Towards a complete description of spectra and polarization of black hole accretion discs: albedo profiles and returning radiation

Accretion discs around stellarmass black holes (BHs) emit radiation peaking in the soft X-rays when the source is in the thermal state. The emerging photons are polarized and, for symmetry reasons, the polarization integrated over the source is expected to be either parallel or perpendicular to the (projected) disc symmetry axis, because of electron scattering in the disc. However, due to general relativity effects photon polarization vectors will rotate with respect to their original orientation, by an amount depending on both the BH spin and the observer's inclination. Hence, X-ray polarization measurements may provide important information about strong gravity effects around these sources. Along with the spectral and polarization properties of radiation which reaches directly the observer once emitted from the disc, in this paper we also include the contribution of returning radiation, i.e. photons that are bent by the strong BH gravity to return again on the disc, where they scatter until eventually escaping to infinity. A comparison between our results and those obtained in previous works by different authors shows an overall good agreement, despite the use of different code architectures. We finally consider the effects of absorption in the disc material by including more realistic albedo profiles for the disc surface. Our findings in this respect show that considering also the ionization state of the disc may deeply modify the behaviour of polarization observables.