There are a number of methods in use to calculate line opacities. The classical methods are statistical and construct tables that are subsequently used in the calculation. The Opacity Distribution Function (ODF) and its derivative the k-coefficient method have been used successfully in a number of atmosphere and opacity table codes . This method works well for opacity table and model construction but cannot be used to calculate detailed synthetic spectra. A second approach is the opacity sampling (OS) method . This is a statistical approach in which the line opacity is sampled on a fine grid of wavelength points using detailed line profiles for each individual spectral line. In classical OS implementation, tables of sampling opacities are constructed for given wavelengths grids and for different elements. These OS tables are then used to calculate model atmospheres and, e.g., Rosseland mean opacities. The OS method has the advantage that is more flexible than the ODF approach and it also allows the construction of (typically) low resolution synthetic spectra. The drawback of tables in general is, however, an inherent inflexibility in terms of, e.g., the wavelength grid or the tables's resolution. For example, to properly account for the pressure broadening of lines an opacity sampling table would have to be a function of temperature and gas pressure, which leads to very large tables if many wavelength points are tabulated (this is not a problem for ODF tables as the number of wavelength bins in such models is typically very small). In addition, a different code is typically required to calculate high-resolution spectra from the model atmosphere constructed with the ODF or OS tables, which has the potential of introducing systematic errors (e.g., if the atmosphere/table and the synthetic spectrum codes are not synchronized).
In direct opacity sampling (dOS) these problems are avoided by replacing the tables with a direct calculation of the total line opacity at each wavelength point for all layers in a model atmosphere . In the dOS method the relevant lines (defined by a suitable criterion) are first selected from master spectral line databases which include all available lines. The line selection procedure will typically select more lines than can be stored in memory and thus temporary line database files are created during the line selection phase. The file size of the temporary database can vary, in theory, from zero to the size of the original database or larger, depending on the amount of data stored for the selected lines and their number. For large molecular line databases this can easily lead to temporary databases of several GB in size. This is in part due the storage for the temporary line database: its data are stored for quick retrieval rather than in the compressed space saving format of the master line databases. The number and identity of lines that are selected from the master databases depends on the physical conditions for which the line opacities are required (temperatures, pressures, abundances for a model atmosphere) and thus the line selection has to be repeated if the physical conditions change significantly. As an optimization, it is easily possible to include only lines in the temporary database that can be ``seen'' by the wavelength grid that will be used in the calculation of the line opacities later on. This is important if, for example, only a narrow range in wavelength is considered at high resolution in order to generate a synthetic spectrum.
The temporary line databases are used in the next phase to calculate the actual line opacity for each wavelength point in a prescribed (arbitrary) wavelength grid. This makes it possible to utilize detailed line profiles for each considered spectral line on arbitrary wavelength grids. For each wavelength grid point, all (selected) lines within prescribed search windows (large enough to include all possibly important lines but small enough to avoid unnecessary calculations) are included in the line opacity calculations for this wavelength point. This procedure is thus very flexible, it can be used to calculate line opacities for both model atmosphere construction (with relatively few wavelength points) and for the generation of high-resolution synthetic spectra. Its main drawback is that the line selection and (in particular) line profile calculations are more costly than table interpolations.
. In the dOS method the relevant lines (defined by a suitable criterion) are first selected from master spectral line databases which include all available lines. The line selection procedure will typically select more lines than can be stored in memory and thus temporary line database files are created during the line selection phase. The file size of the temporary database can vary, in theory, from zero to the size of the original database or larger, depending on the amount of data stored for the selected lines and their number. For large molecular line databases this can easily lead to temporary databases of several GB in size. This is in part due the storage for the temporary line database: its data are stored for quick retrieval rather than in the compressed space saving format of the master line databases. The number and identity of lines that are selected from the master databases depends on the physical conditions for which the line opacities are required (temperatures, pressures, abundances for a model atmosphere) and thus the line selection has to be repeated if the physical conditions change significantly. As an optimization, it is easily possible to include only lines in the temporary database that can be ``seen'' by the wavelength grid that will be used in the calculation of the line opacities later on. This is important if, for example, only a narrow range in wavelength is considered at high resolution in order to generate a synthetic spectrum.
The temporary line databases are used in the next phase to calculate the actual line opacity for each wavelength point in a prescribed (arbitrary) wavelength grid. This makes it possible to utilize detailed line profiles for each considered spectral line on arbitrary wavelength grids. For each wavelength grid point, all (selected) lines within prescribed search windows (large enough to include all possibly important lines but small enough to avoid unnecessary calculations) are included in the line opacity calculations for this wavelength point. This procedure is thus very flexible, it can be used to calculate line opacities for both model atmosphere construction (with relatively few wavelength points) and for the generation of high-resolution synthetic spectra. Its main drawback is that the line selection and (in particular) line profile calculations are more costly than table interpolations.