Speed limits for radiation driven SMBH winds

Ultra Fast Outflows (UFOs) are an established feature in X-ray spectra of AGNs. According to the standard picture, they are launched at accretion disc scales with relativistic velocities, up to 0.3-0.4 c. Their high kinetic power is enough to induce an efficient feedback on galactic-scale, possibly contributing to the co-evolution between the central supermassive black hole (SMBH) and the host galaxy. It is therefore of paramount importance to fully understand the UFO physics, in particular the forces driving their acceleration and the relation with the accretion flow they originate from. In this paper we investigate the impact of special relativity effects on the radiative pressure exerted onto the outflow. The radiation received by the wind decreases for increasing outflow velocity v, implying that the standard Eddington limit argument has to be corrected according to v. Due to the limited ability of the radiation to counteract the SMBH gravity, we expect to find lower typical velocities with respect to the non-relativistic scenario. We integrate the relativistic-corrected outflow equation of motion for a realistic set of starting conditions. We concentrate on UFO typical values of ionisation, column density and launching radius. We explore a one-dimensional, spherical geometry and a 3D setting with a rotating thin accretion disc. We find that the inclusion of relativistic effects leads to sizeable differences in the wind dynamics and that v is reduced up to 50% with respect to the non-relativistic treatment. We compare our results with a sample of UFO from the literature, and we find that the relativistic-corrected velocities are systematically lower than the reported ones, indicating the need for an additional mechanism, such as magnetic driving, to explain the highest velocity components. These conclusions, derived for AGN winds, have a general applicability.