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

Accretion disks around stellar-mass 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) disk symmetry axis, because of electron scattering in the disk. 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 disk, 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 disk, where they scatter until eventually escaping to infinity. A comparison between our results and those obtained in previous works by different authors show an overall good agreement, despite the use of different code architectures. We finally consider the effects of absorption in the disk material by including more realistic albedo profiles for the disk surface. Our findings in this respect show that considering also the ionization state of the disk may deeply modify the behavior of polarization observables.