Xspec Redistribution Functions 

htsmooth: asymmetric broadening function
emcomp: empirical function that reproduces a Compton scattering profile

Preface

These two convolution models empirically reproduce asymmetrically broadened or Compton down-scattered spectra. They use the calcManyLines generic code in the Xspec spectral fitting software in HEASoft, which is used in the gsmooth function and other smoothing functions, and is provided as calcLinesLM.cxx in this distribution.

Model: htsmooth

The htsmooth (Half-Triangle SMOOTH) model redistributes the flux within each spectral bin (Ebin) to a half-triangular distribution. The model includes a single parameter, MaxVel, in units of km/s, which represents the maximum absolute radial velocity at the end of the half-triangle. A negative MaxVel value indicates a blueshift, while a positive value indicates a redshift, extending the triangle into the higher- or lower-energy range, respectively.

Model: emcomp

The emcomp (EMpirical COMPton) model redistributes the flux within each spectral bin (Ebin) to a trapezoidal distribution, defined down to the 180-degree Compton backscattering energy ($E_{\rm BS}$) using the Smallest Scattering Cut (SSC), Smallest Scattering Fraction (SSF), Largest Scattering Cut (LSC), and Largest Scattering Fraction (LSF). The 180-degree Compton backscattering energy ($E_{\rm BS}$) is:

$$E_{\rm BS} = \frac{E_{\rm bin}}{1+2(E_{\rm bin}/511~{\rm keV})}$$

The Compton Flux Ratio (CFR) parameter is the ratio of the Compton-scattering flux to the source flux.

The CFR parameter controls the Compton scattering flux, and the CSF and LSF parameters only define the trapezoid shape. Therefore, either the CSF or the LSF parameter must be fixed to obtain a single solution. Meanwhile, the model breaks when LSC < SSC, so users must manually limit their parameter ranges if both vary. Because the scattering signal tends to be strong when the scattering matter is located behind the irradiating source, the default setup sets both the LSC and LSF parameters to 1.

This model does not account for the angular dependence of the Compton-scattering cross section. The redistribution function is, therefore, a combination of the spatial distribution of the scattering material and the Compton-scattering cross section. It is important to note that in a cold medium, photoelectric absorption occurs with Compton scattering. The Compton scattering cross-section is relatively constant in the soft X-ray energy range, while the absorption cross-section is smaller at a higher X-ray energy. Consequently, the optical depth changes, and the total Compton-scattering flux changes with energy. The current model does not account for this effect and, therefore, is not suitable for wide-band fitting.

Installing the Model

Follow the guidance in Appendix C in the Xspec manual for installing local models.

For example,

term> xspec

XSPEC12>initpackage redistmodels /path/to//lmodel.dat /path/to/redistmodels/
XSPEC12>lmod models /path/to/redistmodels/