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

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 f target=0.1 of the primary bulge mass is redistributed into equal-mass perturbers of 10 7,M (mu p about3.2 times10-3) and 10 8,M (mu p about3.2 times10-2), with four realisations per scenario. The control gives sigma e about0.11, consistent with the Poisson noise floor at this resolution. The 10 7,M case gives sigma e about0.115, indistinguishable from the control, whereas the 10 8,M case gives sigma e about0.26, a factor of 2.4 above the floor, although 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 mu p: the 10 7,M case remains diffusive, whereas the 10 8,M case approaches the near-impulsive regime. Because the expected perturber population in massive ellipticals lies mostly below this regime, perturber-driven eccentricity randomisation is unlikely to affect GWB-relevant MBHB mergers.