | 908. | 226. | 8.65 | -1.347 | O |
| 377 | 20234-1357 | 2.62 | 1.09 | 1164. | -532. | 7.63 | -0.285 | O |
| 321 | 20296-2151 | 2.65 | 0.76 | 1181. | -617. | 7.58 | -1.386 | O |
| 225 | 21069-3843 | 2.00 | 0.93 | 875. | -596. | 7.86 | -0.720 | O |
| 212 | 21206-4054 | 1.85 | 0.94 | 817. | -584. | 7.93 | -0.663 | O |
| 785 | 21262+7000 | 1.41 | 1.32 | 667. | 160. | 8.71 | -0.557 | C |
| 169 | 21453-4708 | 1.75 | 0.74 | 778. | -590. | 8.00 | -1.480 | O |
| 791 | 22348+7149 | 3.27 | 0.93 | 1566. | 322. | 9.20 | -0.711 | O |
| Index | IRAS name | [2.20] | [2.20-3.77] |
|
z |
|
log
|
composition |
| pc | pc | kpc | 10
|
|||||
| 787 | 02588+6956 | 3.55 | 0.79 | 1788. | 313. | 9.80 | -1.248 | O |
| 754 | 03287+6249 | 3.55 | 0.74 | 1782. | 176. | 9.93 | -1.487 | O |
| 609 | 05334+3057 | 4.87 | 1.56 | 3275. | -33. | 11.77 | -0.288 | C |
| 411 | 06230-0930 | 6.43 | 2.65 | 4455. | -784. | 12.24 | 0.526 | C |
| 331 | 07098-2012 | 3.92 | 2.88 | 1184. | -98. | 9.25 | 0.647 | C |
| 189 | 07178-4429 | 5.84 | 1.59 | 5126. | -1249. | 10.82 | 0.517 | O |
| 21 | 10342-7027 | 3.22 | 0.86 | 1533. | -286. | 8.05 | -0.961 | O |
| 2 | 12593-7355 | 4.73 | 0.95 | 3071. | -608. | 7.27 | -0.641 | O |
| 24 | 13408-7021 | 2.39 | 0.78 | 1046. | -150. | 7.91 | -1.384 | C |
| 242 | 17107-3611 | 3.42 | 0.79 | 1680. | 42. | 6.85 | -1.218 | O |
| 258 | 17215-3237 | 3.46 | 1.01 | 1711. | 52. | 6.80 | -0.469 | O |
| 301 | 17380-2429 | 3.92 | 0.91 | 2118. | 113. | 6.39 | -0.759 | O |
| 339 | 17540-1919 | 2.17 | 1.19 | 947. | 45. | 7.57 | -0.059 | O |
| 432 | 18050-0518 | 4.02 | 1.28 | 2213. | 278. | 6.54 | 0.102 | O |
| 472 | 18125+0447 | 3.79 | 0.83 | 1994. | 356. | 6.94 | -1.046 | O |
| 489 | 19426+0650 | 3.34 | 0.85 | 1620. | -243. | 7.46 | -0.968 | O |
The results of the present study are given in Table 4.
They concern the 126 objects that passed
all our selection criteria: detection by the MIRS of a compact stellar source
without PAH-emission, association to an IRAS source, colors typical of a
mass-losing AGB star and a NIRS spectrum typical of an M, C or S-type star.
Each source is refered to with an index that we use throughout the present
work and by its IRAS name. We give the dereddened [2.20] magnitude and
[2.20-3.77] color, the estimated distance from the Sun,
,
the distance above the galactic plane, z, the distance
to the Galactic Centre,
,
the mass-loss rate,
,
estimated using the relations given in Sect. 3.4
and finally a label
defining the chemical composition of the circumstellar shell (C for
carbon-rich, O for oxygen-rich). The 16 sources observed at 3 kbps are
reported separately at the end of the table.
As we have checked individually every spectrum of the 130 candidates, we can be confident that the 126 sources reported in Table 4 are bona-fide AGB stars. For this selection, only 2 sources were misclassified with the Epchtein et al. (1987) criterion and this has been corrected for the present work.
Nevertheless, for future works, it is important to evaluate the contamination of the region defined in Sect. 2.5 by other sources which are not genuine mass-losing AGB stars. In the sample of 130 stars found in this region after dereddening, only 4 are not unambiguously related to the AGB; this includes the special cases of GM CMa, a carbon star, and of TW Cam, an RV Tauri star. It thus seems that the contamination is at a level <5%. It is noteworthy that the 10 stars in Table 1 are all late-type giants.
On the other hand, it is possible that many early-type stars have been
removed from our initial sample together with the H II regions
(see Sect. 2.3).
Another bias that could have affected early-type stars
arises from the difficulty of extracting NIRS sources close to the Galactic
Plane, because of the large beam. Therefore we could have underestimated
the contamination by this type of source. This discussion illustrates
the importance of spectrophotometric data in the 1-5
m region which
allows to pin down early-type stars.
In Fig. 6, we present the projection of the final sample on the
Galactic Plane (GP). One notes a clear preference for carbon stars to be
located outside the solar circle and the opposite, for oxygen-rich sources.
At more than 10 kpc from the Galactic Centre, we have 17 carbon stars and
3 oxygen-rich ones. Between 8 and 10 kpc, we get respectively 17 and 23
sources. Finally at less than 8 kpc, we get 6 carbon sources and
60 oxygen-rich ones. The two populations seem to balance at about the
distance of the Sun to the Galactic Centre, in agreement with Jura
& Kleinmann (1989). In previous studies (Jura 1991; Guglielmo et al. 1998),
it has been found that the surface density of carbon sources is almost
constant within 3 kpc of the Sun. With the present selection of 40 sources,
we cannot confirm this distribution, but we should be able to revisit it
on the basis of the complete NIRS data set which should provide 10-15
times more sources.
![]() |
Figure 6:
Projection on the Galactic Plane of the final sample (126
sources). The carbon stars are represented with diamonds (
|
| Open with DEXTER | |
In the Z direction, most of the sources (74) are within 200 pc of the GP, 32 are found between 200 and 400 pc, and 20, beyond 400 pc. The carbon-rich sources tend to be more concentrated towards the GP, but in view of the present size of the sample this effect is only marginal.
Our ultimate goal is to quantify the contributions of the 2 different kinds of mass-losing AGB stars to the replenishment of the ISM at different distances from the Galactic Centre and different distances from the GP. Our present selection of 126 AGB sources suffers from many biases coming from the extraction of NIRS sources. Nevertheless, for a first step, we assume that these biases affect equally the carbon-rich and the oxygen-rich sources.
In Table 5, we sum up the contributions of our sources in 3 belts. As our sample is not complete the absolute values have no
immediate meaning.
Also, it appears that the contributions from the sources with largest mass
loss rates dominate these sums which therefore are strongly affected by
the small number statistics (see below, and Table 6).
In spite of that, it is clear that the oxygen-rich sources dominate
the replenishment of the ISM by AGB stars for
kpc,
by a factor 10-12, and the carbon-rich sources, for
kpc, by a factor 3-4. It means that the composition
of the ISM, especially in its dust component, should vary considerably
between
6 and 12 kpc from the Galactic Centre.
In Table 6,
we sum up the contributions of our 126 sources in mass-loss-rate
bins. The 20 sources with
in the range 10-6-10
yr-1 contribute about as much as the rest of the sample
to the replenishment of the ISM. Two objects with
yr-1 contribute
1/4 of the total from all the
sources. These two sources (503 and 428) are found to have mass-loss rates
yr-1. Our sample is limited in size
and we do not get AGB mass losing sources with larger rates, although such
sources are known to exist with rates up to
yr-1
(Habing 1996). It would be important to evaluate their contribution because,
although they seem to be extremely rare, they might still contribute
substantially to the replenishment of the ISM.
From these remarks, it becomes clear that a proper determination of the
replenishment of the ISM close to the Sun requires the exploration of a large
volume inside a torus centered on the Galactic Centre and enclosing the Sun,
in order to overcome the effect of small number statistics.
|
|
C-rich | O-rich | ||
| N |
|
N |
|
|
| 6-8 kpc | 6 | 4.47 | 58 | 51.46 |
| 8-10 kpc | 17 | 10.18 | 23 | 4.60 |
| 10-12 kpc | 14 | 13.06 | 2 | 3.66 |
| C-rich | O-rich | |||
| ( |
N |
|
N |
|
|
|
14 | 0.87 | 33 | 1.50 |
| 10-7-10-6 | 15 | 6.36 | 42 | 13.80 |
| 10-6-10-5 | 11 | 25.96 | 9 | 24.33 |
| 10-5-10-4 | 0 | 2 | 23.48 |
We have shown that the data acquired by the Near-Infrared Spectrometer of the
IRTS can be used to obtain an estimate of the contribution of carbon-rich
and oxygen-rich mass-losing AGB stars to the replenishment of the ISM
at different distances (
3 kpc) from the Sun. The combination with
IRAS data helps to sort out the sources. This approach will be developed
in Paper II on the basis of the complete NIRS data.
We note that an experiment similar to the NIRS/IRTS with a smaller entrance
aperture and a better sensitivity could allow to easily extend such a study
to the whole Galaxy. For sources which have no good IRAS fluxes at 12 and 25
m, low-resolution spectroscopy (
)
in the 1-5
m
range may as well be used to discriminate O-rich from C-rich stars in most
situations. Also, this kind of spectral data is useful to identify
contaminating and misclassified sources.
Acknowledgements
T. Le Bertre is grateful to the Institute of Space and Astronautical Science (ISAS) for an invitation to stay in Japan and for the permission to work on IRTS data. J. M. Winters acknowledges financial support by the CNRS. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This work has been supported by the Paris Observatory through the fund BQR2000. We gratefully acknowledge useful comments from A. Jorissen and K. Justtanont.
![]() |
Figure A.1:
BCK versus
|
![]() |
Figure A.2:
|
![]() |
Figure A.3: BCK versus K - [12] for the samples of O-rich (circles) and C-rich (dots) sources discussed in the Appendix. Solid line: recommended relation. |
The results are presented in Fig. A.1. A similar work has been performed
by van Loon et al. (1999) who obtained comparable results. They find that
there is virtually no difference between C-rich and O-rich sources. The
fit to all their data is shown as a dashed line (
![]()
3.6). From
our samples it is not clear if there is a difference between the corrections
for the 2 kinds of sources. We have 4 (carbon-rich) sources
with
![]()
3.6
which deviate from an extrapolation of the van Loon et al. relation.
Therefore, we adopt the relations (common to O and C-rich sources):
BCK = 2.7,
for (
)
2.1, and
BCK = 6.1 - 1.62
(
),
for 2.1
(
)
7.
Instead of evaluating the bolometric correction with respect to K,
we can evaluate it with respect to
.
This approach has also been
followed by Wood et al. (1998), but they used L (3.59
m) instead
of
(3.79
m) so that a direct comparison is not feasible. Our
data can be represented with Fig. A.2:
= 2.7 + (
),
for (
)
2.1, and
= 6.10 - 0.62
(
),
for (
)
2.1.
Another index which can be useful to consider is K - [12], where [12] is
the IRAS 12
m magnitude. The results are presented in Fig. A.3.
The data are well represented by the relations:
BCK = 2.8,
for (K - [12])
4.8, and
BCK = 7.12 - 0.9
(K - [12]),
for (K - [12])
4.8.