week ending PRL 116, 241102 (2016) PHYSICAL REVIEW LETTERS 17 JUNE 2016 Properties of the Binary Black Hole Merger GW150914 B. P. Abbott et al.* (LIGO Scientific Collaboration and Virgo Collaboration) (Received 18 February 2016; revised manuscript received 18 April 2016; published 14 June 2016) On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general þ5 relativity. GW150914 was produced by a nearly equal mass binary black hole of masses 36−4 M⊙ and þ4 29−4 M⊙; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be < 0.7 (at 90% probability). 410þ160 0 09þ0.03 The luminosity distance to the source is −180 Mpc, corresponding to a redshift . −0.04 assuming standard cosmology. The source location is constrained to an annulus section of 610 deg2, primarily 62þ4M 0 67þ0.05 in the southern hemisphere. The binary merges into a black hole of mass −4 ⊙ and spin . −0.07 . This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime. DOI: 10.1103/PhysRevLett.116.241102 I. INTRODUCTION nonprecessing binary systems that affects waveforms used in the analysis. The parameter values reported here, in In Ref. [1] we reported the detection of gravitational waves (GWs), observed on September 14, 2015 at 09:50:45 Table I and the figures, are the updated values and should UTC, by the twin instruments of the twin instruments of be used for future studies. The only value different from the Laser Interferometer Gravitational-Wave Observatory what was reported in Ref. [1] is the total energy radiated, 3 0þ0.5M c2 (LIGO) located at Hanford, Washington, and Livingston, which previously was . −0.5 ⊙ and now rounds to 3 0þ0.5M c2 Louisiana, in the USA [2,3]. The transient signal, named . −0.4 ⊙ ). GW150914, was detected with a false-alarm-probability of In general relativity, two objects in orbit slowly spiral < 2 × 10−7 and has been associated with the merger of a together due to the loss of energy and angular momentum binary system of black holes (BHs). through gravitational radiation [7,8]. This is in contrast Here we discuss the properties of this source and its to Newtonian gravity where bodies can follow closed, inferred parameters. The results are based on a complete elliptical orbits [9,10]. As the binary shrinks, the frequency analysis of the data surrounding this event. The only and amplitude of the emitted GWs increase. Eventually the information from the search stage is the time of arrival two objects merge. If these objects are BHs, they form a of the signal. Crucially, this analysis differs from the search single perturbed BH that radiates GWs as a superposition of in the following fundamental ways: it is coherent across the quasinormal ringdown modes. Typically, one mode domi- LIGO network, it uses waveform models that include nates soon after merger, and an exponentially damped the full richness of the physics introduced by BH spins, oscillation at constant frequency can be observed as the BH and it covers the full multidimensional parameter space settles to its final state [11,12]. of the considered models with a fine (stochastic) sampling; An isolated BH is described by only its mass and spin, we also account for uncertainty in the calibration of the since we expect the electric charge of astrophysical BHs measured strain. The results of this analysis provide the to be negligible [13–16]. Merging (BBHs) are therefore parameter values quoted in Ref. [1] describing the proper- relatively simple systems. The two BHs are described by ties of the source of GW150914. (Following the publication eight intrinsic parameters: the masses m1;2 (defined as the of Ref. [1] we repeated the analysis after fixing minor errors gravitational masses of the BHs in isolation) and spins S1;2 in the coordinate transformation between precessing and (magnitude and orientation) of the individual BHs. For a BH of mass m, the spin can be at most Gm2=c; hence, *Full author list given at the end of the article. it is conventional to quote the dimensionless spin magni- tude a ¼ cjSj=ðGm2Þ ≤ 1. Nine additional parameters are Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- needed to fully describe the binary: the location (luminosity bution of this work must maintain attribution to the author(s) and distance DL, right ascension α, and declination δ); orien- the published article’s title, journal citation, and DOI. tation (the binary’s orbital inclination ι and polarization ψ); 0031-9007=16=116(24)=241102(19) 241102-1 Published by the American Physical Society week ending PRL 116, 241102 (2016) PHYSICAL REVIEW LETTERS 17 JUNE 2016 TABLE I. Summary of the parameters that characterize GW150914. For model parameters we report the median value as well as the range of the symmetric 90% credible interval [4]; where useful, we also quote 90% credible bounds. For the logarithm of the Bayes factor for a signal compared to Gaussian noise we report the mean and its 90% standard error from 4 parallel runs with a nested sampling algorithm [5]. The source redshift and source-frame masses assume standard cosmology [6]. The spin-aligned EOBNR and precessing IMRPhenom waveform models are described in the text. Results for the effective precession spin parameter χp used in the IMRPhenom model are not shown as we effectively recover the prior; we constrain χp < 0.71 at 90% probability, see left panel of Fig. 5. The Overall results are computed by averaging the posteriors for the two models. For the Overall results we quote both the 90% credible interval or bound and an estimate for the 90% range of systematic error on this determined from the variance between waveform models. The sky location associated with GW150914 is presented in Fig. 4 and discussed in the text. EOBNR IMRPhenom Overall M=M 70 3þ5.3 70 9þ4.0 70 6þ4.6Æ0.5 Detector-frame total mass ⊙ . −4.8 . −3.9 . −4.5Æ1.3 M=M 30 2þ2.5 30 6þ1.8 30 4þ2.1Æ0.2 Detector-frame chirp mass ⊙ . −1.9 . −1.8 . −1.9Æ0.5 m =M 39 4þ5.5 38 5þ5.6 38 9þ5.6Æ0.6 Detector-frame primary mass 1 ⊙ . −4.9 . −3.6 . −4.3Æ0.4 m =M 30 9þ4.8 32 2þ3.6 31 6þ4.2Æ0.1 Detector-frame secondary mass 2 ⊙ . −4.4 . −4.8 . −4.7Æ0.9 M =M 67 1þ4.6 67 6þ3.6 67 4þ4.1Æ0.4 Detector-frame final mass f ⊙ . −4.4 . −3.5 . −4.0Æ1.2 Msource=M 65 0þ5.0 65 0þ4.0 65 0þ4.5Æ0.8 Source-frame total mass ⊙ . −4.4 . −3.6 . −4.0Æ0.7 Msource=M 27 9þ2.3 28 1þ1.7 28 0þ2.0Æ0.3 Source-frame chirp mass ⊙ . −1.8 . −1.6 . −1.7Æ0.3 msource=M 36 3þ5.3 35 3þ5.2 35 8þ5.3Æ0.9 Source-frame primary mass 1 ⊙ . −4.5 . −3.4 . −3.9Æ0.1 msource=M 28 6þ4.4 29 6þ3.3 29 1þ3.8Æ0.1 Source-frame secondary mass 2 ⊙ . −4.2 . −4.3 . −4.3Æ0.7 Msource=M 62 0þ4.4 62 0þ3.7 62 0þ4.1Æ0.7 Source-frame final mass f ⊙ . −4.0 . −3.3 . −3.7Æ0.6 q 0 79þ0.18 0 84þ0.14 0 82þ0.17Æ0.01 Mass ratio . −0.19 . −0.20 . −0.20Æ0.03 χ −0 09þ0.19 −0 05þ0.13 −0 07þ0.16Æ0.01 Effective inspiral spin parameter eff . −0.17 . −0.15 . −0.17Æ0.05 a 0 32þ0.45 0 32þ0.53 0 32þ0.49Æ0.06 Dimensionless primary spin magnitude 1 . −0.28 . −0.29 . −0.29Æ0.01 a 0 57þ0.40 0 34þ0.54 0 44þ0.50Æ0.08 Dimensionless secondary spin magnitude 2 . −0.51 . −0.31 . −0.40Æ0.02 a 0 67þ0.06 0 66þ0.04 0 67þ0.05Æ0.01 Final spin f . −0.08 . −0.06 . −0.07Æ0.02 D = 390þ170 440þ150 410þ160Æ20 Luminosity distance L Mpc −180 −180 −180Æ40 Source redshift z 0.083þ0.033 0.093þ0.029 0 088þ0.032Æ0.005 −0.036 −0.036 . −0.037Æ0.008 Upper bound on primary spin magnitude a1 0.65 0.74 0.69 Æ 0.08 Upper bound on secondary spin magnitude a2 0.93 0.78 0.89 Æ 0.13 Lower bound on mass ratio q 0.64 0.68 0.66 Æ 0.03 Log Bayes factor ln Bs=n 288.7 Æ 0.2 290.3 Æ 0.1 ÁÁÁ time tc and phase ϕc of coalescence, and two parameters the Results; for methodological studies, we refer the reader describing eccentricity (the magnitude e and the argument to Refs. [4,19–24] and references therein. of periapsis) of the system. In general relativity, gravitational radiation is fully Radiation reaction is efficient in circularizing orbits [17] described by two independent, and time-dependent polar- h h k before the signal enters the sensitive frequency band of the izations, þ and ×. Each instrument measures the strain instruments (∼20–1000 Hz). In our analysis, we assume h FðþÞh Fð×Þh ; circular orbits (we therefore do not include the eccentricity k ¼ k þ þ k × ð1Þ parameters), and we find no evidence for residual eccen- a linear combination of the polarizations weighted by the tricity, see the Discussion.