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

TL;DR

This paper investigates how triple system dynamics influence black hole and neutron star binary mergers, focusing on merger rates, orbital eccentricities, and spin-orbit misalignments, with implications for gravitational wave observations.

Contribution

It provides analytical and numerical analysis of merger fractions and spin-orbit misalignments in triple systems, highlighting the role of Lidov-Kozai oscillations and octupole effects.

Findings

Merger fraction increases with perturber eccentricity, reaching 10-20% at e_out=0.9.

Wide range of spin-orbit misalignments can be generated, peaking around 90 degrees.

Distinct effective spin parameter distribution can identify this formation channel.

Abstract

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-orbital-averaged and double-orbital-averaged secular dynamics equations of triples, we determine the merger window (the range of companion inclinations that allows the inner binary to merge) and the merger fraction as a function of various system parameters. For typical BH binaries, the merger fraction increases rapidly with the perturber eccentricity $e_{\rm out}$ because of the octupole perturbation, reaching $10-20\%$ at $e_{\rm out}=0.9$. We derive the analytical expressions 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. Starting from aligned spin axes, a wide range of final spin-orbit misalignment angle $\theta_{\rm sl}^{\rm f}$ can be generated when the binary enters the LIGO band. For systems where the octupole effect is small (such as equal mass binaries or $e_{\rm out}\sim 0$), the distribution of $\theta_{\rm sl}^{\rm f}$ peaks around $90^\circ$. As the octuple 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 spin parameter $\chi_{\rm eff}$; this may be used to distinguish this formation channel from others.