Binary super-massive black hole environments diminish the
  gravitational-wave signal in the pulsar timing band
  We assess the effects of super-massive black hole (SMBH) environments on the
gravitational-wave (GW) signal from binary SMBHs. To date, searches with pulsar
timing arrays for GWs from binary SMBHs, in the frequency band
$\sim1-100$\,nHz, include the assumptions that all binaries are circular and
evolve only through GW emission. However, dynamical studies have shown that the
only way that binary SMBH orbits can decay to separations where GW emission
dominates the evolution is through interactions with their environments. We
augment an existing galaxy and SMBH formation and evolution model with
calculations of binary SMBH evolution in stellar environments, accounting for
non-zero binary eccentricities. We find that coupling between binaries and
their environments causes the expected GW spectral energy distribution to be
reduced with respect to the standard assumption of circular, GW-driven
binaries, for frequencies up to $\sim20$\,nHz. Larger eccentricities at binary
formation further reduce the signal in this regime. We also find that GW bursts
from individual eccentric binary SMBHs are unlikely to be detectable with
current pulsar timing arrays. The uncertainties in these predictions are large,
owing to observational uncertainty in SMBH-galaxy scaling relations and the
galaxy stellar mass function, uncertainty in the nature of binary-environment
coupling, and uncertainty in the numbers of the most massive binary SMBHs. We
conclude, however, that low-frequency GWs from binary SMBHs may be more
difficult to detect with pulsar timing arrays than currently thought.
