Implementing and investigating the numerical accuracy of the exact Compton scattering in the x-ray reflection from the black hole accretion disk

The polarized radiative transfer equation (PRTE) deals with the Compton scattering of the radiation by the elections in the accretion disk. The scattering part of the PRTE contains all the information of the photon momentum change due to the Compton scattering in terms of a Compton scattering matrix (CSM). The treatment of Compton electron scattering and its effect in the reflected spectrum in XILLVER (Garcı́a and Kallman 2010; Garcı́a et al. 2013) is done in an approximated way based on a simple redistribution function. This approximation is accurate at relatively low temperatures and for photon energies (E ≪ mec 2 = 511keV). However, at higher energies and temperatures, significant discrepancies with an exact solution become important. We are going to use the exact expression of the RFs from Poutanen paper (Poutanen 1993) in XILLVER, which includes Klein-Nishina corrections, as well as relativistic corrections that become important at high temperatures. Our present work will numerically calculate the CSM values for a 3D grid using the same parameters value applicable for an accretion disk high energies and temperature. This 3D grid values will be imported as a fits file and read into the XILLVER code. We will also investigate the numerical accuracy for different parameters ranges and cut-off energies. Finally, the output from the XILLVER code will be fed into a GR raytracing code written by Henric Krawczynski to study and analyze the Fe Kα line from the future X-ray mission i.e., NASA’s IXPE and XL-calibur.