Plane polarisation in Comptonization process: A Monte Carlo study

Abstract

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 ($k \times k^{\prime}$)-coordinate (in which, ($k \times k^{\prime}$) 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 $\sim$0.33. At the scattering angle $\theta$ = 0 or $\theta \equiv$ [0,25$^{\circ}$], 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^′ ($k^{\prime}_{e}$) 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 $\theta$-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. $\langle N_{sc}\rangle$ $\sim$1.1 the PD is independent of energy and PA $\sim 90^{\circ}$ ($k^{\prime}_{e}$ is parallel to the disc plane), and for $\langle N_{sc}\rangle$ $\sim$5 the PD value is maximum for $i=45^{\circ}$. We also compare the results qualitatively with observation of IXPE for five sources.