## 3. The mapped core regionWe describe in this section the results of our mapping as well as our measurements at selected positions. ## 3.1. Maps in (10) and (21)Our integrated intensity maps in (21) and (10) are presented in Fig. 1a and 1b respectively. The main feature of the maps Fig. 1 is a structure of dimension roughly N-S (0.27 pc) which extends further in the E-W direction than the boundaries of our map. While peaks are clearly observable in our integrated map (e.g. at
offsets (0,0) and
(,)),
there is rather little contrast over the main structure. If one
considers only that part of the cloud with integrated
(10)
intensity above 1 Kkms Our data do show evidence of velocity structure within the cloud.
This is evident when one examines Fig. 2 which shows observed spectra
towards the central region of our map. There are clearly regions (e.g.
around (0,)) where we observe two or
more distinct velocity components. The line widths of individual
components are relatively small and range down to 0.4 km
s
More typical is a single Gaussian shaped line profile with a
typical width of kms ## 3.2. The velocity fieldChannel maps (Fig. 3) and position-velocity plots of the
data reveal better than the maps of
integrated intensities the fragmented spatial and kinematic structure
of the observed region. At velocities
kms
## 3.3. The distribution of clumpsIn order to quantify the structure better we decomposed the
observed
(10)
dataset iteratively into 26 Gaussian shaped clumps using an automated
algorithm developed by Stutzki & Güsten (1990) and discussed
recently by Kramer et al. (1998b). The residual emission not
decomposed into clumps is 5 above
the noise level. From the decomposed clumps we only selected clumps
with deconvolved widths of at least 50% of the resolutions in all
three dimensions
(,, Most clumps show deconvolved radii close to the limit set by the resolution, though the size number distribution extends to radii of 0.1 pc (). The average beam deconvolved aspect ratio of the larger clumps is 2.8. Clumps are generally aligned with the filamentary structure already found in the channel maps (Fig. 3). The number distribution of position angles of the clump elongations shows two maxima, a strong at and a weaker at , which correspond to the position angles of the two filaments described above. The number distribution of deconvolved clump line widths shows a
maximum at kms In Fig. 4 we plot the dependence of the velocity FWHM
and mass
To calculate clump masses from
intensities and column densities we assume optically thin emission, an
excitation temperature of 10 K, LTE, and a standard abundance ratio
[]/[H The dynamical timescale of the clumps should be roughly
where For comparison with LTE masses we also calculated virial masses
from linewidths assuming
gravitational boundedness and neglecting e.g. external pressure. All
clumps are near, but slightly above, virial equilibrium:
(Fig. 5). The average ratio is
.
## 3.4. spectraThe simplest check on whether the lines are optically thick is to measure the spectra of the rarer CO isotopomer . We thus took spectra at 24 positions (see Fig. 1b) mainly along a diagonal cut through the mapped core region, including the position of the peak in visual extinction of 28 mag (Fig. 1a), and at 7 positions in the direction of background stars. To estimate upper limits for, or if possible to determine, the optical depth , we then applied two techniques. First, we obtained a limit on the (10) optical depth using the measured relative intensities of the three hyperfine satellites of this transition (see Frerking & Langer 1981 for the 10 transition, and Lovas & Krupenie 1974, Townes & Schawlow 1975 for 21, cf. Ladd et al. 1998). Deviations from the intrinsic relative line strengths are an indication of high optical depth. We transform this into a limit on the (10) optical depth using an assumed relative abundance for []/[] of 3.65 (Wilson & Rood 1994, Penzias 1981). At all positions observed in we find . A second technique is simply to use the measured ratio of integrated intensities of the and corresponding lines. With the plausible assumptions of equal excitation temperatures and beam filling factors for both isotopomers one then has for the ratio of integrated and line intensities that: This may be solved to determine the optical depth , averaged over the spectral line, in the 10 or 21 transitions. This latter technique yields more critical limits since it measures directly saturation effects in the more abundant isotope. The limits obtained are given in Table 1. We find 3.0 at all positions observed in . In other words, no evidence is found in our data for compact clumps with (10) optical depths higher than 0.5. We believe that 0.5 is a conservative upper limit and our data set
is consistent with optically thin
(10)
emission at To make this clearer, we used integrated intensities
(Table 1) of
, which is certainly optically thin,
to calculate the corresponding
intensities, , and to compare the
ratio
/
with the corresponding ratio
/
(Table 1) calculated from the One could in principle apply the same techniques as above to derive
upper limits on the optical depth in the
(21)
line. However, we conclude that the quality of our
(10) data is such that it is more
accurate to use the fact that (see next section) the excitation
temperature between the For in the range 6-10 K, varies between 1.2 and 1.9. Thus, we expect the (21) optical depth to be relatively well constrained by the limits obtained for (10), and that at all positions observed in , the (21) optical depth is less than 1. From this analysis, we can only put limits on the optical depth over the region covered by our measurements. We cannot exclude the possibility that the optical depth becomes high in regions of our map for which data are unavailable. This possibility however seems unlikely. There is no evidence for example (see next section) that the molecular excitation is different outside the region observed in . There is also no evidence for larger linewidths. We conclude therefore that the optical depth is low, i.e. , throughout the region mapped and that can be used to obtain reliable estimates of CO column density. ## 3.5. excitationIn Fig. 6, we display our map of the integrated main beam intensity ratios defined by:
The mean and scatter are =0.830.22. Note that the observational error on the line ratio is very similar, %. Another view is given by Fig. 8b which shows that the (21)/(10) ratio varies between 0.4 and 1.3 along a NW-SE cut. Assuming optically thin emission in both lines, and equal excitation temperature and beam filling factor for both transitions, we find for the ratio of integrated intensities: where , , (21), and (10). The quantity is a slowly varying function of of order unity. From Eq. 4, we find that varies between 4 K and 9 K along the cut. The average ratio of 0.8 corresponds to an excitation temperature of 6 K. We conclude that either the kinetic temperatures in the shielded cloud interiors are small ( K) or the excitation is sub-thermal, i.e. densities are low. We can investigate the latter point using an LVG analysis for
using collision rates from McKee et
al. (1982). This radiative transfer model assumes a constant kinetic
temperature, column- and volume density to calculate the emergent line
temperatures and optical depths as well as the level populations and
excitation temperatures. Since the observed lines are essentially
optically thin, the magnitude of
column densities has only little influence on the ratios, i.e.
trapping plays a negligible role. In Fig. 7 we show computed values of
the line ratio (Eq. 3) as a
function of local densities
(H
## 3.6. Column density ofOne can slightly improve the accuracy of the column density determination relative to the simple LTE method, because we have two transitions and can thus estimate the molecular excitation. We assume a kinetic temperature of 10 K and use the LVG model to determine the fraction of molecules in rotational states from the observed intensity ratio . Then the "LVG column density" is determined on the basis of the observed intensity in (10) assuming it is optically thin. The results are shown in Fig. 8c along a NW-SE cut (see Fig. 1). A lower limit was computed assuming only the two lowest levels to be populated and an "upper limit" computed on the basis of the (10) intensity assuming LTE with = 6 K, the lowest temperature consistent with the average ratio of 0.8 (Fig. 7). One sees from this that the column density is certainly determined by our measurements to better than a factor of two.
Next, we used the same method to derive LVG column densities over the mapped region for all positions with integrated intensities a factor 6 above the noise level (Fig. 9). To allow a comparison with the NIR data, we smoothed the (10) and (21) maps with a Gaussian to a resolution of sampled on a grid.
The LVG column density varies by
less than a factor of 3 between and
cm obtained with the above ratios. The visual extinction thus derived
from the above H Using the LVG model, our limits on the
opacity show that a
column density of
cm © European Southern Observatory (ESO) 1999 Online publication: December 22, 1998 |