Plane polarisation in Comptonization process: A Monte Carlo study

High energies emissions observed in X-ray binaries (XRBs), active galactic nuclei (AGNs) are linearly polarised. The prominent mechanism for X-ray is the Comptonization process. We revisit the theory for polarisation in Compton scattering with unpolarised electrons and note that the (kxk')-coordinate (in which, (kx 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 polarisation PD after single scattering for randomly oriented low-energy unpolarised incident photons is similar to 0.33. At the scattering angle theta = 0 or theta = [0,25 degrees], the modulation curve of k' exhibits the same PD and PA (angle of polarisation) 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 polarisation 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 disc inclination angle i) on a meridian plane (i.e. the laws of darkening, formulated by Chandrasekhar (1946, ApJ, 103, 351) after single scattering with unpolarised 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. (N-sc) similar to 1.1 the PD is independent of energy and PA similar to 90 degrees (k(e') is parallel to the disc plane), and for (N-sc) similar to 5 the PD value is maximum for i = 45 degrees. We also compare the results qualitatively with observation of IXPE for five sources.