Evolution Of Massive Black Hole Binaries In Rotating Stellar Nuclei: Implications For Gravitational Wave Detection

TL;DR

This paper models the gravitational wave background from supermassive black hole binaries in galactic nuclei, incorporating binary orbital plane evolution and galaxy rotation effects, which refines predictions for gravitational wave detection.

Contribution

It introduces the first model including binary orbital plane evolution and galaxy rotation effects, reducing predicted gravitational wave signals and addressing previous overestimations.

Findings

Predicted GW background is 2-3 times lower than previous models.

High binary eccentricities (>0.9) are common before GW-dominated inspiral.

Model aligns better with current non-detections by PTAs.

Abstract

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.