Astron. Astrophys. 342, 809-822 (1999)

6. Discussion

Comparing the two models allows us to contrast the gas-phase halo chemistry sampled by the single line of sight model and the mixed gas-phase and mantle-evaporation chemistry sampled by the beam-averaged model. In particular it will allow us to determine the most probable origins of certain species, i.e. can the observed column densities be reproduced by gas-phase chemistry alone or do they depend upon the grain mantle-evaporation chemistry sampled in the fringes of the beam? The limitations of the column densities derived from the observations and the predictions of the model have already been mentioned in Sect. 5; in this section we dwell upon them in more detail. We will interpret the predictions of our models below and discuss what can be done to enhance the chemical modelling of hot cores, in particular the radial chemical model of G34.26+0.15, in the next section.

Firstly, what are the similarities between both models? Broadly speaking the ratios of the model to observed column density are fairly similar in both models for most molecules (CH₃OH is the notable exception, as is SO₂ when core evolution is considered). The column densities predicted by the beam-averaged model are higher than the corresponding column densities predicted by the single line of sight model, which is due to the beam-averaged column density being larger than the "pencil-beam" column density by roughly 7. In the early halo both models do not predict sufficient CO (by a factor of up to 5) and overestimate the column densities of the other species by factors of up to several hundred at early halo ages. The model values when compared to the observations suggest a halo age of 10⁶ years (apart from CH₃OH, SO₂ and to a lesser extent HCO⁺). The column densities of CS are not well reproduced by either model.

Secondly, what are the differences between the single line of sight model and the beam-averaged model? The only molecule for which the inclusion of beam-averaging significantly alters the column density at all times in the model is CH₃OH. The methanol in the halo alone decays rapidly over the timescale of the halo evolution whereas in the beam-averaged case the methanol abundance remains roughly constant. The chemical evolution of the core tends to have little effect upon the column densities of most molecules, but the column densities of CH₃OH and SO₂ change over the core evolution timescale. The CH₃OH column density is reduced by a factor of almost 2 as the core evolves from 3.2 to 10⁴ years. The column density of SO₂ is strongly affected by the core evolution in the early halo (the model/observed ratio changes from 0.017 5.00). This occurs because relatively little SO₂ is initially present in the halo gas but is formed in core gas as H₂S is broken down. At older times in the halo, SO₂ is made efficiently and the core makes a difference to the total column density at the 5 level (at a halo age of 10⁶ years the model/observed ratio changes from 94.9 99.9). HCN is also slightly affected by the evolution of the core with the greatest change occurring with a halo age of 10⁶ years.

A key factor in both models is that they overestimate the column densities of almost every species considered. The simplest explanation for this is that our observed column densities are all lower limits based upon one or two detections of each species. The true column density may be higher than our derived lower limit and this would bring the model predictions better into line with the actual column densities. However some of the model column densities are factors of several hundred larger than the observed column densities and the true column density is unlikely to be several hundred times the observed lower limit. We have examined this in the case of the E-type form of methanol, for which we have sufficient transitions to form a rotation diagram. A lower limit to the methanol column density can be evaluated for each line used in the rotation diagram. The lower limits when compared to the strict value determined from the rotation diagram do not differ by more than a factor of 2. On the evidence of E-type methanol the lower limits do not underestimate the true column density by a significant amount. This may not be true for all the molecules detected in our survey but we can be reasonably confident that the lower limits do not underestimate the true value by more than a factor of ten.

We also note that the column densities predicted by the model will be affected by departures from our assumptions about the molecular cloud (e.g. a spherical cloud at an assumed distance of 3.1 kpc). Column density is simply the number density of the species integrated through the depth of the cloud. If the cloud is not spherical to any great degree (as can be seen in Fig. 1 the HCO⁺ emission traces a kidney-shaped cloud) the model cloud depth will not match the actual cloud depth and will give rise to errors in the predicted column density. The structural model on which the chemical model is based is that derived from the radiative transfer modelling of Heaton et al. (1993). The authors note the same problem and that the line profiles are reproduced excellently by assuming a spherical cloud.

Our model takes no account of optical depth, implicitly assuming that emission from all species is optically thin by integrating the column densities throughout the entire depth of the cloud. Optically thick emission arises predominantly from the surface layers of the cloud and column densities derived from optically thick lines will underestimate the actual column density throughout the whole cloud (i.e. the derived lower limits to column density in Table 2 are true lower limits even in the optically thick case). The lower limit to the column density of CO was obtained from the C¹⁷O 3-2 line, which is likely to be optically thin (the CO column density is obtained by assuming a ¹⁶O/¹⁷O ratio of 2400). CS is also likely to be optically thin or at most moderately optically thick as the isotopomer C³⁴S is not detected (the maximum optical depth of CS is 2-3 if C³⁴S is below the 5 level). Other species may well possess some degree of optical depth and will in consequence have a larger actual column density than is observed. We note that CH₃OH observed towards hot core sources by Hatchell et al. (1998a) had optical depths of 10, however these values are for observations towards the cores and not specifically towards the halo.

Given the above caveats we must reconcile the model predictions with the observations of the halo, in particular to estimate the degree of influence by the core. The model predicts that the column densities of methanol are strongly affected by the high column densities present toward the core (the core column density of methanol is some 4 orders of magnitude greater than the halo, Millar et al. 1997). The observational evidence for this is somewhat limited. Methanol does not display an overly high rotation temperature ( 30 K, as compared to the core temperature of 300 K) as would be expected if the emission was predominantly from the core and the widths of the lines seen in the halo survey are roughly a third of those seen in the hot core survey of Paper I. This suggests that the methanol emission is more likely to originate from the halo rather than from dense hot gas picked up in the fringes of the beam. Other species, such as CS and HCN, have comparable linewidths in both core and halo and their halo emission might be due to pickup from the core. The beam-averaged model predicts no change in the column density of CS and a marginal change in the column density of HCN when the core is taken into account through beam-averaging. Further observations at larger angular distances from the core are necessary to confirm the core origins of HCN and CS.

The line widths and rotation temperature of the methanol suggest that the methanol emission is predominantly from the halo. This is at odds with the predictions of the beam-averaged model where the observed column densities of methanol are reproduced by the inclusion of warmer gas toward the core. The beam-averaged model does not however take into account the possibility of grain mantle evaporation in the halo. Temperatures in the inner regions of the halo may be high enough to evaporate volatile non-polar ices from grain mantles and enrich the gas-phase chemistry. If the temperature from the methanol rotation diagram is taken to be representative of the gas temperature, then the halo has an average temperature of 30 K at this position. This compares to the predicted temperature from the structural model of 44 K at this position (0.3 pc from the core centre). The temperature of the innermost halo layers should be around 75 K, according to the structural model.

Large quantities of CO are present in grain mantle ices (Chiar et al. 1994, 1995). CO can react on the grain surface with hydrogen atoms, maintained by cosmic-ray processes, to produce CH₃OH (van Dishoeck & Blake 1998 and references therein). The constituents of the grain mantle ices evaporate at different temperatures, which may lead to a chemical stratification of the cloud. CO in non-polar ices is thought to evaporate at temperatures of 15-20 K, or if trapped in polar ices is expected to sublime at temperatures of 60 K (Tielens et al. 1991). The temperature in the region of the halo sampled by the beam is certainly high enough to evaporate CO ice from grains, which may explain why the model does not reproduce the observed CO column densities.

Methanol has a higher sublimation temperature than CO; perhaps 90 K if present in mixed polar ices (Sandford & Allamandola 1993). Methanol may sublime at lower temperatures than this if it is trapped in more volatile non-polar ices. However a greater understanding of the sublimation processes in molecular ice mantles is required to say whether this is plausible at the temperatures within the halo ( 30 K). Alternatively the methanol in the halo may be the legacy of a higher temperature period in the halo, perhaps caused by shocks. The lack of core pickup predicted by the model must also be explained. If the column density of methanol is larger than expected in the halo, the core column density must be correspondingly reduced. In this case pickup of methanol from the core is much less important to the column density. Or more simply, the methanol core may be smaller than expected. Further observations of methanol in the halo at greater distances from the core are required to address these possibilities.

We have also investigated the model predictions of the column density of propyne (CH₃CCH) in the halo of G34.3. The observed propyne column density of 4.6 cm^-2 at an offset (0, ) from the cloud centre (Hatchell et al. 1998a) was used. The model/observed ratios from both of our models at this position are 0.327 5.85 as the halo ages from years in the single line of sight model and as the halo ages from years in the beam-averaged model. The beam-averaged model propyne column density is altered by core evolution, most notably in medium and old halo models (10⁵ and 10⁶ years) where the column density increases by an order of magnitude over 10⁴ years. Neither the beam-averaged nor single line of sight model can reproduce the observed column density of propyne at late times. Propyne is likely to originate in the core, the linewidths seen in the halo are comparable to those in the core. The main production route of propyne in the model is via mantle-evaporated C₂H₄. However the high column density seen by Hatchell et al. (1998a) in the halo implies that the chemistry of propyne is not well understood.

The model overestimates the column densities of most species, particularly CS at all times of the model. One reason why the column density of CS in the model is much higher than observed may be that the initial abundance of sulphur is too high. In the compact and ultracompact cores sulphur is injected into the gas phase from grain mantles in the initial form of H₂S, with an abundance of 10^-6, following observations of the Orion Hot Core by Minh et al. (1990). A recent study of sulphur chemistry in hot cores (Hatchell et al. 1998b) shows that a lower initial abundance of H₂S (10^-7) may help to reproduce the observed column densities of CS. The column density of SO₂ also depends upon the intial sulphur abundance as both SO₂ and CS are mainly produced in the halo gas by reactions with atomic sulphur. A decrease of the initial abundance of atomic sulphur present in the halo corresponding to that of Hatchell et al. (1998b) would reduce model column densities by a factor of 10. A reduction in the elemental sulphur abundance in the halo by a factor of 10-50 would predict CS abundances much closer to those observed and alter the prediction of SO₂ for the halo age much more in line with other species, i.e. to an age of roughly 10⁶ years.

Combining the predictions of all the species modelled leads to a rough timescale for the evolution of the halo, with a cautionary warning that the final results are sensitively dependent upon the initial abundances of the model (as seen above for the CS and SO₂ abundances). Different molecular tracers predict different ages for the halo and core (as can be seen in Tables 4 and 5). The consideration of the initial sulphur abundance and mantle-evaporation chemistry in the halo may remove the discrepancies between the different molecules, although further investigation is necessary to resolve their effects. If the initial sulphur abundance is too high then the halo is likely to be old (10⁵-10⁶ years), whereas if the evaporation of grain mantles is important for halo chemistry then the halo may be considerably younger. However when all of the molecules and their predicted column densities are considered the most likely age for the halo is 10⁵-10⁶ years. A young halo contains roughly two orders of magnitude more of HCN and CN than is observed. The column densities of certain molecules (CS and propyne) cannot be reproduced by either the beam-averaged or single line of sight models. The column density of methanol can be reproduced by the beam-averaged model but observational evidence (low rotational temperature and narrow linewidths) points to the methanol emission originating from the halo. We will discuss possible improvements to the radial chemical model in the next section.

© European Southern Observatory (ESO) 1999

Online publication: February 23, 1999
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