4 Discussion

  In this section, we look at the survey as a whole, drawing together the results from individual molecules. We discuss the features that the cores have in common and the differences between them. We bring together what we have learned about physical conditions and structure from the various molecular tracers. Implications for our understanding of the environment for models of UC HII regions are discussed. The chemistry in hot cores is considered and we look at whether chemical models can predict the observed column densities.

4.1 Physical conditions and structure

 The first striking point about this survey is that the number of lines detected varies greatly from source to source. In the 239 GHz spectra, which cover 13 out of 14 sources, more than 30 molecular lines are detected in G10.47, G34.26 and G31.41 but only two low-excitation CH₃OH lines are detected in G45.12, G45.45, 45.47, and 13.87. If the transitions observed in the survey are roughly divided into groups of low (< 50 K) and high excitation energy, the low excitation lines are detected towards all sources whereas the high excitation lines are not. Examples of low excitation lines in this survey are C¹⁸O and C¹⁷O, C³⁴S (though this was not detected towards G10.30) and the CH₃OH lines at 241.767 and 241.797 GHz. High excitation lines include the CH₃CN J=13-12 lines, which were observed towards thirteen sources and detected towards eight of them (J=19-18 was detected in the fourteenth); CH₃OH lines such as $J=12(1)-12(0)\pm$ at 336.865 GHz; and the CH₃CCH lines in the 249 GHz band.

High excitation energy lines require high temperatures to excite, so the non-detections mean that for a number of sources in this survey we have no evidence for hot cores. However, these sources have all previously been detected in NH₃ (4,4) line which is >200 K above ground, and therefore are known to have associated hot gas. The main reason for the non-detection of hot gas in the weakest emitters is simply limited sensitivity. The six line-poor sources in our survey are also the weakest NH₃ (4,4) emitters (Cesaroni et al. 1991; Olmi et al. 1993), suggesting that the non-detections correspond to sources with a low column density of hot gas or small source size. The brightness of the high-excitation lines does not correlate with distance, pointing to intrinsic differences in the source properties, rather than simply beam-dilution effects.

Another factor which may have some effect on the line brightnesses is any offset between the pointing centre of the JCMT beam, which is 20'' FWHM at 349 GHz, and the centre of the hot core. Such offsets could arise because of poor pointing or because the molecular cores are offset from the UC HII regions with which they are associated. However, an emission region with lines as bright as G34.26 or G10.47 would have to be offset by $\sim\!10''$ or more from the beam centre in order to fail to be detected by this survey.

In the eight line-rich sources, the strength of high excitation energy lines of CH₃CN, CH₃OH, CH₃CCH, SO₂ and other molecules indicate the existence of hot, dense gas. CH₃OH and CH₃CN are our best tracers of the physical conditions in the hot gas as we observed many emission lines of each spanning a wide range of excitation energies. From our LTE analyses of CH₃CN and CH₃OH in the five strongest sources (G9.62, G10.47, G29.96, G31.41 and G34.26), we found that the high excitation lines are emitted from a source or sources with a small beam filling factor. Both the detection of CH₃¹³CN and ¹³CH₃OH lines and the pattern of emission in CH₃¹²CN and ¹²CH₃OH are inconsistent with an extended, low column density source.

We have assumed for the purposes of our analysis that the small beam filling factor comes about because the emission comes from a single central condensation rather than widely scattered clumps. Interferometric observations of a few of the sources in the sample have shown single cores of 1 - 2'' in hot CH₃CN, NH₃ and other molecules (Cesaroni et al. 1994a,b; Olmi et al. 1996a,b; Mehringer & Snyder 1996, Cesaroni et al. 1998) though in G9.62 multiple cores are resolved (Hofner et al. 1996). In some cores we have made observations 20'' from the position of the UC HII region. These show little emission from hot gas: only in G9.62 and G34.26 do we see emission at the at (0, $20\hbox{$^{\prime\prime}$}$) offset position in CH₃CCH, but not CH₃OH or CH₃CN. If the cores were offset or scattered widely, we would expect to see hot gas in the 20'' off positions. Our single-dish observations give no information on the shape of the core. Where necessary in the calculations we assume spherical symmetry.

In both CH₃CN and CH₃OH, the hot cores are 0.02 - 0.1 pc in diameter (1 - 5'' at the distance of G34.26). We see differences in the core size in different molecular tracers. The region of the hot core traced by CH₃OH is larger than the CH₃CN, and there is some evidence that the lower energy transitions of CH₃CN trace larger cores than the higher energy transitions. This is consistent with a model of hot cores in which there is a gradient of density and temperature increasing towards the centre, rather than a sharply defined boundary.

The physical conditions in the hot cores are extreme. On the 0.02 - 0.1 pc scales traced by CH₃CN and CH₃OH, densities are a few times $10^7 \hbox{ cm}^{-3}$ to $10^8 \hbox{ cm}^{-3}$, from virial masses. Even more extreme densities in G34.26, G10.47 and G31.41 are suggested by the observation of ¹³CH₃OH, as the implied optically thick CH₃OH component can be explained if densities reach $10^9 \hbox{ cm}^{-3}$. Where we have sufficiently accurate temperature determinations, we see that temperatures rise towards the centres of the cores: we see CH₃OH with an average temperature of 50 K; within that, the CH₃CN region is 70 K or more; and within this region the excitation of vibrationally excited CH₃OH suggests the presence of hot dust at temperatures of several hundred kelvin.

Strong emission in low excitation lines is visible in all sources. These low excitation lines account for all the line emission from the line-poor sources. From the temperatures ($\sim\!20-30$ K) and source sizes ($\sim\!0.5$ pc) estimated from the analysis of C¹⁷O and C¹⁸O, the low excitation emission is from cool gas that is more extended than the hot core. This "cold halo" component is also required for the CH₃OH LTE model. Even in the cool gas, column densities in all the sources are high: as measured by CO, H₂ column densities range from $10^{23} \hbox{ cm}^{-2}$ to $5 \ 10^{24} \hbox{ cm}^{-2}$. We note that high column densities were an indirect requirement of our selection procedure: these sources are all emitters of the NH₃ (4,4) transition, and with typical ammonia fractional abundances of 10^-7 column densities of $10^{23}-10^{24} \hbox{ cm}^{-2}$ are required (Cesaroni et al. 1991).

The line-poor sources may have lower column densities in the halo than the line-rich sources. The cold halo CH₃OH component varies in beam-averaged column density from less than $1\ 10^{14} \hbox{ cm}^{-2} \hbox{ to } 2 \ 10^{15} \hbox{ cm}^{-2}$, with upper limits only for the line-poor sources. This variation in CH₃OH column density could be due to either underlying column density variation or to CH₃OH abundance variation. However, the line-poor sources also lie at the low end of the H₂ column density determinations from CO, assuming (as we argue in the section on CO) that the column density lower limits are in fact fairly good estimates of the true column densities. Differences in halo column density could be linked with the non-detection of hot cores in some sources.

The line-poor sources appear to be missing the hot core component. In both CH₃CN and CH₃OH, our excitation analysis shows that sources are less bright because they are smaller hot cores rather than because the source density is lower or because of temperature variations. Carried to its conclusion, this would suggest that the line-poor sources contain very small hot cores. We can put an upper limit on the CH₃OH and CH₃CN core sizes in the line-poor sources where we do not see any emission from hot gas. The smallest angular diameter core that we detect in CH₃OH is G12.21 with a size of 1.3''. The high excitation CH₃OH lines in this source are 3 and 4-$\sigma$detections. We would have detected CH₃OH lines of half this strength, equivalent to a source size of 1''. Similarly, a CH₃CN hot core less than 0.8'' would not have been detected. We observed CH₃CN J=13-12 in all sources in the survey, so we can rule out CH₃CN hot cores bigger than 0.8'' in the line-poor sources where this was not detected. Alternatively, the line-poor sources may contain hot gas of insufficient density to excite the high excitation transitions of CH₃CN and CH₃OH but yet be detectable in NH₃. CH₃CCH emission from hot gas is detected in more sources than CH₃CN and CH₃OH and could be tracing lower-density hot cores.

4.2 Implications for UC HII models

  Wood & Churchwell (1989) suggested that UC HII regions must have lifetimes of 10⁵ years in order to explain their numbers. Various models have been proposed to explain the expansion of the UC regions in a way that reconciles their long lifetimes with their small sizes. Contenders include the bow shock model (Van Buren & Mac Low 1992), champagne flow (Tenorio-Tagle et al. 1979), mass-loaded winds (Dyson et al. 1995; Redman et al. 1996; Williams et al. 1997; Lizano et al. 1996), modified Strömgen sphere models including neutral gas pressure (De Pree et al. 1995; Akeson & Carlstrom 1996) and turbulence (Xie et al. 1996). These models all depend to some extent on the physical conditions in the immediate environment of the HII region.

The two environmental parameters which we have measured that are most likely to affect the HII region expansion are density and linewidth (a measure of turbulence). We found no correlation of either of these parameters with size, when considering either hot core or halo tracers. In particular, we plotted our linewidths from CH₃CN, CH₃OH, C³⁴S and C¹⁷O and C¹⁸O against size to look for correlations, following Xie et al. (1996). Of the transitions chosen, the high excitation transitions of CH₃OH at least fulfil Xie et al.'s conditions of high critical density and low optical depth, yet we found no correlation with UC HII size. The hot core sizes do not correlate with the UC HII sizes. We also looked for any evolution of shape or size of the HII region in line with the chemical evolution of the core, without a positive result. In total, none of our measured environmental parameters correlates with UC HII region shape or size. The absence of correlation could be because we measure average conditions with a large beam rather than the conditions immediately surrounding the HII region. Also both HII region and core evolve with time, and the conditions that we see now may not explain how the HII region has evolved in the past. A third option is that the HII region expansion depends on some environmental or other parameter that we have not measured in this study.

The cloud chemistry does provide a constraint on the HII region ages. In our study of the chemical evolution of hot cores based on this survey, we calculate that the cold halos are less than 10⁵ years old (Hatchell et al. 1998, in preparation). Assuming that the UC HII regions in our sample formed in the clouds in which they now lie, they must also be younger than 10⁵ years.

4.3 Chemistry

  Hot cores have a rich and unique chemistry. Unlike cold dense clouds, hot cores have high densities of saturated molecules such as NH₃ and H₂S. These molecules are believed to form in icy mantles on dust grains, created from constituents deposited during the high density phases of collapse. As the cores heat up in the star formation process, the grain mantles are evaporated and the mantle species are released into the gas phase. A rich gas-phase chemistry proceeds in the hot gas, transforming many of the grain mantle products into daughter species on timescales of 100000 years.

We see high column densities of saturated molecules such as H₂S and CH₃OH. High abundances of saturated molecules are formed in grain ices as a result of rapid hydrogenation, so these observations confirm that grain mantle evaporation is important in hot cores (Millar et al. 1995; Mehringer & Snyder 1996). Other direct or indirect products of grain surface chemistry that we observe in the hot cores are CH₃OCH₃ and HCOOCH₃.

  

Figure 5: Measured column densities compared to model predictions for column density through the core, from Millar et al. (1997) with a core age of 104 years and a halo age of 105 years. The model predictions are marked by circles. The range of column densities observed in the survey is shown by a line. Where the measured column densities are lower limits to the column density through the core this is shown by an arrow

We have developed a model of hot core chemistry which follows the evolution of the chemistry in the core from the turn-on of core heating (Millar et al. 1997). The physical conditions used in this model were specifically tailored for G34.26 but can be generally applied to the other hot cores assuming they have similar temperatures and densities. In Fig. 5 we compare the column densities predicted by the model with those we have measured. The model predicts the total column density through the centre of the core, including contributions from core and halo, rather than the beam-averaged column density that we calculate for most molecules. The beam-averaged column density that we calculate is a lower limit on the column density through the core because of the effects of beam dilution on the core components.

Three species in particular are observed in larger amounts than the model predicts, as shown in Fig. 5. CH₃CN column densities of $10^{16} \hbox{ cm}^{-2}$ are marginally too high for this molecule to have formed in the gas phase, and if column densities are as large as $10^{17}\hbox{ cm}^{-2}$ this suggests that there is also a surface chemistry route to its formation. HCOOCH₃ column densities of 10$^{16}\hbox{ cm}^{-2}$ are larger than can be made in the gas in a hot core (Millar et al. 1997) and may indicate that grain surface reactions can produce this molecule, although the gas phase routes to HCOOCH₃ are probably not yet clearly identified. The production of such a highly unsaturated molecule has not normally been considered to be a sign of grain chemistry and is at odds with the paradigm that surface reactions produce saturated molecules. This of course is only the case as long as there is sufficient atomic hydrogen to hydrogenate the surface radicals but it is possible that, in the final stages of grain accretion, the gas is depleted in atomic hydrogen so that saturation does not occur. In this context it is interesting to note that HCOOCH₃ has been detected in Comet C/1995 O1 (Hale-Bopp) by Colom et al. (1997).

Although the model predicts enough CH₃CCH to account for the column densities observed in some sources, in others the observed beam-averaged column density lower limit exceeds the amount of CH₃CCH that can be produced by the model.

The chemistry of CH₃CCH contained in Millar et al. (1997) is obviously inadequate in its description of CH₃CCH in hot cores. A recently studied reaction which may be of importance in hot gas is that between CH and C₂H₄ (Canosa et al. 1997). Although the products have not been deterined as yet - the lowest energy products are CH₃CCH and CH₂CCH₂, however - the reaction is fast with a rate coefficient of $\sim\!4 \ 10^{-10} \hbox{ cm}^{3}~ \hbox{s}^{-1}$ over the temperature range 23 - 300 K. If CH₃CCH is the end product of this reaction, then methyl acetylene production can be enhanced in regions in which C₂H₄ is abundant, i.e. in the hot gas where it evaporates from grains. Using the above rate coefficient and abundances calculated by Millar et al. (1997) we find that production of methyl acetylene is enhanced most in the compact core of G34.3 where the CH + C₂H₄ reaction is around a factor of ten larger than that due to C₃H$_5^+ + \rm{e}$.

For most species in the survey for which we have column density estimates or limits (CH₃OH, CO, H₂S, SO₂, SO, and CS) the chemical model predicts column densities which are consistent with the data.

Because of the relatively rapid evolution of the chemistry, molecular abundances in hot cores can be used as chemical clocks to determine the onset of heating. We explore this possibility fully in a subsequent paper based on this survey (Hatchell et al. 1998, in preparation).