Stellar hardening of massive black hole binaries: the impact of the host rotation

TL;DR

This study investigates how the rotation of the stellar environment influences the hardening process of massive black hole binaries, revealing that prograde binaries in rotating hosts harden faster due to enhanced stellar interactions.

Contribution

The paper introduces a model describing the impact of host rotation on binary black hole dynamics, highlighting the role of center of mass oscillations and their effect on binary shrinking rates.

Findings

Prograde binaries in rotating hosts exhibit faster hardening.

Center of mass oscillations are induced by stellar interactions.

Binary shrinking rate doubles with net orbital motion of the CoM.

Abstract

Massive black hole binaries (MBHBs) with masses of ~ 10^4 to ~ 10^10 of solar masses are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is approximately 0.25 ( approximately 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems.