Routing protocol

Physics

LIGO

Computer network

Mathematics

Black hole (networking)

Link-state routing protocol

Mass ratio

Gravitational wave

Neutron star

Computer science

Astrophysics

Routing (electronic design automation)

Binary number

Arithmetic

The Astrophysical Journal

Black hole (BH) mergers driven by gravitational perturbations of external companions constitute an important class of formation channels for merging BH binaries detected by LIGO. We have studied the orbital and spin evolution of binary BHs in triple systems, where the tertiary companion excites large eccentricity in the inner binary through Lidov–Kozai oscillations, causing the binary to merge via gravitational radiation. Using the single-averaged and double-averaged secular dynamics of triples (where the equations of motion are averaged over the inner orbit and both orbits, respectively), we perform a large set of numerical integrations to determine the merger window (the range of companion inclinations that allows the inner binary to merge within ∼10 Gyr) and the merger fraction as a function of various system parameters (e.g., the binary masses m 1 , m 2 and initial semimajor axis a 0 , the mass, semimajor axis, and eccentricity <?CDATA ${e}_{\mathrm{out}}$?> of the outer companion). For typical BH binaries ( <?CDATA ${m}_{\mathrm{1,2}}\simeq 20\,{M}_{\odot }\mbox{--}30\,{M}_{\odot }$?> and a 0 ≳ 10 au), the merger fraction increases rapidly with e out because of the octupole perturbation, ranging from ∼1% at <?CDATA ${e}_{\mathrm{out}}=0$?> to 10%–20% at e out = 0.9. We derive analytical expressions and approximate scaling relations for the merger window and merger fraction for systems with negligible octupole effect, and apply them to neutron star binary mergers in triples. We also follow the spin evolution of the BHs during the companion-induced orbital decay, where de Sitter spin precession competes with Lidov–Kozai orbital precession/nutation. Starting from aligned spin axes (relative to the orbital angular momentum axis), a wide range of final spin–orbit misalignment angle θ sl f can be generated when the binary enters the LIGO sensitivity band. For systems where the octupole effect is small (such as those with m 1 ≃ m 2 or e out ∼ 0), the distribution of <?CDATA ${\theta }_{\mathrm{sl}}^{{\rm{f}}}$?> peaks around 90°. As the octupole effect increases, a more isotropic distribution of final spin axis is produced. Overall, merging BH binaries produced by Lidov–Kozai oscillations in triples exhibit a unique distribution of the effective (mass-weighted) spin parameter χ eff ; this may be used to distinguish this formation channel from other dynamical channels.

Black Hole and Neutron Star Binary Mergers in Triple Systems: Merger Fraction and Spin–Orbit Misalignment