rfxconv: angle-dependent reflection from an ionized disk

This convolution model from Chris Done combines the ionized disk table model from Ross and Fabian with the Magdziarz & Zdziarski Compton reflection code. It is described in Kolehmainen, Done & Diaz Trigo (2011) and is a modification of the model first described in Done & Gierlinski (2006).

The algorithm used is as follows.

1. Determine the average power-law index of the input spectrum between 2 and 10 keV. For this index and the other input parameters interpolate on the table models to generate the reflected spectrum from the ionized disk.
2. Estimate the average power-law index of the reflected spectrum over the range 12 - 14 keV.
3. Iterate over the Compton reflection models changing the cross-section at 10 keV until a match is found with the index calculated in the previous step.
4. Renormalize the reflection spectrum calculated in step 1 to match the Compton reflection calculated in step 3 at 14 keV.
5. Calculate the final reflection spectrum by using the renormalized ionized disk spectrum below 14 keV and the Compton reflection spectrum above 14 keV.

When using this model it is essential to extend the energy range over which the model is calculated because photons at higher energies are Compton down-scattered into the target energy range. The energy range can be extended using the extend command. The upper limit on the energies should be set above that for which the input spectrum has significant flux. To speed up the model, calculation of the output spectrum can be limited to energies below a given value by using xset to define RFXCONV_MAX_E (in units of keV). For instance, suppose that the original data extends up to 100 keV. To accurately determine the reflection it may be necessary to extend the energy range up to 500 keV. Now to avoid calculating the output spectrum between 100 and 500 keV use the command xset RFXCONV_MAX_E 100.0.

The core of this model is a Greens' function integration with one numerical integral performed for each model energy. The numerical integration is done using an adaptive method which continues until a given estimated fractional precision is reached. The precision can be changed by setting RFXCONV_PRECISION eg xset RFXCONV_PRECISION 0.05. The default precision is 0.01 (ie 1%).

To use different ionized disk table model files than those installed change the directory searched for these files using xset RFXCONV_DIR.

The model parameters are as follows.

par1 = $rel_{refl}$	the relative reflection normalization. If $rel_{refl}$ is negative then only the reflected component is returned.
par2 = $redshift$
par3 = $Fe_{abund}$	the iron abundance relative to Solar. All other elements are assumed to have Solar abundance.
par4 = $cosIncl$	cosine of the inclination angle (degrees).
par5 = $log(xi)$	the ionization parameter used by the table models.