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Maximum black-hole spin from quasicircular binary mergers

Kesden, Michael and Lockhart, Guglielmo and Phinney, E. Sterl (2010) Maximum black-hole spin from quasicircular binary mergers. Physical Review D, 82 (12). Art. No. 124045. ISSN 0556-2821.

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Black holes of mass M must have a spin angular momentum S below the Kerr limit (χ ≡ S/M^2 ≤ 1), but whether astrophysical black holes can attain this limiting spin depends on their accretion history. Gas accretion from a thin disk limits the black-hole spin to χ_(gas) ≲ 0.9980 ± 0.0002, as electromagnetic radiation from this disk with retrograde angular momentum is preferentially absorbed by the black hole. Extrapolation of numerical-relativity simulations of equal-mass binary black-hole mergers to maximum initial spins suggests these mergers yield a maximum spin χ_(eq) ≲ 0.95. Here we show that for smaller mass ratios q ≡ m/M ≪ 1, the superradiant extraction of angular momentum from the larger black hole imposes a fundamental limit χ_(lim) ≲ 0.9979 ± 0.0001 on the final black-hole spin even in the test-particle limit (q→0) of binary black-hole mergers. The nearly equal values of χ_(gas) and χ_(lim) imply that measurement of supermassive black-hole spins cannot distinguish a black hole built by gas accretion from one assembled by the gravitational inspiral of a disk of compact stellar remnants. We also show how superradiant scattering alters the mass and spin predicted by models derived from extrapolating test-particle mergers to finite mass ratios.

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Additional Information:© 2010 American Physical Society. Received 29 October 2010; published 20 December 2010. We thank Scott Hughes for generously allowing us to use a version of his GREMLIN (Gravitational Radiation in the Extreme Mass ratio LIMit) code to calculate the energy and angular momentum radiated during the inspiral. We also thank Andrew Benson, Chris Hirata, Pedro Marronetti, Uli Sperhake, and Kip Thorne for useful conversations. The authors acknowledge support from NASA BEFS Grant No. NNX07AH06G (PI:Phinney). M. Kesden also acknowledges support from NSF Grant No. PHY- 0601459 (PI: Thorne).
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Classification Code:PACS: 04.70.Bw, 04.25.Nx, 04.30.Db, 04.30.Tv
Record Number:CaltechAUTHORS:20110302-090724602
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22592
Deposited By: Benjamin Perez
Deposited On:03 Mar 2011 04:44
Last Modified:26 Dec 2012 12:59

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