Birth, Life, and Death of Black Hole Binaries around Supermassive Black Holes: Dynamical Evolution of Gravitational Wave Sources

This paper explores 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, 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 the lifetime of binaries. We find that the merging probability weakly depends on the SMBH mass in the 10(6)-10(9) M-circle dot range, leading to a merger rate Gamma similar or equal to 3-8 yr(-1) Gpc(-3) at redshift zero. Nearly 40% of the mergers have masses in the "BH mass gap," 50-140 M-circle dot, thus indicating that galactic nuclei are ideal places to form BHs in this mass range. We argue that gravitational wave (GW) sources with component masses m(1) > 40 M-circle dot and m(2) < 30 M-circle dot would represent a strong indicator of a galactic nucleus 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.