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Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

Zhao, Xinyu and Kesden, Michael and Gerosa, Davide (2017) Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems. Physical Review D, 96 (2). Art. No. 024007. ISSN 2470-0010. http://resolver.caltech.edu/CaltechAUTHORS:20170711-143334459

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Abstract

In the post-Newtonian (PN) regime, the time scale on which the spins of binary black holes precess is much shorter than the radiation-reaction time scale on which the black holes inspiral to smaller separations. On the precession time scale, the angle between the total and orbital angular momenta oscillates with nutation period τ, during which the orbital angular momentum precesses about the total angular momentum by an angle α. This defines two distinct frequencies that vary on the radiation-reaction time scale: the nutation frequency ω≡2π/τ and the precession frequency Ω≡α/τ. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency Ω−nω for integer n. As black holes inspiral, they can pass through nutational resonances (Ω=nω) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than 10−3 radians for nutational resonances at binary separations r>10M. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate n=0 nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with n providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.96.024007DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.024007PublisherArticle
https://arxiv.org/abs/1705.02369arXivDiscussion Paper
Additional Information:© 2017 American Physical Society. Received 5 May 2017; published 11 July 2017. M. K. is supported by the Alfred P. Sloan Foundation Grant No. FG-2015-65299 and NSF Grant No. PHY-1607031. D. G. is supported by NASA through Einstein Postdoctoral Fellowship Grant No. PF6-170152 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under Contract No. NAS8-03060. Computations were performed on the Caltech computer cluster “Wheeler,” supported by the Sherman Fairchild Foundation and Caltech. D. G. acknowledges partial support from NSF Award CAREER PHY-1151197.
Group:TAPIR
Funders:
Funding AgencyGrant Number
Alfred P. Sloan FoundationFG-2015-65299
NSFPHY-1607031
NASA Einstein FellowshipPF6-170152
NASANAS8-03060
Sherman Fairchild FoundationUNSPECIFIED
CaltechUNSPECIFIED
NSFPHY-1151197
Record Number:CaltechAUTHORS:20170711-143334459
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170711-143334459
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78965
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Jul 2017 21:45
Last Modified:11 Jul 2017 21:45

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