Astron. Astrophys. 324, 185-195 (1997)

2. CIA opacities from existing quantum mechanical sources

2.1. H₂ -H₂ roto-translational band

The existing model of the roto-translational (RT) band (Zheng & Borysow 1995b) in H₂ -H₂ has been designed specifically for astrophysical applications. It provides absorption intensities at temperatures from 600 to 7500 K. We based our model on the available induced dipole functions due to Meyer et al. (1989), designed to work well at low temperatures (i.e. at moderate intermolecular distances), and on the isotropic, effective H₂ -H₂ interaction potential by Ross et al. (1983). We have upgraded the dipole data to meet the demands of the high temperature predictions of CIA. The model accounts for hot bands involving vibrational transitions with , which are populated at temperatures below 7000 K. Variables and denote vibrational quantum numbers of each hydrogen molecule.

2.2. H₂ -H₂ fundamental band

The existing model of the fundamental band (Borysow & Frommhold 1990) is available at temperatures from 600 to 5000 K. It includes, however, only one vibrational transition, i.e. , although at high temperatures also hot bands (with ) corresponding to the same frequency range are expected to be present. We tried to correct for this fact, although it is apparent that an updated model is necessary. An extrapolation of the models to temperatures other than those they are designed for can give very undependable results. We have therefore chosen to use the results for 5000 K to represent opacities of the transition also at 6000 and 7000 K. However, in order to account for the missing transitions (giving rise to the hot bands) with , corresponding to , with , (we account, in fact, globally for two cases: , and , , both bands are identical, due to the symmetry), we rescaled the intensities of the transition by dividing them by the probability of the population of state at each temperature (see , Table 1).

Table 1. Population probability of the ground vibrational state of H₂ at temperatures between 1000 and 7000 K.

Such a procedure is correct if we assume that the shape and the intensity of the unweighted (by the P(v) ) translational, rotational, and vibrational transitions with =1 are identical. Whereas it is not generally the case, we think that this procedure significantly improves the data over those available from the existing program.

2.3. H₂ -He roto-translational band

The existing model of the band predicts CIA intensities of this band at temperatures below 3000 K (Borysow et al. 1988). In the absence of any newer data we have applied similar rescaling procedure as we did for the fundamental band of H₂ -H₂. Again, initially we have computed intensities at all temperatures up to 3000 K, and then copied the results for 3000 K to all higher temperatures. Next, in order to account for the hot bands, we divided those intensities by . We expect quite large uncertainties associated with this procedure, but we note that the far infrared intensities, corresponding to the band, are less important than those in the near infrared. In addition, the H₂ -He intensities are expected to matter much less that those due to H₂ -H₂, on account of lower abundance of helium in the stellar atmospheres. Also, CIA usually matters less at high temperatures, so the inaccuracy of the high temperature predictions is less relevant. A better CIA model of this band is certainly being called for.

2.4. H₂ -He fundamental band

The models of all relevant vibrational transitions corresponding to the fundamental band frequency region are available for the H₂ -He complex. The models are applicable for all temperatures up to 7000 K, and involve transitions, including the transition (Borysow et al. 1989) and many hot bands (Borysow & Frommhold 1989).

2.5. H₂ -He higher overtones

Models of several vibrational transitions corresponding to are available (Borysow & Frommhold 1989) at temperatures up to 7000 K. We have incorporated all of them into our opacity code.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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