  Central supermassive black holes (SMBHs) are a ubiquitous feature of
locally-observed galaxies, and ample evidence suggests that the growth of SMBHs
and their host galaxies is closely linked. However, in the event of a merger,
gravitational-wave (GW) recoil may displace a SMBH from its galactic center, or
eject it entirely. To explore the consequences of this phenomenon, we use
hydrodynamic simulations of gaseous galaxy mergers that include a range of BH
recoil velocities. We have generated a suite of over 200 simulations with more
than 60 merger models, enabling us to identify systematic trends in the
behavior of recoiling BHs -- specifically (i) their dynamics, (ii) their
observable signatures, and (iii) their effects on BH/galaxy co-evolution. (i)
Recoiling BH trajectories depend heavily on the gas content of the host galaxy;
maximal BH displacements from the center may vary by up to an order of
magnitude between gas-rich and gas-poor mergers. In some cases, recoil
trajectories also depend on the timing of the BH merger relative to the
formation of the galaxy merger remnant. (ii) Recoiling BHs may be observable as
offset active galactic nuclei (AGN) via either kinematic offsets (v > 800 km
s^-1) or spatial offsets (R > 1 kpc) for lifetimes of about 1 - 100 Myr. In
addition, recoil events affect the total AGN lifetime. GW recoil generally
reduces the lifetimes of bright AGN, but may extend lower-luminosity AGN
lifetimes. (iii) Rapidly-recoiling BHs may be up to about 5 times less massive
than their stationary counterparts. These mass deficits lower the normalization
of the M - sigma relation and contribute to both intrinsic and overall scatter.
Furthermore, recoil events displace AGN feedback from the galactic center,
which enhances central star formation rates. This results in longer starburst
phases and higher central stellar densities in merger remnants.
