Long-Term Evolution of and X-Ray Emission from a Recoiling Supermassive Black Hole in a Disk Galaxy

Recent numerical relativity simulations have shown that the emission of gravitational waves at the merger of two black holes gives a recoil kick to the final BH. We follow the orbits of a recoiling supermassive black hole (SMBH) in a fixed background potential of a disk galaxy including the effect of dynamical friction. If the recoil velocity of the SMBH is smaller than the escape velocity of the galaxy, the SMBH moves around in the potential along a complex trajectory before it spirals into the galactic center through dynamical friction. We consider the accretion of gas onto the SMBH from the surrounding interstellar medium and estimate the X-ray luminosity of the SMBH. We find that it can be larger than 3 × 10³⁹ erg s^-1 or the typical X-ray luminosity of ultra-luminous X-ray sources, when the SMBH passes the galactic disk. In particular, the luminosity could exceed ~10⁴⁵ erg s^-1, if the SMBH is ejected into the galactic disk. The average luminosity gradually increases as the SMBH spirals into the galactic center. We also estimate the probability of finding recoiling SMBHs with X-ray luminosities of >3 × 10³⁹ erg s^-1 in a disk galaxy.