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Hybrid method for understanding black-hole mergers: Inspiralling case

Nichols, David A. and Chen, Yanbei (2012) Hybrid method for understanding black-hole mergers: Inspiralling case. Physical Review D, 85 (4). Art. No. 044035. ISSN 2470-0010. doi:10.1103/PhysRevD.85.044035.

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We adapt a method of matching post-Newtonian and black-hole-perturbation theories on a timelike surface (which proved useful for understanding head-on black-hole-binary collisions) to treat equal-mass, inspiralling black-hole binaries. We first introduce a radiation-reaction potential into this method, and we show that it leads to a self-consistent set of equations that describe the simultaneous evolution of the waveform and of the timelike matching surface. This allows us to produce a full inspiral-merger-ringdown waveform of the l=2, m=±2 modes of the gravitational waveform of an equal-mass black-hole-binary inspiral. These modes match those of numerical-relativity simulations well in phase, though less well in amplitude for the inspiral. As a second application of this method, we study a merger of black holes with spins antialigned in the orbital plane (the superkick configuration). During the ringdown of the superkick, the phases of the mass- and current-quadrupole radiation become locked together, because they evolve at the same quasinormal-mode frequencies. We argue that this locking begins during the merger, and we show that if the spins of the black holes evolve via geodetic precession in the perturbed black-hole spacetime of our model, then the spins precess at the orbital frequency during the merger. In turn, this gives rise to the correct behavior of the radiation, and produces a kick similar to that observed in numerical simulations.

Item Type:Article
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Chen, Yanbei0000-0002-9730-9463
Additional Information:© 2012 American Physical Society. Received 31 August 2011; published 13 February 2012. We thank Jeandrew Brink, Tanja Hinderer, Lee Lindblom, Yasushi Mino, Mark Scheel, Belá Szilágyi, Kip Thorne, Huan Yang, and Aaron Zimmerman for discussing various aspects of this work with us. In particular, we acknowledge Scheel for letting us use the waveform from the numerical-relativity simulation, Szilagyi for his input on numerical algorithms, Mino and Yang for their remarks on the validity of PN and BHP theories in the early stage of this work, and Thorne for his constant encouragement and for reminding us that spin precession must lock the spins to the orbital frequency. This work is supported by NSF Grants No. PHY-0653653 and No. PHY-1068881 and CAREER Grant No. PHY-0956189, and by the David and Barbara Groce start-up fund. D. N. was supported by the David and Barbara Groce Fund at Caltech.
Funding AgencyGrant Number
David and Barbara Groce startup fundUNSPECIFIED
Caltech David and Barbara Groce FundUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 04.25.Nx, 04.30.-w, 04.70.-s
Record Number:CaltechAUTHORS:20120314-133435118
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Official Citation:Hybrid method for understanding black-hole mergers: Inspiralling case David A. Nichols and Yanbei Chen Published 13 February 2012 (24 pages) 044035
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29721
Deposited By: Ruth Sustaita
Deposited On:14 Mar 2012 21:01
Last Modified:09 Nov 2021 19:28

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