An estimate of the stochastic gravitational wave background from the MassiveBlackII simulation

A population of super-massive black hole binaries is expected to generate a stochastic gravitational wave background (SGWB) in the pulsar timing array (PTA) frequency range of $10^{-9}$--$10^{-7}$ Hz. Detection of this signal is a current observational goal and so predictions of its characteristics are of significant interest. In this work we use super-massive black hole binary mergers from the MassiveBlackII simulation to estimate the characteristic strain of the stochastic background. We examine both a gravitational wave driven model of binary evolution and a model which also includes the effects of stellar scattering and a circumbinary gas disk. Results are consistent with PTA upper limits and similar to estimates in the literature. The characteristic strain at a reference frequency of $1 yr^{-1}$ is found to be $A_{yr^{-1}} = 6.9 \times 10^{-16}$ and $A_{yr^{-1}} = 6.4 \times 10^{-16}$ in the gravitational-wave driven and stellar scattering/gas disk cases, respectively. Using the latter approach, our models show that the SGWB is mildly suppressed compared to the purely gravitational wave driven model as frequency decreases inside the PTA frequency band.