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Redshift factor and the small mass-ratio limit in binary black hole simulations

Navarro Albalat, Sergi and Zimmerman, Aaron and Giesler, Matthew and Scheel, Mark A. (2022) Redshift factor and the small mass-ratio limit in binary black hole simulations. Physical Review D, 106 (4). Art. No. 044006. ISSN 2470-0010. doi:10.1103/physrevd.106.044006.

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We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from m_A/m_B = 1 to m_A/m_B = 9.5 we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order 10⁻⁵ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio ν does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, z_A + z_B, which is symmetric under the exchange of the masses, a reexpansion in ν accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.

Item Type:Article
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URLURL TypeDescription Paper
Navarro Albalat, Sergi0000-0003-2554-7486
Zimmerman, Aaron0000-0002-7453-6372
Giesler, Matthew0000-0003-2300-893X
Scheel, Mark A.0000-0001-6656-9134
Additional Information:© 2022 American Physical Society. (Received 25 April 2022; accepted 30 June 2022; published 2 August 2022). We would like to thank Serguei Ossokine for sharing with us the q = 3.5 – q = 9.5 SKS simulations used in this work. We also thank Jooheon Yoo for sharing the q = 14 and q = 15 simulations from [80] and Keefe Mitman for sharing the redshift data from the recent SHK simulations of q = 1 and q = 4 from [81]. For the simulations used in this work, computations were performed on the Wheeler cluster at Caltech, which is supported by the Sherman Fairchild Foundation and by Caltech; and on Frontera at the Texas Advanced Computing Center [82]. We also thank the developers of Scri [70,71], which was used to calculate the energy and angular momentum fluxes and angular velocity of the corotating frame. We thank the participants of a number of Capra conferences for valuable discussions on the topics of this work over several years, especially Takahiro Tanaka, Adam Pound, Leor Barack, Abraham Harte, Soichiro Isoyama, Eric Poisson, and Alexandre Le Tiec. S. N. A. and A. Z. are supported by NSF Grants No. PHY-1912578 and No. PHY-2207594. M. G. is supported by NSF Grant Number PHY-1912081 at Cornell. M. A. S. is supported in part by the Sherman Fairchild Foundation and by National Science Foundation (NSF) Grants No. PHY-2011961, No. PHY-2011968, and No. OAC-1931266 at Caltech.
Group:TAPIR, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20220803-224707000
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116065
Deposited By: George Porter
Deposited On:03 Aug 2022 20:18
Last Modified:03 Aug 2022 20:18

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