Gravitational Waves from the Inspiral of Supermassive Black Holes in Galactic-scale Simulations

We study the orbital evolution and gravitational wave (GW) emission of supermassive black hole (SMBH) binaries formed in gas-free mergers of massive early-type galaxies using the hybrid tree-regularized N-body code KETJU. The evolution of the SMBHs and the surrounding galaxies is followed self-consistently from the large-scale merger down to the final few orbits before the black holes coalesce. Post-Newtonian corrections are included up to PN3.5-level for the binary dynamics, and the GW calculations include the corresponding corrections up to PN1.0-level. We analyze the significance of the stellar environment on the evolution of the binary and the emitted GW signal during the final GW emission dominated phase of the binary hardening and inspiral. Our simulations are compared to semi-analytic models that have often been used for making predictions for the stochastic GW background emitted by SMBHs. We find that the commonly used semi-analytic parameter values produce large differences in merger timescales and eccentricity evolution, but result in only $\sim 10\%$ differences in the GW spectrum emitted by a single binary at frequencies $f\gtrsim 10^{-1} \, \rm yr^{-1}$, which are accessible by current pulsar timing arrays. These differences are in part caused by the strong effects of the SMBH binaries on the surrounding stellar population, which are not included in the semi-analytic models.