Abstract
Results from pulsar timing arrays (PTAs) show evidence of a gravitational wave background (GWB) consistent with a population of unresolved supermassive black hole binaries (BHBs). The observed spectrum shows a flattening at lower frequencies that can be explained by a population of eccentric BHBs. This study aims to determine the dynamical evolution and merger timescales of the most massive BHBs, which are potential sources of the GWB. We selected successive galactic major mergers from the IllustrisTNG100-1 cosmological simulation and re-simulated them at high resolution with the N-body code Griffin down to binary separations of the order of a parsec. Coalescence timescales were estimated using a semi-analytical model that incorporates gravitational wave emission and stellar hardening. Throughout our investigation, we considered the impact of prior mergers on the remnant galaxy in the form of core scouring and anisotropy, which can influence the subsequent formation and evolution of BHBs. We find that all the binaries in our sample enter the PTA band with an eccentricity of e>0.85: such a large eccentricity can impact the shape of the PTA observed GWB spectrum, and it highlights the importance of including the eccentricity of binaries when interpreting the PTA signal. Furthermore, we find that: (i) starting from initial separations of a few tens of kiloparsecs, the dynamical friction phase lasts for a few hundred million years; (ii) the binary formation time is not resolution-dependent; (iii) the scatter on the eccentricity at binary formation decreases with increasing resolution; and (iv) triple systems form whenever a third galaxy interacts with a binary that has not yet reached coalescence.