Recoiling black holes in merging galaxies: relationship to active galactic nucleus lifetimes, starbursts and the MBH-Σ* relation

Gravitational-wave recoil of merging supermassive black holes (SMBHs) may influence the co-evolution of SMBHs and their host galaxies. We examine this possibility using smoothed particle hydrodynamic/N-body simulations of gaseous galaxy mergers, including SMBH accretion, in which the merged BH receives a recoil kick. This enables us to follow the trajectories and accretion of recoiling BHs in self-consistent, evolving merger remnants. In contrast to recent studies on similar topics, we conduct a large parameter study, generating a suite of over 200 simulations with more than 60 merger models and a range of recoil velocities (v(k)). With this, we can identify systematic trends in the behaviour of recoiling BHs. Our main results are as follows. (1) BHs kicked at nearly the central escape speed (v(esc)) may oscillate on large orbits for up to a Hubble time, but in gas-rich mergers, BHs kicked with up to similar to 0.7v(esc) may be confined to the central few kpc of the galaxy, owing to gas drag and steep central potentials. (2) v(esc) in gas-rich mergers may increase rapidly during final coalescence, in which case recoil trajectories may depend sensitively on the timing of the BH merger relative to the formation of the central potential well. Delays of even a few times 107 yr in the BH merger time may substantially suppress recoiling BH motion for a fixed kick speed. (3) Recoil events generally reduce the lifetimes of bright active galactic nuclei (AGNs), but short-period recoil oscillations may actually extend AGN lifetimes at lower luminosities. (4) Bondi-Hoyle accretion dominates recoiling BH growth for v(k)/v(esc) less than or similar to 0.6-0.8; for higher v(k), the BH accretes primarily from its ejected gas disc, which we model as a time-dependent accretion disc. (5) Kinematically offset AGNs may be observable either immediately after a high-velocity recoil or during pericentric passages through a gas-rich remnant. In either case, AGN lifetimes may be up to similar to 10 Myr (for delta v > 800 km s-1), though the latter generally have higher luminosities. (6) Spatially offset AGNs can occur for v(k) greater than or similar to 0.5-0.7v(esc) (for delta R > 1 kpc); these generally have low luminosities and lifetimes of similar to 1-100 Myr. (7) Rapidly recoiling BHs may be up to approximately five times less massive than their stationary counterparts. These mass deficits lower the normalization of the M-BH-Sigma(*) relation and contribute to both intrinsic and overall scatter. (8) Finally, the displacement of AGN feedback after a recoil event enhances central star formation rates in the merger remnant, thereby extending the starburst phase of the merger and creating a denser, more massive stellar cusp.