In this paper , we explore the mechanisms that regulate the formation and evolution of stellar black hole binaries ( BHBs ) around supermassive black holes ( SMBHs ) .
We show that dynamical interactions can efficiently drive ” in-situ ” BHB formation if the SMBH is surrounded by a massive nuclear cluster ( NC ) , while orbitally segregated star clusters can replenish the BHB reservoir in SMBH-dominated nuclei .
We discuss how the combined action of stellar hardening and mass segregation sculpts the BHB orbital properties .
We use direct N-body simulations including post-Newtonian corrections up to 2.5 order to study the BHB-SMBH interplay , showing that the Kozai-Lidov mechanism plays a crucial role in shortening binaries lifetime .
We find that the merging probability weakly depends on the SMBH mass in the 10 ^ { 6 } -10 ^ { 9 } { \leavevmode \nobreak M } _ { \odot } mass range , leading to a merger rate \Gamma \simeq 3 - 8 yr ^ { -1 } Gpc ^ { -3 } at redshift zero .
Nearly 40 \% of the mergers have masses in the ” BH mass gap ” , 50 - 140 { \leavevmode \nobreak M } _ { \odot } , thus indicating that galactic nuclei are ideal places to form BHs in this mass range .
We argue that gravitational wave ( GW ) sources with components mass m _ { 1 } > 40 { \leavevmode \nobreak M } _ { \odot } and m _ { 2 } < 30 { \leavevmode \nobreak M } _ { \odot } would represent a strong indicator of a galactic nuclei origin .
The majority of these mergers could be multiband GW sources in the local Universe : nearly 40 \% might be seen by LISA as eccentric sources and , a few years later , as circular sources by LIGO and the Einstein Telescope , making decihertz observatories like DECIGO unique instruments to bridge the observations during the binary inspiral .