  We compute the isotropic gravitational wave (GW) background produced by
binary supermassive black holes (SBHs) in galactic nuclei. In our model,
massive binaries evolve at early times via gravitational-slingshot interaction
with nearby stars, and at later times by the emission of GWs. Our expressions
for the rate of binary hardening in the "stellar" regime are taken from the
recent work of Vasiliev et al., who show that in the non-axisymmetric galaxies
expected to form via mergers, stars are supplied to the center at high enough
rates to ensure binary coalescence on Gyr timescales. We also include, for the
first time, the extra degrees of freedom associated with evolution of the
binary's orbital plane; in rotating nuclei, interaction with stars causes the
orientation and the eccentricity of a massive binary to change in tandem,
leading in some cases to very high eccentricities (e>0.9) before the binary
enters the GW-dominated regime. We argue that previous studies have
over-estimated the mean ratio of SBH mass to galaxy bulge mass by factors of 2
- 3. In the frequency regime currently accessible to pulsar timing arrays
(PTAs), our assumptions imply a factor 2 - 3 reduction in the characteristic
strain compared with the values computed in most recent studies, removing the
tension that currently exists between model predictions and the non-detection
of GWs.
