Binary mergers near the supermassive black hole-Secular effect in the orbital evolution

The center of a galaxy is expected to contain a supermassive black hole (SMBH) surrounded by a nuclear star cluster. Inside the cluster, there is a broad distribution of stars, compact objects, and even binary systems. In such an environment, the evolution of binaries can be affected by a variety of physical processes. With the discovery of gravitational waves (GWs) from merging black hole binaries (BHBs), extensive research has been conducted to understand the formation and merger of compact binaries. Here, we theoretically review how binaries evolve and eventually merge under the long-term influence of a central SMBH. We summarize the key conclusions of this dynamical channel of mergers, including: (1) Gravitational perturbation from the SMBH induces von Zeipel-Lidov-Kozai (ZLK) eccentricity oscillations of the BHB, which leads to enhanced gravitational radiation and merger of the BHB. The maximum eccentricity of the BHB due to ZLK effect can be derived analytically and the modified merger time of the BHB is presented. In this tertiary induced channel, we find that the spins of black holes (BHs) preferentially lie in the orbital plane when the BHB enters the LIGO band. (2) Because the tertiary (SMBH) mass is much larger than the masses of the inner BHB, several general relativity (GR) effects involving the SMBH can generate extra precessions on the binary orbits and qualitatively change the dynamics, significantly increasing the inclination window for mergers and producing a wide range of spin orientations when the BHB enters LIGO band. For the BHBs that emit GWs in the low-frequency band (0.001-1 Hz), we show that the rate of change of the angular momentum vector of the BHB encodes the information on the spin of the SMBH due to the GR effects. Detecting GWs from compact binaries around SMBHs can provide a new probe of the spins of SMBHs. When the BHB moves around the SMBH in a less inclined orbit, we show that the inner binary can encounter an "apsidal precession resonance" and experience eccentricity excitation during the orbital decay due to gravitational radiation. This resonance occurs when the apsidal precession rate of the inner binary matches that of the outer binary, with the precessions driven by both Newtonian interactions and various post-Newtonian effects. The resonance and the associated eccentricity growth may occur while the binary emits gravitational waves in the low-frequency band, and may be detectable by future space-based gravitational wave detectors. The hierarchical mergers in multiple stellar systems can occur. We show that the binaries that have survived the SNe and kicks generally have too wide orbital separations to merge by themselves, but can merge with the aid of an external companion that gives rise to ZLK oscillations. The merging BHBs GW190412, GW190814, and GW190521 from the third LIGO/VIRGO observing run exhibit some extraordinary properties. We suggest that GW190412, GW190814, and GW190521 could all be produced via hierarchical mergers in multiples, likely in a nuclear star cluster, with the final merger induced by a massive BH.