# Post-Newtonian Evolution of Massive Black Hole Triplets in Galactic Nuclei: IV. Implications for LISA

## TL;DR

This paper models the evolution of massive black hole triplets in galactic nuclei to predict their detection rates and characteristics for LISA, highlighting the importance of triple interactions and eccentricities in gravitational wave signals.

## Contribution

It introduces a semi-analytic model including a novel triple interaction channel, providing new insights into the coalescence rates and eccentricities of MBHBs relevant for LISA.

## Key findings

- LISA may detect 25-75 MBHB events per year.
- Triple interactions could account for up to 30% of detections.
- High eccentricities (up to 0.9) are possible at LISA entry, affecting waveform templates.

## Abstract

Coalescing 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 {\it 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 $\approx 25$ and $\approx 75$ events per year depending on the seed model. We show that triple-induced coalescences can range from a few detected events up to $\sim 30\%$ 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 $\approx 10$ to $\approx 20$ LISA detections per year. Remarkably, triple interactions among the black holes can produce coalescing binaries with large eccentricities ($\gtrsim 0.9$) upon entrance into the LISA band. This eccentricity will remain significant ($\sim 0.1$) also at merger, requiring suitable templates for parameter estimation.