High-temperature (1000–7000 K) collision-induced absorption of H 2 pairs computed from the first principles, with application to cool and dense stellar atmospheres

Abstract

The collision-induced absorption (CIA) spectra of H 2–H 2 and H 2–He are known to play an important role for modelling of low-metallicity cool and dense stellar atmospheres. In this paper we present collision-induced absorption spectra of H 2–H 2 complexes in the rototranslational (Δ v=0), the fundamental (Δ v=1), the first (Δ v=2) and the second (Δ v=3) overtone bands in the temperature range from 1000 to 7000 K, and in the frequency region from 0 to 20 000 cm −1. The translational spectral density functions are computed quantum mechanically, based on: (1) the newly developed ab initio collision-induced H 2–H 2 dipole functions of Zheng (Computational study of collision induced dipole moments and absorption spectra of H 2–H 2. Ph.D. thesis, Michigan Technological University, 1997), which account for the short-range H 2–H 2 intermolecular distances (as small as 2.5 a.u.) and for larger H 2 internuclear distances (as large as 2.15 a.u.); (2) semiempirical isotropic H 2–H 2 potential (Ross et al, J Chem Phys 1983;79(3):1487) suitable for high temperatures. We include the collision-induced absorption coefficient of the vibrational transitions as v 1, v 2, v′ 1, v′ 2≤3 which we computed rigorously. We also give our estimate for the collision-induced absorption coefficients of single vibrational transitions such as v i<3, v′ i>3 in the first and second overtone bands. The dependence of CIA spectra on rotational states of H 2 molecules is accounted for in our computations. We have previously (Borysow et al, Astronom Astrophys. 1997;324:185–95) studied the effect of CIA for stars of a wide range of fundamental stellar parameters (effective temperature, gravity, and chemical composition), and determined for which combinations of these parameters it is necessary to include CIA in the model and spectrum computation. These calculations showed that CIA from H 2–H 2 plays an important, and often even a dominating role for stellar atmospheres of a wide range of stars. The approximate character of the estimates of the H 2–H 2 absorption coefficient we used in our previous work combined with the large effect CIA had on the stellar atmospheres, were the main inspirations to initiate the more accurate computations of the absorption coefficient we present here. The absorption coefficient we compute in the present analysis is in qualitative agreement with our preliminary estimates (Borysow et al, Astronom Astrophys 1997;324:185–95), but in some spectral regions of high importance for the stellar structure, our computed absorption coefficient is up to a factor of 3 larger than our preliminary estimates. We therefore fully confirm our previous suspicion that H 2–H 2 CIA will have a pronounced effect on the atmosphere for a wide range of stars. In this paper we therefore quantify the effect the new data have on a typical cool dense stellar atmosphere, and compare our new results with our previous estimates.