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Astron. Astrophys. 320, 972-992 (1997)

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3. Results and analysis

3.1. G 353.1+0.6

3.1.1. Morphology

Fig. 1 shows all the 12 CO(1-0) spectra taken towards this source, with the emission between -20 and 20  [FORMULA], while in Fig. 2 and 3 we present all the spectra taken along the strips at [FORMULA] = [FORMULA] and [FORMULA] =- [FORMULA], respectively. The bulk of the emission is between [FORMULA] =-10 and +6  [FORMULA], and shows a rather complex behaviour, with shape and intensity (max. [FORMULA] [FORMULA] 40 K) changing significantly over separations of a single beam. This broad emission feature is likely to be made up of individual, narrower components, with different velocities which contribute at different locations. We shall later discuss this broad emission in terms of individual components. In addition there is weaker and narrower emission at about -40  [FORMULA], with a maximum temperature of a few K, which does not change appreciably with position. This latter component is probably not related to the radio source [the [FORMULA] of the ionized gas is [FORMULA]   [FORMULA] (H109 [FORMULA], Wilson et al. 1970)], and it will not be considered further.

[FIGURE] Fig. 1. All 12 CO(1-0) spectra taken towards G353.1+0.6. Velocity and temperature scale are indicated in the upper right-hand corner.
[FIGURE] Fig. 2. Spectra of all observed lines in G353.1+0.6 along the strip at [FORMULA]. Transitions and temperature scale are indicated above each column; velocity ranges are indicated below.

[FIGURE] Fig. 3. Same as Fig. 2, for the strip at [FORMULA].

Comparison of 12 CO(1-0) integrated intensity with the red plate of the ESO/SRC Atlas (see Fig. 16 of Fea90) shows that the lower contours in the southern part of the molecular cloud run parallel to the ionization front, which is north of the optically visible diffuse emission, at the border of a region of strong obscuration. The 12 CO emission peaks further north in the region of obscuration.

Based on channel maps and velocity-position contour diagrams, we have identified several distinct emission components (clouds) within the observed field. Fig. 4 shows velocity-declination contour diagrams of 5 transitions along the two strips at [FORMULA] [FORMULA] and [FORMULA]. Individual clouds are indicated by letters. Their position on the plane of the sky can be seen from integrated intensity contour plots over the appropriate velocity intervals (see Fig. 5). All components are incompletely mapped, and all, with the exception of A, have their peak emission outside the observed field. Note that the strong, narrow feature at [FORMULA][FORMULA] in the [FORMULA] -diagrams is not of interstellar origin, but is probably an interference spike.

[FIGURE] Fig. 4. [FORMULA] - [FORMULA] contour diagrams for the two strips in G353.1+0.6. Contour intervals ([FORMULA]) are: for 12 CO(1-0) and 12 CO(2-1) steps of 3 K from 2 K; for 13 CO(1-0) steps of 1 K from 0.5 K; for 13 CO(2-1) steps of 3 K from 2 K; for [FORMULA] (1-0) steps of 0.5 K from 0.5 K. Clouds discussed in the text are indicated by letters.
[FIGURE] Fig. 5. 12 CO(1-0) integrated intensity contour plots of G353.1+0.6. Velocity ranges are indicated at the bottom of each panel. Contour values, in the format low(step)high, are: 1(2)7, 10(10)50, 70(20)150 K [FORMULA]. The 10 K [FORMULA] contour is drawn thicker. The clouds discussed in the text are indicated by letters.

The narrow component D at 6  [FORMULA] (see Fig. 4) does not seem to be related to the ionization front. In fact it is visible over the whole field, with [FORMULA] [FORMULA] 9 K and a line width [FORMULA] 1.4  [FORMULA], thus resembling a quiescent dark cloud. It has been detected only in 12 CO(1-0), 12 CO(2-1) and 13 CO(1-0) and the ratio of 12 CO(2-1) and 12 CO(1-0) peak temperatures is on average [FORMULA] 1, implying the emission comes from a cold, extended region with a relatively low density. The signature of this cloud has also been found through narrow absorption lines in H2 CO (Whiteoak & Gardner 1974) and OH (at 1667 MHz; Goss 1968). This, together with the radial velocity, forbidden according to the galactic circular rotation model, suggests that component D is due to a line-of-sight cloud, closer to the Sun than NGC 6357. Consequently, it will be excluded from further analysis. This cloud might be identified as dark cloud Kh 348 (Khavtassi 1955).

Figs. 4 and 5 show that the molecular cloud is composed of several distinct components. The most conspicuous structure is component A, which appears as an extended bright ([FORMULA] [FORMULA] 39 K) emission region centered near position ([FORMULA], [FORMULA])=(0,80) and covering the velocity interval from -12 to +2  [FORMULA]. Cloud A clearly lies north of the ionization front, but its lower isophotes in the southern part overlap the radio-continuum emission and tend to run parallel with it, suggesting an interaction between molecular and ionized gas. Component E represents an east-west filamentary structure, blue-shifted with respect to the peak velocity of component A, and clearly overlaps the ionization front. In the east, component E dominates the emission with [FORMULA] [FORMULA] 21 K. This suggests that cloud E lies in front of the ionized gas and obscures it, while cloud A bounds the HII region in the north. Component C consists essentially of a peak near the south-western edge of the VLA image, and is red-shifted with respect to the peak velocity of cloud A. Although our observations only partially cover it, it seems that molecular emission with roughly the same velocity as cloud C may be associated with the "West Arm" of Fea90 (see Fig. 5). Fig. 4 shows component B with [FORMULA] [FORMULA] 17 K north of component A. Since the corresponding peaks at [FORMULA] = [FORMULA] and [FORMULA] =- [FORMULA] have different velocities, component B may be composed of two clouds, to the east and west, but we have no observations at [FORMULA] outside the two strips. However, both clouds are very far from the ionization front and probably unrelated to it. Other weaker structures (F and H) lie south of the ionization front and have low [FORMULA] ; it is therefore difficult to say whether or not these represent small fragments associated with the HII region.

3.1.2. Self-absorption

At [FORMULA] [FORMULA] 0.7 [FORMULA] and around [FORMULA] [FORMULA] the 12 CO(1-0) contours have a `dip' in the line profiles over an area larger than the beam. This is well illustrated in the [FORMULA] - [FORMULA] diagram of Fig. 6. This feature might be due either to two components with slightly different velocities, or to absorption by cooler foreground material.

[FIGURE] Fig. 6. [FORMULA] - [FORMULA] contour diagrams at [FORMULA] for G353.1+0.6. a (left) 12 CO(1-0), b (right) 13 CO(1-0). Contour intervals ([FORMULA]) are in steps of 4 K from 2 K (a) and in steps of 1 K from 1 K (b).

The 13 CO spectra show no dip, and can be satisfactorily fitted by a combination of several gaussian emission components, which favours a (self-)absorption interpretation. On the other hand, the dip is not evident in the 12 CO(2-1) profile at [FORMULA], where self-absorption effects are expected to be more pronounced (Phillips et al. 1981). However, the 12 CO(1-0) and 12 CO(2-1) line profiles at the locations where the 12 CO(1-0) clearly shows a dip can be best approximated by the sum of up to four gaussians, one of which is in absorption, with roughly the same velocities in the two transitions, while emission-only gaussians never give good fits. The negative gaussian needed to fit the 12 CO(2-1) profiles is weaker than that for the 12 CO(1-0) transition.

The self-reversal is strongest at (0,0). We note that the dip is also clearly visible in the HCO [FORMULA] (1-0) line. Unfortunately, observations have been made with different beam widths, and in particular the HCO [FORMULA] and 12 CO(1-0) spectra are more beam diluted than those of 12 CO(2-1).

Given the similarity between the [FORMULA] - [FORMULA] diagrams of  Fig. 6 and the results of model computations of the emission profiles expected from a cloud surrounded by a colder shell (cf. Fig. 4 of Phillips et al. 1981) we believe that the dip is due to colder material surrounding component A, rather than due to a foreground cloud. Adopting a two-layer cloud model in which an absorbing layer with excitation temperature [FORMULA] and optical depth [FORMULA] surrounds a cloud with brightness temperature [FORMULA] ([FORMULA]), the observed main beam temperature of the dip, [FORMULA], is given by (Phillips et al. 1981)

[EQUATION]

where [FORMULA], [FORMULA], and [FORMULA] =2.7 K is the temperature of the background radiation.

Taking [FORMULA] equal to the peak [FORMULA] of the 12 CO(1-0) transition (39 K), an upper limit to [FORMULA] can be obtained assuming [FORMULA]. We find [FORMULA] 23 K at (0,0) and [FORMULA] 31 K at (0,40), two positions that we shall use as examples. But obviously [FORMULA] cannot be [FORMULA], otherwise we would see the absorbing component in the 13 CO(1-0) transition as well. Conversely, lower limits to [FORMULA] can be obtained from Eq. (1), assuming an excitation temperature [FORMULA]. Table 1 lists [FORMULA] for [FORMULA] = 5, 10, 15 K, the velocity dispersion [FORMULA] of the absorbing layer in the 12 CO(1-0) transition derived from the gaussian fits, and the FWHM [FORMULA] CO).


[TABLE]

Table 1. 12 CO(1-0) self-reversals and line widths at two positions in G353.1+0.6.


As noted above, the self-reversal is less strong in the 12 CO(2-1) than in the 12 CO(1-0) transition. This implies that either physical conditions in the absorbing layer cause the 12 CO(2-1) optical depth [FORMULA] to be smaller than [FORMULA], or the absorption is produced by many small clumps and their contribution is greater in the 12 CO(1-0) beam than in the 12 CO(2-1) beam. As shown by Loren et al. (1981), if the kinetic temperature is 5 K, then [FORMULA] for any density, and if [FORMULA] =10, 15 K, then with densities in the absorbing layer of [FORMULA] 500 cm-3, when [FORMULA] [FORMULA] 1 we still have [FORMULA].

Since we detect the dip in the [FORMULA] (1-0) transition, we can obtain a lower limit to [FORMULA] from Eq. (1) by assuming that [FORMULA] (HCO [FORMULA])= 3 K, roughly the background radiation temperature. At (0,0) we find [FORMULA] (HCO [FORMULA] 0.94.

In summary, a clumpy layer surrounding cloud A, at least 20 K cooler than the inside cloud, and with moderate optical depth, could explain the observed dip.

The 13 CO(1-0) line profile at the position where the 12 CO(1-0) dip is stronger can be fit by 2 main gaussian components and the dip is closer to the more red-shifted one ([FORMULA] [FORMULA]   [FORMULA]). The difference in velocity between the dip and the gaussian component is positive and of the order of 0.5  [FORMULA]. This could be indicative of a large scale motion of the external layers towards the inner parts of the cloud.

3.1.3. Variations in molecular emission across the ionization front

The total molecular emission along the line-of-sight towards G353.1+0.6 is the result of the combined emission of several individual components. In separating that part of the emission which is actually associated with the HII region under study, it would help if we could deconvolve each emission profile into gaussian components. We first fitted gaussians to the optically thin 13 CO(1-0), C18 O(1-0) and C18 O(2-1) emission profiles; then we tried to fit gaussians at the same velocities to the optically thick profiles, including a negative component where necessary (see previous section). In general this procedure worked quite satisfactorally, except that the optically thick profiles could not always be fitted with gaussians at exactly the same velocity as those for the optically thin lines, because saturation affects the line shapes, and since the optically thick and thin emission originate in different parts of the cloud. In the majority of cases the velocity differences between gaussian fits to optically thin and thick profiles at the same position are within 0.5  [FORMULA], but sometimes differences of up to 1  [FORMULA] are found.

Although emission is found at velocities between -12 and +4  [FORMULA], it seems clear that there are two main components (at -5 and -1  [FORMULA]) which are present along the whole extent of the strips. Other components appear at a few positions at higher and lower velocities along the strips. Between [FORMULA] and [FORMULA] (the VLA continuum emission is from [FORMULA] to [FORMULA]) the first moment of the emission of any line lies at [FORMULA] [FORMULA]   [FORMULA] at [FORMULA], and at [FORMULA] [FORMULA]   [FORMULA] at [FORMULA] = [FORMULA]. Note that the ionized gas is at [FORMULA] =-4.1 [FORMULA] 0.9  [FORMULA], the same velocity as, or slightly bluer than that of the molecular gas. To the south and north the centroid of the molecular emission moves to higher velocities (to become lower again further from the ionization front), due to the appearance of other clouds at different velocities.

In Fig. 7 a,b we show the integrated 12 CO(1-0) and 13 CO(1-0) emission between -6 and 0 [FORMULA] (component A), associated with the HII region, while in Fig. 7 c,d we show the integrated emission along the two strips in [FORMULA], for all the lines with sufficient signal-to-noise. Figs. 7 a,b show that there is a sharp decrease in integrated emission at the location of the ionization front, with contour lines running more or less parallel to it. From Figs. 7 c,d we see that this rapid decrease occurs in all measured lines, although much more so at [FORMULA], but also that the behaviour differs for the various tracers. At [FORMULA] both [FORMULA] O and [FORMULA] (i.e. the high density tracers) peak closer to the ionization front than do 12 CO and 13 CO, indicating the front is associated with a density enhancement, as would be expected for a shock front preceding the ionization front. This effect is not so clear in the optically thick lines, because the high optical depth may mask the density increase. The strip at [FORMULA] shows a much more gradual north-south decrease of the total emission. At this [FORMULA], the radio emission detected by Fea90 becomes bifurcated, as relatively weak radio-continuum emission has been detected at (-80,-20), while the intensity of the emission increases again at position (-80,-80). At the latter position H [FORMULA] emission has been detected (see Fea90), and the radio peak has been interpreted as a local density enhancement produced by the interaction between the stellar UV radiation and a molecular fragment, of which the outer layer is ionized. The fact that the [FORMULA] (1-0) emission has a slightly slower decrease than the other transitions is perhaps due to a similar density enhancement when moving towards the shock front or, alternatively, to its higher beam dilution.

[FIGURE] Fig. 7. a,b Contour plots of 12 CO(1-0) and 13 CO(1-0) integrated emission ([FORMULA] [FORMULA] [FORMULA][FORMULA]) from component A. Contour values are in steps of 20 K [FORMULA] from 20 K [FORMULA] for 12 CO(1-0), and in steps of 5 K [FORMULA] from 5 K [FORMULA] for 13 CO(1-0). The dashed lines indicate the ionization front. c and d Distribution of the normalized integrated intensity along the two declination strips for the various transitions observed. Codes are indicated below the panels. Dashed lines as in a and b.

3.1.4. Column densities

Column densities can be determined in three ways. The first method uses 12 CO(1-0) and 13 CO(1-0) data, and yields LTE column densities [FORMULA] (see e.g. Martin and Barrett 1978; Harju et al. 1990). We have adopted an H [FORMULA] 13 CO ratio of [FORMULA] (Dickman 1978).

The second method is based on the LVG model of Goldsmith et al. (1983) and uses the (2-1) and (1-0) brightness temperatures of any isotopic species of CO (in our case we shall use 13 CO) and an assumption of its abundance relative to H2.

Finally, column densities can also be derived from 12 CO(1-0) data alone, by making use of the empirical relation between [FORMULA] [FORMULA] [FORMULA] (12 CO) [FORMULA] and [FORMULA]

[EQUATION]

with X =(2.3 [FORMULA] 0.3) [FORMULA] 1020  cm-2 (K [FORMULA])-1 (Strong et al. 1988).

For each component we have calculated [FORMULA] using the gaussians fitted to the 13 CO(1-0) line profiles. The excitation temperatures have been determined from 12 CO(1-0) by superimposing the 13 CO(1-0) gaussians on the 12 CO(1-0) spectra and reading off the 12 CO(1-0) [FORMULA] at the peak velocity of each gaussian. The same has been repeated for 12 CO(2-1) in order to calculate 12 CO(2-1)/12 CO(1-0) for single components. Where possible, we have checked that the column densities obtained using [FORMULA] 's from optically thin 13 CO or [FORMULA] O line ratios are similar. We have also calculated total column densities from 12 CO(1-0) integrated emission, using Eq. (2) with the value of X given above, and compared them both with the sum of [FORMULA] along the same line of sight and with the column densities obtained from the LVG model. [FORMULA] O(1-0) LTE column densities were transformed into [FORMULA] by using the conversion given by Frerking et al. (1982). In all cases we found values to be the same within a factor [FORMULA] 2-3, with greater differences at positions of low column density. The mean ratio of [FORMULA] column density to total [FORMULA] (derived from 13 CO summing all contributions of single components along the line of sight) is [FORMULA] but only in few (6 out of 43) locations it is [FORMULA] or even much greater. The total [FORMULA] mass in the field, including a 1.36 correction for helium, is 3000 [FORMULA], while the total LTE mass, also corrected for helium, is 1600 [FORMULA]. The total LTE mass was obtained correcting also for locations with no 13 CO(1-0) observations using a LTE- [FORMULA] relation derived from a linear fit to all available couples of data.

Fig. 8 shows [FORMULA] of component A along the two strips, as a function of [FORMULA]. Note that component A has been deconvolved in two subcomponents at [FORMULA] and [FORMULA]   [FORMULA] (see Sect. 3.1.3). In both strips the column density peaks north of the ionization front, but at [FORMULA] that occurs nearer to the front and [FORMULA] suddenly decreases when approaching it. Maximum values are of the order of 1022  cm-2 and are clearly greater at [FORMULA]. Component E (not shown in Fig. 8) peaks at the ionization front with column densities of the order of 1021  cm-2 and up to 1022  cm-2 at [FORMULA], where it dominates the emission. Component C (not shown) peaks south of the ionization front with [FORMULA] of the order of 1021  cm-2. Both E and C show a limited extent in declination, so their emission is probably somewhat beam diluted and their column densities underestimated.

[FIGURE] Fig. 8. LTE column density of the two main subcomponents of A: A1 ([FORMULA] [FORMULA][FORMULA] ; filled squares) and A2 ([FORMULA] [FORMULA][FORMULA] ; open squares), along the two strips in G353.1+0.6.

Lower resolution IR maps (see e.g. McBreen et al. 1983; Persi et al. 1986) are quite similar to low resolution radio-continuum maps (see e.g. Schraml & Mezger 1969); since IR emission traces dust, this suggests that the total (molecular, atomic and ionized) hydrogen column density can be quite high also at the ionization front. PDR models (Tielens & Hollenbach 1985; Hollenbach et al. 1991) indicate that CO forms at [FORMULA]  mag; assuming

[EQUATION]

(e.g. Bertoldi & McKee 1992), this implies [FORMULA]  cm-2. Since in G353.1+0.6 the PDR is illuminated from below and is viewed almost edge-on, the width of the VLA image of Fea90 at [FORMULA] ([FORMULA] or [FORMULA] 0.5 pc) gives an upper limit to the depth of the region where CO is dissociated. The mean density of this region is then [FORMULA]  cm-3 ; assuming an extent along the line of sight of the order of the size of A (1 pc), we find that the total hydrogen column density is quite high, of the order of [FORMULA]  cm-2.

3.1.5. Masses and mean densities

To obtain the masses of the single components we have considered contour plots of the area of all gaussians with roughly the same central velocity on the plane of the sky, and have determined the size of each component as [FORMULA], where [FORMULA] and [FORMULA] are maximum and minimum angular sizes (in radians) at half maximum integrated intensity and D is the distance (in pc). The mean densities have then been calculated both from the H2 mass divided by the volume of a sphere of radius R and from the peak column density ([FORMULA]) divided by linear size, assuming the extent along the line of sight to be equal to [FORMULA]. The two methods give similar values (within a factor of 3 in the worst case). The physical parameters are given in Table 2. We have also calculated the virial masses using the relation of MacLaren et al. (1988) for a homogeneous sphere and the FWHM of the gaussians fitted to the 13 CO(1-0) line profiles. They tend to be systematically larger (by a factor of 2.4-12) than LTE masses, which is not surprising if we consider that [FORMULA] may not represent only gravitational interaction.


[TABLE]

Table 2. Physical parameters of components related to the ionization front of G353.1+0.6. A distance of 1.7 kpc has been assumed. All LTE masses are corrected for He. All densities, unless explicitly stated, are derived from H2 mass divided by volume.


3.1.6. Temperatures and relative abundances

The excitation temperature of 12 CO(1-0), [FORMULA], can be used as a first approximation of [FORMULA] because 12 CO(1-0) thermalizes at low densities ([FORMULA] cm-3). The warmest component is A, with [FORMULA] [FORMULA] 42 K at (0,40) which rapidly decreases when approaching the ionization front. [FORMULA] can also be obtained from the (2-1)/(1-0)-line ratios of optically thin isotopes (e.g. Levreault 1988); generally 13 CO and [FORMULA] O line ratios give lower values than those of 12 CO, but while the 12 CO brightness temperature of A peaks at (0,40), its [FORMULA] O excitation temperature clearly peaks at (0,0) where the integrated emission of the high density tracers (including [FORMULA] O) also peaks. At [FORMULA], all [FORMULA] 's (12 CO, 13 CO and [FORMULA] O) are smaller and decrease more gently, and also column densities are lower suggesting that smaller [FORMULA] 's are due to a weaker coupling between radiation and gas at lower density. Clearly, the kinetic temperature cannot have the same behaviour as the 12 CO(1-0) excitation temperature (i.e. decreasing towards the edges) since at the cloud border the beam filling factor becomes dominant.

Abundances were derived from the LVG model of Goldsmith et al. (1983). We have adopted a (constant) kinetic temperature of 50 K, which is the model value that allows to reproduce the observed peak temperatures of A, C and E. From 12 CO, this yields densities of 10 [FORMULA]  cm-3. The same values have been obtained from 13 CO and [FORMULA] O, although [FORMULA] O shows a density increase at (0,0), further substantiating what was already suggested by the integrated emission of the high density tracers. Using the FWHM of the gaussians as a first approximation of the velocity field, we also estimated abundances of [FORMULA] a few [FORMULA] for 12 CO, [FORMULA] for 13 CO, and [FORMULA] for [FORMULA] O, which are more or less "standard values" for a molecular cloud (see e.g. Dickman 1978, Frerking et al. 1982). It is uncertain whether abundances decrease towards the edges of the clouds, due to the different beam dilution of (2-1) and (1-0) transitions. The LVG column density is generally lower than, though within a factor of 2, the corresponding LTE values.

3.1.7. Optical depths

The degree of saturation of the CO emission can be assessed from line ratios (e.g. Levreault 1988). Along both strips we find [FORMULA] T[12 CO(2-1)]/T[12 CO(1-0)] [FORMULA] 1, with an increase towards the edges of the field (where, however, the signal-to-noise ratio is smaller [between 1 and 5]). The mean value is [FORMULA] for the subcomponent of A at [FORMULA] km s-1, but does not change if we include all available data. We have also examined the dependence of [FORMULA] on H2 column density or, alternatively, on [FORMULA]. In fact, as indicated by Eq. (3), the two quantities are directly related (see also Harjumpää & Mattila 1996). [FORMULA] was obtained from Eq. (3) using only the H2 contribution to N. [FORMULA] values tend to cluster between 0.9 and 1.2, especially at high [FORMULA]. The highest [FORMULA] 's are at the cloud center, so they are less likely to be affected by beam dilution differences in 2-1 and 1-0 transitions; the dispersion is consequently lower. Ratios [FORMULA] T[12 CO(1-0)]/T[13 CO(1-0)] are [FORMULA] 5 along the strip at [FORMULA] and [FORMULA] 10 along the strip at [FORMULA]. These values are typical of optically thick 12 CO(1-0) emission. For 13 CO we obtain [FORMULA] 2 along the two strips (indicating optically thin emission), except at [FORMULA] between [FORMULA] and [FORMULA], where [FORMULA]. There 13 CO(2-1) is at most moderately optically thick. In fact these observed line ratios with the assumption of optical thin emission give [FORMULA] (13 CO) much less than [FORMULA] ([FORMULA] O) and [FORMULA] (12 CO), whereas [FORMULA] (13 CO) is expected to lie between [FORMULA] (12 CO) and [FORMULA] ([FORMULA] O). At (0,0) the line ratio [FORMULA] (1-0)/ [FORMULA] CO [FORMULA] (1-0) is [FORMULA] 8, much less than the local interstellar medium 12 C/13 C abundance ratio ([FORMULA] 70; Wilson & Matteucci 1992), suggesting that also [FORMULA] (1-0) is optically thick.

3.1.8. Isotopic ratios

Fig. 9 shows T[13 CO(1-0)]/T[ [FORMULA] O(1-0)] and T[13 CO(2-1)]/T[ [FORMULA] O(2-1)] for component A along the strip at [FORMULA]. Along the strip at [FORMULA] we observe values (and lower limits) of the order of 5-10 for both transitions. The subcomponent of A at [FORMULA][FORMULA] shows a steady decrease of line ratios from the northern edge to the ionization front (from 12.5 to 7 for [FORMULA] and from 8.4 to 3 for [FORMULA]). The same behaviour is observed if ratios are determined from the integrated emission, although then the decrease is more gentle (e.g. from 9.5 to 7.7 for [FORMULA]). The two main sources of uncertainties arise from the gaussian fits and the temperature calibration. We estimate that errors are about 15-20% for (1-0). For the subcomponent at -1  [FORMULA] the situation is less clear, as the uncertainties are larger (up to 30% for [FORMULA]) because gaussian fits to this component are less accurate. If both 13 CO and [FORMULA] O are optically thin, line ratios are equal to abundance ratios; because 13 CO is moderately optically thick, a correction for optical depth has been applied.

[FIGURE] Fig. 9. T(13 CO)/T([FORMULA] O) ratios both for (1-0) and (2-1) of the two main subcomponents of A: A1 ([FORMULA] [FORMULA][FORMULA], filled squares) and A2 ([FORMULA] [FORMULA][FORMULA], open squares), along the strip at [FORMULA] in G353.1+0.6.

Because of chemical fractionation and selective photo-dissociation, chemical models predict an increase of X (13 CO) [FORMULA] ([FORMULA] O) at the edges of a cloud (which instead occurs only at the northern edge of A). Even though the optical depth of 13 CO(1-0) obtained from the ratio 13 CO(1-0)/12 CO(1-0) increases towards the ionization front from 0.2 to 0.3, this can account for at most 6% decrease of line ratios. Beam dilution cannot explain the observed decrease, since [FORMULA] O is less abundant and is likely to be more beam diluted than 13 CO at the edge. However saturation of 13 CO accounts for the lower values of (2-1) line ratios, since 13 CO(2-1) is generally more optically thick than 13 CO(1-0) (and is moderately thick as noted in Sect. 3.1.7). Since at (0,0) the 13 CO and [FORMULA] O emission seem to come from different regions (a more diffuse one and a high density one), excitation effects can affect line ratios. Also, chemical fractionation may be inhibited near the ionization front because of high temperature and density (Langer et al. 1984).

Assuming [FORMULA] 500 (Wilson & Matteucci 1992), and using an optical depth correction and the ratios of gaussian areas, we find [FORMULA], more or less in agreement with the local interstellar medium value of [FORMULA] 70 (Wilson & Matteucci 1992).

3.2. G 353.2+0.9

3.2.1. Morphology

In Fig. 10 we present the 12 CO(1-0) spectra taken towards this source. The weak feature at about -40  [FORMULA] has been detected at virtually every position in this field as well and will not be considered further as it is probably unrelated [ [FORMULA])= [FORMULA]   [FORMULA] (Wilson et al. 1970)]. Spectra of all species, observed along the strips at [FORMULA] and [FORMULA], are presented in Fig. 11 and 12 respectively. The bulk of the emission occurs at velocities roughly between -14 and +4  [FORMULA]. From Fig. 10 it is evident that the velocity structure of the gas observed towards this region is quite complex: line profiles change considerably from one position to the next, sometimes abruptly (as along the strip at [FORMULA]), sometimes more gradually (as along [FORMULA]). This is illustrated more clearly by the diagrams presented in Fig. 13, which show the integrated 12 CO(1-0) emission in intervals of 1  [FORMULA] ; the central values of the bins are indicated in each panel. From these diagrams we see first of all that the emission in the south-eastern corner of the map is blue-shifted with respect to rest of the emission. Comparison with the red ESO/SRC plate (see Fig. 2 of Fea90) shows that this "South-Eastern Complex" (S.E.C.) is not associated with the HII region under consideration, but coincides with a filament of obscuration, whose edges are outlined by diffuse emission. The emission towards the remainder of the mapped region coincides with the HII region and is a collection of several different velocity components within the beam. The most relevant of these have been indicated with letters in Fig. 13.

[FIGURE] Fig. 10. All 12 CO(1-0) spectra taken towards G353.2+0.9. Velocity and temperature scale are indicated in the upper right-hand corner.
[FIGURE] Fig. 11. Spectra of all observed lines in G353.2+0.9 along the strip at [FORMULA]. Only spectra at intervals of [FORMULA] are shown. Transitions and temperature scale are indicated above each column; velocity ranges below.
[FIGURE] Fig. 12. Same as Fig. 11, for [FORMULA].

[FIGURE] Fig. 13. Channel maps of 12 CO(1-0) emission in G353.2+0.9. The channel width is 1  [FORMULA], and the central velocity is indicated in each panel. Contour levels are 2(2)20, 25(5)40 K [FORMULA]. The 20 K [FORMULA] contour is drawn thick.

The emission integrated between -14 and [FORMULA] [FORMULA] is completely dominated by component "B", with its peak to the NW of the optical HII region, and the S.E.C. There is a strong gradient in the emission towards the SW quadrant of the mapped region; the region at [FORMULA] and [FORMULA] is characterized by emission at a level of [FORMULA] 20 K [FORMULA]. At the northern boundary of this region the contours run almost parallel to the ionization front (which coincides with the sharp edge in H [FORMULA] emission; see Fig. 7 of Fea90). The early-type stars of the cluster Pis24 (Neckel 1984) are located just north of the cavity, in a region of relatively little molecular emission, and one might suspect that these stars have blown the region surrounding them clear of molecular material. While this may be so, the stars of Pis24 are not the cause of the HII region (Fea90) because the ionization front is located between the Pis24 cluster and the diffuse H [FORMULA] emission. Rather, the HII region is excited by sources located inside the nebula (Fea90). These authors concluded that the obscuration causing the sharp boundary in H [FORMULA] must therefore be connected to the ionization front. In fact, components E, G and H, indicated in Fig. 13, form a chain of lower [FORMULA] cloudlets parallel to the edge of the H [FORMULA] emission, and lying just south of it. Of these 3 clouds, E and G have the most intense emission, and are presumably also the densest. They are bordering the western half of the ionization front, where the H [FORMULA] emission has its sharpest boundary. The weaker component, H, lies along the eastern half of the front, where the H [FORMULA] emission has a more fuzzy edge.

Other features visible in Fig. 13 can account for the obscuration seen towards other parts of the H [FORMULA] emission (see Fig. 7b in Fea90). Component C coincides with the `elephant trunk'-shaped obscuration cutting through the H [FORMULA] emission, and which houses two compact radio sources (called A and B by Fea90). It has been detected in all lines, including [FORMULA] and [FORMULA] CO [FORMULA], implying it must have a high density ([FORMULA] 105  cm-3).

Components B and F cause the obscuration seen towards the NW and NE of the H [FORMULA] emission respectively. They may be located partly behind the HII emission, as weak diffuse emission can be seen in the lower part of both components (Fig. 7 of Fea90).

In summary, contrary to the situation in G353.1+0.6, where most of the molecular gas is located beyond the ionization front as seen from the exciting stars and viewed in an edge-on geometry, in G353.2+0.9 most of the molecular emission is located either along the line of sight or north of the optical emission, with only weaker components bordering the southern edge of the ionization front. That is, this star forming complex is essentially viewed face-on. Components B and F, which are on either side of the brightest part of the optical nebulosity (and consequently are partly behind it) peak at [FORMULA] [FORMULA][FORMULA], so that with respect to these clouds the ionized gas at [FORMULA] =-3.8  [FORMULA] is streaming towards the observer, while component C, which coincides with the elephant trunk (and therefore must be in front of the optical nebula) peaks at [FORMULA] [FORMULA] 5.5  [FORMULA]. This geometry implies that the PDR extends over the whole of the mapped region, i.e. lies in front of the molecular clouds, at least for components B and F, so that we should find "PDR-values" for physical parameters at all positions, rather than a north-south trend across the ionization front.

3.2.2. The ionization front

In G353.2+0.9 the emission profile at each position is the combination of various components at different velocities. For positions north of the ionization front (i.e. [FORMULA]) the dominant emission has central velocities between -6 and -1  [FORMULA]. The emission at each position can be roughly separated into four velocity ranges: [FORMULA] [FORMULA][FORMULA] (S.E.C), [FORMULA] [FORMULA] [FORMULA]   [FORMULA] (A and C), [FORMULA] [FORMULA] [FORMULA]   [FORMULA] (B and F), and [FORMULA] [FORMULA][FORMULA] (E), which has been confirmed by first fitting gaussians to the (relatively) optically thin 13 CO(1-0) and [FORMULA] O(1-0) emission and then to the optically thick 12 CO(1-0) spectra. At all positions the spectra could be deconvolved in 2 to 4 gaussian components with central velocities that are the same within 0.5  [FORMULA] (1  [FORMULA] in a few cases). The corresponding temperatures of the optically thick transitions were derived by the same procedure as for G353.1+0.6 (see Sect. 3.1.4).

With temperatures determined in this way, we can assess the behaviour of the molecular emission with respect to the ionization front along the two strips. The emission of all molecular species changes in the same manner (see Figs. 11 and 12) and the intensities drop very rapidly at the location of the front. At [FORMULA], the emission between -7 and -3  [FORMULA] peaks at two locations, namely component A ([FORMULA] - [FORMULA]) and C ([FORMULA]). Whereas the 12 CO(1-0) and 13 CO(1-0) lines have their primary peak in component A, the transitions more sensitive to density, such as [FORMULA] (1-0) and [FORMULA] CO [FORMULA] (1-0), only have a secondary maximum there, and are stronger in component C, indicating that C is the denser one. [FORMULA] O also peaks at C, but only this region was covered for this molecule. Between [FORMULA] and 15 [FORMULA] components with [FORMULA] between -7 to -3  [FORMULA] (i.e. A and C) have lower level emission, while components B and F have their peaks. The (2-1) intensities show essentially the same features, although 12 CO(2-1) is as strong at component C as it is at A. There are slight offsets between the locations of the peak 12 CO(2-1) and 12 CO(1-0) emission: the 12 CO(2-1) has the same sampling, [FORMULA], as the 12 CO(1-0) with a resolution twice that of 12 CO(1-0), and is therefore expected to better resolve the peak. For the emission between -7 and -3  [FORMULA] component A seems to peak more to the north in 12 CO(2-1) than in 12 CO(1-0).

The behaviour of the peak temperatures along the strip at [FORMULA] is similar to that at [FORMULA], except that the former does not pass through component C, and so there is only one peak for components with [FORMULA] between -7 and -3  [FORMULA].

South of the ionization front ([FORMULA]), all molecules have much lower intensities, so it is difficult to follow variations. Component E, which dominates at these locations, has a peak [FORMULA] [12 CO(1-0)] of only [FORMULA] 7 K, while along the strip at [FORMULA] components A, B, and C reach a peak [FORMULA] [12 CO(1-0)] of [FORMULA] 39, [FORMULA] 31, and [FORMULA] 25 K, respectively. The lower temperature of component E could be explained by its small size and therefore by its being more beam-diluted.

As both 12 CO transitions are certainly optically thick, the ratio [FORMULA] should be about 0.8 - 1.0 for the range of [FORMULA] we find here (10-40 K; Levrault 1988). Because the beam size at 230 GHz is smaller, we expect [FORMULA] to be larger than its real value, especially if the gas is clumpy on scale sizes comparable to the 12 CO(2-1) beam. [FORMULA] has been calculated for each velocity component, at each position where both transitions have been detected, and lies between 0.5 and 1.4, with a mean value of 0.9 [FORMULA] 0.2. [FORMULA] tends to values between 0.6 and 0.9 at high [FORMULA] (where the effect of beam dilution decreases; see Sect. 3.1.7). This means that on average the cloud is not very clumpy on scales of [FORMULA]. However, to explain the lower values of [FORMULA] may require a two-layer model with an optically thick inner layer and a diffuse optically thin warmer front layer which, because of [FORMULA], preferentially absorbs the (2-1) emission, as discussed by Pagani et al. (1993) for the case of RCW 34.

3.2.3. Column densities

We determined column densities as for G353.1+0.6. Again, different methods give column densities generally within a factor of 2-3, with larger differences at positions with lower emission. The total mass of the molecular gas in our observations has been determined using Eq. (2), from [FORMULA] [12 CO(1-0)] integrated between [FORMULA] =-10 or -16 (including the S.E.C.) and 4  [FORMULA] summed over all positions. With the 1.36 correction for He, this yields 5700  [FORMULA]. Adding all [FORMULA] values from gaussian components yields a total mass of 3500  [FORMULA], corrected for He and with a contribution from positions not observed in 13 CO(1-0) estimated as in G353.1+0.6. The mean ratio of [FORMULA] column density to total LTE column density (determined by adding all contributions of single components along the line of sight) is 2.5 [FORMULA] 1.8, lower than in G353.1+0.6. The difference may be due to a different fraction of positions with low-level emission in the two regions. However, 13 CO was observed over a smaller area than 12 CO, and furthermore 13 CO was not always detected. LTE masses of single components are reported in Table 3. [FORMULA] masses are roughly twice as much.


[TABLE]

Table 3. Physical parameters of molecular clouds in G353.2+0.9. A distance of 1.7 kpc has been assumed. All LTE masses are corrected for He. All densities are derived from H2 mass divided by volume


Fig. 14 shows [FORMULA] along the strips at [FORMULA] and [FORMULA] for components A, B, C and E. With the exception of E, peak [FORMULA] 's are [FORMULA]  cm-2, similar to those obtained for component A of G353.1+0.6, although line profiles are deconvolved in finer detail there. Component E, which dominates south of the ionization front, has a peak [FORMULA] of [FORMULA]  cm-2, with a relatively large uncertainty because 13 CO is very weak. [FORMULA] is much larger, at [FORMULA]  cm-2. It is evident from Fig. 14 that [FORMULA] rapidly decreases towards the ionization front and has a minimum value south of the ionization front, confirming the fact that there is a relative scarcity of molecular gas there.

[FIGURE] Fig. 14. LTE column density of several velocity components in G353.2+0.9 along the two main strips. Components A and C are indicated by filled squares; B by open squares; E by triangles. [FORMULA] coincides with the position of the ionization front.

Sizes and mean densities, reported in Table 3, were determined in the same way as for G353.1+0.6. Densities are generally of the order of 103 -104  cm-3 ; the density of components E, G and H has been determined from the [FORMULA] column density. For comparison with the other values, note that the maximum [FORMULA] 's of E, G and H divided by 2R are only [FORMULA] 200 cm-3. Virial masses (assuming each cloud is a homogeneous sphere) are also given in Table 3 ; for components C, E and H these are much higher than their LTE or [FORMULA] -masses, indicating that these are not in virial equilibrium. However, since it is not clear if the line width is due to turbulence or to ordered motions, it is difficult to say whether the clouds may be collapsing or expanding.

3.2.4. Temperatures and relative abundances

As for G353.1+0.6, we estimated [FORMULA] from [FORMULA] [12 CO(1-0)]. At least along the two main strips, [FORMULA] rapidly decreases both south and north of the peaks. Line ratios suggest that 13 CO and [FORMULA] O excitation temperatures are lower than [FORMULA] (12 CO), at least in the northern part of the field. Components A and B have a peak [FORMULA] (12 CO) [FORMULA] 40 K, while C reaches [FORMULA] 30 K, and components E and G have [FORMULA] (12 CO) [FORMULA] 10-16 K. Since C, E and G are very small features, their [FORMULA] [12 CO(1-0)] may be underestimated because of beam dilution. Thus, as for G353.1+0.6, we have adopted a constant [FORMULA] [FORMULA] K to use as input for the LVG model of Goldsmith et al. (1983). The low [FORMULA] ratios and high 12 CO(1-0) brightness temperatures of components A, B and F requires densities [FORMULA] - [FORMULA] cm-3 and abundances X (12 CO) [FORMULA] to be explained. But 13 CO and [FORMULA] O yield densities [FORMULA] - [FORMULA] cm-3 and abundances X (13 CO) [FORMULA] and X ([FORMULA] O) [FORMULA], so a low density absorbing layer that reduces [FORMULA] may exist. Component C has densities [FORMULA] cm-3 (for [FORMULA] O , [FORMULA] cm-3) and abundances X (12 CO) [FORMULA], X (13 CO) [FORMULA] and X ([FORMULA] O) [FORMULA]. Both E and H have densities [FORMULA] cm-3 and X (12 CO) [FORMULA] - [FORMULA] ; their emission in 13 CO and [FORMULA] O has not been detected. Finally, component G has a density [FORMULA] cm-3 and abundances X (12 CO) [FORMULA] - [FORMULA] and X (13 CO) [FORMULA]. LVG column densities are generally lower (but within a factor of 2-3) than the corresponding [FORMULA].

3.2.5. Optical depths

As we have shown in Sect. 3.2.2, line ratios [FORMULA] are generally [FORMULA] 1 with many values [FORMULA] 0.7. This indicates either low excitation temperatures or low opacities (Levreault 1988). However, [FORMULA] is [FORMULA] 10 almost everywhere, implying that 12 CO is optically thick. Along the two main strips, T[13 CO(2-1)]/T[13 CO(1-0)] is generally between 1 and 2 for A, B and C, suggesting that at least 13 CO(2-1) may be moderately thick in some locations (and consequently excitation temperatures derived from line ratios may be in error at those positions). [FORMULA] O line ratios, where available, are indicative of low opacities. Finally, T[ [FORMULA] (1-0)]/T[ [FORMULA] CO [FORMULA] (1-0)] is 5 and 8 for A and C at the locations of their maxima, indicating that [FORMULA] (1-0) is optically thick. At other locations, only lower limits are available; these range from 2 to 5.

3.2.6. Isotopic ratios

Both for the (1-0) and for the (2-1) transition the ratio T(13 CO)/T([FORMULA] O) has a large scatter around a mean value of 12.8 for (1-0) and 10 for (2-1) and is generally [FORMULA]. No clear trend with position is evident, although there is a marginal indication of an increase of the line ratios at the cloud edges, as predicted by many PDR models (e.g. Minchin et al. 1995). The mean values are greater than the terrestrial isotopic ratio of 5.5 (Taylor & Dickman 1989). Correcting for 13 CO opacity and under the same assumptions as used for G353.1+0.6 (see Sect. 3.1.8), we find [FORMULA] between 22 and 61, with 52 near the A-peak and 61 at the C-peak. Unfortunately, all components south of the ionization front are undetected in [FORMULA] O, so only scarcely significant lower limits (T(13 CO) /T([FORMULA] O) [FORMULA] -4) are available there.

3.2.7. Clouds at the ionization front

As mentioned in Sect. 3.2.1 the molecular clouds labeled E, G, and H (see Fig. 13) form the material into which the ionization front is proceeding. They are in the shape of a thin strip of gas south of the ionization front. In many respects this situation is reminiscent of the bright bar in the Orion Nebula, which is bounded by a thin strip of molecular gas on the side opposite to that of the exciting stars of the Trapezium cluster. Also in Orion the CO emission from this strip is much weaker than that of the molecular clouds associated with the BN/KL region (see Wilson & Mauersberger 1991). The G353.2+0.9 complex presents many similarities with the Orion complex, in the sense that we see the HII region produced by the new-born massive stars at the edge of a large molecular complex where star formation may just begin and with a similar orientation with respect to the observer. Perhaps G353.2+0.9 is in an earlier stage, since there the equivalent of the Trapezium stars are not visible because the surroundings have not yet been sufficiently cleared by the stellar ionizing radiation.

An indication of the properties of the gas in this strip has been obtained by using the models published by Köster et al. (1994), who consider the CO spectra emerging from clumpy molecular clouds in PDR's. They present models for two cases: clouds that are illuminated from one side (their model B) and those that are illuminated on both sides (model A). The visual extinction through the clouds and the illumination (by far UV [FUV] radiation) are both varied, and for each case the thermal and chemical structure of the clouds are calculated. They present their results in a series of figures, showing the change of the brightness temperature at the center of the emergent 12 CO and 13 CO profiles as a function of the upper level of the rotational transition, for various combinations of cloud density, [FORMULA], velocity dispersion, and intensity of the incident FUV radiation. For G353.2+0.9 their model B is the more appropriate, with the clouds along the ionization front being illuminated by the embedded sources responsible for the excitation of the HII region. As indicated by Fea90, the ionizing sources embedded in G353.2+0.9 are the equivalent of 5 O9V stars, which implies that the FUV flux density ([FORMULA] eV) is [FORMULA] times the average interstellar field. In fact, 5 O9 V stars yield [FORMULA] erg s-1 (Panagia 1973). Assuming the HII region is 1.2 pc in diameter and the stars lie at its center yields a FUV flux density [FORMULA] erg cm-2 s-1 (the inequality comes from the photons with [FORMULA] eV). The average interstellar FUV flux density is [FORMULA] 1.6 10-3 erg s-1 cm2 (Tielens & Hollenbach 1985), then the local FUV flux density is [FORMULA] times greater. However, since the ionizing sources are located along the southern edge of the HII region (Fea90) at a projected distance of at most [FORMULA] from the radio border, the FUV flux density provided by even a single O9 V star on a cloud surface 0.1 pc away from it may be as high as [FORMULA] times the average interstellar flux density. Because the exact geometry and the amount of FUV radiation being absorbed by matter surrounding the stars are unknown, this must be considered an upper limit.

As can be seen in Fig. 14, component E has [FORMULA] [FORMULA] 3 to 6 [FORMULA] cm-2, corresponding to [FORMULA] 2 mag. We find that for cloud E, G and H the best agreement between model and observations is found for FUV field [FORMULA] times the average interstellar value, density [FORMULA] cm-3, [FORMULA] mag and velocity dispersion 1 [FORMULA]. According to the model of Köster et al. (1994), the 12 CO(1-0) emission has [FORMULA] in this case.

The parameters that best fit the observations of component C, the narrow "elephant trunk" of obscuration which houses a compact radio component (Fea90), are [FORMULA], density of the order of 105-6 cm-3, [FORMULA] mag, and velocity dispersion 3 [FORMULA].

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Online publication: June 30, 1998
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