Introduction

Vander Meulen et al. 2023 describe the X-ray implementation in SKIRT and perform a number of benchmark tests, comparing the SKIRT simulation results to the published results of other codes to verify its operation. This web page discusses the RXTORUS benchmark test, presented in their section 4.2.2, which compares the results for a smooth torus model originally calculated with the REFLEX code (Paltani & Ricci 2017). REFLEX implements a complete set of X-ray physics in cold-gas media, including bound-electron scattering and a large collection of fluorescent line transitions. It implements the same interaction cross sections as those that are incorporated in SKIRT, forming an ideal reference for benchmarking these processes.

References and downloads

Publications	Vander Meulen et al. 2023 [ADS] Paltani & Ricci 2017 [ADS]
Ski files	RXTORUS.ski RXTORUS_CS.ski
Input files	RXTORUS_CUTOFFPL.txt RXTORUS_WLG.txt RXTORUS_CS_WLG.txt

Benchmark results

Overall comparison

The RXTORUS model represents a ring torus of cold gas with a uniform density and a variable covering factor, which models scattering on bound electrons in addition to photo-absorption and fluorescence. We reproduce the RXTORUS model in SKIRT with a uniform ring torus of cold gas centered around an X-ray point source. We fix the torus opening angle to 60 deg, and run SKIRT simulations for an unobscured (i = 45 deg) and an obscured (i = 75 deg) sightline. The equatorial hydrogen column density of the torus is varied between \(10^{22}\) and \(10^{25}~\mathrm{cm}^{−2}\), which are the \(N_\mathrm{H}\)-limits of the RXTORUS model. The following figure compares the SKIRT and REFLEX results.

The results are found to be in excellent agreement over the entire simulation domain, for both sightlines and all considered column densities. The noise levels in the SKIRT results are significantly lower, in part because of the generic optimisation mechanisms implemented in SKIRT. Furthermore, the simulated SKIRT spectra have a much higher spectral resolution, producing narrower fluorescent lines and smoother reflection continua.

Zoom on narrow spectral range

The following figure shows a zoom into the important 6.0 to 7.5 keV spectral range for the same ring torus model with \(N_\mathrm{H} = 10^{24}~\mathrm{cm}^{−2}\) and i = 45 deg. This spectral range contains the three most prominent fluorescent lines (Fe Kα, Fe Kβ, and Ni Kα), plus the Fe Kα Compton shoulder.

Despite the limited spectral resolution of the REFLEX results, we distinguish clear Compton shoulders in both simulations, with similar strengths and consistent spectral shapes.

Performing this benchmark

To perform this benchmark, download the ski files, input spectrum, and wavelength grid data files provided above in References and downloads.

To reproduce the results discussed above in Overall comparison, make a copy of the RXTORUS.ski file with a descriptive name for each variation of column density and open these copies in a text editor to adjust the column density value in the model:

Parameter	XML element	XML attribute
column density	`NumberColumnMaterialNormalization`	numberColumnDensity

Note that the SKIRT normalization occurs along the full X-axis, so the column density value must be doubled:

Radial column density	Value of numberColumnDensity
\(10^{22}~\mathrm{cm}^{−2}\)	`2e22 1/cm2`
\(10^{23}~\mathrm{cm}^{−2}\)	`2e23 1/cm2`
\(10^{24}~\mathrm{cm}^{−2}\)	`2e24 1/cm2`
\(10^{25}~\mathrm{cm}^{−2}\)	`2e25 1/cm2`

The RXTORUS_CS.ski file has already been adjusted to produce the results for the narrow spectral range discussed in Zoom on narrow spectral range.

Once all files are in place, pass the name of each ski file to SKIRT as a single command line argument. Higher number column densities lead to longer simulation run times.