Interpolation Issue

The APEC model, as implemented in XSPEC, has been found to have issues modeling certain plamsas accurately due to interpolation issues. We have prepared a report describing the effects in detail, but in the meantime, here is an executive summary, and suggested fixes.

How APEC works

The APEC model stores the emisivities of the lines and the continuum components of thermal plasma emission at 51 temperatures from 10⁴ to 10⁹K. These tables are formed by multiplying the emissivity of a line (or other feature, but we'll use lines in this example) due to a single ion by the elemental abundance and the fraction of that ion present in collisional ionization equilbirium (CIE). The APEC table store all 51 of these.

The Issue

Recent work (link to be inserted when published) by François Mernier et al. have shown both that the interpolation grid is not fine enough and that the ion fractions are, in effect, always rounded down, as shown here:

The red line in this sketch represent the ``real'' ion fraction, while the green shown the ion fraction on a regular log(T) grid. Because the ion fraction is always equal to or less than the real value, element abundances are increased to compensate.

The non-equilibrium model

The rnei model in Xspec uses the same data, but presented in a slightly different way. The emissivities are calculated and stored for each ion on the same temperature grid, but the ionization fraction is calculated on the fly each time. This removes interpolation over the ion fraction as an issue. Interpolation of the emissivities is still an approximation which is made, but this is a significantly reduced issue, as shown in the attached memo.

The Remedy

In short, the suggested remedy is to either:

• Replace the APEC model in XSPEC with the RNEI model and then tie kT=kT_init, and freeze Tau at 10^13.
• Use a finer grained APEC model, such as atomdb_v3.0.9_201.tar.bz2 201 temperature one

As the nature of this bug is highly instrument and plasma condition dependent, we have a simple python script to run to test how any particular analysis may have been affected. While we work to make this widely available, please contact us with any questions/requests