Are $^{12}$CO lines good indicators of the star formation rate in galaxies?
ABSTRACT In this paper, we investigate the relevance of using the $^{12}$CO line emissions as indicators of star formation rates (SFR). For the first time, we present this study for a relatively large number of $^{12}$CO transitions (12) as well as over a large interval in redshift (from z$\sim$0 to z$\sim$6). For the nearby sources (D$\leq$10 Mpc), we have used homogeneous sample of $^{12}$CO data provided by Bayet et al. (2004, 2006), mixing observational and modelled line intensities. For higher-z sources (z $\geq$ 1), we have collected $^{12}$CO observations from various papers and have completed the data set of line intensities with model predictions which we also present in this paper. Finally, for increasing the statistics, we have included recent $^{12}$CO(1-0) and $^{12}$CO(3-2) observations of intermediate-z sources. Linear regressions have been calculated for identifying the tightest SFR-$^{12}$CO line luminosity relationships. We show that the \emph{total} $^{12}$CO, the $^{12}$CO(5-4), the $^{12}$CO(6-5) and the $^{12}$CO(7-6) luminosities are the best indicators of SFR (as measured by the far-infrared luminosity). Comparisons with theoretical approaches from Krumholz and Thompson (2007) and Narayanan et al. (2008) are also performed in this paper. Although in general agreement, the predictions made by these authors and the observational results we present here show small and interesting discrepancies. In particular, the slope of the linear regressions, for J$_{upper}\geq$ 4 $^{12}$CO lines are not similar between theoretical studies and observations. On one hand, a larger high-J $^{12}$CO data set of observations might help to better agree with models, increasing the statistics. On the other hand, theoretical studies extended to high redshift sources might also reduce such discrepancies. Comment: 10 pages, 3 figures and 4 tables, Accepted in MNRAS
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Mon. Not. R. Astron. Soc. 000, 1–10 (2008)Printed 16 June 2009(MN LATEX style file v2.2)
Are12CO lines good indicators of the star formation rate
in galaxies?
E. Bayet1?; M. Gerin2; T. G. Phillips3and A. Contursi4
1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
2LERMA, Observatoire de Paris and Ecole Normale Sup´ erieure, 24 rue Lhomond, F-75005 Paris, France (CNRS-UMR 8112)
3California Institute of Technology, Downs Laboratory of Physics 320-47, Pasadena, CA 91125, USA
4Max Planck Institute f¨ ur Extraterrestrische Physik, Postfach 1312, 85741, Garching, Germany
Accepted ; Received ; in original form
ABSTRACT
In this paper, we investigate the relevance of using the12CO line emissions as in-
dicators of star formation rates (SFR). For the first time, we present this study for
a relatively large number of12CO transitions (12) as well as over a large interval
in redshift (from z∼0 to z∼6). For the nearby sources (D?10 Mpc), we have used
homogeneous sample of12CO data provided by Bayet et al. (2004, 2006), mixing
observational and modelled line intensities. For higher-z sources (z ? 1), we have col-
lected12CO observations from various papers and have completed the data set of line
intensities with model predictions which we also present in this paper. Finally, for
increasing the statistics, we have included recent12CO(1-0) and12CO(3-2) observa-
tions of intermediate-z sources. Linear regressions have been calculated for identifying
the tightest SFR-12CO line luminosity relationships. We show that the total
the12CO(5-4), the12CO(6-5) and the12CO(7-6) luminosities are the best indicators
of SFR (as measured by the far-infrared luminosity). Comparisons with theoretical
approaches from Krumholz and Thompson (2007) and Narayanan et al. (2008) are
also performed in this paper. Although in general agreement, the predictions made
by these authors and the observational results we present here show small and inter-
esting discrepancies. In particular, the slope of the linear regressions, for Jupper? 4
12CO lines are not similar between theoretical studies and observations. On one hand,
a larger high-J12CO data set of observations might help to better agree with mod-
els, increasing the statistics. On the other hand, theoretical studies extended to high
redshift sources might also reduce such discrepancies.
12CO,
Key words:
infrared:galaxies
Galaxies: starburst-nuclei-ISM – Submillimeter – ISM: molecules –
1 INTRODUCTION
Fifty years ago, it has been showed that the star formation
rate (hereafter SFR) is intimately linked with the reservoir
of the gas from which stars are forming (Schmidt 1959). The
Kennicutt-Schmidt power law parameterized on local galax-
ies by Kennicutt (1998a,b); Kennicutt et al. (2007) has led
to an SFR index of N=1.4±0.15. Since late 90s, researchers
have converted the Kennicutt-Schmidt law into a more in-
teresting relationship connecting the SFR (traced by the
infrared luminosity - hereafter Lir) to the mass of molecular
gas, investigating various molecular tracers. Firstly, Sanders
et al. (1991); Sanders & Mirabel (1996) have showed that
?E-mail:
tgp@submm.caltech.edu; contursi@mpe.mpg.de
eb@star.ucl.ac.uk;gerin@@lra.ens.fr;
the SFR is roughly proportional to the
(hereafter CO(1-0)) luminosity (slope of 1.4-1.6, consistent
with the Kennicutt-Schmidt law index). This SFR-CO(1-
0) relationship has been broadly interpreted as an increase
of star formation efficiency as a function of molecular gas
mass (and density). More recent analysis focussing on trac-
ers of dense molecular gas such as the HCN(1-0) line (Gao
& Solomon 2004a,b; Wu et al. 2005), the HCN(3-2) line
(Bussmann et al. 2008) or the CO(3-2) line (Yao et al. 2003;
Narayanan et al. 2005), have shown that these transitions
are likely to be better indicators of star formation rate than
the total H2 content (traced by the CO(1-0) luminosity).
Indeed, the CO(1-0) line can be excited at rather low den-
sities (∼ 102−103cm−3) and low temperature (∼ 5K above
ground) whereas the higher-J CO transitions and the HCN
lines trace denser and warmer gas, more closely connected
12CO(J=1-0) line
arXiv:0906.2975v1 [astro-ph.CO] 16 Jun 2009
Page 2
2Bayet et al.
with the stars in formation. However, recent modelling work
(Krumholz & Thompson 2007; Narayanan et al. 2008) show
that this situation is more complex than it appears, involv-
ing in particular the values of the molecular line critical den-
sities as compared with the mean gas density of the observed
regions.
So far, none of observational or modelling work in-
vestigate the relationship between the SFR and molecular
gas tracers both for several transitions (>2) of the same
molecule (here CO) and over several factors of redshift (here
z≈0-6). In this paper, the influence of the high-J CO lines
is especially studied. This is motivated by the fact that,
in addition to obtain much more accurate estimation of the
CO line luminosities when adding the high-J transitions (see
Bayet et al. 2004, 2006), more subtle effect may be revealed
by these lines, when considering their respective critical den-
sities.
The knowledge of the global star formation history, and
for individual galaxies, of their actual and past star forma-
tion rate, is a key item for understanding galaxy evolution,
and for comparing with state-of-the-art models. Statistical
relations linking star formation properties with other galaxy
global characteristics established by observing nearby galax-
ies, have been already used to understand the processes rul-
ing the large scale star forming activities (e.g. Malhotra et al.
2001; Boselli et al. 2002). Such trends can afterwards be used
in the large scale cosmological models, which lack the spatial
and temporal resolution to describe the local details of star
formation in individual galaxies.
In this paper, we have thus compared the CO lines emis-
sions (from J=1-0 to J=12-11 transitions) with the infrared
emission, for the nearby galaxies we have surveyed using
the Caltech Submillimeter Observatory (CSO) (see Bayet
et al. 2004, 2006). We extended this comparison to higher
redshifted sources (z = 1.4-6.4) for which CO line emissions
have been previously observed (Cox et al. 2002; Bertoldi
et al. 2003; Pety et al. 2004; Walter et al. 2004; Greve et al.
2005; Solomon & Vanden Bout 2005; Tacconi et al. 2006;
Weiß et al. 2007). For these distant objects, we derived the
total and the individual CO line emissions (from J=1-0 to
J=12-11) by the same approach as the one presented in
Bayet et al. (2004, 2006). In order to strengthen the results
in a more statistical point of view, we finally have included
additional literature CO(1-0) and CO(3-2) data from Gao &
Solomon (2004a,b); Yao et al. (2003) and Narayanan et al.
(2005), respectively.
The paper is divided straightforwardly as followed: Sect.
2 presents the data sample while Sect. 3 lists the results we
have obtained, focussing especially on the comparison with
the model predictions from Krumholz & Thompson (2007)
and Narayanan et al. (2008). Finally, we conclude in Sect.
4.
2 SAMPLE SELECTION
It has been crucial to determine, or find in the literature, the
total CO line emission as well as the individual line emis-
sions of the CO transitions from J=1-0 to J=12-11. The
total infrared luminosity (from 8 to 1000 µm) for both the
nearby and the high-z sources has also been crucial to deter-
mine. Here, we have converted all the gathered data, for the
Table 1. List of the detected CO lines for nearby galaxies in-
cluded in this study. These CO lines detections are from Bayet
et al. (2004, 2006). Similar information for distant sources is found
in Fig. 1 (observations represented by black bullets). When the
line is not detected, we have used its corresponding predicted
emission from modelling work (see Subsects. 2.1 and 2.2). For the
Antennae sources (NGC 4038 and Overlap), the12CO(4-3) and
12CO(7-6) lines have been observed by Bayet et al. (2006) but
they suffer from large uncertainties. Therefore, we used for these
two objects and two transitions, rather the corresponding best
model predictions.
Name Distance detected12CO lines
Nearby sources
IC 10
NGC 253
IC 342
He 2-10
NGC 4038
Overlapa
M 83
NGC 6946
(Mpc)
1.01
2.52
1.83
9.04
13.85
13.85
3.56
5.57
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5, 7-6
1-0, 2-1, 3-2, 4-3, 6-5
1-0, 2-1, 3-2, 4-3, 6-5
a: Overlap corresponds to a shifted position from the NGC 4039
nucleus in the Antennae Galaxy which shows a high gas density
(see Bayet et al. 2006). References:1: Massey & Armandroff
(1995);2: Adopted value from Mauersberger et al. (1996);3:
McCall (1989);4: Kobulnicky & Johnson (1999);5: Saviane
et al. (2004);6: Thim et al. (2003) and7: Tully (1988).
first time, into a coherent and homogeneous sample we have
corrected for various effects, as described below. In Table 1
and Fig. 1, the observed CO data for nearby and distant
sources are presented, respectively. Model predictions go up
to the J=15-14 transition of CO, consistently to the work of
Bayet et al. (2004, 2006). However, we have restricted our
study to only the first 12 CO transitions, higher-J CO lines
having very weak intensity (see Bayet et al. 2004, 2006 and
Fig. 1). In the rest of the paper, the total CO will thus refer
to the sum of only the first 12 CO transitions.
2.1Nearby sources
The CO data we are using in this study for the nearby
sources are from the observational and modelling work of
Bayet et al. (2004, 2006). They already provided a consis-
tent line intensity sample for 8 nearby (<10 Mpc) galaxies:
NGC 253, IC 10, IC 342, NGC 6946, M 83, Henize 2-10
and the Antennae (NGC 4038 and Overlap) from CO(1-0)
to CO(15-14). We converted the first twelve CO integrated
line intensities into luminosities (in Kkms−1pc2) using the
formulae in Solomon & Vanden Bout (2005):
L?
CO= 3.25 × 107× SCO∆v × ν−2
where z is the redshift1, νobs is the observed frequency2
(in GHz) of the CO line, SCO∆v is the CO integrated line
intensities (in Jykms−1) and DL is the luminosity distance
obs× (1 + z)−3× D2
L
(1)
1For nearby sources we used the NED database values of z.
2The observed frequency is equal to the rest frequency νrest
divided by (1+z).
Page 3
Star formation indicators3
(in Mpc)3. The total CO luminosity has been obtained by
summing the individual CO line luminosities converted pre-
viously from Eq. 1 into solar luminosity units (L?) to avoid
any frequency bias in the SFR-total CO relationship. Table
2 summaries the results obtained.
The infrared data used for the nearby sources and, more
generally in the whole paper, are from Sanders et al. (2003).
For consistency with the additional literature data described
in Subsect. 2.3, we chose to use the total infrared luminosity
from 8 µm to 1000 µm (LIR:8−1000µm), thereby including
the continuum emission shorter than 60 µm affected by the
contribution from very small grains. This total infrared lu-
minosity is known to be contaminated by a possible AGN
contribution (see also Graci´ a-Carpio et al. 2008). In partic-
ular, the AGN yield can be fairly large in the MIR range
(e.g Rowan-Robinson & Crawford 1989) in active galaxies
such as LIRGs and ULIRGs. However, for the sample of the
nearby sources we are studying here, this AGN contamina-
tion is considered as negligible since none of the 8 sources
(IC 10, NGC 253, IC 342, Henize 2-10, NGC 4038, Overlap,
M 83 and NGC 6946) is known for hosting an AGN (see
e.g. Leroy et al. 2006; Mart´ ın et al. 2006; Usero et al. 2006;
Wilson et al. 2000; Kramer et al. 2005; Israel & Baas 2001,
respectively).
A more important aspect for nearby sources is that
the CO measurements (both observations and model predic-
tions) referred to an aperture of 22??, as described by Bayet
et al. (2004, 2006), while the infrared data from Sanders
et al. (2003) showed a higher aperture (80??). Thus, in Fig. 2
where we present various SFR-CO luminosity relationships
(see Sect. 3), we compare, for nearby sources, two emit-
ting regions which are not spatially identical. Indeed, the
region which emits the infrared luminosity is larger than
the region where CO is detected. It is the same case for the
intermediate-z data (Subsect. 2.3) but this problem does
not appear in the case of higher-z sources since they are
seen as point-like sources in both the sub-mm/mm and in-
frared wavelengths. To correct this effect on nearby and
intermediate-z sources, we have estimated a factor between
the CO and the infrared luminosities resolution via the dust
emission traced by SCUBA maps at 850 µm. We have de-
rived from these maps the luminosity (removing the back-
ground contribution) of the 850 µm emission at a spatial
resolution of 22??and 80??, for the sources available in the
SCUBA archive. We have then calculated the ratio between
the emissions observed at 22??and 80??that we have applied
to the infrared data. We have obtained ratios varying from
2.3 to 6.5, depending on the source. Rather than the 450
µm SCUBA maps, we have chosen the 850µm SCUBA maps
because they show a better signal-to-noise ratio. Neverthe-
less, we checked that the factors obtained at 850µm were
in agreement with the ones at 450µm (difference obtained
being less than 2%). After having applied such correction to
the infrared data of the galaxies in common to this paper
and the SCUBA archive, we have however obtained similar
results to those listed in Table 3 and presented in Fig. 2
3For
nosity
http://www.astro.ucla.edu/∼wright/CosmoCalc.html, within a
cosmology of Ho= 77 kms−1Mpc−1, ΩM=0.27 and ΩV =0.73.
all
distance
thesources,
using
weobtained
site
thelumi-
the webcalculator of
which show non-aperture corrected data. The slopes did not
show changes greater than 5% in their values, depending on
the SFR-CO line luminosity relationship studied. Due to the
fact that all the data could not be corrected consistently for
this effect since the galaxies presented here have not been all
observed by SCUBA (e.g IC 342), we thus have decided to
keep non-corrected infrared data in Fig. 2, increasing how-
ever the error bars on the slope values by 5% in Table 3.
Both the (non-aperture corrected) infrared and the CO
luminosities used in the Fig. 2 are listed in Table 2.
2.2High-z sources
So far, a complete observed CO SED does not exist for J=1-0
to J=12-11 neither for nearby nor high-z sources.
At high redshift, various CO transitions have been how-
ever already detected (e.g. Cox et al. 2002; Bertoldi et al.
2003; Pety et al. 2004; Walter et al. 2004; Greve et al.
2005; Solomon & Vanden Bout 2005; Tacconi et al. 2006;
Weiß et al. 2007). Most of these data are summarized in
Solomon & Vanden Bout (2005). In our study, we restricted
the number of studied sources presented in Solomon & Van-
den Bout (2005) to ten objects : 4C60.07, APM 082794,
Cloverleaf QSO, SMM J14011, VCV J1409, PSSJ2322, TN
J0924, SDSS J1148, IRAS F10214 and HR 10, keeping only
those which show at least two CO line detections. Indeed,
to correctly constrain the models which estimate the miss-
ing line emissions (LVG models, see Appendix A) and derive
relevant predicted CO line intensities, it is crucial to have
as many CO line detections as possible. This is why we have
rejected from our study high-z sources presented in Solomon
& Vanden Bout (2005) with only one CO line observed.
To estimate the total CO luminosity as well as the in-
dividual missing molecular CO line luminosities in these
sources, we have used a single-component Large Velocity
Gradient (LVG) model as done in Bayet et al. (2004, 2006).
The obtained line intensity predictions (see Fig. 1) corre-
spond to a beam size of 22??, consistently with other data
sets. The goal of the paper is to investigate the SFR-
molecular CO line luminosity relationships. Thus, we will
not discuss further the physical properties of the molecular
gas we have obtained using the LVG model. Nonetheless, we
present them in Appendix A.
In Fig. 1, we have superimposed on the CO observa-
tions (black bullets with error bars), the predicted emis-
sions of both the observed and the missing CO lines (grey
filled triangles). Similarly to the nearby sources case, the
total CO luminosity has been obtained by summing the in-
dividual CO line luminosities converted previously from Eq.
1 into solar luminosity units (L?) to avoid any frequency
bias in the SFR-total CO relationship. More precisely, we
have used the observed velocity-integrated CO line fluxes
(SCO∆v in Jykms−1) when detected and the predicted val-
ues when not. The redshift values used in Eq. 1 are those
presented in Solomon & Vanden Bout (2005).
We did not need to correct the CO line luminosities
for any beam dilution effect since the high-z galaxies are
4For this source, we rather used more recent CO data from Weiß
et al. (2007)
Page 4
4 Bayet et al.
point-like sources within telescope beams and show unre-
solved emissions whatever these wavelengths. However, some
of these distant objects are lensed. Thus, we have applied
the factor of lens magnification listed in Solomon & Vanden
Bout (2005) to all the CO line luminosities. The underlying
assumption of such a correction is that the gravitational lens
magnifies similarly the emission from compact and warm re-
gions usually traced by high-J CO lines such as the CO(7-6)
line and the regions more extended normally traced by typ-
ical low-J lines such as the CO(1-0) transition. In principle,
this is a relevant assumption since the properties of the lens
does not depend on the magnified source but only on the
properties of the galaxies separated the observer from the
studied source.
For the infrared luminosity, we used the integrated val-
ues (“LFIR(int.)”) listed in Table 1 of Solomon & Vanden
Bout (2005), corresponding to infrared emission corrected
for lens magnification. After having checked several refer-
ences in this table, it appears that the “LFIR(int.)” values
are similar to the LIR:8−1000µm presented in Sanders et al.
(2003) (see the example of HR 10 for which Dey et al. 1999
derived the infrared luminosity by fitting the dust SED on
a rest wavelength range from 10 µm to 2 cm.).
For these distant sources, we also present in Table 2,
both the infrared and the CO luminosities we have used in
Fig. 2.
2.3 Intermediate-z data from the literature
We have included in our study CO data from observations
at intermediate redshift (within similar beam sizes) to bet-
ter constrain the SFR-molecular CO line luminosity rela-
tionships, and especially increase the statistics. These data
are either from Gao & Solomon (2004a,b) (CO(1-0) tran-
sition observed with a 22??beam size), or from Yao et al.
(2003) and Narayanan et al. (2005) (CO(3-2) line observed
with a 15??and 22??beam sizes, respectively). We have not
included the CO(2-1) data reported in Rigopoulou et al.
(1996) (beam size of 23??) because they appear inconsistent
with those presented in Yao et al. (2003); Gao & Solomon
(2004a,b); Narayanan et al. (2005). We have included in our
SFR-CO relationships the observed and modelling results
dedicated to Markarian 231 (Papadopoulos et al. 2007), pro-
viding CO line luminosities estimations up to the CO(10-9).
For the infrared luminosity values, we have used the values
reported in Sanders et al. (2003) and not those listed in each
corresponding papers.
The additional sources included here are seen to be
mostly LIRGs and ULIRGs (at a distance > 10 Mpc). Ra-
dio continuum maps (Condon et al. 1990), and the HI and
SCUBA 850 µm maps (Thompson et al. 2002), show that
much of the emission of the objects is extended with re-
spect to the beam size of 15??. However, in recent high-
resolution (2??-3??) millimeter wave observations of seven
LIRGs/ULIRGs, Bryant & Scoville (1999) find that nearly
all of the detected CO(J=1-0) emission is concentrated
within the central 1.6kpc in six of seven objects. Because it
is unlikely that there will be significant high-J CO emission
where there is no CO(1-0) detected, we assume that all of the
emitting gas in these additional sources is confined within
the same region. Consequently, we have not converted the
14??beam data into that for a 22??beam.
As for nearby galaxies, the infrared luminosities of these
sources are expressed for a larger aperture than the one used
for the CO data. As previously mentioned (see Subsect. 2.1),
this effect on the SFR-CO line luminosity relationship has
been investigated through SCUBA data. Unfortunately, as
for the case of nearby galaxies, the intermediate-z sources we
are using here have indeed not been all observed by SCUBA,
therefore no correction on their infrared data has been per-
formed directly. We have however taken fully into account
the effect of different spatial resolutions on the slope val-
ues listed in Table 3 (increased error bars as explained in
Subsect. 2.1).
In the samples presented in Yao et al. (2003); Gao &
Solomon (2004a,b); Narayanan et al. (2005), some sources
such as ARP 220 are in common. For removing any calibra-
tion effects on the SFR-CO relationships, we have followed
the recommendation of Narayanan et al. (2005) and applied
their scaling factor equal to 0.26 for the CO(3-2) and to 0.45
for the CO(1-0). They specified that this effect may indeed
occur when various instruments (and thus various calibra-
tion processes) are used.
Note that the intermediate-z sources increase signifi-
cantly the number of CO observations used in the correla-
tions either in the SFR-CO(1-0) line luminosity or in the
SFR-CO(3-2) line luminosity relationships (see triangles in
Fig. 2 as well as the fourth column in Table 3). This strength-
ens the corresponding results.
3 RESULTS
3.1General arguments
We present in Fig. 2, the SFR-CO line luminosity relation-
ships we have obtained for the total CO line emission, the
CO(1-0), CO(3-2) and CO(7-6) line emissions. In the same
vein, we have obtained the SFR-CO line luminosity relation-
ships for the other CO transitions: J=2-1 and from J=4-3
to J=12-11. SFR-CO luminosity relationships for CO data
higher than CO(7-6) are less relevant than the correlation in-
volving lower-J CO lines. Indeed, most of the data in CO(8-
7), CO(9-8), CO(10-9), CO(11-10) and CO(12-11) are from
modelled fit, similarly to the fits presented in Fig. 1. In such
cases, correlations between the SFR and the CO luminosity
are not constrained by many observational measures. Thus,
we exclude these correlations from the following analysis.
As one can see in Fig. 2, a proportionality exists be-
tween the CO and infrared luminosities over a large range
of redshift (galaxies from z∼ 0 up to z∼ 6 sources). This
characteristic has been previously seen (Sanders et al. 1991;
Sanders & Mirabel 1996 and references therein) although
this sample was more restricted in redshift than the one we
present in this paper. It has been interpreted as an increas-
ing star formation efficiency (SFE; SFR divided by M(H2))
as a function of molecular gas mass. Here, our data sample
confirms this broad interpretation.
To quantify better these relationships, we performed
linear regressions (using the software xmgrace). The corre-
sponding output parameters are listed in Table 3. Note that
IC 10 has been excluded from these calculations. For the
SFR-CO(3-2) relationship we have also excluded NGC 7817,
as Narayanan et al. (2005) suggested. Indeed these two
Page 5
Star formation indicators5
Figure 1. Observed and predicted CO spectral energy distributions (Jykms−1) of the following high redshift sources (from top to bottom,
and by increasing order of redshift): HR 10, IRAS F10214, The Cloverleaf QSO, SMM J14011, VCV J1409, 4C60.06, APM 08279, PSS
J2322, TN J0924 and SDSS J1148 (see plots). Observations and their corresponding error bars are represented by black bullets (see
references listed in Solomon & Vanden Bout 2005) while LVG predictions (see Appendix A) are symbolized with grey triangles. To make
the plots more easily readable, we have connected the CO LVG predictions (grey lines). One could notice that, except for the source
HR 10, the position of the maximum of the SED is located at rather high-J (Jupper ?4).