Astron. Astrophys. 361, 1079-1094 (2000)

4. Discussion

4.1. Comparison with other HNCO data

Most of our HNCO sources are new detections. Only few were included in the surveys of Jackson et al. (1984) and Churchwell et al. (1986). A direct comparison with the intensities measured by Jackson et al. is impossible due to different temperature scales. Common detected sources are Orion KL and W51. Their upper limit for W3(OH) does not contradict our value if we take into account the difference in the temperature scales. The upper limits for the transition obtained by Churchwell et al. do not contradict our results taking into account the differences in the beam sizes and efficiencies.

As mentioned above, towards Orion KL several HNCO lines were observed at 220 GHz by Sutton et al. (1985). Their results agree in general with our measurements though there is a discrepancy concerning the intensity of the transition (Sect. 3.3).

It is worth noting that while at 22 GHz and at 110 GHz (as obtained by Jackson et al. 1984) the brightest source of HNCO emission is the Galactic center, at 220 GHz the situation changes and Orion becomes the brightest source with several other sources approaching Sgr A in intensity. Apparently this is caused by differences in excitation.

4.2. Rotational diagrams

As a first step in the excitation analysis we construct traditional rotational diagrams for our sources. For a recent discussion of this method see e.g. Goldsmith & Langer (1999). This means a plot of the column density () per statistical weight () of a number of molecular energy levels, as a function of their energy above the ground state (). In local thermodynamic equilibrium (LTE), this will just be a Boltzmann distribution, so a plot of versus will yield a straight line with a slope of . The temperature inferred is often called the "rotational temperature".

Actually from the measurements we do not obtain directly the column densities. The measured quantity is the line intensity. In an optically thin case for ( is the excitation temperature of the transition and is the background temperature)

where W is the integrated line intensity, is the beam dilution factor, S is the line strength, is the appropriate component of the dipole moment, N is the total column density and is the partition function.

The quantity on the left hand side of Eq. (1) can be derived from the molecular data. Plotting it versus we can find the rotational temperature (from the slope) and the total column density (from the intercept).

Some problems can arise from an uncertainty in the beam filling factor. As shown in Fig. 4 the sources are probably unresolved. Assuming that the source size is the same for all HNCO transitions in a given source and that the source size is small with respect to the beam, we reduced all data to the same beam size, the SEST HPBW at 220 GHz, i.e. 24".

For Orion the highest observed transition lies  K above the ground level. For other sources we managed to observe transitions up to  K above the ground state. Examples of the rotational diagrams are presented in Fig. 7, Fig. 8.

Fig. 7. Rotational diagrams for selected sample sources (, S is the line strength). Filled squares correspond to the measured values and the open squares to the values corrected taking into account the beam sizes (see text). The diamond on the Sgr A plot corresponds to the data from Lindqvist et al. (1995)

Fig. 8. Logarithm of integrated line intensity divided by the line strength and frequency versus upper-state excitation energy for Orion A. The filled squares correspond to the measured values and the open squares represent the values corrected for beam width ratios (see text). The points corresponding to transitions are encircled

The measured integrated intensities are represented by filled squares (). The corrected results are plotted by open squares in Fig. 7, Fig. 8. One can see that they much better correspond to each other than the uncorrected values.

The rotational diagram for Orion is presented in Fig. 8. The rotational temperature from this plot is  K for the lowest transitions and  K for the highest transitions. The latter one is a very high value even for Orion KL. But in principle the diagram shows a range of rotational temperatures. We represent it by 3 components as shown in Table 15. A separate fit to the transitions gives  K (although this fit is not very satisfactory).

Table 15. HNCO rotational temperatures, column densities and relative abundances.

The rotational temperatures and column densities derived from rotational diagrams are summarized in Table 15. In this analysis we assume that the sources are optically thin in the observed transitions. This contradicts the tentative detection of HN¹³CO in G 301.12-0.20. The effects of high optical depth on rotational diagrams have been analyzed recently by Goldsmith & Langer (1999). In optically thick case the column density in the upper level of the transition () is underestimated by the factor of and, therefore, corresponding points in the population diagram lie lower than they should. In general, for linear molecules it produces a curvature resembling that seen in the diagrams for Orion and some other sources. It is caused by the fact that the optical depth exhibits a peak for transitions with the excitation energy (Goldsmith & Langer 1999). However, for nonlinear molecules the optical depth effect rather leads to a "scatter" in the population diagram, because transitions with significantly different optical depth can have similar excitation energies.

There is a strong argument against high optical depth at least for transitions with  K in Orion. In this range transitions with similar energies of the upper state but with very different frequencies (belonging to different ladders) were observed. It is easy to estimate the expected ratio of peak optical depths in the lines which is

For the exponential factor is close to unity.

In our data there are pairs of transitions with similar upper state energies. The and transitions have similar  K. However, the first one has higher line strength and higher transition frequency; therefore, according to Eq. (2) it should have higher optical depth than the second one. Then, it should be stronger influenced by possible optical depth effects and the corresponding point in Fig. 8 should lie lower than the point corresponding to the transitions. However, this is not a case. Actually, the points are very close to each other and perhaps slightly shifted in the opposite sense. The same is true for the and transitions with  K. We conclude that the optical depth for Orion in these transitions should be low. Perhaps in some other transitions or in other sources optical depths are as high as indicated by our tentative HN¹³CO detection. There is however no reason to apply optical depth corrections to the bulk of our sources.

Transitions with low values are fitted by rather low temperature models,  K. Transitions between higher excited states are related to higher rotational temperatures up to  K. In Table 15 we also present estimates of the HNCO relative abundances. The hydrogen column densities have been calculated from the C¹⁸O data under the assumptions of LTE and a C¹⁸O relative abundance of (Frerking et al. 1982). Typical HNCO abundances are . Sgr A does not look very exceptional here. The relative HNCO abundance in Sgr A is about the same as in Orion but the rotational temperature is much lower. In contrast to many other sources there is no high excitation temperature component in Sgr A, indicating that the dense gas is probably cool. This agrees with results from Hüttemeister et al. (1998) based on SiO and C¹⁸O. The opposite scenario, a hot highly subthermally excited low density gas component (n(H₂) cm^-3) as observed by Hüttemeister et al. (1993) in ammonia toward Sgr B2 is less likely, due to the correlations between HNCO and SiO that will be outlined in Sects. 4.4 and 4.6.

It is important to emphasize that our estimates give lower limits to the relative abundance X(HNCO) = N(HNCO)/N(H₂) for at least two reasons. First, the HNCO sources are much more compact than their C¹⁸O counterparts and tend to be spatially unresolved. Our estimates give beam averaged values and "real" abundances in regions of HNCO line formation should be significantly higher. Second, if the HNCO optical depth is high we would underestimate its column densities.

Next, we have to mention that all these estimates refer to the bulk of the cores. In the high velocity gas the HNCO abundances are apparently much higher.

One might think that better estimates of HNCO abundances can be obtained from comparison with the dust emission rather than with C¹⁸O. As shown, HNCO probably arises in "warm" environments and in the dust emission we see preferentially a high temperature medium while in C¹⁸O the reverse is true. However, interferometric observations in Orion (Blake et al. 1996) show that HNCO and dust distributions do not entirely coincide. At the same time, as shown in Sect. 4.5, there is a tight correlation between the FIR emission at 100 µm and C¹⁸O(2-1) integrated line intensity. Therefore, no large differences between estimates of HNCO abundances by both methods can be expected. There are detailed studies of dust emission towards some of our sources with comparable angular resolution. E.g. Henning et al. (2000) show that total gas column densities derived from dust and from C¹⁸O(2-1) in G301.12-0.20 coincide within a factor of 3.

In Fig. 9 we plot the HNCO abundances versus the HNCO line widths. There is a trend of increasing the HNCO abundance with increasing HNCO line width. This shows that the HNCO production can be related to dynamical activity in the sources.

Fig. 9. HNCO relative abundance versus the HNCO line width for sources observed at SEST (filled squares) and in Onsala (open squares)

Table 15 and Fig. 9 indicate that abundances derived for the sources which belong to the inner and to the outer Galaxy, respectively, are about the same. Therefore, there is no significant galactic gradient in HNCO abundance.

4.3. Physical conditions in regions of HNCO emission

Now we shall try to understand the physical conditions in regions of HNCO emission detected by us. An important question to start with is which excitation mechanism dominates, radiative or collisional? And which gas parameters are implied by each of them? To answer these questions properly would require a numerical model taking both into account. Useful conclusions can, however, also be obtained by semi-qualitative consideration presented below. We concentrate here on Orion KL as the best studied source.

At first, we need an estimate for the size of the HNCO emission region. Our map presented in Fig. 4 gives an upper limit of for the transition. Interferometric results (Blake et al. 1996) give a size of for the transition at 220 GHz. This can be probably considered as an upper limit also for higher ladders. On the other hand we can obtain a lower limit on the source size from the comparison of the brightness and excitation temperatures. For  K (as follows from the population diagram) we obtain that the lower limit on the beam filling factor for the transitions in Orion is . Therefore, the effective size of the emitting region is " or  pc, i.e.  cm.

Let us consider the physical requirements in the case of collisional excitation. The critical densities defined as ( is the spontaneous decay rate and is the collisional de-excitation rate; Scoville et al. 1980) are  cm^-3 for the transition and  cm^-3 for the transition (the collisional rates are  s^-1cm³ as obtained from Sheldon Green's program available on Internet - http://www.giss.nasa.gov/data/mcrates/ ). Much higher densities are needed for excitation of the transitions in the ladders. This is caused by fast b-type transitions between different ladders. E.g. the spontaneous emission rate from the ladder to the ladder is  s^-1. This implies a critical density of  cm^-3. The gas kinetic temperature should be  K.

Such conditions cannot be excluded. Walker et al. (1994) derived from observations of vibrationally excited CS  cm^-3 and  K in a region  cm from the stellar core toward IRAS 16293-2422. The question is whether the required amount of such gas is consistent with the observations.

Taking into account the lower limit on the source size the mass of the hot dense gas ( cm^-3,  K) would be  . Estimates of the hot core mass from dust continuum measurements give values of   (Masson & Mundy 1988; Wright et al. 1992). Taking into account the uncertainties in our estimations we cannot entirely exclude the possibility of collisional excitation even for the ladder but this appears to be an unlikely scenario.

For the lower ladders the density requirements can be significantly relaxed. E.g. for the b-type transitions from the to the ladder the spontaneous decay rate is  s^-1 and the critical density is  cm^-3.

The transitions in the ladder, of course, will be also excited in this hot dense gas. However, the emission in these lines will be dominated by a more extended lower density component.

Now let us turn to radiative excitation. It requires sufficient photons at the wavelengths corresponding to the b-type transitions between different ladders, from to  µm. If the dilution factor is close to unity we need an optical depth and a radiation temperature  K at least at 30 µm. As an upper limit to the source size we can take the mean interferometric value of ". However, what will be the IR flux and luminosity of such a source? For the flux at 30 µm we obtain  Jy. The observational value is  Jy (van Dishoeck et al. 1998). Therefore, the angular source size should be and the linear size  cm. This practically coincides with the lower limit on the source size derived from the beam dilution (see above). Taking the dust absorption coefficient of  cm²/g (Ossenkopf & Henning 1994) we conclude that the gas density in this region should be  cm^-3. In this case we have no problem to reconcile the mass estimates with the available data.

However, at longer wavelengths the IR pumping from such a source might be not sufficient. Say, for the optical depth at 300 µm will be only . Therefore, we need even higher gas column and volume densities and/or larger source sizes at longer wavelengths. The latter implies the presence of a temperature gradient in the source which is natural for an internally heated object. The lower ladders are apparently excited by radiation with a lower effective temperature.

To conclude, it is much easier to explain the excitation of the higher ladders by the radiative process. The source size in Orion should be which agrees with the interferometric image in the transition at 1.3 mm (Blake et al. 1996).

The emission in the ladder should be more extended. For Orion again from a comparison between the brightness and excitation temperatures the source size should be . Such a large source size for the transitions implies that the radiative excitation via ladders will become inefficient. Therefore, for the ladder collisional excitation may dominate which implies gas densities  cm^-3. This scenario is supported by several sources where the HNCO emission peak is significantly displaced from any known IR source. The most obvious example is G 270.26+0.83 (Fig. 4). This implies either the presence of a very dense prestellar core or a highly obscured young stellar object at this location.

4.4. Comparison with C¹⁸O, CS and SiO data

An obvious step ahead to understand the properties of interstellar HNCO emission is to compare our results with data from other better studied species. The most reliable comparison can be done with our C¹⁸O data which were observed simultaneously with HNCO.

Fig. 10 shows a noticeable correlation between the HNCO and C¹⁸O integrated line intensities. However, it is produced apparently by the correlation between the line widths since the correlation between HNCO and C¹⁸O peak line temperatures is rather weak.

Fig. 10. HNCO integrated line intensities, peak main beam temperatures and line widths versus corresponding C18O and SiO peak temperatures for the SEST sample. Open squares correspond to those SiO data which were obtained at slightly different positions than HNCO. The dashed lines in the panel (c) correspond to equal line widths of the compared species

The plot of versus looks rather interesting. Concerning the 220 GHz transitions for the narrowest C¹⁸O lines the HNCO line width is smaller than that of C¹⁸O. With increasing C¹⁸O linewidth, however, the HNCO lines broaden faster and become broader than the C¹⁸O lines. An exception is Sgr A (not shown in the plot) but its C¹⁸O spectrum is strongly distorted by emission from the reference position.

A similar comparison with the CS(2-1) data from Zinchenko et al. (1995, 1998) and Juvela (1996) (not shown here) shows even lower correlations between the line parameters than in the case of C¹⁸O. However, in this case the beam sizes for CS and HNCO are different and even the central positions not always coincide.

In contrast, much better correlations exist between the HNCO and SiO line parameters (the latter ones are taken from Harju et al. 1998). Good correlations exist for both integrated and peak intensities. The correlation between the line widths is somewhat worse but one should take into account that the SiO line widths were derived from the second moments of the line profiles while the HNCO widths represent results of the gaussian fits. Anyway, the correlation does exist and the SiO lines are almost always broader than the HNCO lines.

A more detailed comparison with other species should include the line profiles. For Orion, such a comparison is displayed in Fig. 11. It shows that HNCO lines possess an extra wing emission which is less pronounced than in SiO. A similar picture is seen in some other sources.

Fig. 11. The HNCO line in Orion (thick line) in comparison with the C18O(2-1) (dotted line) and SiO(2-1) (thin solid line). The latter ones are scaled to the same peak intensity as HNCO

This comparison shows that HNCO is closely related to SiO which is thought to be produced primarily in shocks and other energetic processes. The comparison with the presumably optically thin C¹⁸O(2-1) line shows that the HNCO/CO abundance ratio is apparently enhanced in high velocity gas although to a lower degree than for SiO. Since the CO abundance is usually assumed to be constant in bipolar flows (e.g., Cabrit & Bertout 1992; Shepherd & Churchwell E. 1996) we see that HNCO abundances are enhanced relative to hydrogen, too.

It is interesting to note that the interferometric data for Orion (Blake et al. 1996) show that the spatial distributions of SiO and HNCO are rather different. However, this does not exclude a common production mechanism. E.g. these species can be formed at different stages in the postshock gas.

4.5. Comparison with IR data

The correlation between HNCO integrated line intensities and FIR flux, e.g. at 100 µm taken from IRAS data (Fig. 12), looks rather similar to the relationship between HNCO and C¹⁸O (Fig. 10). This is natural because there is a rather tight correlation between the 100 µm flux and the C¹⁸O integrated line intensity (Fig. 13). Such a good correlation shows that C¹⁸O relative abundances are rather constant and justifies the usage of the HNCO/C¹⁸O ratio for estimation of HNCO abundances.

Fig. 12. HNCO integrated line intensities versus the FIR flux at 100 µm for the SEST sample. The open squares correspond to the cases where there is a large ( HPBW) displacement between the position observed in HNCO and the IRAS position

Fig. 13. C18O(2-1) integrated line intensities versus the FIR flux at 100 µm for the SEST sample. The open squares correspond to the cases where there is a large ( HPBW) displacement between the position observed in C18O and the IRAS position

4.6. HNCO chemistry

In the early work of Iglesias (1977) HNCO was suggested to form via ion-molecule reactions. The sequence leading to HNCO via electron recombination of H₂NCO⁺ is initiated by the formation of NCO⁺ (either by a reaction between CN and or between He⁺ and NCO; see also Brown 1981). The predicted HNCO abundances from this reaction scheme are low. The steady state fractional abundance is of the order for a model with cm^-3 (Iglesias 1977), and still lower for higher densities, because the fractional ion abundances are roughly inversely proportional to the square root of the gas density.

The abundances derived from ion-molecule chemistry are in contradiction with the observations, especially when HNCO is believed to trace high density gas. Recently, a new neutral gas-phase pathway has been suggested by Turner et al. (1999) for translucent clouds: followed by . The importance of these reactions can however be questioned, since 1) the abundance of O₂ in the interstellar space is poorly known; and 2) the second reaction probably has an activation barrier of about 1000 K (Turner et al. 1999).

Chemistry models predict high fractional O₂ abundances (up to ) at late stages of chemical evolution in dense cores and in postshock gas (e.g Caselli et al. 1993; Bergin et al. 1998). However, the upper limits derived from observations towards several GMC cores (most recently by the SWAS satellite; Melnick et al. 1999) are about , which indicates that the oxygen chemistry is not well understood, yet. O₂ is destroyed by UV radiation and in powerful shocks (with shock velocities greater than 26 kms^-1; Bergin et al. 1998), and is therefore likely thriving in relatively quiescent dense gas or in regions associated with low velocity shocks. The same should be true for HNCO if the reaction suggested by Turner et al. (1999) is relevant.

The observed correlation between SiO and HNCO integrated line intensities indicates the prevalence of shocks in the HNCO emission regions. Shock heating can therefore provide the means of overcoming the energy barrier in the reaction between NCO and H₂, and thereby intensify the HNCO production. On the other hand, the fact that the HNCO line widths are smaller than those of SiO could be understood by the destruction of O₂ in high velocity shocks.

In the light of the present observations the neutral reactions suggested by Turner et al. (1999) appear to provide a plausible production pathway of HNCO also in warm GMC cores. The formation of HNCO via grain surface reactions, e.g. through the desorption and subsequent fragmentation of some more complex molecule is an alternative, which to our knowledge has not yet been investigated.

© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000
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