Computation of Collision-Induced Absorption by Simple Molecular Complexes, for Astrophysical Applications

The absorption due to pairs of H₂ molecules is an important opacity source in the atmospheres of various types of planets and cool stars, such as late stars, low mass main sequence stars, brown dwarf stars, cool white dwarf stars, the ambers of the smaller, burnt out main sequence stars, exoplanets, etc., and therefore of special astronomical interest. Astronomers are interested in the outer planets as they still contain primordal matter. Furthermore, recent observations by the Hubble space telescope (in operation since 1990) have revealed several thousand cool white dwarf stars with temperatures of several thousand Kelvin. It is surprising that none of them has temperatures lower than roughly 4000 K. This means that the white dwarf stars have not had enough time to cool down to the temperature of the cosmic background radiation. Astrophysicists believe that this information can be used for an alternative and more accurate method of cosmochronology. However, the emission spectra of cool white dwarf stars differ significantly from the expected blackbody spectra of their cores, largely due to collision-induced absorption by collisional complexes of residual hydrogen and helium in the stellar atmospheres. In order to model the radiative processes in these atmospheres, which have temperatures of several thousand kelvin, one needs accurate knowledge of the induced dipole and potential energy surfaces of the absorbing collisional complexes, such as H₂--H₂, H₂--He, and H₂--H. These come from quantum-chemical calculations, which, for the high temperatures and high photon energies under consideration in this work, need to take into account that the H₂ bonds can be stretched or compressed far from equilibrium length. Since no laboratory measurements for these high temperatures and photon energies exist, one has to undertake \textit{ab initio} calculations which take into account the high vibrational and rotational excitation of the involved hydrogen molecules. However, before one attempts to proceed to higher temperatures and photon energies where no laboratory measurements exist it is good to check that the formalism is correct and reproduces the results at temperatures and photon energies where laboratory measurements exist, that is, at and below room temperature and for photon energies up to about 1.5 eV. In this work a formalism is developed to compute the binary collision-induced absorption of simple molecular complexes up to temperatures of thousands of kelvin and photon energies up to 2.5 eV, properly taking into account vibrational and rotational dependencies of the induced dipole and potential energy surfaces. In order to make the computational effort feasible, the isotropic potenial approximation is employed. The formalism is applied to collisional complexes of H₂--H₂, D₂--D₂, H₂--He, D₂--He, T₂--He, and H₂--H, and compared with existing laboratory measurements.