1 Introduction

With an ever-increasing number of secure detections, supermassive black holes (SBHs) have evolved, in the span of a few years, from exotic possibilities to well-established components of galaxies. While it was understood since the 1960’s that the energy sources of quasars must be gravitational [185 ], it was thirty years before the existence of SBHs was firmly established, through measurements of the Keplerian rise in the rotation velocity of stars or gas at the very centers of galactic nuclei [106 ]. It is now generally accepted that the formation and evolution of galaxies and SBHs are tightly intertwined, from the early phases of proto-galactic formation [200

], through hierarchical build-up in CDM-like cosmogonies [83

], to recent galaxy mergers [150

SBHs appear to be linked in fundamental ways to the dynamics of the stellar component in galaxies, both on large and small scales. An astonishingly tight correlation exists between SBH mass and the central velocity dispersion of the stellar component, $M • ~ sa$ , $a ~~ 4.5$ [51 ]; the correlation with the velocity dispersion averaged over kiloparsec scales is weaker but still impressive [64 , 49 ]. Similar correlations exist between SBH mass and bulge luminosity [131 , 129 ] and central concentration of the light [77 , 38 ], indicating that SBHs “know” about the depth of the gravitational potential well in which they live. These tight correlations probably reflect a degree of feedback in the growth of SBHs [200 ].

On small scales, SBHs are embedded in stellar cusps, parsec-scale regions where the stellar density increases approximately as a power law with distance from the SBH into the smallest resolvable radii [29 , 52 , 138 , 65 ]. Faint galaxies have steep nuclear density profiles, $r ~ r- g$ , $1.5 <~ g <~ 2.5$ , while bright galaxies typically have weaker cusps, $g <~ 1$ . Steep cusps form naturally as the growth of the SBH pulls in stars [163 ]. In small dense galaxies where the star-star relaxation time is shorter than $10 10 yr$ , steep cusps may also form via collisional relaxation [8 , 171 ]. Weak cusps may be remnants of strong cusps that were destroyed by binary SBHs during galaxy mergers; in fact the structure and kinematics of galactic nuclei are now believed to be fossil relics of the merger process [135 ].

Larger galaxies grow through the agglomeration of smaller galaxies and protogalactic fragments. If more than one of the fragments contained a SBH, the SBHs will form a bound system in the merger product [18 , 187 ]. This scenario has received considerable attention because the ultimate coalescence of such a pair would generate an observable outburst of gravitational waves [209 ]. The evolution of a binary SBH can be divided into three phases [18 ]:

As the galaxies merge, the SBHs sink toward the center of the new galaxy via dynamical friction where they form a binary.
The binary continues to decay via gravitational slingshot interactions [191 ] in which stars on orbits intersecting the binary are ejected at velocities comparable to the binary’s orbital velocity, while the binary’s binding energy increases.
If the binary’s separation decreases to the point where the emission of gravitational waves becomes efficient at carrying away the last remaining angular momentum, the SBHs coalesce rapidly.

The transition from (2) to (3) is understood to be the bottleneck of a SBH binary’s path to coalescence, since the binary will quickly eject all stars on intersecting orbits, thus cutting off the supply of stars. This is called the “final parsec problem” [151 ]. But there are other possible ways of continuing to extract energy and angular momentum from a binary SBH, including accretion of gas onto the binary system [4 ] or refilling of the loss cone via star-star encounters [228 , 152 ] or triaxial distortions [143 ]. Furthermore there is circumstantial evidence that efficient coalescence is the norm. The X-shaped radio sources [32 ] are probably galaxies in which SBHs have recently coalesced, causing jet directions to flip. The inferred production rate of the X-sources is comparable to the expected merger rate of bright ellipticals, suggesting that coalescence occurs relatively quickly following mergers [137 ]. If binary SBHs failed to merge efficiently, uncoalesced binaries would be present in many bright ellipticals, resulting in 3- or 4-body slingshot ejections when subsequent mergers brought in additional SBHs. This would produce off-center SBHs, which seem to be rare or non-existent, as well as (perhaps) too much scatter in the $M$ - $s$ and $M$ - $Lbulge$ relations [83 ].

While the final approach to coalescence of binary SBHs is not well understood, much of their dynamical effect on the surrounding nucleus takes place very soon after the binary forms. The binary quickly (in less than a galactic crossing time) ejects from the nucleus a mass in stars of order its own mass [177 , 150 ] significantly lowering the central density on parsec scales. There is reasonable quantitative agreement between this model and the observed structure of nuclei: The “mass deficit” - the stellar mass that is “missing” from the centers of galaxies, assuming that they once had steep cusps like those observed at the centers of faint ellipticals - is of order the black hole mass [153 , 181 , 76 ].

While the binary SBH model is compelling, there is still not much hard evidence in its support. Observationally, no bona fide binary SBH (i.e. gravitationally bound pair of SBHs) has definitely been detected, although there is circumstantial evidence (precessing radio jets; periodic outburst activity) for SBH binaries in a number of active galaxies, as reviewed briefly below (see [104 ] for a more complete review of this topic). But the binary SBH model has one great advantage: the postulated effects are accessible to observation, since they extend to scales of $1 -100 pc$ , the distance out to which a binary SBH can significantly influence stellar motions. Much of the recent theoretical work in this field has been directed toward understanding the influence of a binary SBH on its stellar surroundings and looking for evidence of that influence in the distribution of light at the centers of galaxies.

Following the definition of terms and time scales in Section 2, we present a brief overview of the observational evidence for binary SBHs in Section 3. Interaction of a binary SBH with stars is discussed in Section 4. The possibility of multiple SBHs in galactic nuclei, and the implications for coalescence, are discussed in Section 5. Section 6 summarizes $N$ -body work on the evolution of binary SBHs, with an emphasis on the question of binary wandering. Observational evidence for the destruction of nuclear density cusps is reviewed in Section 7. In some galaxies, the predominant source of torques leading to decay of the binary may be gas; this topic is reviewed in Section 8. Finally, the influence of binary coalescence on SBH spins is summarized in Section 9.