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

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 ($θ_\rm {sl}^\rm f$) 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 $e_{\mathrm{m}}>0.9$. The majority of the mergers have significant eccentricities in the LISA band. The BH spin evolution and $θ_\rm {sl}^\rm f$ are correlated with the orbital evolution and $e_{\mathrm{m}}$. Mergers with $e_{\mathrm{m}}\lesssim 10^{-3}$ have a distribution of $θ_\rm {sl}^\rm f$ that peaks around $90^{\circ }$ (and thus favoring a projected binary spin parameter ${\chi }_{\mathrm{eff}}\sim 0$), while mergers with larger $e_{\mathrm{m}}$ 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 $θ_\rm {sl}^\rm f$ from LIGO/VIRGO and LISA would provide useful diagnostics on the dynamical formation of merging BH or NS binaries in triples.

13 pages, 15 figures. Published in ApJ

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