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Published December 15, 2020 | Published + Accepted Version
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Spin and eccentricity evolution in triple systems: From the Lidov-Kozai interaction to the final merger of the inner binary


We study the spin and eccentricity evolution of black-hole (BH) binaries that are perturbed by tertiary masses and experience the Lidov-Kozai (LK) excitation. We focus on three aspects. First, we study the spin-orbit alignment of the inner binary following the approach outlined by Antonini et al. [Mon. Not. R. Astron. Soc. 480, L58 (2018)] and Liu and Lai [Astrophys. J. 863, 68 (2018)], yet allowing the spins to have random initial orientations. We confirm the existence of a dynamical attractor that drives the spin-orbit angle at the end of the LK evolution to a value given by the initial angle between the spin and the outer orbital angular momentum (instead of to a specific value of the effective spin). Second, we follow the (inner) binary's evolution further to the merger to study the final spin-spin alignment. We generalize the effective potential theory to include orbital eccentricity, which allows us to efficiently evolve the system in the early inspiral stages. We further find that the spin-spin and spin-orbit alignments are correlated and the correlation is determined by the initial spin-orbit angle. For systems with the spin vectors initially in the orbital plane, the final spins strongly disfavor an aligned configuration and could thus lead to a greater value of the GW recoil than a uniform spin-spin alignment would predict. Lastly, we study the maximum eccentricity excitation that can be achieved during the LK process, including the effects of gravitational-wave radiation. We find that when the tertiary mass is a supermassive BH and the inner binary is massive, then even with the maximum LK excitation, the residual eccentricity is typically less than 0.1 when the binary's orbital frequency reaches 10 Hz, and a decihertz detector would be necessary to follow such a system's orbital evolution.

Additional Information

© 2020 American Physical Society. (Received 27 July 2020; accepted 12 November 2020; published 7 December 2020) We thank Nathan Johnson-McDaniel for pointing out the error that the quadrupole-monopole interaction was not properly accounted for in an earlier version of the manuscript. We also thank Fabio Antonini, Linqing Wen, Ling Sun, Ka-Lok Rico Lo, Dong Lai, Yubo Su, and the referee for useful comments and discussions. H. Y. and M. G. are supported by the Sherman Fairchild foundation. S. M. and Y. C. are supported by the Brinson Foundation and the Simons Foundation (Grant No. 568762). S. M., M. G., and Y. C. are additionally supported by the National Science Foundation (Grants No. PHY-1708212 and No. PHY-1708213). The authors also gratefully acknowledge the computational resources provided by the LIGO Laboratory and supported by NSF Grants No. PHY-0757058 and No. PHY-0823459.

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Accepted Version - 2007.12978.pdf

Published - PhysRevD.102.123009.pdf


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August 20, 2023
August 20, 2023