4. Comparison with the observations
The observations of the 234 GHz line of 16 O18 O have been made during four consecutive winters at POM-2 telescope from December 1992 to January 1996 and have been presented in Pagani et al. (1993) and MPLC. The sources are four cold, dark molecular clouds ( 10 K): B5, TMC2, L134N and B335, three lukewarm clouds ( 20 K): OMC3, NGC2264(IRS2) and DR21, and one warm cloud ( 40 K): NGC7538.
As the line has not been detected in any of the observed clouds except for one possible case, namely L134N (0', 0') for which we can get a tentative value, only upper limits of the 16 O18 O column densities have been derived. To analyse the observations, we have performed model calculations of the observed clouds. In cloud modeling, an important free parameter is the visual extinction throughout the cloud; this parameter is correlated with the H2 column densities. Since CO is a good tracer of H2 in the interstellar medium, we have deduced the H2 column densities of the observed clouds from those of C18 O using the relation derived by Frerking et al. (1982) in the Taurus region:
Fig. 6 shows the 16 O18 O column density as a function of the H2 column density throughout the cloud computed for several series of homogeneous steady state models (this work) as well as for four fragmented cloud models developed by Spaans (private communication). The upper limits of the 16 O18 O column densities derived for the eight clouds observed by MPLC are also plotted in Fig. 6. As the hydrogen density and the temperature do not affect the column density of the molecular oxygen in the ranges 500 105 cm-3 and 10 100 K, all models represented in Fig. 6 have the same density = 104 cm-3 and the same temperature T = 10 K. The full line on Fig. 6 represents "standard" models with C/O = 0.4 (X = 3.6 10-5, X = 8.5 10-5) and = 1. We have also performed calculations by varying only one parameter with respect to the standard model: The long dashed curve displays results obtained in an enhanced UV field, with = 1000; the dotted and dash dotted curves display results obtained for an enhanced C/O ratio of 0.7 with X and X kept constant, respectively.
One can see that, for half of the observed clouds (NGC2264(IRS2), DR21, OMC3, L134N (4', -1') and TMC2), the upper limits of the column densities obtained for 16 O18 O are significantly lower than the column densities computed with standard conditions. The model overestimates the amount of 16 O18 O by factors between 2 and 10 if the true column densities are near the derived upper limits. The discrepancy can be much larger if the true column densities are well below, indicating a clear problem for the standard O2 chemistry.
An increase of the ultraviolet radiation field could be compatible with the low column densities of 16 O18 O derived for L134N and TMC2. However, it cannot explain the results for NGC2264(IRS2), DR21 and OMC3. Furthermore, all sources have been chosen without intense UV radiation field on the scale of the beamsize, so that it is difficult to emphasize a high UV radiation field to explain the observations of these three clouds.
As the C/O elemental ratio plays a dominant role on the abundance of molecular oxygen and the emissivities of its rotational lines (see discussion of MVB), an increase of the C/O ratio in the gaseous phase with respect to its "standard" value can account for the underabundance of 16 O18 O. Fig. 6 shows that C/O 0.7 makes the model compatible with the observed upper limits of N (16 O18 O).
The case of L134N (0', 0'), if real, is clearly atypical because it stands above the "standard" model (Fig. 6) and thus requires a C/O ratio between 0.1 and 0.4. Because L134N is considered to be a peculiar oxygen-rich cloud, there is a real possibility to find anomalous oxygen abundance at this place and nowhere else. Indeed each observed molecule traces a different volume which means that the chemistry is highly inhomogeneous (Swade 1989). On top of that, the case seems to be stronger now as a recent paper (Stark at al. 1996) has shown that in that direction two CI lines could be seen, a main one at the bulk gas velocity (2.5 km/s) and a satellite line at 1.3 km/s which corresponds to our third 16 O18 O component towards that position (Pagani et al. 1993). Thus all three lines could be 16 O18 O features. If true the chemistry and/or excitation of molecular oxygen in this cloud is a complete puzzle still to be elucidated.
In the general case of non-detection, the variation of the C/O ratio is not the only possible explanation to the low abundance of 16 O18 O in molecular clouds. An efficient destruction of molecular oxygen can occur if the cloud is clumpy because the UV photons can penetrate deeper into the cloud. This effect is illustrated in Fig. 6, in which we have included the four 16 O18 O column densities computed from the inhomogeneous model of Spaans (private communication) for different clump volume filling factors (F). In these models, F varies from 10 to 50 %, the clump-interclump density ratio is 30 and the clump size is 0.1 pc. Though strong observational evidences of the clumpiness of the interstellar clouds exist, they are still qualitative and do not allow to estimate the filling factor, the density ratio or the clump size. The clumpiness of the clouds could be a good way to reduce the discrepancy between theory and observations. In some cases however, it does not appear sufficient to explain some low values of the molecular oxygen abundance. For instance, the upper limit upon N (16 O18 O) for NGC2264(IRS2) still remains a factor of 2 lower than the value expected with a low filling factor (10 %).
To conclude this section, let us point out the main uncertaintly on our model calculations: the collisional excitation 16 O18 O is rather uncertain. If extrapolation of collisional rates (see appendix) from the main isotope can be warranted, in the first approximation, for collisions between odd-odd N levels or even-even N levels, it is more questionable for collisions between odd N and even N levels, i.e. for =1, 3, 5... The possibility that these rates are much smaller than the ones corresponding to even can not be excluded. To check this, we have run a "standard" cloud model ( 11, =104 cm-3 and T =10 K) with the collisional rates for odd reduced by a factor 100 with respect to the ones tabulated in Table 4. Table 3 gives
Table 3. Population of the first sixteen rotational levels of 16 O18 O and emissivities of the 234, 298 and 402 GHz lines in a "standard" dark cloud ( 11, =104 cm-3 and T =10 K) for two series of collisional rates: the one tabulated in Table 4 (Rates 1) and those with the odd rates reduced by a factor 100 (Rates 2).
the population of the first sixteen levels of 16 O18 O and the emissivities of the 234, 298 and 402 GHz lines obtained with the normal odd collisional rates and rates reduced by a factor 100. Differences between the two series of calculations are very small and never exceed 10 %, indicating that collisions with odd have little influence on the 16 O18 O rotational population, at least for the physical conditions prevailing in dense dark clouds.
© European Southern Observatory (ESO) 1997
Online publication: March 26, 1998