Astron. Astrophys. 324, 221-236 (1997)

4. Conclusion

Several projects are planned in the near future to detect rotational lines of O₂ using millimeter and submillimeter receivers embarked on satellites or stratospheric balloons: ODIN for the 119 and 487 GHz lines, SWAS for the 487 GHz line, PRONAOS-SMH for the 368 GHz line and PIROG 8 for the 425 GHz line. As a theoretical preparation to these projects, we have used an interstellar cloud model to compute the abundance and rotational populations of O₂ in order to predict the intensities of its main rotational lines. The model, which assumes steady-state equilibrium, solves a coupled set of equations: 1) The chemical balance equation for 136 species, mainly the simplest C- and O-bearing compounds and their ¹³ C and ¹⁸ O substitutions, leading to the distribution of their fractional abundances throughout the cloud. 2) The statistical equilibrium equations leading to the rotational population of the molecules H₂, CO and O₂ and the fine structure population of C, C and O. 3) The thermal balance equation with gives the gas temperature distribution. 4) The transfer equation for the UV photons giving the photo-destruction rates of the chemical species as a function of depth within the cloud. The cloud model has been adapted from the one developed by Warin et al. (1996) by including the first 24 rotational levels of O₂. Their population is computed by using recent calculations of the collisional rates O₂ -He from which we estimated O₂ -H₂ rates; we also computed the spectroscopic parameters (energy levels and line strenghts) necessary to obtain the radiative rates. The main conclusions of this work can be summarized as follow:

• With the standard C/O abundance ratio of 0.4, the abundance of molecular oxygen increases very sharply with cloud visual extinction, so as to be comparable to that of CO, with O₂ /CO ranging for 0.25 to 0.4 as increases from 10 to 30, whatever the temperature and the hydrogen density. It must be noted that, even in the densest and most opaque clouds computed here, atomic oxygen remains more abundant than O₂ and represents between 20 and 30 % of the available gas phase oxygen.
• With the sensitivities expected for the receivers of the forthcoming missions, the detection of interstellar O₂ will be limited to dark clouds, with a possible exception for the ODIN receiver which could observe the 119 GHz line in translucent clouds (  5) provided the temperature is less than 50 K.
• Unlike the overall abundance of O₂, its rotational population, and consequently the intensity of its rotational lines are fairly sensitive to the temperature. The 368 GHz receiver of PRONAOS and the 487 GHz receivers of ODIN and SWAS are able to detect O₂ in opaque clouds (  10) with temperatures  25-50 K, somewhat larger than usually expected in dark clouds. Due to larger line intensities, the PIROG 8 receiver could detect the 425 GHz line in less opaque clouds (  6-7) in the same range of temperatures.
• Because O₂ is rather easily photodissociated, the regions submitted to an intense UV radiation field are very unfavourable to the detection of O₂. Typically, if the external UV radiation field is enhanced by a factor 1000 with respect to the local standard value, only the ODIN receiver at 119 GHz is able to detect O₂ in dark clouds with  10, while the three other lines will be observable in more opaque clouds (  20).
• The most drastic parameter that controls the abundance of O₂ (as well as that of OH and H₂ O) and, consequently, the detectability of its rotational lines, is the C/O elemental abundance ratio in the gas phase. The molecule CO is so easily formed in interstellar clouds and so stable that its abundance is very rapidly limited by the available gas phase carbon or oxygen depending to wether C O or C O. As the carbon abundance increases and approches that of oxygen, the amount of oxygen available to produce oxygen-bearing molecules other than CO is considerably reduced. For typical dark cloud conditions, as C/O increases from the standard value of 0.4 to 2, O being fixed, the O₂ abundance drops by a factor  4 10⁴ ; at the same time, the H₂ O and OH abundances are also decreased, but to a lesser extent, by a factor 2500 and 30, respectively. If C/O 1, the 119 GHz line of O₂ appears accessible to the ODIN receiver only in very opaque clouds (  20), the three other lines being unobservable as soon as the C/O ratio is larger than 0.7. Because of this strong sensitivity to C/O, the detection of O₂ could serve to constrain the carbon and oxygen abundances if parameters like density, temperature, UV field... could be derived by another way; it must be however noted that the amount of O₂ is very sensitive to other physical conditions such as the ionization degree, as indicated by alternative model calculations.
• In regions where the O₂ column densities are large enough to be detectable, the rate coefficient of the reaction O+OH O₂ +H, the main route to O₂, has little influence on its abundance. It however controls the OH abundance since it is the main destruction process of this molecule. An experimental study of the O+OH O₂ +H reaction at low temperatures would be of great interest for this problem.
• Our model calculations also predict that radiative de-excitation of O₂ could be an important cooling agent of cold molecular gas, to be included in models. Under favourable conditions for the formation of O₂, its cooling efficiency is comparable to that of CO mainly because the lower line strenghts of the O₂ lines are compensated by their lower opacities.

Table 8. Analytic fit of the O₂ -He collision de-excitation rate (in cm³ s^-1):

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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