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

4. Comparison with previous data

Although quantum mechanical computations of CIA have been available at high temperatures for some time, they have been used in stellar studies only recently. In more widespread use are Linsky's (1969) analytical expressions for CIA transitions - sometimes applied in combination with a limited set of quantum mechanical results. Linsky's data include estimates of the roto-translational band of H₂ -H₂ at temperatures from 600 to 3000-4000 K, the fundamental roto-vibrational band at temperatures up to 3000 K, and its first overtone band for temperatures up to 4000 K. No hot bands or higher overtones are included. Linsky's treatment of the roto-vibrational band has been superseded by the ab initio computations of Patch (1971). As already stressed by these authors, the adopted lineshapes are, however, modelled by highly 'ad hoc' analytical functions that are designed to reproduce the desired absorption intensities within strictly limited ranges of temperatures and frequencies - let's say where the intensity of each band falls off by one order of magnitude compared to its peak value. In this sense Linsky's data have not been intended for use for wavenumbers above 10 000 cm^-1 (i.e., 1 µm), or for temperatures outside the range described above. In addition, Linsky's opacities given for H₂ -He rely on simple rescaling of the absorption coefficients of H₂ -H₂, which is now known to give quite incorrect results (compare Figs. 1 and 2, this paper).

Although the data by Linsky and Patch were, hence, intended for a rather limited range in frequency and temperature, simple programming of their analytical expressions will of course give answers also outside this range, and great caution should obviously be taken in the interpretation of results based on such "extrapolations". For example, the default continuum opacities in recent versions (e.g., Jorgensen et al. 1992, Plez et al. 1992) of the widely used MARCS code include Linsky's roto-translational band and Patch's fundamental band (the first overtone is missing). The expression for these two bands should be used only between 0 and 9 000 cm^-1. In default computations they will, however, be included at any frequency range, and any temperature demanded by the program. In Fig. 3 we demonstrate the difference between our new quantum mechanical CIA opacities as applied in the MARCS code and the Linsky/Patch-continuum CIA opacities as given by the MARCS code, when computed at 4000 K at the frequency range from 0 to 20 000 cm^-1. It is easily seen that at higher frequencies, overlapping well with the black body radiation flux, the data by Linsky and Patch overestimate the realistic opacities by as much as three orders of magnitude. In fact, numerical experiments showed that the Linsky/Patch data may often give artificially larger effects on the model atmosphere, because of such an erroneous extrapolation, than will application of the more realistic quantum mechanical CIA, in spite of the fact that the values of the Linsky/Patch data are considerably lower around the maximum CIA absorption intensity. We would like to draw the attention of all users of analytical CIA expressions in any atmospheric code to this point; they should examine carefully their inputs, and have in mind the comparison in Fig. 3 and the limitations in analytical expressions alluded to above.

Fig. 3. Comparison of our results for the H H2 CIA opacities with those due to Linsky and Patch.

We would also like to extend this warning to all other cases of indiscriminate use of all analytical opacity models which are designed to reproduce certain values within a given (and tested) range. As another example, we mention the use of the model of roto-translational CIA for H₂ pairs by Borysow et al. (1985), designed to model CIA intensities at temperatures up to 300 K, but instead used (for example in the work by Lenzuni et al. 1991) to model CIA opacities at 3000 K. The user needs to have in mind that whereas authors who publish their opacity data can make certain that the selected analytical, multi-parametric spectral lineshapes reproduce well their quantum mechanical computations within certain range of temperatures and frequencies, there is no attempt made, and in fact it is highly unlikely, that the same lineshapes will give correct results at temperatures different by one order of magnitude from those tested. Therefore, such "extrapolation" procedures will inadvertently lead to unpredictable results and should be strictly avoided.

Our Figs. 1 and 2 above show a very large range of intensities, up to five orders of magnitude for H₂-H₂ and 3-5 orders for H₂ -He. As we mentioned above, analytical lineshapes used by us to model spectral lineshapes reproduce real profiles well within the 1:100 range of intensities. Their far wing behaviour is rather unpredictable, though on some occasions they were seen to perform impressively well over extended frequency/intensity range. We need to remind the reader that whereas at shorter frequencies the spectral bands overlap each other, making the far wings more irrelevant in the presence of the next, more intense band, the intensities at frequencies higher than those due to the first and the second overtones ( 15000 cm^-1) may be prone to more uncertainties. Thus, even though great care has been placed on making the present models as realistic as possible under current circumstances, it needs to be understood that uncertainties of such models are also unavoidable.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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