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Published September 15, 2016 | Supplemental Material + Submitted + Published
Journal Article Open

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


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 M_z ∈[64  M_⊙−82  M_⊙], mass ratio 1/q = m_2/m_1 ∈[0.6,1], and effective aligned spin χ_(eff) ∈[−0.3,0.2], where χ_(eff)=(S_1/m_1+S_2/m_2)⋅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 χ_(eff) 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 ɑ_(1,2) 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 ɑ_f = 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)].

Additional Information

© 2016 American Physical Society. Received 10 June 2016; published 14 September 2016. The authors gratefully acknowledge helpful feedback from an anonymous referee. The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), India, Ministry of Human Resource Development, India, the Spanish Ministerio de Economía y Competitividad, the Conselleria d'Economia i Competitivitat and Conselleria d'Educació, Cultura i Universitats of the Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the National Science and Engineering Research Council Canada, the Brazilian Ministry of Science, Technology, and Innovation, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS, and the State of Niedersachsen/Germany for provision of computational resources. The SXS Collaboration also gratefully acknowledges Compute Canada, the Research Corporation, and California State University Fullerton for computational resources, as well as the support of the National Science Foundation, the Research Corporation for Science Advancement,and the Sherman Fairchild Foundation. The RIT team gratefully acknowledges the NSF for financial support, as well as Blue Waters and XSEDE for computational resources. This paper has been assigned the document number LIGO-P1500263.

Attached Files

Published - PhysRevD.94.064035.pdf

Submitted - 1606.01262v1.pdf

Supplemental Material - paper-tables-long.pdf


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