Astron. Astrophys. 328, 617-627 (1997)

3. The most intense rotational lines of O O

In all model calculations presented hereafter, the clouds are assumed to be homogeneous and submitted to the interstellar UV radiation field of Mathis et al. (1983) with a possible scaling factor constant over the range 913-4000 Å. For the elemental abundances, we adopted the solar values from the compilation of Anders & Grevesse (1989) with the same depletion factor of 10 for C and O and a depletion of 10⁴ for sulfur and metals (i.e. H:He:C:O:S:Mg:Fe:Si = 1:0.098:3.8 10^-5:8.5 10^-5: 1.6 ^-9:3.8 10^-9:4.7 10^-9:3.5 10^-9). As the abundance of ¹⁶ O¹⁸ O is quite similar to the one of ¹⁶ O₂ divided by 250, we do not present it here, the interested reader can find the information in MVB. We will only present here the emissivities of ¹⁶ O¹⁸ O (expressed in mK km s^-1) as a function of some selected cloud parameters.

Our model allows to compute the emissivity of the 71 ¹⁶ O¹⁸ O rotational lines taken into account in the model. Following what has been done for the rotational excitation of ¹⁶ O₂ (MVB), the ¹⁶ O¹⁸ O line emissivities have been computed for different kinds of interstellar clouds and several parameters characterizing these clouds and their environment. We only present here the results obtained for the lines which are accessible from the ground. The most intense transition of ¹⁶ O¹⁸ O is the 119 GHz (N, J):(1, 1)-(1, 0) line as for ¹⁶ O₂ but this frequency is strongly blocked by the telluric ¹⁶ O₂ line. The most intense transitions of ¹⁶ O¹⁸ O which are accessible by ground-based telescopes are the 234 GHz (2, 1)-(0, 1), 298 GHz (2, 2)-(0, 1) and 402 GHz (3, 2)-(1, 2) lines for which receivers exist.

Fig. 1 displays the predicted emissivities of the 234, 298 and 402 GHz ¹⁶ O¹⁸ O lines versus the visual extinction for various values of the hydrogen density. The temperature distributions are obtained from the thermal balance equation. The temperature distribution throughout the cloud varies from cloud to cloud according to the total visual extinction and the density: it decreases with increasing and . Typically for =500 cm^-3, the temperature decreases from 56 K at the edge of the cloud to 17 K in the core; for the densest clouds considerated here, with =10⁵ cm^-3, the temperature ranges from 32 K to 8 K. It can be noted that the 234 GHz line is the most intense one which could be observed by ground-based telescopes. This is fortunate as it is also the easiest one to observe in terms of receiver sensitivity and atmospheric transparency.

Fig. 1. Emissivities of 16 O18 O lines as a function of the total visual extinction throughout different kinds of clouds and as a function of hydrogen density . Temperature distributions throughout the clouds are computed by solving the thermal balance equation.

The second series of models represents clouds with uniform temperature from T = 10 up to 100 K and =10⁴ cm^-3. Fig. 2 displays the emissivities of the 234, 298 and 402 GHz lines versus the visual extinction. Unlike the ¹⁶ O¹⁸ O abundance, the line intensities, controlled by the rotational population, are really sensitive to the temperature. Our model calculations show that the rotational population of ¹⁶ O¹⁸ O is close to LTE in opaque clouds ( 10-20) where lines have the best chance to be detected. In all situations, the (2, 1)-(0, 1) 234 GHz is more intense than the (2, 2)-(0, 1) 298 GHz and the (3, 2)-(1, 2) 402 GHz lines.

Fig. 2. Emissivities of 16 O18 O lines as a function of the total visual extinction throughout different kinds of clouds and as a function of temperature for clouds with nH = 104cm-3

In the third series of models, the incident ultraviolet radiation field has been multiplied by a scaling factor =10, 100 and 10³ to take into account molecular clouds near HII regions. All cloud models were run with =10⁴ cm^-3 and T =10 K and the emissivities of the 234, 298 and 402 GHz lines are plotted in Fig. 3.

Fig. 3. Emissivities of 16 O18 O lines as a function of the total visual extinction throughout different kinds of clouds and UV radiation field for clouds with =104 cm-3 and T =10 K

The global decrease of the intensities is due to the decrease of abundance of ¹⁶ O¹⁸ O which is more efficiently destroyed when the UV field is stronger. For a same visual extinction, the UV radiation field is a determinant parameter for the emissivity of the ¹⁶ O¹⁸ O lines until the visual extinction becomes large enough ( 20) to attenuate its effect. Typically, even for a cloud with an opacity as large as 20, the emissivities are divided by 4 as increases from 1 to 10³, implying a factor of 16 increase of the required integration time for a given receiver. With the present status of mm receivers, detection of ¹⁶ O¹⁸ O appears completely excluded in molecular clouds where massive star formation occurs.

Finally, the last two series of models check the influence of the C/O ratio on ¹⁶ O¹⁸ O detectability. We have computed two series of models with C/O=0.1, 0.4 and 0.7, one series with a constant carbon abundance X =3.8 10^-5 and the other one with the oxygen abundance fixed to X =8.5 10^-5. All models are run with T =10 K and =10⁴ cm^-3. Figs. 4 and 5

display the predicted emissivities of the ¹⁶ O¹⁸ O lines at 234, 298 and 402 GHz versus the visual extinction for the two series of models. The C/O ratio is a dramatic parameter for the abundance and, consequently, for the emissivities of the ¹⁶ O¹⁸ O lines: when X is divided by 7 (Fig. 4) while the carbon abundance remains constant, the emissivities decrease by a factor of about 40. When the oxygen abundance is constant and X is increased by a factor of 7 (Fig. 5), the emissivities decrease by a factor of about 10. This means an increase of the integration time for a given receiver by a factor 1600 and 100, respectively. With the sensitivities of present receivers, ¹⁶ O¹⁸ O could only be detected if the C/O ratio is lower or of the same order than the "standard" cosmic value (C/O 0.4).

Fig. 4. Emissivities of 16 O18 O lines as a function of the total visual extinction throughout different kinds of clouds and as a function of C/O ratio for isothermal clouds ( =104 cm-3 and T =10 K). The fractional abundance of carbon is constant: X =3.8 10-5

Fig. 5. Emissivities of 16 O18 O lines as a function of the total visual extinction througout different kinds of clouds and as a function of C/O ratio for isothermal clouds ( =104 cm-3 and T =10 K). The fractional abundance of oxygen is constante: X =8.5 10-5,

For nearly all the different sets of parameters presented in this section, the intensity of the 234 GHz is from 2 to 4 times higher than that of the 298 and 402 GHz lines. As the 234 GHz line has not been detected, detections of the two other lines seem presently unrealistic.

© European Southern Observatory (ESO) 1997

Online publication: March 26, 1998

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