Astrophysical and relativistic modeling of the recoiling black-hole candidate in quasar 3C 186

The compact object in quasar 3C 186 is one of the most promising recoiling black-hole candidates, exhibiting both an astrometric displacement between the quasar and the host galaxy as well as a spectroscopic shift between broad and narrow lines. 3C 186 also presents a radio jet which, when projected onto the plane of the sky, appears to be perpendicular to the quasar/galaxy displacement. Assuming a gravitational-wave kick is indeed responsible for the properties of 3C 186 and using state-of-the-art relativistic modeling, we show that current observations allow for exquisite modeling of the recoiling black hole. Most notably, we find that the kick velocity, the black-hole spin, and the line of sight are almost collinear and the former appear perpendicular to each other only because of a strong projection effect. The targeted configuration requires substantial fine-tuning: while there exists a region in the black-hole binary parameter space that is compatible with 3C 186, the observed system appears to be a rare occurrence. Using archival radio observations, we explore different strategies that could potentially confirm or rule out our interpretation. In particular, we develop two observational tests that rely on the brightness ratio between the approaching and receding jet as well as the asymmetry of the jet lobes. While the available radio data provide loose constraints, deeper observations have the unique potential of unveiling the nature of 3C 186.