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. In astrophysical sources, the electron's spin direction are generally randomly oriented, so the Comptonized spectrum would be linearly polarized. 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, at the scattering angle $\theta$ = 0 or $\theta$ $\equiv$ [0,25degree], the modulation curve of scattered photon exhibits the same PD (degree of polarization) and PA (angle of polarization) of incident photon, 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 $\theta$-angle (or alternatively, the disk inclination angle i) on a meridian plane after single scattering with unpolarized incident photons (which was first formulated by Chandrasekhar, 1946). We explore the energy dependency of polarization by considering a general spectral parameter set corresponding to hard and soft states of XRBs. We also compare the results qualitatively with observation of IXPE.