Binary super-massive black hole environments diminish the gravitational-wave signal in the pulsar timing band

TL;DR

This study shows that the gravitational-wave signals from super-massive black hole binaries are weaker than previously estimated due to environmental interactions and eccentricities, complicating detection efforts with pulsar timing arrays.

Contribution

It introduces a model incorporating environmental effects and eccentricities into SMBH binary evolution, refining predictions of gravitational-wave signals in the pulsar timing band.

Findings

Environmental coupling reduces GW signal strength up to 20 nHz.

Higher initial eccentricities further diminish the GW signal.

Detection of individual eccentric SMBH GW bursts is unlikely with current arrays.

Abstract

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.