Spectral and polarization properties of reflected X-ray emission from black-hole accretion discs for a distant observer: the lamp-post model

Rebirth of X-ray polarimetric instruments will have a significant impact on our knowledge of compact accreting sources. The properties of inner-accreting regions of active galactic nuclei (AGNs) or X-ray binary systems (XRBs), such as black-hole spin, their disc inclination and orientation, shape and size of their corona, can be polarimetrically studied, parallelly to the well-known X-ray spectroscopic and timing techniques. In this work, we provide a new spectropolarimetric numerical estimate of X-rays in the lamp-post coronal model for a distant observer, including a polarized reflected radiation from the accretion disc. The local disc reflection was simulated using the codes TITAN and STOKES and includes variable disc ionization as well as Monte Carlo treatment of Compton multiple scatterings. We introduce a relativistic code KYNSTOKES based on our well-tested KY package that accounts for all relativistic effects on radiation near a black hole, apart from the returning radiation, and adds a possibility of polarized coronal emission. We study the spectrum, polarization degree and polarization angle at spatial infinity for various global system parameters and we demonstrate the difference at infinity, if analytical local reflection computations are used. We newly predict that in the hard X-rays the reflected component can be 25% polarized and the total emission can be 9% polarized in the most favourable, yet realistic configurations of radio-quiet AGNs. Thus, the relativistic disc reflection remains important for the interpretation of X-ray polarimetric observations.