Gravitational Waves from the Inspiral of Supermassive Black Holes in Galactic-scale Simulations

TL;DR

This study uses detailed simulations to analyze the orbital evolution and gravitational wave emission of supermassive black hole binaries, highlighting differences from semi-analytic models and their implications for pulsar timing array observations.

Contribution

It provides the first self-consistent, high-precision simulation of SMBH binary evolution from galaxy merger to coalescence, including relativistic effects and stellar environment impacts.

Findings

Semi-analytic models differ significantly in merger timescales and eccentricity evolution.

GW spectrum differences are about 10% at frequencies relevant for pulsar timing arrays.

Stellar environment effects are crucial and often neglected in simplified models.

Abstract

We study the orbital evolution and gravitational wave (GW) emission of supermassive black hole (SMBH) binaries formed in gas-free mergers of massive early-type galaxies using the hybrid tree-regularized N-body code KETJU. The evolution of the SMBHs and the surrounding galaxies is followed self-consistently from the large-scale merger down to the final few orbits before the black holes coalesce. Post-Newtonian corrections are included up to PN3.5-level for the binary dynamics, and the GW calculations include the corresponding corrections up to PN1.0-level. We analyze the significance of the stellar environment on the evolution of the binary and the emitted GW signal during the final GW emission dominated phase of the binary hardening and inspiral. Our simulations are compared to semi-analytic models that have often been used for making predictions for the stochastic GW background emitted by SMBHs. We find that the commonly used semi-analytic parameter values produce large differences in merger timescales and eccentricity evolution, but result in only $\sim 10\%$ differences in the GW spectrum emitted by a single binary at frequencies $f\gtrsim 10^{-1} \, \rm yr^{-1}$, which are accessible by current pulsar timing arrays. These differences are in part caused by the strong effects of the SMBH binaries on the surrounding stellar population, which are not included in the semi-analytic models.