Plane Polarization in Comptonization process : a Monte Carlo study

High energies emissions observed in X-ray binaries (XRBs), active galactic nuclei (AGNs) are linearly polarized. The prominent mechanism for X-ray is the Comptonization process. We revisit the theory for polarization in Compton scattering with unpolarized electrons, and note that the (k×k′)-coordinate (in which, (k×k′) acts as a z-axis, here k and k′ are incident and scattered photon momentum respectively) is more convenient to describe it. Interestingly, for a fixed scattering plane the degree of polarization PD after single scattering for random oriented low-energy unpolarized incident photons is ~0.3. At the scattering angle θ = 0 orθ≡ [0,25◦], the modulation curve of k′ exhibits the same PD and PA (angle of polarization) of k, and even the distribution of projection of electric vector of k′ (k′e) on perpendicular plane to the k indicates same (so, an essential criteria for detector designing). We compute the polarization state in Comptonization process using Monte Carlo methods with considering a simple spherical corona. We obtain the PD of emergent photons as a function of =-angle (or alternatively, the disk inclination angle i) on a meridian plane (i.e., the laws of darkening, formulated by Chandrasekhar, 1946) after single scattering with unpolarized incident photons. To explore the energy dependency we consider a general spectral parameter set corresponding to hard and soft states of XRBs, we find that for average scattering no. 〈Nsc〉 ~1.1 the PD is independent of energy and PA ~ 90◦ (k′e is parallel to the disk plane), and for hNsci ~5 the PD value is maximum for i = 45◦. We also compare the results qualitatively with observation of IXPE for five sources.