Astron. Astrophys. 360, 562-574 (2000)
5. Results
Table 1 lists the derived parameters and their uncertainties
obtained from the for the different
bands. The corresponding best fits can be seen in Figs. 10 to 14.
For all the bands the derived parameters yield a maximum
optical depth for each of the
spectral windows. As the optically thin models are a subset of the
parameter space we studied, the first obvious conclusion is that the
observations are better explained by an optically thick model than an
optically thin one.
![[FIGURE]](img140.gif) |
Fig. 10. The 13.48 µm region. The SWS observations are the diamonds connected with the grey line; the observational uncertainties are indicated by the vertical lines. The solid line is the best fitting model (see Table 1). The dotted line is the continuum as in Fig. 2 ; the dashed line indicates the continuum shift derived by the minimization procedure. Note the fringe residuals in this wavelength region.
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![[FIGURE]](img144.gif) |
Fig. 12. Same as Fig. 10 for the 14.98 µm region. Note the sharp peak indicating the presence of a much cooler layer on top of a warmer layer.
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![[TABLE]](img152.gif)
Table 1. The derived parameters for all the bands using a single layer LTE model. The errors stated are the formal errors based on the analysis.
It can easily be seen from Eq. (14) that for the case of
optically thick bands and hence in
our model the observed peak intensity is a good measure of the extent
R of the emitting region.
5.1. Temperatures
The whole spectrum cannot be reproduced at once by a single layer
model. The temperatures derived for the individual bands are
significantly different, reminiscent of a temperature stratification
in the extended atmosphere. Q-branch bands arising from higher
vibrational levels are then probing the hotter material closer to the
central star, while the emission from lower vibrational levels arises
from cooler material further out.
However, as can be seen from Fig. 5, any given band becomes
stronger when increasing the temperature. When deriving the parameters
for a given band, one might therefore expect to see a significant
contribution from the hotter layers as those hotter layers always show
stronger emission in the bands arising from lower vibrational levels
(see Fig. 5). However, as a consequence of all the bands being
optically thick, emission from the hotter layers is shielded from view
at those wavelengths where a cooler layer shows prominent emission
features. On the other hand, a contribution from the cooler layers
might be present at those wavelengths in the spectrum where the hotter
layers are visible if the cooler material is optically thin at those
wavelengths.
As a consistency check we therefore performed a test calculation
for the 13.48 and 13.87 µm bands with a two-layer model
using the parameters from Table 1. The 13.87 µm band
is indeed quite unaffected by the presence of the
K layer, but the flux in the 13.48
µm band shows a significant contribution due to the
K layer. The main effect is that
the extent for the warmer layer
decreases when compared to the single layer model and thus the
values listed in Table 1 are
probably too high.
All the bands are reasonably well reproduced by a single layer
model except for the 14.98 µm band. Upon inspection of
the peak position, it is obvious that an extra cool
( K) and optically thin emission
component is necessary on top of the warmer component to reproduce the
overall band shape. This component is probably the result of the
dissociation of water into OH molecules by the interstellar UV field
followed by a reaction with CO which could produce CO2 with
a maximum CO2 abundance of typically
10 at a few hundred stellar radii
where the temperature is of the order of 100 K Willacy & Millar
1997. Moreover, as the hot bands are consecutively shifted to the blue
(see Fig. 3) and as these Q-branch transitions (fundamental as
well as hot bands) have the highest Einstein A values in the
observed wavelength range, it can be expected that this band is
optically thick at all wavelengths. The shape of this band will
therefore be the most sensitive to a temperature stratification and
the temperature derived for this band with the single-layer model is
probably somewhere in between the warmer and the coolest layers. A
two-layer model with K,
10
and 100-150
for the second layer is indeed able
to reproduce the observed spectrum much better. Also the other derived
parameters are probably not very reliable for this band. As the
Einstein A coefficients for this band are rather high, one
could expect to find the same problem for the fundamental
13CO2 bending mode at 15.40 µm even
though the 13CO2 column density is much lower.
This band however is buried in the forest of P-branch lines of the
14.98 µm 12CO2 band and therefore
this effect is not obvious. Nevertheless the observations clearly show
that the CO2 layer is extended and that the temperature
decreases with increasing radius (see Fig. 15).
![[FIGURE]](img162.gif) |
Fig. 15. The filled circles are the temperatures and corresponding radii derived from the observation. The solid lines are temperature profiles with (from top to bottom) =0.4,0.5,0.7.
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5.2. Column densities
The derived column densities are 10
cm-2 for all bands except for the 14.98 µm
band, where the column density is slightly higher. As discussed in the
previous paragraph, this is a consequence of a temperature
stratification and the presence of hot bands in the spectrum as well
as the presence of a much cooler layer.
5.3. Isotopic ratio
On first sight there is not a single value for the
12C/13C ratio that is compatible with the
results derived for the bands individually. However, the problem with
the temperature stratification mentioned above will influence the
12C/13C ratio derived for both the 14.98 and
15.40 µm bands and hence the values for these bands are
doubtful. The 16.18 µm band on the other hand is rather
insensitive for the adopted 12C/13C ratio as can
be seen from the uncertainties. As the 13.48 µm band has
the lowest optical depth, this would be the best band to derive the
12C/13C ratio. However, this is the weakest band
and unfortunately the quality of the spectrum in this region is not
too good (see Fig. 10) due to fringe residuals, which hampers a
good determination of the 12C/13C ratio. The
best guess for the 12C/13C ratio is probably the
one derived for the 13.87 µm band which is both very
sensitive to the contribution of 13CO2 and not
too optically thick. We find a 12C/13C ratio
value of 10 for this band.
© European Southern Observatory (ESO) 2000
Online publication: August 17, 2000
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