# Black Hole and Neutron Star Binary Mergers in Triple Systems: II. Merger Eccentricity and Spin-Orbit Misalignment

## TL;DR

This paper investigates the dynamical signatures of black hole and neutron star binary mergers in triple systems, focusing on eccentricity and spin-orbit misalignment, using various secular and N-body methods to predict observable features.

## Contribution

It provides detailed distributions of eccentricity and spin-orbit misalignment for BH-BH and BH-NS mergers in hierarchical triples, incorporating multiple dynamical effects and evolution methods.

## Key findings

- Majority of mergers have significant eccentricities in the LISA band.
- Mergers with low eccentricity tend to have spin misalignments around 90 degrees.
- A notable fraction of BH-NS mergers exhibit high eccentricities and random spin orientations.

## Abstract

We study the dynamical signatures of black hole (BH) and neutron star (NS) binary mergers via Lidov-Kozai oscillations induced by tertiary companions in hierarchical triple systems. For each type of binaries (BH-BH and BH-NS), we explore a wide range of binary/triple parameters that lead to binary mergers, and determine the distributions of eccentricity ($e_\mathrm{m}$) and spin-orbit misalignment angle ($\theta_\rm {sl}^\rm f$) when the binary enters the LIGO/VIRGO band. We use the double-averaged (over both orbits) and single-averaged (over the inner orbit) secular equations, as well as N-body integration, to evolve systems with different hierarchy levels, including the leading-order post-Newtonian effect, spin-orbit coupling and gravitational radiation. We find that for merging BH-BH binaries with comparable masses, about $7\%$ have $e_\mathrm{m}>0.1$ and $0.7\%$ have $e_{\rm m}>0.9$. The majority of the mergers have significant eccentricities in the LISA band. The BH spin evolution and $\theta_\rm {sl}^\rm f$ are correlated with the orbital evolution and $e_{\rm m}$. Mergers with $e_{\rm m} \lesssim 10^{-3}$ have a distribution of $\theta_\rm {sl}^\rm f$ that peaks around $90^\circ$ (and thus favoring a projected binary spin parameter $\chi_{\rm eff}\sim 0$), while mergers with larger $e_{\rm m}$ have a more isotropic spin-orbit misalignments. For typical BH-NS binaries, strong octuple effects lead to more mergers with non-negligible $e_\mathrm{m}$ (with $\sim 18\%$ having $e_\mathrm{m}>0.1$ and $2.5\%$ having $e_\mathrm{m}>0.9$), and the final BH spin axis tends to be randomly orientated. Measurements or constraints on eccentric mergers and $\theta_\rm {sl}^\rm f$ from LIGO/VIRGO and LISA would provide useful diagnostics on the dynamical formation of merging BH or NS binaries in triples.