Massive black hole binary mergers in dynamical galactic environments

Gravitational waves (GWs) have now been detected from stellar-mass black hole binaries, and the first observations of GWs from massive black hole (MBH) binaries are expected within the next decade. Pulsar timing arrays (PTA), which can measure the years long periods of GWs from MBH binaries (MBHBs), have excluded many standard predictions for the amplitude of a stochastic GW background (GWB). We use coevolved populations of MBHs and galaxies from hydrodynamic, cosmological simulations (`Illustris') to calculate a predicted GWB. The most advanced predictions so far have included binary hardening mechanisms from individual environmental processes. We present the first calculation including all of the environmental mechanisms expected to be involved: dynamical friction, stellar `loss-cone' scattering, and viscous drag from a circumbinary disc. We find that MBH binary lifetimes are generally multiple gigayears, and only a fraction coalesce by redshift zero. For a variety of parameters, we find all GWB amplitudes to be below the most stringent PTA upper limit of A_{yr^{-1}} ≈ 10^{-15}. Our fairly conservative fiducial model predicts an amplitude of A_{yr^{-1}} ≈ 0.4× 10^{-15}. At lower frequencies, we find A_{0.1 yr^{-1}} ≈ 1.5× 10^{-15} with spectral indices between -0.4 and -0.6 - significantly flatter than the canonical value of -2/3 due to purely GW-driven evolution. Typical MBHBs driving the GWB signal come from redshifts around 0.3, with total masses of a few times 10⁹ M_⊙, and in host galaxies with very large stellar masses. Even without GWB detections, our results can be connected to observations of dual active galactic nuclei to constrain binary evolution.