Perturber-Driven Dynamics of Supermassive Black Hole Binaries in Galaxy Mergers

The orbital eccentricity of massive black hole binaries (MBHBs) at binary formation shapes the stochastic gravitational-wave background (GWB) detectable by pulsar timing arrays (PTAs). Previous N-body simulations show large run-to-run scatter in this quantity, dominated by Poisson noise, raising the question of whether physical substructure adds genuine astrophysical stochasticity. We test this with high-resolution re-simulations of a major merger from IllustrisTNG100-1, evolved with the Griffin N-body code. A no-perturber control is compared with two matched suites in which ftarget = 0.1 of the primary bulge mass is redistributed into equal-mass perturbers of 10⁷\, M (μp ≈ 3.2 × 10−3) and 10⁸\, M (μp ≈ 3.2 × 10−2), with four realisations per scenario. The control gives σe ≈ 0.11, consistent with the Poisson noise floor at this resolution. The 10⁷\, M case gives σe ≈ 0.115, indistinguishable from the control in its scatter, whereas the 10⁸\, M case gives σe ≈ 0.26, a factor of 2.4 above the floor, though statistically marginal given only four realisations. This excess scatter coincides with larger event-aligned residuals in orbital energy and angular momentum and stronger torque spikes, consistent with near-impulsive perturber–MBHB encounters. In binary–single scattering theory the transition is set by the perturber–MBHB mass ratio μp: the 10⁷\, M case remains diffusive while the 10⁸\, M case approaches the near-impulsive regime. As the expected perturber population in massive ellipticals lies mostly below this regime, perturber-driven eccentricity randomisation is unlikely to matter for GWB-relevant MBHB mergers.