Merging Compact Binaries in Hierarchical Triple Systems: Resonant Excitation of Binary Eccentricity

Abstract

We study the secular dynamics of compact binaries (consisting of white dwarfs, neutron stars or black holes) with tertiary companions in hierarchical triple systems. As the inner binary (with initially negligible eccentricity) undergoes orbital decay due to gravitational radiation, its eccentricity can be excited by gravitational forcing from the tertiary. This excitation occurs when the triple system passes through an "apsidal precession resonance", when the precession rate of the inner binary, driven by the gravitational perturbation of the external companion and general relativity, matches the precession rate of the outer binary. The eccentricity excitation requires the outer companion to be on an eccentric orbit, with the mutual inclination between the inner and outer orbits less than $\sim 40^{\circ }$. Gravitational wave (GW) signals from the inner binary can be significantly modified as the system evolves through the apsidal precession resonance. For some system parameters (e.g., a white dwarf binary with a brown dwarf tertiary), the resonance can happen when the binary emits GWs in the $10^{-4}-10^{-1}$~Hz range (the sensitivity band of LISA).

Another typo in Eq.(38) is corrected. In Eq.(38): (a1/a2)^{3} should be (a1/a2)^{-3}. Two previous typos are as follows: in Eq.12: (1-e_2^2)^{5/2} should be (1-e_2^2)^2, and in Eq.14: (4+3e_1) should be (4+3 e_1^2). Thanks to Ryan Miranda for pointing this out

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