Gravitational-Wave Signatures from Compact Object Binaries in the Galactic Center

Almost every galaxy has a supermassive black hole (SMBH) residing at its center, the Milky Way included. Recent studies suggest that these unique places are expected to host a high abundance of stellar and compact object binaries. These binaries form hierarchical triple systems with the SMBH and undergo the eccentric Kozai-Lidov (EKL) mechanism. Here we estimate the detectability of potential Gravitational-Wave emissions from these compact objects within the frequency band of the Laser Interferometer Space Antenna (LISA) and Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo detectors. We generate a post EKL population of stars at the onset of Roche limit crossing and follow their evolution to compact object binaries. As a proof-of-concept, we adopt two metallicities, solar metallicity ($Z = 0.02$) and $15\%$ of it ($Z = 0.003$). We demonstrate that over the observation timescale of LISA, black hole binaries (BH-BH) and white dwarf binaries provide the most prominent GW sources via the EKL assisted merger channel. Systems involving neutron stars are less observable but possibly abundant through different merger channels. Our population synthesis of BH-BH with $Z = 0.02$ ($Z = 0.003$) translate to $\sim$ $4$ ($24$) events per year with LIGO within a 1 ${\rm Gpc}^3$ sphere. We also estimated the number of binaries visible in the LISA band within the inner parsec of our galactic center (and possibly other galaxies) to be about 14 - 150 WD-WD, 0 - 2 NS-BH, 0.2 - 4 NS-NS, and 0.3 - 20 BH-BH.