Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence

(LIGO Scientific Collaboration and Virgo Collaboration)

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Abstract

We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations - including sources with two independent, precessing spins - we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90% credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulations performed using previously estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz [64 M-82 M], mass ratio 1/q=m2/m1 [0.6,1], and effective aligned spin χeff [-0.3,0.2], where χeff=(S1/m1+S2/m2)·L/M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z in the range 64.0 M-73.5 M and the final black hole's dimensionless spin parameter is consistent with af=0.62-0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].

Original languageEnglish
Article number064035
JournalPhysical Review D
Volume94
Issue number6
DOIs
StatePublished - 14 Sep 2016

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Einstein equations
coalescing
mass ratios
simulation
relativity
precession
complement
radiation
approximation

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(LIGO Scientific Collaboration and Virgo Collaboration). / Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence. In: Physical Review D. 2016 ; Vol. 94, No. 6.
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title = "Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence",
abstract = "We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations - including sources with two independent, precessing spins - we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90{\%} credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulations performed using previously estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz [64 M-82 M], mass ratio 1/q=m2/m1 [0.6,1], and effective aligned spin χeff [-0.3,0.2], where χeff=(S1/m1+S2/m2)·L/M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z in the range 64.0 M-73.5 M and the final black hole's dimensionless spin parameter is consistent with af=0.62-0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].",
author = "{(LIGO Scientific Collaboration and Virgo Collaboration)} and Abbott, {B. P.} and R. Abbott and Abbott, {T. D.} and Abernathy, {M. R.} and F. Acernese and K. Ackley and C. Adams and T. Adams and P. Addesso and Adhikari, {R. X.} and Adya, {V. B.} and C. Affeldt and M. Agathos and K. Agatsuma and N. Aggarwal and Aguiar, {O. D.} and L. Aiello and A. Ain and P. Ajith and B. Allen and A. Allocca and Altin, {P. A.} and Anderson, {S. B.} and Anderson, {W. G.} and K. Arai and Araya, {M. C.} and Arceneaux, {C. C.} and Areeda, {J. S.} and N. Arnaud and Arun, {K. G.} and S. Ascenzi and G. Ashton and M. Ast and Aston, {S. M.} and P. Astone and P. Aufmuth and C. Aulbert and S. Babak and P. Bacon and Bader, {M. K.M.} and Baker, {P. T.} and F. Baldaccini and G. Ballardin and Ballmer, {S. W.} and Barayoga, {J. C.} and Barclay, {S. E.} and Barish, {B. C.} and D. Barker and F. Barone and Marc Favata",
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Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence. / (LIGO Scientific Collaboration and Virgo Collaboration).

In: Physical Review D, Vol. 94, No. 6, 064035, 14.09.2016.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Directly comparing GW150914 with numerical solutions of Einstein's equations for binary black hole coalescence

AU - (LIGO Scientific Collaboration and Virgo Collaboration)

AU - Abbott, B. P.

AU - Abbott, R.

AU - Abbott, T. D.

AU - Abernathy, M. R.

AU - Acernese, F.

AU - Ackley, K.

AU - Adams, C.

AU - Adams, T.

AU - Addesso, P.

AU - Adhikari, R. X.

AU - Adya, V. B.

AU - Affeldt, C.

AU - Agathos, M.

AU - Agatsuma, K.

AU - Aggarwal, N.

AU - Aguiar, O. D.

AU - Aiello, L.

AU - Ain, A.

AU - Ajith, P.

AU - Allen, B.

AU - Allocca, A.

AU - Altin, P. A.

AU - Anderson, S. B.

AU - Anderson, W. G.

AU - Arai, K.

AU - Araya, M. C.

AU - Arceneaux, C. C.

AU - Areeda, J. S.

AU - Arnaud, N.

AU - Arun, K. G.

AU - Ascenzi, S.

AU - Ashton, G.

AU - Ast, M.

AU - Aston, S. M.

AU - Astone, P.

AU - Aufmuth, P.

AU - Aulbert, C.

AU - Babak, S.

AU - Bacon, P.

AU - Bader, M. K.M.

AU - Baker, P. T.

AU - Baldaccini, F.

AU - Ballardin, G.

AU - Ballmer, S. W.

AU - Barayoga, J. C.

AU - Barclay, S. E.

AU - Barish, B. C.

AU - Barker, D.

AU - Barone, F.

AU - Favata, Marc

PY - 2016/9/14

Y1 - 2016/9/14

N2 - We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations - including sources with two independent, precessing spins - we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90% credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulations performed using previously estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz [64 M-82 M], mass ratio 1/q=m2/m1 [0.6,1], and effective aligned spin χeff [-0.3,0.2], where χeff=(S1/m1+S2/m2)·L/M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z in the range 64.0 M-73.5 M and the final black hole's dimensionless spin parameter is consistent with af=0.62-0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].

AB - We compare GW150914 directly to simulations of coalescing binary black holes in full general relativity, including several performed specifically to reproduce this event. Our calculations go beyond existing semianalytic models, because for all simulations - including sources with two independent, precessing spins - we perform comparisons which account for all the spin-weighted quadrupolar modes, and separately which account for all the quadrupolar and octopolar modes. Consistent with the posterior distributions reported by Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)] (at the 90% credible level), we find the data are compatible with a wide range of nonprecessing and precessing simulations. Follow-up simulations performed using previously estimated binary parameters most resemble the data, even when all quadrupolar and octopolar modes are included. Comparisons including only the quadrupolar modes constrain the total redshifted mass Mz [64 M-82 M], mass ratio 1/q=m2/m1 [0.6,1], and effective aligned spin χeff [-0.3,0.2], where χeff=(S1/m1+S2/m2)·L/M. Including both quadrupolar and octopolar modes, we find the mass ratio is even more tightly constrained. Even accounting for precession, simulations with extreme mass ratios and effective spins are highly inconsistent with the data, at any mass. Several nonprecessing and precessing simulations with similar mass ratio and χeff are consistent with the data. Though correlated, the components' spins (both in magnitude and directions) are not significantly constrained by the data: the data is consistent with simulations with component spin magnitudes a1,2 up to at least 0.8, with random orientations. Further detailed follow-up calculations are needed to determine if the data contain a weak imprint from transverse (precessing) spins. For nonprecessing binaries, interpolating between simulations, we reconstruct a posterior distribution consistent with previous results. The final black hole's redshifted mass is consistent with Mf,z in the range 64.0 M-73.5 M and the final black hole's dimensionless spin parameter is consistent with af=0.62-0.73. As our approach invokes no intermediate approximations to general relativity and can strongly reject binaries whose radiation is inconsistent with the data, our analysis provides a valuable complement to Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016)].

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