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We study the dynamical evolution of the stellar mass binary black holes(BBHs) in a galactic nucleus that contains a massive black hole (MBH). For acomprehensive study of their merging events, we consider simultaneously thenon-resonant and resonant relaxations of the BBHs, the binary-single encountersof the BBHs with the field stars, the Kozai-Lidov (KL) oscillation and theclose encounters between the BBHs and the central MBH, which usually lead tobinaries' tidal disruptions. As the BBHs are usually heavier than thebackground stars, they sink to the center by mass segregation, making the KLoscillation an important effect in merging BBHs. The binary-single encounterscan not only lead to softening and ionization of the BBHs, it can also makethem hardening, that increases the merging rates significantly. The mergers ofBBHs are mainly contributed by galaxies containing MBHs less massive than $10^8M_\odot$ and the total event rates are likely in orders of $1$--$10$ Gpc$^{-3}$yr$^{-1}$, depending on the detailed assumptions of the nucleus clusters. About$3-10\%$ of these BBH mergers are with eccentricity $\ge 0.01$ when theirgravitational wave oscillating frequencies enter the LIGO band ($10$\,Hz). Ourresults show that merging the BBHs within galactic nuclei can be an importantsource of the merging events detected by the Advanced LIGO/Virgo detectors, andthey can be distinguished from BBH mergers from the galactic fields andglobular clusters when enough events are accumulated.

Gravitational-wave merging events from the dynamics of stellar mass binary black holes around the massive black hole in a galactic nucleus