Post-Newtonian evolution of massive black hole triplets in galactic nuclei – IV. Implications for LISA

International audienceCoalescing massive black hole binaries (MBHBs) of |$10^{4-7}~\rm M_{\odot }$|⁠, forming in the aftermath of galaxy mergers, are primary targets of the space mission LISA, the Laser Interferometer Space Antenna. An assessment of LISA detection prospects requires an estimate of the abundance and properties of MBHBs that form and evolve during the assembly of cosmic structures. To this aim, we employ a semi-analytic model to follow the co-evolution of MBHBs within their host galaxies. We identify three major evolutionary channels driving the binaries to coalescence: two standard paths along which the binary evolution is driven by interactions with the stellar and/or gaseous environment, and a novel channel where MBHB coalescence occurs during the interaction with a third black hole. For each channel, we follow the orbital evolution of MBHBs with physically motivated models that include a self-consistent treatment of the orbital eccentricity. We find that LISA will detect between ≈25 and ≈75 events per year depending on the seed model. We show that triple-induced coalescences can range from a few detected events up to |${\sim } 30{{\ \rm per\ cent}}$| of the total detected mergers. Moreover, even if the standard gas/stars-driven evolutionary channels should fail and MBHBs were to stall, triple interactions would still occur as a result of the hierarchical nature of galaxy formation, resulting in about ≈10 to ≈20 LISA detections per year. Remarkably, triple interactions among the black holes can produce coalescing binaries with large eccentricities (≳ 0.9) upon entrance into the LISA band. This eccentricity will remain significant (∼0.1) also at merger, requiring suitable templates for parameter estimation