Frequency Dependent Opacity Spectrum Limitations

The opacity calculations are intended primarily for users interested in integrated opacities. The "gray" opacities (Rosseland or Planck) are obtained by integrating over all photon energies while the "multigroup" opacities are integrated between the energy boundaries, giving one opacity number for each energy range. This range is assumed to be large compared with individual line profile widths. Under these assumptions, several approximations are made in the calculations that will reduce spectroscopic accuracy.

1.Most of the atomic energy levels used in the opacity code are obtained from single configuration LS Hartree-Fock calculations, with relativistic corrections. These energy levels are then fit with a quantum defect model in order to reduce this massive data base to a managable set. This can result in errors of 1% or more, especially for inner shell transitions. Errors of this magnitude have little effect on the integrated opacity, but are large in terms of spectroscopic accuracy.

2. For the higher Z elements, even the reduced LS coupled data base becomes too large. Switching to jj coupling, which is usually the preferred model for these elements, would require even more data. For this reason, the opacity code uses an Unresolved Transition Array (UTA) model for many bound-bound transitions calculations. This model replaces the actual transition array with a single Gaussian profile to approximate all of the actual lines (which can number in the millions). This overestimates the opacity for low densities, so a Random Line model is used to replace the single Gaussian with a relatively small set of randomly generated, plasma broadened lines that distribute the total oscillator strength over the same energy interval as the original transition array. For obvious reasons, none of these random lines can be matched spectroscopically, but looking at a broad enough energy range, this model will preserve the oscillator strength within the correct photon energy range.

3. The individual element opacities are all calculated at the same u (u = hv/kT) grid for all temperatures and densities. This allows the elements to be mixed together to form opacities for multi-element materials. Since this is a fixed grid, the contributions from the different processes (such as bound-bound transitions) are calculated and summed only at the grid points and no effort is made to preserve the line centers. Therefore, line ratios could be reversed from their normal ratio by the choice of grid points. In addition to this, since the u's are constant, each temperature samples the opacity cross sections at different photon energies. If the lines are broad enough, this makes little difference, but the narrow line distribution could look entirely different at two adjoining temperatures.

All attempts are made to insure the most accurate possible opacity calculations, but because of the above inherent limitations, use of the frequency dependent opacities to match spectra is discouraged.