Spin–Orbit Misalignment of Merging Black Hole Binaries with Tertiary Companions

Bin Liu,Dong Lai

doi:10.3847/2041-8213/aa8727

Abstract

Abstract We study the effect of an external companion on the orbital and spin evolution of merging black hole (BH) binaries. A sufficiently nearby and inclined companion can excite Lidov–Kozai (LK) eccentricity oscillations in the binary, thereby shortening its merger time. During such LK-enhanced orbital decay, the spin axis of the BH generally exhibits chaotic evolution, leading to a wide range (0°–180°) of the final spin–orbit misalignment angle from an initially aligned configuration. For systems that do not experience eccentricity excitation, only modest ( ) spin–orbit misalignment can be produced, and we derive an analytic expression for the final misalignment using the principle of adiabatic invariance. The spin–orbit misalignment directly impacts the gravitational waveform and can be used to constrain the formation scenarios of BH binaries and dynamical influences of external companions.

Highlights

We show that as the BH binary undergoes LK-enhanced decay from a wide orbit and eventually enters the LIGO band, the spin axis of individual BHs can experience chaotic evolution, so that a significant spin-orbit misalignment can be produced prior to merger even for binaries formed with zero initial misalignment
We have studied the effect of external companion on the orbital and spin evolution of merging BH binaries due to gravitational radiation
A sufficiently close by and inclined companion can excite Lidov-Kozai eccentricity oscillation in the binary, shortening its merger time compared to circular orbits [see Fig.3]

Summary

INTRODUCTION

The recent breakthrough in the detection of gravitational waves (GWs) from merging black hole (BH) binaries by advanced LIGO (Abbott et al 2016a,b, 2017) has generated renewed interest in understanding the formation mechanisms of compact BH binaries, from the evolution of massive stellar binaries (Lipunov et al 1997; Belczynski et al 2010, 2016; Mandel & de Mink 2016; Lipunov et al 2017) and triples (Silsbee & Tremaine 2017; Antonini et al 2017) in the galactic fields, to dynamical interactions in galactic nuclei (Antonini & Perets 2012; Petrovich & Antonini 2017) and in the dense core of globular clusters (Miller & Hamilton 2002; Rodriguez et al 2015; Chatterjee et al 2017). We study the merger and spin-orbit misalignment of BH binaries in the presence of tertiary companion Such triple BH systems could be a direct product of massive triple stars in the galactic field (Silsbee & Tremaine 2017; Antonini et al 2017), or could be produced dynamically in a dense cluster (Miller & Hamilton 2002; Rodriguez et al 2015; Antonini & Rasio 2016). It is well known that a tertiary body on an inclined orbit can accelerate the decay of an inner binary by inducing Lidov-Kozai (LK) eccentrcity/inclination oscillations (Lidov 1962; Kozai 1962) This has been studied before in the contexts of supermassive BH binary merger (Blaes et al 2002) and stellar mass BH binaries (e.g., Miller & Hamilton (2002); Thompson (2011); Antonini et al (2014); Silsbee & Tremaine (2017)). We expect that similar spin dynamics may take place in other types of triple systems, e.g., those with much larger initial separations, but experience extreme eccentricity excitation due to non-secular forcing from tertiary companions (Silsbee & Tremaine 2017; Antonini et al 2017)

Setup and Orbital Evolution

Eccentricity Excitation and Merger Time

Spin-Orbit Coupling

Analytical Calculation of θSf L for Circular Binaries

SUMMARY AND DISCUSSION