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Astron. Astrophys. 341, 579-586 (1999)

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3. The carbon dioxide rotation-vibration bands

The [FORMULA] bending-mode, rotation-vibrational band at [FORMULA] or [FORMULA], is a [FORMULA] transition of the linear and symmetric molecule CO2, see e.g. Herzberg (1966). The selection rules for this perpendicular band, [FORMULA] and [FORMULA], result in a Q, P, and R-branch. The Q-branch will appear strongest since it will correspond to an overlap of [FORMULA] transitions, whereas the P- and R-branches will be smeared out and will hardly be detectable at the resolution used in the observations. If the rotational constant [FORMULA], determining the energy separations of the rotational levels within a vibrational state, would be the same for the upper vibrational state as for the lower one, the [FORMULA] transitions would all have the same frequency. The rotational constant for the upper vibrational level ([FORMULA]) is in the [FORMULA] band case, however, modestly larger than that of the lower level ([FORMULA]), leading to a small increase in frequency for high J-values. Therefore, the Q-branch is expected to be slightly asymmetric to the blue. For the 13.9 and [FORMULA] bands (cf. Fig. 3) [FORMULA] implying a reversed asymmetry. The width of a thermal band reveals the underlying temperature since as the temperature increases, higher rotational levels will be populated, resulting in a broader band. The difference of the rotational constant of the upper and lower levels gives an indication of how sensitive the broadening is to the temperature. In Table 2 the band oscillator strength, [FORMULA] and the difference between the rotational constants of the upper and the lower level of the transition, [FORMULA], are given for the three bands discussed here.


Table 2. Parameters of the CO2 Q-bands. The band oscillator strengths were derived from Rothman et al. (1992) and the rotational constants are directly given in the same reference

[FIGURE] Fig. 3. The vibrational energy-level diagram of some states in CO2. A number of infrared transitions are indicated. The labels identifying the different levels indicate the number of quanta in the three fundamental vibrational modes. The superscript denotes the quantum number associated with vibrational angular momentum, l

The [FORMULA] Q-band is a transition from a state where the molecule vibrates in the [FORMULA]-mode and de-excites to the upper level of the [FORMULA] band. The Q-band at [FORMULA] is a de-excitation of a molecule vibrating in the second level of the [FORMULA] mode down to the upper level of the [FORMULA] band. See Fig. 3.

The resolution of the measurements ([FORMULA]) will allow the asymmetry of the observed features (FWHM[FORMULA]) to be measurable, which is also observed. The rotational fine structure, i.e. the individual Q-lines will, however, not be detectable in the SWS06 mode of the spectrometer. In the high resolution mode (SWS07, [FORMULA]) the Q-lines will show up as separated symmetric lines, since the typical separation for the lowest Q-lines is approximately [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998