4 Presentation of the data

Table 5 gives a summary of the results obtained, indicating which lines were observed and detected towards each source.

The amount of data that we have obtained is very large, considering that for each source and for each transition a data cube ( $\alpha$ , $\delta$ ,velocity) can be created. It is also difficult to express our results in the form of tables of line parameters. Some lines have very large signal-to-noise ratio (S/N) and allow detailed studies of line profiles, namely absorption dips and asymmetries in the core of the line and wings at large velocities (outflows). In other cases, the S/N is so low that we have a marginal detection only at the central position and very little information on the line profile. We stress that in all tracers with sufficiently good S/N, the emission peaks at the position of the water masers (within the uncertainty related to the angular resolution and sampling of our maps). Thus, it seems highly probable that the gas clumps mapped by us are associated with the water maser as well as with the YSO.

While the individual spectra in our maps are available upon request, we have decided to present here the following information:

1.: Spectra of all the transitions observed towards the peak position of our maps (namely the position of the H₂O maser). These figures show the velocity structure of the lines and the relative intensities of the transitions.
2.: Contour plots of the velocity integrated intensity for each transition where we have sufficient S/N to allow mapping.
3.: Tables with line parameters and other quantities of interest derived from the maps.
4.: Contour plots in selected velocity ranges for the transitions with good S/N. These are shown only when asymmetries in the spatial distribution of the low or high velocity emission are present.

**Table 5:** Summary of observed lines
$\begin{tabular} {lccccccccccc} \hline Source & \mbox{HCO$^+$}$(1-0$) & CS$(3-2)$... ...3151+5912 & Y & Y & Y & Y & N & Y & --- & --- & Y & N & N \\ \hline\end{tabular}$ Note: Y = detected; N = non detected; -- = non observed.

4.1 Spectra of molecular transitions

In Fig. 1 we plot the spectra of the ¹³CO, HCO⁺, CS, C³⁴S, and HCN lines observed towards all the sources. When one or several spectra are missing, this means that the corresponding lines were either not observed or not detected. We present in Fig. 2 the spectra of the CH₃CN and CH₃OH transitions.

We note that the strongest lines observed by us such as ¹³CO, HCN, HCO⁺, and - to some extent - CS show complex line profiles with wings suggestive of "outflow activity'' (see for example Fig. 1 for NGC 281-W). In the case of less abundant species (e.g. C³⁴S), this is usually not the case but this may just be a question of sensitivity. It is interesting however that in some sources, the velocity of the C³⁴S(3-2) line (obtained with a Gaussian fit) corresponds to a dip in the profile of CS(3-2) (see e.g. IC 1396-N) suggesting high optical depth. In general, as discussed below, there is reason to believe that the "strong lines'' are thick but one should note also that there are cases (e.g. S233) where the C³⁴S peak coincides with a peak in CS(3-2) suggesting the presence of distinct spatial and velocity components in the molecular cloud. A more detailed investigation of such line profiles and of their origin will be given in Sect. 5.

4.2 Integrated velocity contour plots

The simplest description of the emitting region in a given transition is obtained from the integrated emission in the line of interest. In Figs. 3 to 8 we show maps for all cases where the line emission was strong enough to be detected away from the central position. In particular, Figs. 3 and 4 refer to the "strong line'' tracers, namely ¹³CO, HCN, HCO⁺, and CS, whereas Figs. 5 to 7 illustrate the distribution of the "weak line'' tracers i.e. C³⁴S, CH₃CN, and CH₃OH. One sees that the latter transitions arise from regions smaller than those traced by the "strong lines''. Moreover, in all sources the C³⁴S emission coincides with the H₂O maser spots: although this is true for all lines, the C³⁴S emission is particularly significant since it is most probably optically thin whereas at least the "strong lines'' are likely to be somewhat optically thick (see discussion in Sect. 4.5). Thus C³⁴S can be expected in crude fashion to be "representative'' of the mass distribution in the dense molecular gas. We consider this to be strong evidence that we have identified the clump from which the young stars in the cluster surrounding the water masers have formed.

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1a.ps}}\end{figure}$

Figure 1: a) Spectra of some rotational transitions observed towards the H₂O maser position (i.e. the map centre, see Table 1) in NGC 281-W. The main beam brightness temperature ( $T_{\rm MB}$ ) is plotted against the local standard of rest (LSR) velocity. The conversion factor from $T_{\rm MB}$ to flux density is 4.7 Jy K^-1. The dotted horizontal and vertical lines correspond respectively to $T_{\rm MB}$ = 0 K and to the $V_{\rm LSR}$ of the C³⁴S(3-2) line obtained with a Gaussian fit. The vertical lines in the bottom panel indicate the F=0-1 (left), 2-1 (centre), and 1-1 (right) hyperfine components of the HCN(1-0) transition

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1b.ps}}\end{figure}$

Figure 1: b) Same as previous figure, for AFGL5142

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1c.ps}}\end{figure}$

Figure 1: c) Same as previous figure, for S233

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1d.ps}}\end{figure}$

Figure 1: d) Same as previous figure, for GGD4

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1e.ps}}\end{figure}$

Figure 1: e) Same as previous figure, for S235B

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1f.ps}}\end{figure}$

Figure 1: f) Same as previous figure, for MONR2

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1g.ps}}\end{figure}$

Figure 1: g) Same as previous figure, for GGD12-15

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1h.ps}}\end{figure}$

Figure 1: h) Same as previous figure, for NGC 2264-C

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1i.ps}}\end{figure}$

Figure 1: i) Same as previous figure, for IRAS20126+4104

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1j.ps}}\end{figure}$

Figure 1: j) Same as previous figure, for IC 1396-N

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1k.ps}}\end{figure}$

Figure 1: k) Same as previous figure, for L1204-G

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f1l.ps}}\end{figure}$

Figure 1: l) Same as previous figure, for IRAS23151+5912

4.3 Tables of relevant quantities

The line parameters at the peak position in the maps (corresponding to the maser position) are given in Tables 7 to 10. We have separated transitions with "simple'' line profiles (such as e.g. ¹³CO) from those where we have detected many components (such as CH₃OH) and hence give their parameters in different tables.

In Table 7, we list the measured line parameters for ¹³CO, HCO⁺, CS, C³⁴S, and HCN. We give in column: 1) the source name; 2) the two extreme velocities ( $V_{\rm min}$ and $V_{\rm max}$ ) at which the line intensity becomes less than twice the RMS noise: thus $\mbox{$V_{\rm min}$}-\mbox{$V_{\rm max}$}$ is the the full width at zero intensity (FWZI); 3) the peak temperature $T_{\rm peak}$ ;4) the velocity of the peak $V_{\rm LSR}$ ;5) the integral of the area under the profile; 6) the 1 $\sigma$ RMS of the spectrum. We note that, in the case of HCN, $V_{\rm min}$ and $V_{\rm max}$ are strongly affected by the F=0-1 and 1-1 hyperfine satellites which clearly widen the velocity range over which emission is detected.

There are a number of indications of high optical depth in the transitions observed by us. In the case of CS for example, we have observed both CS(3-2) and C³⁴S(3-2) in seven of the sources of our sample. From Table 7, one finds (excepting L1204-G where C³⁴S is very weak) that the ratio of CS(3-2)/C³⁴S(3-2) integrated intensities varies between 14.3 (IC 1396) and 8.5 (S233) whereas the corresponding ratio of peak intensities varies between 12.9 (AFGL5142) and 7.8 (23151+5912). These ratios should be compared with the local ISM value for ³²S/³⁴S of 22 (Wilson & Rood 1994). We conclude that the difference is due to moderate optical depth in CS(3-2). We also think it probable that HCN(1-0) is optically thick in many cases. Although the hyperfine satellites are usually blended with one another, from Table 8 it is clear that the intensity ratios vary substantially from the 5:3:1 (2-1:1-1:0-1) ratio expected in optically thin LTE.

Tables 9 and 10 list the parameters of the CH₃OH and CH₃CN transitions. These have been obtained by Gaussian fits, fixing the separation in frequency of different K-components to the laboratory values and forcing their line widths to be identical. We give the $V_{\rm LSR}$ and full width at half maximum (FWHM), and for each line the integrated intensity. Note that Table 10 contains only the rotational transitions for which at least one K component was detected.

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2a.ps}}\end{figure}$

Figure 2: a) Spectra of the CH₃CN and CH₃OH rotational transitions towards the H₂O maser position (i.e. the map centre, see Table 1) in NGC 281-W. The main beam brightness temperature ( $T_{\rm MB}$ ) is plotted against the frequency. The conversion factor from $T_{\rm MB}$ to flux density is 4.7 Jy K^-1. The dotted lines indicate the CH₃CN (lines above the spectrum) and C ${{\rm H}_3}^{13}$ CN (from below), and the CH₃OH transitions; the corresponding quantum numbers are also shown

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2b.ps}} \end{figure}$

Figure 2: b) Same as previous figure, for AFGL5142

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2c.ps}} \end{figure}$

Figure 2: c) Same as previous figure, for GGD4

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2d.ps}} \end{figure}$

Figure 2: d) Same as previous figure, for S235B

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2e.ps}} \end{figure}$

Figure 2: e) Same as previous figure, for MONR2

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2f.ps}} \end{figure}$

Figure 2: f) Same as previous figure, for NGC 2264-C

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2g.ps}} \end{figure}$

Figure 2: g) Same as previous figure, for IRAS20126+4104. Also the CH₃CH₃O 7₁₇-6₀₆ line at 147024.8 MHz, the HNCO 10₁₉-9₁₈ line at 220584.766 MHz, and the C₃H₂ 3₁₂-2₂₁ line at 145089.63 MHz can be seen in the spectra

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2h.ps}} \end{figure}$

Figure 2: h) Same as Fig. 2a, for IC 1396-N

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f2i.ps}} \end{figure}$

Figure 2: i) Same as previous figure, for L1204-G

In Table 11 we give the measured full width at half power (FWHP) of the maps and the angular diameter after deconvolution ( $\Theta_{\rm S}$ ) for a Gaussian source. The FWHP has been obtained as the diameter of a circle with the same area as that inside the 50% contour in the corresponding map. From this table, one sees that ¹³CO typically traces a component which extends beyond the borders of our map and thus the observed emission emanates only in part from the dense core associated with the water masers. HCN and HCO⁺ appear to trace extended material surrounding the core whereas the C³⁴S and CH₃OH transitions arise from gas relatively close to the water maser. It is plausible that the optically thick lines have more extended emission than optically thin transition and this may explain for example the slightly higher angular sizes seen in HCN, HCO⁺, and CS than in C³⁴S. In the case of methanol, there is evidence in the literature that it has high abundances in high temperature regions (Menten et al. 1986) and this may also influence the observed distribution.

4.4 Line widths and line asymmetries

Because of its low abundance and relatively high critical density, C³⁴S is known to trace dense regions. Such regions are probably well defined, compact clumps characterised by a "simple'' velocity field, as suggested by two facts: the C³⁴S(3-2) profiles observed by us can be fitted with a single Gaussian component with FWHM $\sim$ 1/2 as that of the ¹³CO(1-0) line; and the angular diameter in the C³⁴S(3-2) line is always $$\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil $\displaystyle ...$ 2 times smaller than that in ¹³CO(2-1) (see Table 7). Consequently, the peak velocity of the C³⁴S(3-2) can be assumed to represent the bulk velocity of the high density gas.

All these aspects suggest that the dynamics of the lower density gas (traced by ¹³CO) is decoupled from that of the embedded high density clump (seen in C³⁴S). The greater linewidths and blue/red distribution of the low density gas originate from larger scale turbulence or motions of different sub-clouds and do not seem to be directly related to the presence of a high density clump.

We postpone to Sect. 5 a more detailed analysis of the molecular gas in each source, which requires a study of the cloud structure in different velocity intervals.

With this in mind, in Fig. 9 we have reproduced the ¹³CO(2-1) profiles, aligning them to the C³⁴S(3-2) peak velocity. In this way one can check for possible ¹³CO(2-1) line asymmetries and differences between the ¹³CO and C³⁴S peak velocities. For example, a dip in the ¹³CO profile in correspondence of the C³⁴S peak may indicate self absorption due to temperature gradients in the molecular gas. Indeed, this occurs in two cases (MONR2 and IC 1396-N), although it might be due to absorption of foreground cooler gas at the same bulk velocity. The profile of the ¹³CO(2-1) gas on the blue and red side of the C³⁴S(3-2) peak does not show any systematic trend. In four sources the blue and red sides have almost equal intensity, in the remaining eight cases, four have larger integrated values on the blue side and four on the red side (with ratios of blue to red and vice-versa up to a factor two in both cases).

4.5 Line ratios in C³⁴S

On the basis of our C³⁴S measurements, we can attempt to constrain the density and temperature in the core surrounding the water masers. In Fig. 10, we show our measured $T_{\rm B}$ (3-2)/ $T_{\rm B}$ (2-1) and $T_{\rm B}$ (5-4)/ $T_{\rm B}$ (3-2) line brightness temperature ratios for C³⁴S in our sources; note that $T_{\rm B}$ has been obtained from Table 7, after correction for beam dilution using the sizes from Table 11 or (where not possible) with an assumed size of 20 $^{\prime\prime}$ . We compare these with the results of Cesaroni et al. (1991), who mapped a sample of UC HII regions in the same transitions. It appears that the latter sample has slightly higher values of $T_{\rm B}$ (5-4)/ $T_{\rm B}$ (3-2) than our sources, but the difference is not large. Cesaroni et al. (1991) derived densities of order 10⁶ cm^-3 for their sample and we conclude that the sources in our sample have densities which are not greatly smaller.

We also show in Fig. 10 the results of LVG calculations for C³⁴S carried out assuming an abundance ratio [C³⁴S]/[H₂] of 10^-10 and temperatures of 50 K and 100 K. The abundance chosen is similar to that found for C³⁴S in other sources and has the effect that C³⁴S is optically thin for the parameter range considered by us. Thus, "trapping'' is not of great importance. We have used the rate coefficients discussed by Turner et al. (1992) but note that these are essentially the same as the earlier rates used by Cesaroni et al. (1991).

From Fig. 10 one sees that while the Cesaroni et al. (1991 ) sample is in good agreement with model predictions, our sources tend to have $T_{\rm B}$ (3-2)/ $T_{\rm B}$ (2-1) intensity ratios close to or even larger than the maximum value allowed in LTE (2.25). This suggests that the temperature is high (above 30 K) and that probably there is a contribution to the (3-2) intensity from an unresolved hot compact source. The $T_{\rm B}$ (5-4)/ $T_{\rm B}$ (3-2) ratios suggest moreover that H₂ densities are approximately 5 10⁵ cm^-3: such a value is probably somewhat lower than found in the Cesaroni et al. (1991) study although the difference is small.

4.6 Boltzmann plots

The large number of methanol transitions detected in NGC 281-W, IRAS20126+4104, IC 1396-N, and L1204-G make possible to derive temperature and column density estimates by means of the rotational diagram method, which assumes that the CH₃OH molecule is populated according to LTE. The corresponding Boltzmann plots are shown in Fig. 11 and the derived rotation temperatures and source averaged column densities are given in Table 12. We have assumed source angular diameters equal to those given in parentheses in Table 11.

One sees that, with the sole exception of IRAS20126+4104, the values of $T_{\rm rot}$ are quite low, even lower than the peak brightness temperature of the ¹³CO(2-1) line (see Table 7), which very likely represents just a lower limit to the kinetic temperature of the ¹³CO gas. Since the CH₃OH gas is confined to a much smaller region than ¹³CO (see Table 11), this might suggest a temperature decrease towards the centre of the molecular clumps. However, we believe this is not the case, because it is well known (see e.g. Johnston et al. 1992) that the CH₃OH molecule is subthermally excited, namely that $T_{\rm rot}$ underestimates the true CH₃OH kinetic temperature. Indeed, better temperature indicators such as CH₃CN give larger values of $T_{\rm rot}$ than CH₃OH, i.e. $\sim$ 30 K for NGC 281-W and $\sim$ 150 K for IRAS20126+4104. Also, the latter source has been observed in the CH₃CN(6-5) transition with high angular resolution (Cesaroni et al. 1997a), confirming the existence of a small ( $\sim$ 1 $^{\prime\prime}$ ) dense core much hotter ( $\sim$ 200 K) than the gas on larger scales, such as ¹³CO and CH₃OH.

Unlike $T_{\rm rot}$ , the column density derived from CH₃OH is quite reliable. For an assumed CH₃OH abundance with respect to H₂ of 10^-7, one derives an H₂ column density of 10²² cm^-2, which is about an order of magnitude below the value derived for clumps associated with UC HII regions (Cesaroni et al. 1991). This result is consistent with the conclusion of Sect. 4.5 that the densities of our sample are lower than those derived by Cesaroni et al. (1991) for their clumps.

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3a.ps}\end{figure}$

Figure 3: a) Maps towards NGC 281-W of the integrated emission in the ¹³CO(2-1) (top left panel), HCN(1-0) (bottom left), CS(3-2) (top right), and HCO⁺(1-0) (bottom right) lines. Thick contours correspond to 50% of the maximum in each map. The $\times$ indicate the observed positions, and the filled triangles the positions of the H₂O maser spots. The values of the contour levels are given in Table 6

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3b.ps} \end{figure}$

Figure 3: b) Same as previous figure, for AFGL5142

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3c.ps} \end{figure}$

Figure 3: c) Same as previous figure, for S233

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3d.ps} \end{figure}$

Figure 3: d) Same as previous figure, for IRAS20126+4104

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3e.ps} \end{figure}$

Figure 3: e) Same as previous figure, for IC 1396-N

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3f.ps} \end{figure}$

Figure 3: f) Same as previous figure, for L1204-G

$\begin{figure} \includegraphics[angle=-90,width=8cm]{h1279f3g.ps} \end{figure}$

Figure 3: g) Same as previous figure, for IRAS23151+5912

$\begin{figure} \includegraphics[angle=-90,width=7cm]{h1279f4a.ps}\end{figure}$

Figure 4: a) Maps towards GGD4 of the integrated emission in the ¹³CO(2-1) (top panel) and HCN(1-0) (bottom) lines. Thick contours correspond to 50% of the maximum in each map. The filled triangles indicate the positions of the H₂O maser spots, the $\times$ the observed positions. The values of the contour levels are given in Table 6

$\begin{figure} \includegraphics[angle=-90,width=7cm]{h1279f4b.ps} \end{figure}$

Figure 4: b) Same as previous figure, for S235B

$\begin{figure} \includegraphics[angle=-90,width=7cm]{h1279f4c.ps} \end{figure}$

Figure 4: c) Same as previous figure, for MONR2

$\begin{figure} \includegraphics[angle=-90,width=7cm]{h1279f4d.ps} \end{figure}$

Figure 4: d) Same as previous figure, for GGD12-15

$\begin{figure} \includegraphics[angle=-90,width=7cm]{h1279f4e.ps} \end{figure}$

Figure 4: e) Same as previous figure, for NGC 2264-C

$\begin{figure} \resizebox{7cm}{!}{\includegraphics{h1279f5.ps}}\end{figure}$

Figure 5: Maps towards IRAS20126+4104 of the integrated bulk emission in the CH₃OH(3-2) (top panel), CH₃CN(8-7) (middle), and C³⁴S(3-2) (bottom) transitions. Thick contours correspond to 50% of the maximum in each map. The HPBW is $\sim$ $17\hbox{$^{\prime\prime}$}$ . The filled triangles indicate the positions of the H₂O maser spots, the $\times$ the observed positions. Contour levels for CH₃CN(8-7) range from 4.9 to 14 by 1.5 K km s^-1; the values of the contour levels for the other maps are given in Table 6

Up: High density molecular clumps