Detecting Supermassive Black Hole-Induced Binary Eccentricity Oscillations with LISA

Stellar-mass black hole binaries (BHBs) near supermassive black holes (SMBH) in galactic nuclei undergo eccentricity oscillations due to gravitational perturbations from the SMBH. Previous works have shown that this channel can contribute to the overall BHB merger rate detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo Interferometer. Significantly, the SMBH gravitational perturbations on the binary's orbit may produce eccentric BHBs which are expected to be visible using the upcoming Laser Interferometer Space Antenna (LISA) for a large fraction of their lifetime before they merge in the LIGO/Virgo band. For a proof-of-concept, we show that the eccentricity oscillations of these binaries can be detected with LISA for BHBs in the local universe up to a few Mpcs, with observation periods shorter than the mission lifetime, thereby disentangling this merger channel from others. The approach presented here is straightforward to apply to a wide variety of compact object binaries with a tertiary companion.