Analytical ray-tracing of synchrotron emission around accreting black holes

Polarimetric images of accreting black holes encode important information about laws of strong gravity and relativistic motions of matter. Recent advancements in instrumentation have enabled such studies of two objects: the supermassive black holes M87* and Sagittarius A*. Light coming from these sources is produced by a synchrotron mechanism whose polarization is directly linked to magnetic field lines, and propagates toward the observer in a curved spacetime. We studied the distortions of the gas image by employing the analytical ray-tracing technique for polarized light ARTPOL, which is adapted for the case of synchrotron emission. We derived analytical expressions for fast conversion of the intensity or flux, polarization degree, and polarization angle from the local coordinates to those of the observer. We placed an emphasis on the nonzero matter elevation above the equatorial plane and noncircular matter motions. Applications of the developed formalism include static polarimetric imaging of the black hole vicinity and dynamic polarimetric signatures of matter close to the compact object.