《力学改变生活》课程教学资源（文献资料）Observation of Gravitational Waves from a Binary Black Hole Merger

Selected for a Viewpoint in Physics week ending PRL116,061102(2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 g Observation of Gravitational Waves from a Binary Black Hole Merger B.P.Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) (Received 21 January 2016:published 11 February 2016) On September 14,2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal.The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 x 10-21.It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole.The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years,equivalent to a significance greater than5..The source lies at aluminosity distance of 1Mpcomresponding to a redshift0.09 In the source frame,the initial black hole masses are 36+M and 29M and the final black hole mass is 62M,with 3.0Mc2 radiated in gravitational waves.All uncertainties define 90%credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems.This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. DOI:10.1103/PhysRevLett.116.061102 I.INTRODUCTION The discovery of the binary pulsar system PSR B1913+16 In 1916,the year after the final formulation of the field by Hulse and Taylor [20]and subsequent observations of equations of general relativity,Albert Einstein predicted its energy loss by Taylor and Weisberg [21]demonstrated the existence of gravitational waves.He found that the existence of gravitational waves.This discovery, the linearized weak-field equations had wave solutions: along with emerging astrophysical understanding [22], transverse waves of spatial strain that travel at the speed of led to the recognition that direct observations of the light,generated by time variations of the mass quadrupole amplitude and phase of gravitational waves would enable moment of the source [1.2].Einstein understood that studies of additional relativistic systems and provide new gravitational-wave amplitudes would be remarkably tests of general relativity,especially in the dynamic small;moreover,until the Chapel Hill conference in strong-field regime. 1957 there was significant debate about the physical Experiments to detect gravitational waves began with reality of gravitational waves [3]. Weber and his resonant mass detectors in the 1960s [23], Also in 1916,Schwarzschild published a solution for the followed by an international network of cryogenic reso- field equations [4]that was later understood to describe a nant detectors [24].Interferometric detectors were first black hole [5,6],and in 1963 Kerr generalized the solution suggested in the early 1960s [25]and the 1970s [26].A to rotating black holes [7].Starting in the 1970s theoretical study of the noise and performance of such detectors [27], work led to the understanding of black hole quasinormal and further concepts to improve them [28],led to modes [8-10],and in the 1990s higher-order post- proposals for long-baseline broadband laser interferome- Newtonian calculations [11]preceded extensive analytical ters with the potential for significantly increased sensi- studies of relativistic two-body dynamics [12,13].These tivity [29-32].By the early 2000s,a set of initial detectors advances,together with numerical relativity breakthroughs was completed,including TAMA 300 in Japan,GEO 600 in the past decade [14-16],have enabled modeling of in Germany,the Laser Interferometer Gravitational-Wave binary black hole mergers and accurate predictions of Observatory (LIGO)in the United States,and Virgo in their gravitational waveforms.While numerous black hole Italy.Combinations of these detectors made joint obser- candidates have now been identified through electromag- vations from 2002 through 2011,setting upper limits on a netic observations [17-19],black hole mergers have not variety of gravitational-wave sources while evolving into previously been observed. a global network.In 2015,Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations [33-36]. Full author list given at the end of the article. A century after the fundamental predictions of Einstein Published by the American Physical Society under the terms of and Schwarzschild,we report the first direct detection of the Creative Commons Attribution 3.0 License.Further distri- gravitational waves and the first direct observation of a bution of this work must maintain attribution to the authors)and binary black hole system merging to form a single black the published article's title,journal citation,and DOI. hole.Our observations provide unique access to the 0031-9007/16/116(6)/061102(16) 061102-1 Published by the American Physical Society

Observation of Gravitational Waves from a Binary Black Hole Merger B. P. Abbott et al.* (LIGO Scientific Collaboration and Virgo Collaboration) (Received 21 January 2016; published 11 February 2016) On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10−21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410þ160 −180 Mpc corresponding to a redshift z ¼ 0.09þ0.03 −0.04 . In the source frame, the initial black hole masses are 36þ5 −4M⊙ and 29þ4 −4M⊙, and the final black hole mass is 62þ4 −4M⊙, with 3.0þ0.5 −0.5M⊙c2 radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. DOI: 10.1103/PhysRevLett.116.061102 I. INTRODUCTION In 1916, the year after the final formulation of the field equations of general relativity, Albert Einstein predicted the existence of gravitational waves. He found that the linearized weak-field equations had wave solutions: transverse waves of spatial strain that travel at the speed of light, generated by time variations of the mass quadrupole moment of the source [1,2]. Einstein understood that gravitational-wave amplitudes would be remarkably small; moreover, until the Chapel Hill conference in 1957 there was significant debate about the physical reality of gravitational waves [3]. Also in 1916, Schwarzschild published a solution for the field equations [4] that was later understood to describe a black hole [5,6], and in 1963 Kerr generalized the solution to rotating black holes [7]. Starting in the 1970s theoretical work led to the understanding of black hole quasinormal modes [8–10], and in the 1990s higher-order post￾Newtonian calculations [11] preceded extensive analytical studies of relativistic two-body dynamics [12,13]. These advances, together with numerical relativity breakthroughs in the past decade [14–16], have enabled modeling of binary black hole mergers and accurate predictions of their gravitational waveforms. While numerous black hole candidates have now been identified through electromag￾netic observations [17–19], black hole mergers have not previously been observed. The discovery of the binary pulsar system PSR B1913þ16 by Hulse and Taylor [20] and subsequent observations of its energy loss by Taylor and Weisberg [21] demonstrated the existence of gravitational waves. This discovery, along with emerging astrophysical understanding [22], led to the recognition that direct observations of the amplitude and phase of gravitational waves would enable studies of additional relativistic systems and provide new tests of general relativity, especially in the dynamic strong-field regime. Experiments to detect gravitational waves began with Weber and his resonant mass detectors in the 1960s [23], followed by an international network of cryogenic reso￾nant detectors [24]. Interferometric detectors were first suggested in the early 1960s [25] and the 1970s [26]. A study of the noise and performance of such detectors [27], and further concepts to improve them [28], led to proposals for long-baseline broadband laser interferome￾ters with the potential for significantly increased sensi￾tivity [29–32]. By the early 2000s, a set of initial detectors was completed, including TAMA 300 in Japan, GEO 600 in Germany, the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States, and Virgo in Italy. Combinations of these detectors made joint obser￾vations from 2002 through 2011, setting upper limits on a variety of gravitational-wave sources while evolving into a global network. In 2015, Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations [33–36]. A century after the fundamental predictions of Einstein and Schwarzschild, we report the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging to form a single black hole. Our observations provide unique access to the * Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri￾bution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PRL 116, 061102 (2016) Selected for a Viewpoint in Physics PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 0031-9007=16=116(6)=061102(16) 061102-1 Published by the American Physical Society

PHYSICAL REVIEW LETTERS week ending PRL116,061102(2016) 12 FEBRUARY 2016 properties of space-time in the strong-field,high-velocity the coincident signal GW150914 shown in Fig.1.The initial regime and confirm predictions of general relativity for the detection was made by low-latency searches for generic nonlinear dynamics of highly disturbed black holes. gravitational-wave transients [41]and was reported within three minutes of data acquisition [43].Subsequently, II.OBSERVATION matched-filter analyses that use relativistic models of com- pact binary waveforms [44]recovered GW150914 as the On September 14,2015 at 09:50:45 UTC,the LIGO most significant event from each detector for the observa- Hanford,WA,and Livingston,LA,observatories detected tions reported here.Occurring within the 10-ms intersite Hanford,Washington(H1) Livingston,Louisiana (L1) 1.0 0.5 0.0 -0.5 -1.0 .1 observed -H1 observed -H1 observed(shifted,inverted) 1.0 0.5 0.0 -0.5 -1.0 -Numerical relativity Numerical relativity Reconstructed (wavelet) Reconstructed (wavelet) Reconstructed (template) Reconstructed (template) 0.5 0.0 hiw-/wwhwwhiwwrwbwl.wwi/wnh -0.5 -Residual 一Residual 512 N 256 8 6 128 4 nba 64 2 32 0 0.30 0.35 0.40 0.45 0.30 0.35 0.40 0.45 Time(s) Time(s) FIG.1.The gravitational-wave event GW150914 observed by the LIGO Hanford(H1,left column panels)and Livingston (L1.right column panels)detectors.Times are shown relative to September 14,2015 at 09:50:45 UTC.For visualization,all time series are filtered with a 35-350 Hz bandpass filter to suppress large fluctuations outside the detectors'most sensitive frequency band,and band-reject filters to remove the strong instrumental spectral lines seen in the Fig.3 spectra.Top row,lefi:HI strain.Top row,right:LI strain. GW150914 arrived first at LI and 6.ms later at H1:for a visual comparison,the HI data are also shown,shifted in time by this amount and inverted(to account for the detectors'relative orientations).Second row:Gravitational-wave strain projected onto each detector in the 35-350 Hz band.Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [37.38]confirmed to 99.9%by an independent calculation based on [15].Shaded areas show 90%credible regions for two independent waveform reconstructions.One(dark gray)models the signal using binary black hole template waveforms 39].The other (light gray)does not use an astrophysical model,but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets [40,41].These reconstructions have a 94%overlap,as shown in [39].Third row:Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series.Bottom row:A time-frequency representation [42]of the strain data,showing the signal frequency increasing over time. 061102-2

properties of space-time in the strong-field, high-velocity regime and confirm predictions of general relativity for the nonlinear dynamics of highly disturbed black holes. II. OBSERVATION On September 14, 2015 at 09:50:45 UTC, the LIGO Hanford, WA, and Livingston, LA, observatories detected the coincident signal GW150914 shown in Fig. 1. The initial detection was made by low-latency searches for generic gravitational-wave transients [41] and was reported within three minutes of data acquisition [43]. Subsequently, matched-filter analyses that use relativistic models of com￾pact binary waveforms [44] recovered GW150914 as the most significant event from each detector for the observa￾tions reported here. Occurring within the 10-ms intersite FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filtered with a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain. GW150914 arrived first at L1 and 6.9þ0.5 −0.4 ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [37,38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credible regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms [39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets [40,41]. These reconstructions have a 94% overlap, as shown in [39]. Third row: Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series. Bottom row:A time-frequency representation [42] of the strain data, showing the signal frequency increasing over time. PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-2

week ending PRL116,061102(2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 propagation time,the events have a combined signal-to- Inspiral Merger Ring- noise ratio (SNR)of 24 [45]. down Only the LIGO detectors were observing at the time of GW150914.The Virgo detector was being upgraded, and GEO 600,though not sufficiently sensitive to detect this event,was operating but not in observational mode.With only two detectors the source position is 1.0 primarily determined by the relative arrival time and 0.5 localized to an area of approximately 600 deg2(90% credible region)[39,46]. The basic features of GW150914 point to it being 0.5 produced by the coalescence of two black holes-i.e., -1.0 Numerical relativity their orbital inspiral and merger,and subsequent final black Reconstructed (template hole ringdown.Over 0.2 s,the signal increases in frequency and amplitude in about 8 cycles from 35 to 150 Hz,where 0.6 4 the amplitude reaches a maximum.The most plausible 0.5 Black hole separation Black hole relative velocity 32 explanation for this evolution is the inspiral of two orbiting 0.4 masses,m and m2,due to gravitational-wave emission.At 0.3 0 the lower frequencies,such evolution is characterized by 0.30 0.35 0.40 0.45 the chirp mass [11] Time(s) Ms1m2)35 c3「5 3/5 FIG.2. Top:Estimated gravitational-wave strain amplitude (m1+m2)万= from GW150914 projected onto H1.This shows the full bandwidth of the waveforms,without the filtering used for Fig.I. The inset images show numerical relativity models of the black where f and f are the observed frequency and its time hole horizons as the black holes coalesce.Bottom:The Keplerian derivative and G and c are the gravitational constant and effective black hole separation in units of Schwarzschild radii speed of light.Estimating f and f from the data in Fig.1, (Rs =2GM/c2)and the effective relative velocity given by the we obtain a chirp mass of M=30Mo,implying that the post-Newtonian parameter v/c=(GMf/c3)1/3,where f is the total mass M=m+m2 is 270M in the detector frame. gravitational-wave frequency calculated with numerical relativity This bounds the sum of the Schwarzschild radii of the and M is the total mass (value from Table I). binary components to 2GM/c2210 km.To reach an orbital frequency of 75 Hz(half the gravitational-wave detector [33],a modified Michelson interferometer (see frequency)the objects must have been very close and very Fig.3)that measures gravitational-wave strain as a differ- compact;equal Newtonian point masses orbiting at this ence in length of its orthogonal arms.Each arm is formed frequency would be only =350 km apart.A pair of by two mirrors,acting as test masses,separated by neutron stars,while compact,would not have the required Lx=Ly =L =4 km.A passing gravitational wave effec- mass,while a black hole neutron star binary with the tively alters the arm lengths such that the measured deduced chirp mass would have a very large total mass, difference is AL(t)=6Lx-Ly =h(t)L,where h is the and would thus merge at much lower frequency.This gravitational-wave strain amplitude projected onto the leaves black holes as the only known objects compact detector.This differential length variation alters the phase enough to reach an orbital frequency of 75 Hz without difference between the two light fields returning to the contact.Furthermore,the decay of the waveform after it beam splitter,transmitting an optical signal proportional to peaks is consistent with the damped oscillations of a black the gravitational-wave strain to the output photodetector. hole relaxing to a final stationary Kerr configuration. To achieve sufficient sensitivity to measure gravitational Below,we present a general-relativistic analysis of waves,the detectors include several enhancements to the GW150914;Fig.2 shows the calculated waveform using basic Michelson interferometer.First,each arm contains a the resulting source parameters. resonant optical cavity,formed by its two test mass mirrors, that multiplies the effect of a gravitational wave on the light III.DETECTORS phase by a factor of 300 [48].Second,a partially trans- missive power-recycling mirror at the input provides addi- Gravitational-wave astronomy exploits multiple,widely tional resonant buildup of the laser light in the interferometer separated detectors to distinguish gravitational waves from as a whole [49,50]:20 W of laser input is increased to 700 W local instrumental and environmental noise,to provide incident on the beam splitter,which is further increased to source sky localization,and to measure wave polarizations. 100 kW circulating in each arm cavity.Third,a partially The LIGO sites each operate a single Advanced LIGO transmissive signal-recycling mirror at the output optimizes 061102-3

propagation time, the events have a combined signal-to￾noise ratio (SNR) of 24 [45]. Only the LIGO detectors were observing at the time of GW150914. The Virgo detector was being upgraded, and GEO 600, though not sufficiently sensitive to detect this event, was operating but not in observational mode. With only two detectors the source position is primarily determined by the relative arrival time and localized to an area of approximately 600 deg2 (90% credible region) [39,46]. The basic features of GW150914 point to it being produced by the coalescence of two black holes—i.e., their orbital inspiral and merger, and subsequent final black hole ringdown. Over 0.2 s, the signal increases in frequency and amplitude in about 8 cycles from 35 to 150 Hz, where the amplitude reaches a maximum. The most plausible explanation for this evolution is the inspiral of two orbiting masses, m1 and m2, due to gravitational-wave emission. At the lower frequencies, such evolution is characterized by the chirp mass [11] M ¼ ðm1m2Þ3=5 ðm1 þ m2Þ1=5 ¼ c3 G
5 96 π−8=3f−11=3f_ 3=5 ; where f and f_ are the observed frequency and its time derivative and G and c are the gravitational constant and speed of light. Estimating f and f_ from the data in Fig. 1, we obtain a chirp mass of M ≃ 30M⊙, implying that the total mass M ¼ m1 þ m2 is ≳70M⊙ in the detector frame. This bounds the sum of the Schwarzschild radii of the binary components to 2GM=c2 ≳ 210 km. To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) the objects must have been very close and very compact; equal Newtonian point masses orbiting at this frequency would be only ≃350 km apart. A pair of neutron stars, while compact, would not have the required mass, while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency. This leaves black holes as the only known objects compact enough to reach an orbital frequency of 75 Hz without contact. Furthermore, the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration. Below, we present a general-relativistic analysis of GW150914; Fig. 2 shows the calculated waveform using the resulting source parameters. III. DETECTORS Gravitational-wave astronomy exploits multiple, widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise, to provide source sky localization, and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector [33], a modified Michelson interferometer (see Fig. 3) that measures gravitational-wave strain as a differ￾ence in length of its orthogonal arms. Each arm is formed by two mirrors, acting as test masses, separated by Lx ¼ Ly ¼ L ¼ 4 km. A passing gravitational wave effec￾tively alters the arm lengths such that the measured difference is ΔLðtÞ ¼ δLx − δLy ¼ hðtÞL, where h is the gravitational-wave strain amplitude projected onto the detector. This differential length variation alters the phase difference between the two light fields returning to the beam splitter, transmitting an optical signal proportional to the gravitational-wave strain to the output photodetector. To achieve sufficient sensitivity to measure gravitational waves, the detectors include several enhancements to the basic Michelson interferometer. First, each arm contains a resonant optical cavity, formed by its two test mass mirrors, that multiplies the effect of a gravitational wave on the light phase by a factor of 300 [48]. Second, a partially trans￾missive power-recycling mirror at the input provides addi￾tional resonant buildup of the laser light in the interferometer as a whole [49,50]: 20 W of laser input is increased to 700 W incident on the beam splitter, which is further increased to 100 kW circulating in each arm cavity. Third, a partially transmissive signal-recycling mirror at the output optimizes FIG. 2. Top: Estimated gravitational-wave strain amplitude from GW150914 projected onto H1. This shows the full bandwidth of the waveforms, without the filtering used for Fig. 1. The inset images show numerical relativity models of the black hole horizons as the black holes coalesce. Bottom: The Keplerian effective black hole separation in units of Schwarzschild radii (RS ¼ 2GM=c2) and the effective relative velocity given by the post-Newtonian parameter v=c ¼ ðGMπf=c3Þ1=3, where f is the gravitational-wave frequency calculated with numerical relativity and M is the total mass (value from Table I). PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-3

week ending PRL116,061102(2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 (b) Test -H1 Mass -L1 10-21 HI 出 10 ms light travel tir 是 10-22 ∥ (a 10-23 Test 20 100 1000 Mass Frequency(Hz) Power Beam Recycling Splitter Lx=4 km Laser 20W 100 kW Circulating Power Source Test Test Signal Mass Mass Recycling Photodetector FIG.3.Simplified diagram of an Advanced LIGO detector (not to scale).A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave;these length changes are reversed during the other half-cycle.The output photodetector records these differential cavity length variations.While a detector's directional response is maximal for this case,it is still significant for most other angles of incidence or polarizations(gravitational waves propagate freely through the Earth).Inser (a):Location and orientation of the LIGO detectors at Hanford,WA(HI)and Livingston,LA(LI).Inset(b):The instrument noise for each detector near the time of the signal detection;this is an amplitude spectral density,expressed in terms of equivalent gravitational-wave strain amplitude.The sensitivity is limited by photon shot noise at frequencies above 150 Hz,and by a superposition of other noise sources at lower frequencies [47].Narrow-band features include calibration lines (33-38,330,and 1080 Hz),vibrational modes of suspension fibers(500 Hz and harmonics),and 60 Hz electric power grid harmonics. the gravitational-wave signal extraction by broadening the suspensions:the test masses are 40-kg fused silica substrates bandwidth of the arm cavities [51,52].The interferometer with low-loss dielectric optical coatings [58,59],and are is illuminated with a 1064-nm wavelength Nd:YAG laser. suspended with fused silica fibers from the stage above [60]. stabilized in amplitude,frequency,and beam geometry To minimize additional noise sources,all components [53,54].The gravitational-wave signal is extracted at the other than the laser source are mounted on vibration output port using a homodyne readout [55]. isolation stages in ultrahigh vacuum.To reduce optical These interferometry techniques are designed to maxi- phase fluctuations caused by Rayleigh scattering,the mize the conversion of strain to optical signal,thereby pressure in the 1.2-m diameter tubes containing the arm- minimizing the impact of photon shot noise (the principal cavity beams is maintained below I uPa noise at high frequencies).High strain sensitivity also Servo controls are used to hold the arm cavities on requires that the test masses have low displacement noise, resonance [61]and maintain proper alignment of the optical which is achieved by isolating them from seismic noise (low components [62.The detector output is calibrated in strain frequencies)and designing them to have low thermal noise by measuring its response to test mass motion induced by (intermediate frequencies).Each test mass is suspended as photon pressure from a modulated calibration laser beam the final stage of a quadruple-pendulum system [56], [63].The calibration is established to an uncertainty (1o)of supported by an active seismic isolation platform [57]. less than 10%in amplitude and 10 degrees in phase,and is These systems collectively provide more than 10 orders continuously monitored with calibration laser excitations at of magnitude of isolation from ground motion for frequen- selected frequencies.Two alternative methods are used to cies above 10 Hz.Thermal noise is minimized by using validate the absolute calibration,one referenced to the main low-mechanical-loss materials in the test masses and their laser wavelength and the other to a radio-frequency oscillator 061102-4

the gravitational-wave signal extraction by broadening the bandwidth of the arm cavities [51,52]. The interferometer is illuminated with a 1064-nm wavelength Nd:YAG laser, stabilized in amplitude, frequency, and beam geometry [53,54]. The gravitational-wave signal is extracted at the output port using a homodyne readout [55]. These interferometry techniques are designed to maxi￾mize the conversion of strain to optical signal, thereby minimizing the impact of photon shot noise (the principal noise at high frequencies). High strain sensitivity also requires that the test masses have low displacement noise, which is achieved by isolating them from seismic noise (low frequencies) and designing them to have low thermal noise (intermediate frequencies). Each test mass is suspended as the final stage of a quadruple-pendulum system [56], supported by an active seismic isolation platform [57]. These systems collectively provide more than 10 orders of magnitude of isolation from ground motion for frequen￾cies above 10 Hz. Thermal noise is minimized by using low-mechanical-loss materials in the test masses and their suspensions: the test masses are 40-kg fused silica substrates with low-loss dielectric optical coatings [58,59], and are suspended with fused silica fibers from the stage above [60]. To minimize additional noise sources, all components other than the laser source are mounted on vibration isolation stages in ultrahigh vacuum. To reduce optical phase fluctuations caused by Rayleigh scattering, the pressure in the 1.2-m diameter tubes containing the arm￾cavity beams is maintained below 1 μPa. Servo controls are used to hold the arm cavities on resonance [61] and maintain proper alignment of the optical components [62]. The detector output is calibrated in strain by measuring its response to test mass motion induced by photon pressure from a modulated calibration laser beam [63]. The calibration is established to an uncertainty (1σ) of less than 10% in amplitude and 10 degrees in phase, and is continuously monitored with calibration laser excitations at selected frequencies. Two alternative methods are used to validate the absolute calibration, one referenced to the main laser wavelength and the other to a radio-frequency oscillator (a) (b) FIG. 3. Simplified diagram of an Advanced LIGO detector (not to scale). A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave; these length changes are reversed during the other half-cycle. The output photodetector records these differential cavity length variations. While a detector’s directional response is maximal for this case, it is still significant for most other angles of incidence or polarizations (gravitational waves propagate freely through the Earth). Inset (a): Location and orientation of the LIGO detectors at Hanford, WA (H1) and Livingston, LA (L1). Inset (b): The instrument noise for each detector near the time of the signal detection; this is an amplitude spectral density, expressed in terms of equivalent gravitational-wave strain amplitude. The sensitivity is limited by photon shot noise at frequencies above 150 Hz, and by a superposition of other noise sources at lower frequencies [47]. Narrow-band features include calibration lines (33–38, 330, and 1080 Hz), vibrational modes of suspension fibers (500 Hz and harmonics), and 60 Hz electric power grid harmonics. PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-4

PRL116,061102(2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 [64].Additionally,the detector response to gravitational described below.There is no evidence for instrumental waves is tested by injecting simulated waveforms with the transients that are temporally correlated between the two calibration laser. detectors To monitor environmental disturbances and their influ- ence on the detectors,each observatory site is equipped V.SEARCHES with an array of sensors:seismometers,accelerometers, microphones,magnetometers,radio receivers,weather We present the analysis of 16 days of coincident sensors,ac-power line monitors,and a cosmic-ray detector observations between the two LIGO detectors from [65].Another ~105 channels record the interferometer's September 12 to October 20,2015.This is a subset of operating point and the state of the control systems.Data the data from Advanced LIGO's first observational period collection is synchronized to Global Positioning System that ended on January 12,2016. (GPS)time to better than 10 us [66].Timing accuracy is GW150914 is confidently detected by two different verified with an atomic clock and a secondary GPS receiver types of searches.One aims to recover signals from the at each observatory site. coalescence of compact objects,using optimal matched In their most sensitive band.100-300 Hz.the current filtering with waveforms predicted by general relativity. LIGO detectors are 3 to 5 times more sensitive to strain than The other search targets a broad range of generic transient initial LIGO [67];at lower frequencies,the improvement is signals,with minimal assumptions about waveforms.These even greater,with more than ten times better sensitivity searches use independent methods,and their response to below 60 Hz.Because the detectors respond proportionally detector noise consists of different,uncorrelated.events. to gravitational-wave amplitude,at low redshift the volume However,strong signals from binary black hole mergers are of space to which they are sensitive increases as the cube expected to be detected by both searches. of strain sensitivity.For binary black holes with masses Each search identifies candidate events that are detected similar to GW150914,the space-time volume surveyed by at both observatories consistent with the intersite propa- the observations reported here surpasses previous obser- gation time.Events are assigned a detection-statistic value vations by an order of magnitude [681 that ranks their likelihood of being a gravitational-wave signal.The significance of a candidate event is determined IV.DETECTOR VALIDATION by the search background-the rate at which detector noise produces events with a detection-statistic value equal to or Both detectors were in steady state operation for several higher than the candidate event.Estimating this back- hours around GW150914.All performance measures,in ground is challenging for two reasons:the detector noise particular their average sensitivity and transient noise is nonstationary and non-Gaussian,so its properties must behavior,were typical of the full analysis period [69,70]. be empirically determined;and it is not possible to shield Exhaustive investigations of instrumental and environ- the detector from gravitational waves to directly measure a mental disturbances were performed,giving no evidence to signal-free background.The specific procedure used to suggest that GW150914 could be an instrumental artifact estimate the background is slightly different for the two [69].The detectors'susceptibility to environmental disturb- searches,but both use a time-shift technique:the time ances was quantified by measuring their response to spe- stamps of one detector's data are artificially shifted by an cially generated magnetic,radio-frequency,acoustic,and offset that is large compared to the intersite propagation vibration excitations.These tests indicated that any external time,and a new set of events is produced based on this disturbance large enough to have caused the observed signal time-shifted data set.For instrumental noise that is uncor- would have been clearly recorded by the array of environ- related between detectors this is an effective way to mental sensors.None of the environmental sensors recorded estimate the background.In this process a gravitational- any disturbances that evolved in time and frequency like wave signal in one detector may coincide with time-shifted GW150914,and all environmental fluctuations during the noise transients in the other detector,thereby contributing second that contained GW150914 were too small to account to the background estimate.This leads to an overestimate of for more than 6%of its strain amplitude.Special care was the noise background and therefore to a more conservative taken to search for long-range correlated disturbances that assessment of the significance of candidate events. might produce nearly simultaneous signals at the two sites. The characteristics of non-Gaussian noise vary between No significant disturbances were found. different time-frequency regions.This means that the search The detector strain data exhibit non-Gaussian noise backgrounds are not uniform across the space of signals transients that arise from a variety of instrumental mecha- being searched.To maximize sensitivity and provide a better nisms.Many have distinct signatures,visible in auxiliary estimate of event significance,the searches sort both their data channels that are not sensitive to gravitational waves; background estimates and their event candidates into differ- such instrumental transients are removed from our analyses ent classes according to their time-frequency morphology. [69].Any instrumental transients that remain in the data The significance of a candidate event is measured against the are accounted for in the estimated detector backgrounds background of its class.To account for having searched 061102-5

[64]. Additionally, the detector response to gravitational waves is tested by injecting simulated waveforms with the calibration laser. To monitor environmental disturbances and their influ￾ence on the detectors, each observatory site is equipped with an array of sensors: seismometers, accelerometers, microphones, magnetometers, radio receivers, weather sensors, ac-power line monitors, and a cosmic-ray detector [65]. Another ∼105 channels record the interferometer’s operating point and the state of the control systems. Data collection is synchronized to Global Positioning System (GPS) time to better than 10 μs [66]. Timing accuracy is verified with an atomic clock and a secondary GPS receiver at each observatory site. In their most sensitive band, 100–300 Hz, the current LIGO detectors are 3 to 5 times more sensitive to strain than initial LIGO [67]; at lower frequencies, the improvement is even greater, with more than ten times better sensitivity below 60 Hz. Because the detectors respond proportionally to gravitational-wave amplitude, at low redshift the volume of space to which they are sensitive increases as the cube of strain sensitivity. For binary black holes with masses similar to GW150914, the space-time volume surveyed by the observations reported here surpasses previous obser￾vations by an order of magnitude [68]. IV. DETECTOR VALIDATION Both detectors were in steady state operation for several hours around GW150914. All performance measures, in particular their average sensitivity and transient noise behavior, were typical of the full analysis period [69,70]. Exhaustive investigations of instrumental and environ￾mental disturbances were performed, giving no evidence to suggest that GW150914 could be an instrumental artifact [69]. The detectors’ susceptibility to environmental disturb￾ances was quantified by measuring their response to spe￾cially generated magnetic, radio-frequency, acoustic, and vibration excitations. These tests indicated that any external disturbance large enough to have caused the observed signal would have been clearly recorded by the array of environ￾mental sensors. None of the environmental sensors recorded any disturbances that evolved in time and frequency like GW150914, and all environmental fluctuations during the second that contained GW150914 were too small to account for more than 6% of its strain amplitude. Special care was taken to search for long-range correlated disturbances that might produce nearly simultaneous signals at the two sites. No significant disturbances were found. The detector strain data exhibit non-Gaussian noise transients that arise from a variety of instrumental mecha￾nisms. Many have distinct signatures, visible in auxiliary data channels that are not sensitive to gravitational waves; such instrumental transients are removed from our analyses [69]. Any instrumental transients that remain in the data are accounted for in the estimated detector backgrounds described below. There is no evidence for instrumental transients that are temporally correlated between the two detectors. V. SEARCHES We present the analysis of 16 days of coincident observations between the two LIGO detectors from September 12 to October 20, 2015. This is a subset of the data from Advanced LIGO’s first observational period that ended on January 12, 2016. GW150914 is confidently detected by two different types of searches. One aims to recover signals from the coalescence of compact objects, using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals, with minimal assumptions about waveforms. These searches use independent methods, and their response to detector noise consists of different, uncorrelated, events. However, strong signals from binary black hole mergers are expected to be detected by both searches. Each search identifies candidate events that are detected at both observatories consistent with the intersite propa￾gation time. Events are assigned a detection-statistic value that ranks their likelihood of being a gravitational-wave signal. The significance of a candidate event is determined by the search background—the rate at which detector noise produces events with a detection-statistic value equal to or higher than the candidate event. Estimating this back￾ground is challenging for two reasons: the detector noise is nonstationary and non-Gaussian, so its properties must be empirically determined; and it is not possible to shield the detector from gravitational waves to directly measure a signal-free background. The specific procedure used to estimate the background is slightly different for the two searches, but both use a time-shift technique: the time stamps of one detector’s data are artificially shifted by an offset that is large compared to the intersite propagation time, and a new set of events is produced based on this time-shifted data set. For instrumental noise that is uncor￾related between detectors this is an effective way to estimate the background. In this process a gravitational￾wave signal in one detector may coincide with time-shifted noise transients in the other detector, thereby contributing to the background estimate. This leads to an overestimate of the noise background and therefore to a more conservative assessment of the significance of candidate events. The characteristics of non-Gaussian noise vary between different time-frequency regions. This means that the search backgrounds are not uniform across the space of signals being searched. To maximize sensitivity and provide a better estimate of event significance, the searches sort both their background estimates and their event candidates into differ￾ent classes according to their time-frequency morphology. The significance of a candidate event is measured against the background of its class. To account for having searched PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-5

PRL116,061102(2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 multiple classes,this significance is decreased by a trials Detected with nc=20.0,GW150914 is the strongest factor equal to the number of classes [71]. event of the entire search.Consistent with its coalescence signal signature,it is found in the search class C3 of events A.Generic transient search with increasing time-frequency evolution.Measured on a Designed to operate without a specific waveform model, background equivalent to over 67 400 years of data and this search identifies coincident excess power in time- including a trials factor of 3 to account for the search frequency representations of the detector strain data classes,its false alarm rate is lower than I in 22 500 years. [43,72],for signal frequencies up to I kHz and durations This corresponds to a probability 32.1,yielding a of known populations of noise transients(class C1),events false alarm rate for GW150914 of 1 in 8 400 years.This with frequency that increases with time(class C3),and all corresponds to a false alarm probability of 5x 10-6 remaining events (class C2) equivalent to 4.40. Generic transient search Binary coalescence search 2030 40 4.40 4.40 20304g 5.1 >5.10 2g304g4,60 >4.60 2a 30 405.10 >5.10 10 104 ■■■Search Result(C3) ■■■Search Result 101 Search Background (C3) 101 Search Background 100 ◆◆◆Search Result(C2+C3) 100 Background excluding GW150914 Search Background (C2+C3) 9 10-1 10- 10-2 GW150914 GW150914 10 10-3 10-4 10 10-5 10-6 10-6 10- 10- 10-8 10-8 12 14 16 18 20 532 10 18 20 24 Detection statistic nc Detection statistic pc FIG.4.Search results from the generic transient search (left)and the binary coalescence search(right).These histograms show the number of candidate events (orange markers)and the mean number of background events (black lines)in the search class where GW150914 was found as a function of the search detection statistic and with a bin width of 0.2.The scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background.The significance of GW150914 is greater than 5.1o and 4.60 for the binary coalescence and the generic transient searches,respectively.Left:Along with the primary search (C3)we also show the results (blue markers)and background (green curve)for an alternative search that treats events independently of their frequency evolution(C2+C3).The classes C2 and C3 are defined in the text.Right:The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914 in one detector with noise in the other detector.(This type of event is practically absent in the generic transient search background because they do not pass the time-frequency consistency requirements used in that search.)The purple curve is the background excluding those coincidences,which is used to assess the significance of the second strongest event. 061102-6

multiple classes, this significance is decreased by a trials factor equal to the number of classes [71]. A. Generic transient search Designed to operate without a specific waveform model, this search identifies coincident excess power in time￾frequency representations of the detector strain data [43,72], for signal frequencies up to 1 kHz and durations up to a few seconds. The search reconstructs signal waveforms consistent with a common gravitational-wave signal in both detectors using a multidetector maximum likelihood method. Each event is ranked according to the detection statistic ηc ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Ec=ð1 þ En=EcÞ p , where Ec is the dimensionless coherent signal energy obtained by cross-correlating the two reconstructed waveforms, and En is the dimensionless residual noise energy after the reconstructed signal is subtracted from the data. The statistic ηc thus quantifies the SNR of the event and the consistency of the data between the two detectors. Based on their time-frequency morphology, the events are divided into three mutually exclusive search classes, as described in [41]: events with time-frequency morphology of known populations of noise transients (class C1), events with frequency that increases with time (class C3), and all remaining events (class C2). Detected with ηc ¼ 20.0, GW150914 is the strongest event of the entire search. Consistent with its coalescence signal signature, it is found in the search class C3 of events with increasing time-frequency evolution. Measured on a background equivalent to over 67 400 years of data and including a trials factor of 3 to account for the search classes, its false alarm rate is lower than 1 in 22 500 years. This corresponds to a probability < 2 × 10−6 of observing one or more noise events as strong as GW150914 during the analysis time, equivalent to 4.6σ. The left panel of Fig. 4 shows the C3 class results and background. The selection criteria that define the search class C3 reduce the background by introducing a constraint on the signal morphology. In order to illustrate the significance of GW150914 against a background of events with arbitrary shapes, we also show the results of a search that uses the same set of events as the one described above but without this constraint. Specifically, we use only two search classes: the C1 class and the union of C2 and C3 classes (C2 þ C3). In this two-class search the GW150914 event is found in the C2 þ C3 class. The left panel of Fig. 4 shows the C2 þ C3 class results and background. In the background of this class there are four events with ηc ≥ 32.1, yielding a false alarm rate for GW150914 of 1 in 8 400 years. This corresponds to a false alarm probability of 5 × 10−6 equivalent to 4.4σ. FIG. 4. Search results from the generic transient search (left) and the binary coalescence search (right). These histograms show the number of candidate events (orange markers) and the mean number of background events (black lines) in the search class where GW150914 was found as a function of the search detection statistic and with a bin width of 0.2. The scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background. The significance of GW150914 is greater than 5.1σ and 4.6σ for the binary coalescence and the generic transient searches, respectively. Left: Along with the primary search (C3) we also show the results (blue markers) and background (green curve) for an alternative search that treats events independently of their frequency evolution (C2 þ C3). The classes C2 and C3 are defined in the text. Right: The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914 in one detector with noise in the other detector. (This type of event is practically absent in the generic transient search background because they do not pass the time-frequency consistency requirements used in that search.) The purple curve is the background excluding those coincidences, which is used to assess the significance of the second strongest event. PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-6

week ending PRL116,061102(2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 For robustness and validation,we also use other generic TABLE I.Source parameters for GW150914.We report transient search algorithms [41].A different search [73]and median values with 90%credible intervals that include statistical a parameter estimation follow-up [74]detected GW150914 errors,and systematic errors from averaging the results of with consistent significance and signal parameters. different waveform models.Masses are given in the source frame;to convert to the detector frame multiply by (1+z) [90].The source redshift assumes standard cosmology [91]. B.Binary coalescence search This search targets gravitational-wave emission from Primary black hole mass 36tM。 binary systems with individual masses from I to 99M Secondary black hole mass 294M。 total mass less than 100Mo,and dimensionless spins up to Final black hole mass 62M 0.99 [44].To model systems with total mass larger than Final black hole spin 4Mo,we use the effective-one-body formalism [75],which 0.671805 combines results from the post-Newtonian approach Luminosity distance 41010Mpc [11,76]with results from black hole perturbation theory Source redshift z 0.09888 and numerical relativity.The waveform model [77,78] assumes that the spins of the merging objects are aligned with the orbital angular momentum,but the resulting templates can,nonetheless,effectively recover systems When an event is confidently identified as a real with misaligned spins in the parameter region of gravitational-wave signal,as for GW150914,the back- GW150914 [44].Approximately 250 000 template wave- ground used to determine the significance of other events is reestimated without the contribution of this event.This is forms are used to cover this parameter space. The search calculates the matched-filter signal-to-noise the background distribution shown as a purple line in the ratio p(t)for each template in each detector and identifies right panel of Fig.4.Based on this,the second most maxima of p(t)with respect to the time of arrival of the signal significant event has a false alarm rate of I per 2.3 years and [79-81].For each maximum we calculate a chi-squared corresponding Poissonian false alarm probability of 0.02. statistic to test whether the data in several different Waveform analysis of this event indicates that if it is frequency bands are consistent with the matching template astrophysical in origin it is also a binary black hole [82].Values of near unity indicate that the signal is merger [44]. consistent with a coalescence.If is greater than unity.p(r) is reweighted asp=p/[1+()3]/2)1/6 [83.84].The final VI.SOURCE DISCUSSION step enforces coincidence between detectors by selecting The matched-filter search is optimized for detecting event pairs that occur within a 15-ms window and come from signals,but it provides only approximate estimates of the same template.The 15-ms window is determined by the the source parameters.To refine them we use general 10-ms intersite propagation time plus 5 ms for uncertainty in relativity-based models [77,78,87,88],some of which arrival time of weak signals.We rank coincident events based include spin precession,and for each model perform a on the quadrature sum pe of the p from both detectors [45]. coherent Bayesian analysis to derive posterior distributions To produce background data for this search the SNR of the source parameters [89].The initial and final masses, maxima of one detector are time shifted and a new set of final spin,distance,and redshift of the source are shown in coincident events is computed.Repeating this procedure Table I.The spin of the primary black hole is constrained ~107 times produces a noise background analysis time to be <0.7 (90%credible interval)indicating it is not equivalent to 608 000 years. maximally spinning,while the spin of the secondary is only To account for the search background noise varying across weakly constrained.These source parameters are discussed the target signal space,candidate and background events are in detail in [39].The parameter uncertainties include divided into three search classes based on template length. statistical errors and systematic errors from averaging the The right panel of Fig.4 shows the background for the results of different waveform models. search class of GW150914.The GW150914 detection- Using the fits to numerical simulations of binary black statistic value of Pe=23.6 is larger than any background hole mergers in [92,93],we provide estimates of the mass event,so only an upper bound can be placed on its false and spin of the final black hole,the total energy radiated alarm rate.Across the three search classes this bound is I in in gravitational waves,and the peak gravitational-wave 203000 years.This translates to a false alarm probability luminosity [39].The estimated total energy radiated in <2 x 10-7,corresponding to 5.10. gravitational waves is 3.0M.The system reached a A second,independent matched-filter analysis that uses a peak gravitational-wave luminosity of 3.6105 erg/s, different method for estimating the significance of its equivalent to /s. events [85,86],also detected GW150914 with identical Several analyses have been performed to determine signal parameters and consistent significance. whether or not GW150914 is consistent with a binary 061102-7

For robustness and validation, we also use other generic transient search algorithms [41]. A different search [73] and a parameter estimation follow-up [74] detected GW150914 with consistent significance and signal parameters. B. Binary coalescence search This search targets gravitational-wave emission from binary systems with individual masses from 1 to 99M⊙, total mass less than 100M⊙, and dimensionless spins up to 0.99 [44]. To model systems with total mass larger than 4M⊙, we use the effective-one-body formalism [75], which combines results from the post-Newtonian approach [11,76] with results from black hole perturbation theory and numerical relativity. The waveform model [77,78] assumes that the spins of the merging objects are aligned with the orbital angular momentum, but the resulting templates can, nonetheless, effectively recover systems with misaligned spins in the parameter region of GW150914 [44]. Approximately 250 000 template wave￾forms are used to cover this parameter space. The search calculates the matched-filter signal-to-noise ratio ρðtÞ for each template in each detector and identifies maxima of ρðtÞ with respect to the time of arrival of the signal [79–81]. For each maximum we calculate a chi-squared statistic χ2 r to test whether the data in several different frequency bands are consistent with the matching template [82]. Values of χ2 r near unity indicate that the signal is consistent with a coalescence. If χ2 r is greater than unity, ρðtÞ is reweighted as ρˆ ¼ ρ=f½1 þ ðχ2 r Þ3=2g1=6 [83,84]. The final step enforces coincidence between detectors by selecting event pairs that occur within a 15-ms window and come from the same template. The 15-ms window is determined by the 10-ms intersite propagation time plus 5 ms for uncertainty in arrival time of weak signals. We rank coincident events based on the quadrature sum ρˆ c of the ρˆ from both detectors [45]. To produce background data for this search the SNR maxima of one detector are time shifted and a new set of coincident events is computed. Repeating this procedure ∼107 times produces a noise background analysis time equivalent to 608 000 years. To account for the search background noise varying across the target signal space, candidate and background events are divided into three search classes based on template length. The right panel of Fig. 4 shows the background for the search class of GW150914. The GW150914 detection￾statistic value of ρˆ c ¼ 23.6 is larger than any background event, so only an upper bound can be placed on its false alarm rate. Across the three search classes this bound is 1 in 203 000 years. This translates to a false alarm probability < 2 × 10−7, corresponding to 5.1σ. A second, independent matched-filter analysis that uses a different method for estimating the significance of its events [85,86], also detected GW150914 with identical signal parameters and consistent significance. When an event is confidently identified as a real gravitational-wave signal, as for GW150914, the back￾ground used to determine the significance of other events is reestimated without the contribution of this event. This is the background distribution shown as a purple line in the right panel of Fig. 4. Based on this, the second most significant event has a false alarm rate of 1 per 2.3 years and corresponding Poissonian false alarm probability of 0.02. Waveform analysis of this event indicates that if it is astrophysical in origin it is also a binary black hole merger [44]. VI. SOURCE DISCUSSION The matched-filter search is optimized for detecting signals, but it provides only approximate estimates of the source parameters. To refine them we use general relativity-based models [77,78,87,88], some of which include spin precession, and for each model perform a coherent Bayesian analysis to derive posterior distributions of the source parameters [89]. The initial and final masses, final spin, distance, and redshift of the source are shown in Table I. The spin of the primary black hole is constrained to be < 0.7 (90% credible interval) indicating it is not maximally spinning, while the spin of the secondary is only weakly constrained. These source parameters are discussed in detail in [39]. The parameter uncertainties include statistical errors and systematic errors from averaging the results of different waveform models. Using the fits to numerical simulations of binary black hole mergers in [92,93], we provide estimates of the mass and spin of the final black hole, the total energy radiated in gravitational waves, and the peak gravitational-wave luminosity [39]. The estimated total energy radiated in gravitational waves is 3.0þ0.5 −0.5M⊙c2. The system reached a peak gravitational-wave luminosity of 3.6þ0.5 −0.4 × 1056 erg=s, equivalent to 200þ30 −20M⊙c2=s. Several analyses have been performed to determine whether or not GW150914 is consistent with a binary TABLE I. Source parameters for GW150914. We report median values with 90% credible intervals that include statistical errors, and systematic errors from averaging the results of different waveform models. Masses are given in the source frame; to convert to the detector frame multiply by (1 þ z) [90]. The source redshift assumes standard cosmology [91]. Primary black hole mass 36þ5 −4M⊙ Secondary black hole mass 29þ4 −4M⊙ Final black hole mass 62þ4 −4M⊙ Final black hole spin 0.67þ0.05 −0.07 Luminosity distance 410þ160 −180 Mpc Source redshift z 0.09þ0.03 −0.04 PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-7

PRL116,061102(2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 black hole system in general relativity [94].A first background are presented in [115].If the signal from such a consistency check involves the mass and spin of the final population were detected,it would provide information black hole.In general relativity,the end product of a black about the evolution of such binary systems over the history hole binary coalescence is a Kerr black hole,which is fully of the universe. described by its mass and spin.For quasicircular inspirals, these are predicted uniquely by Einstein's equations as a function of the masses and spins of the two progenitor VII.OUTLOOK black holes.Using fitting formulas calibrated to numerical Further details about these results and associated data relativity simulations [921.we verified that the remnant releases are available at [1161.Analysis results for the mass and spin deduced from the early stage of the entire first observational period will be reported in future coalescence and those inferred independently from the late stage are consistent with each other,with no evidence for publications.Efforts are under way to enhance significantly the global gravitational-wave detector network [117]. disagreement from general relativity. These include further commissioning of the Advanced Within the post-Newtonian formalism,the phase of the LIGO detectors to reach design sensitivity,which will gravitational waveform during the inspiral can be expressed allow detection of binaries like GW150914 with 3 times as a power series in fl/3.The coefficients of this expansion can be computed in general relativity.Thus,we can test for higher SNR.Additionally,Advanced Virgo,KAGRA,and a possible third LIGO detector in India [118]will extend consistency with general relativity [95,96]by allowing the the network and significantly improve the position coefficients to deviate from the nominal values,and seeing reconstruction and parameter estimation of sources. if the resulting waveform is consistent with the data.In this second check [94]we place constraints on these deviations, finding no evidence for violations of general relativity. VIIL.CONCLUSION Finally,assuming a modified dispersion relation for gravitational waves [97],our observations constrain the The LIGO detectors have observed gravitational waves Compton wavelength of the graviton to be>1013 km, from the merger of two stellar-mass black holes.The which could be interpreted as a bound on the graviton mass detected waveform matches the predictions of general m<1.2 x 10-22 eV/c2.This improves on Solar System relativity for the inspiral and merger of a pair of black and binary pulsar bounds [98,99]by factors of a few and a holes and the ringdown of the resulting single black hole. thousand,respectively,but does not improve on the model- These observations demonstrate the existence of binary dependent bounds derived from the dynamics of Galaxy stellar-mass black hole systems.This is the first direct clusters [100]and weak lensing observations [101].In detection of gravitational waves and the first observation of summary,all three tests are consistent with the predictions a binary black hole merger. of general relativity in the strong-field regime of gravity. GW150914 demonstrates the existence of stellar-mass black holes more massive than =25M,and establishes that ACKNOWLEDGMENTS binary black holes can form in nature and merge within a The authors gratefully acknowledge the support of Hubble time.Binary black holes have been predicted to form the United States National Science Foundation (NSF)for both in isolated binaries [102-104]and in dense environ- the construction and operation of the LIGO Laboratory ments by dynamical interactions [105-107].The formation and Advanced LIGO as well as the Science and of such massive black holes from stellar evolution requires Technology Facilities Council (STFC)of the United weak massive-star winds,which are possible in stellar Kingdom,the Max-Planck Society (MPS),and the State environments with metallicity lower than =1/2 the solar of Niedersachsen,Germany,for support of the construction value [108,109].Further astrophysical implications of this of Advanced LIGO and construction and operation of the binary black hole discovery are discussed in [110]. GEO 600 detector.Additional support for Advanced LIGO These observational results constrain the rate of stellar- was provided by the Australian Research Council.The mass binary black hole mergers in the local universe.Using authors gratefully acknowledge the Italian Istituto several different models of the underlying binary black hole Nazionale di Fisica Nucleare (INFN).the French Centre mass distribution,we obtain rate estimates ranging from National de la Recherche Scientifique (CNRS),and the 2-400 Gpc-3 yr-!in the comoving frame [111-113].This Foundation for Fundamental Research on Matter supported is consistent with a broad range of rate predictions as by the Netherlands Organisation for Scientific Research. reviewed in [114],with only the lowest event rates being for the construction and operation of the Virgo detector,and excluded. for the creation and support of the EGO consortium.The Binary black hole systems at larger distances contribute authors also gratefully acknowledge research support from to a stochastic background of gravitational waves from the these agencies as well as by the Council of Scientific and superposition of unresolved systems.Predictions for such a Industrial Research of India,Department of Science and 061102-8

black hole system in general relativity [94]. A first consistency check involves the mass and spin of the final black hole. In general relativity, the end product of a black hole binary coalescence is a Kerr black hole, which is fully described by its mass and spin. For quasicircular inspirals, these are predicted uniquely by Einstein’s equations as a function of the masses and spins of the two progenitor black holes. Using fitting formulas calibrated to numerical relativity simulations [92], we verified that the remnant mass and spin deduced from the early stage of the coalescence and those inferred independently from the late stage are consistent with each other, with no evidence for disagreement from general relativity. Within the post-Newtonian formalism, the phase of the gravitational waveform during the inspiral can be expressed as a power series in f1=3. The coefficients of this expansion can be computed in general relativity. Thus, we can test for consistency with general relativity [95,96] by allowing the coefficients to deviate from the nominal values, and seeing if the resulting waveform is consistent with the data. In this second check [94] we place constraints on these deviations, finding no evidence for violations of general relativity. Finally, assuming a modified dispersion relation for gravitational waves [97], our observations constrain the Compton wavelength of the graviton to be λg > 1013 km, which could be interpreted as a bound on the graviton mass mg < 1.2 × 10−22 eV=c2. This improves on Solar System and binary pulsar bounds [98,99] by factors of a few and a thousand, respectively, but does not improve on the model￾dependent bounds derived from the dynamics of Galaxy clusters [100] and weak lensing observations [101]. In summary, all three tests are consistent with the predictions of general relativity in the strong-field regime of gravity. GW150914 demonstrates the existence of stellar-mass black holes more massive than ≃25M⊙, and establishes that binary black holes can form in nature and merge within a Hubble time. Binary black holes have been predicted to form both in isolated binaries [102–104] and in dense environ￾ments by dynamical interactions [105–107]. The formation of such massive black holes from stellar evolution requires weak massive-star winds, which are possible in stellar environments with metallicity lower than ≃1=2 the solar value [108,109]. Further astrophysical implications of this binary black hole discovery are discussed in [110]. These observational results constrain the rate of stellar￾mass binary black hole mergers in the local universe. Using several different models of the underlying binary black hole mass distribution, we obtain rate estimates ranging from 2–400 Gpc−3 yr−1 in the comoving frame [111–113]. This is consistent with a broad range of rate predictions as reviewed in [114], with only the lowest event rates being excluded. Binary black hole systems at larger distances contribute to a stochastic background of gravitational waves from the superposition of unresolved systems. Predictions for such a background are presented in [115]. If the signal from such a population were detected, it would provide information about the evolution of such binary systems over the history of the universe. VII. OUTLOOK Further details about these results and associated data releases are available at [116]. Analysis results for the entire first observational period will be reported in future publications. Efforts are under way to enhance significantly the global gravitational-wave detector network [117]. These include further commissioning of the Advanced LIGO detectors to reach design sensitivity, which will allow detection of binaries like GW150914 with 3 times higher SNR. Additionally, Advanced Virgo, KAGRA, and a possible third LIGO detector in India [118] will extend the network and significantly improve the position reconstruction and parameter estimation of sources. VIII. CONCLUSION The LIGO detectors have observed gravitational waves from the merger of two stellar-mass black holes. The detected waveform matches the predictions of general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. ACKNOWLEDGMENTS 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 GEO 600 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 for 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 PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-8

week ending PRL116,061102(2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 Technology,India,Science Engineering Research Board [21]J.H.Taylor and J.M.Weisberg.Astrophys.J.253,908 (SERB),India,Ministry of Human Resource Development, (1982). India,the Spanish Ministerio de Economia y [22]W.Press and K.Thorne,Annu.Rev.Astron.Astrophys Competitividad,the Conselleria d'Economia 1 10.335(1972). Competitivitat and Conselleria d'Educacio,Cultura i [23]J.Weber,.Phys.Rev.117,306(1960). Universitats of the Govern de les Illes Balears,the [24]P.Astone et al.,Phys.Rev.D 82,022003(2010). [25]M.E.Gertsenshtein and V.I.Pustovoit,Sov.Phys.JETP National Science Centre of Poland,the European 16.433(1962). Commission,the Royal Society,the Scottish Funding [26]G.E.Moss,L.R.Miller,and R.L.Forward,Appl.Opt.10 Council,the Scottish Universities Physics Alliance,the 2495(1971). Hungarian Scientific Research Fund (OTKA),the Lyon [27]R.Weiss,Electromagnetically coupled broadband gravi- Institute of Origins (LIO),the National Research tational antenna,Quarterly Report of the Research Labo- Foundation of Korea,Industry Canada and the Province ratory for Electronics,MIT Report No.105,1972,https:// of Ontario through the Ministry of Economic Development dcc.ligo.org/LIGO-P720002/public/main. and Innovation,the Natural Sciences and Engineering [28]R.W.P.Drever,in Gravitational Radiation,edited by N. Research Council of Canada,Canadian Institute for Deruelle and T.Piran (North-Holland,Amsterdam,1983), p.321. Advanced Research,the Brazilian Ministry of Science, [29]R.W.P.Drever,F.J.Raab,K.S.Thome,R.Vogt,and R. Technology,and Innovation,Russian Foundation for Basic Weiss,Laser Interferometer Gravitational-wave Observa- Research,the Leverhulme Trust,the Research Corporation, tory (LIGO)Technical Report,1989,https://dcc.ligo.org/ Ministry of Science and Technology (MOST),Taiwan,and LIGO-M890001/public/main. the Kavli Foundation.The authors gratefully acknowledge [30]A.Abramovici et al.,Science 256,325 (1992). the support of the NSF,STFC,MPS,INFN,CNRS and the [31]A.Brillet,A.Giazotto et al.,Virgo Project Technical State of Niedersachsen,Germany,for provision of compu- Report No.VIR-0517A-15,1989,https://tds.ego-gw.it/ql/? tational resources.This article has been assigned the c=11247. document numbers LIGO-P150914 and VIR-0015A-16. [32]J.Hough et al.,Proposal for a joint German-British interferometric gravitational wave detector,MPQ Techni- cal Report 147,No.GWD/137/JH(89),1989,http://eprints gla.ac.uk/114852. [33]J.Aasi et al.,Classical Quantum Gravity 32,074001 [1]A.Einstein,Sitzungsber.K.Preuss.Akad.Wiss.1,688 (2015). (1916). [34]F.Acernese et al.,Classical Quantum Gravity 32,024001 [2]A.Einstein,Sitzungsber.K.Preuss.Akad.Wiss.1,154 (2015). (1918). [35]C.Affeldt et al.,Classical Quantum Gravity 31,224002 [3]P.R.Saulson.Gen.Relativ.Gravit.43.3289 (2011). (2014). [4]K.Schwarzschild,Sitzungsber.K.Preuss.Akad.Wiss.1, [36]Y.Aso,Y.Michimura,K.Somiya,M.Ando,O. 189(1916). Miyakawa,T.Sekiguchi,D.Tatsumi,and H.Yamamoto, [5]D.Finkelstein,Phys.Rev.110,965(1958). Phys.Rev.D88.043007(2013). [6]M.D.Kruskal,Phys.Rev.119,1743 (1960). [37]The waveform shown is SXS:BBH:0305,available for [7]R.P.Kerr,Phys.Rev.Lett.11,237 (1963). download at http://www.black-holes.org/waveforms. [8]C.V.Vishveshwara,Nature (London)227,936 (1970) [38]A.H.Mroue er al.,Phys.Rev.Lett.111,241104 [9]W.H.Press,Astrophys.J.170,L105 (1971). (2013). [10]S.Chandrasekhar and S.L.Detweiler,Proc.R.Soc.A344, [39]B.Abbott et al.,arXiv:1602.03840. 441(1975). [40]N.J.Cornish and T.B.Littenberg,Classical Quantum [11]L.Blanchet,T.Damour,B.R.Iyer,C.M.Will,and A.G. Gravity32.135012(2015. Wiseman,Phys.Rev.Lett.74,3515(1995). [41]B.Abbott et al.,arXiv:1602.03843. [12]L.Blanchet,Living Rev.Relativity 17.2 (2014) [42]S.Chatterji,L.Blackburn,G.Martin,and E.Katsavounidis, [13]A.Buonanno and T.Damour,Phys.Rev.D 59,084006 Classical Quantum Gravity 21,S1809(2004). (1999). [43]S.Klimenko et al.,Phys.Rev.D 93,042004 (2016). [14]F.Pretorius,Phys.Rev.Lett.95,121101 (2005) [44]B.Abbott et al.,arXiv:1602.03839. [15]M.Campanelli,C.O.Lousto,P.Marronetti,and Y. [45]S.A.Usman et al.,arXiv:1508.02357 Zlochower,Phys.Rev.Lett.96,111101 (2006). [46]B.Abbott et al.,https://dcc.ligo.org/LIGO-P1500227/ [16]J.G.Baker,J.Centrella,D.-I.Choi,M.Koppitz,and J.van public/main. Meter,Phys.Rev.Lett.96,111102 (2006). [47]B.Abbott et al.,arXiv:1602.03838. [17]B.L.Webster and P.Murdin.Nature (London)235.37 [48]R.W.P.Drever,The Detection of Gravitational Waves, (1972). edited by D.G.Blair (Cambridge University Press. [18]C.T.Bolton,Nature (London)240,124 (1972). Cambridge,England,1991). [19]J.Casares and P.G.Jonker,Space Sci.Rev.183,223 [49]R.W.P.Drever et al.,in Quantum Optics,Experimental (2014). Gravity,and Measurement Theory,edited by P.Meystre [20]R.A.Hulse and J.H.Taylor,Astrophys.J.195,L51 and M.O.Scully.NATO ASI,Ser.B.Vol.94 (Plenum (1975). Press,New York,1983),pp.503-514. 061102-9

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 Natural Sciences and Engineering Research Council of Canada, Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Russian Foundation for Basic Research, 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 compu￾tational resources. This article has been assigned the document numbers LIGO-P150914 and VIR-0015A-16. [1] A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 1, 688 (1916). [2] A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. 1, 154 (1918). [3] P. R. Saulson, Gen. Relativ. Gravit. 43, 3289 (2011). [4] K. Schwarzschild, Sitzungsber. K. Preuss. Akad. Wiss. 1, 189 (1916). [5] D. Finkelstein, Phys. Rev. 110, 965 (1958). [6] M. D. Kruskal, Phys. Rev. 119, 1743 (1960). [7] R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963). [8] C. V. Vishveshwara, Nature (London) 227, 936 (1970). [9] W. H. Press, Astrophys. J. 170, L105 (1971). [10] S. Chandrasekhar and S. L. Detweiler, Proc. R. Soc. A 344, 441 (1975). [11] L. Blanchet, T. Damour, B. R. Iyer, C. M. Will, and A. G. Wiseman, Phys. Rev. Lett. 74, 3515 (1995). [12] L. Blanchet, Living Rev. Relativity 17, 2 (2014). [13] A. Buonanno and T. Damour, Phys. Rev. D 59, 084006 (1999). [14] F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005). [15] M. Campanelli, C. O. Lousto, P. Marronetti, and Y. Zlochower, Phys. Rev. Lett. 96, 111101 (2006). [16] J. G. Baker, J. Centrella, D.-I. Choi, M. Koppitz, and J. van Meter, Phys. Rev. Lett. 96, 111102 (2006). [17] B. L. Webster and P. Murdin, Nature (London) 235, 37 (1972). [18] C. T. Bolton, Nature (London) 240, 124 (1972). [19] J. Casares and P. G. Jonker, Space Sci. Rev. 183, 223 (2014). [20] R. A. Hulse and J. H. Taylor, Astrophys. J. 195, L51 (1975). [21] J. H. Taylor and J. M. Weisberg, Astrophys. J. 253, 908 (1982). [22] W. Press and K. Thorne, Annu. Rev. Astron. Astrophys. 10, 335 (1972). [23] J. Weber, Phys. Rev. 117, 306 (1960). [24] P. Astone et al., Phys. Rev. D 82, 022003 (2010). [25] M. E. Gertsenshtein and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1962). [26] G. E. Moss, L. R. Miller, and R. L. Forward, Appl. Opt. 10, 2495 (1971). [27] R. Weiss, Electromagnetically coupled broadband gravi￾tational antenna, Quarterly Report of the Research Labo￾ratory for Electronics, MIT Report No. 105, 1972, https:// dcc.ligo.org/LIGO‑P720002/public/main. [28] R. W. P. Drever, in Gravitational Radiation, edited by N. Deruelle and T. Piran (North-Holland, Amsterdam, 1983), p. 321. [29] R. W. P. Drever, F. J. Raab, K. S. Thorne, R. Vogt, and R. Weiss, Laser Interferometer Gravitational-wave Observa￾tory (LIGO) Technical Report, 1989, https://dcc.ligo.org/ LIGO‑M890001/public/main. [30] A. Abramovici et al., Science 256, 325 (1992). [31] A. Brillet, A. Giazotto et al., Virgo Project Technical Report No. VIR-0517A-15, 1989, https://tds.ego‑gw.it/ql/? c=11247. [32] J. Hough et al., Proposal for a joint German-British interferometric gravitational wave detector, MPQ Techni￾cal Report 147, No. GWD/137/JH(89), 1989, http://eprints .gla.ac.uk/114852. [33] J. Aasi et al., Classical Quantum Gravity 32, 074001 (2015). [34] F. Acernese et al., Classical Quantum Gravity 32, 024001 (2015). [35] C. Affeldt et al., Classical Quantum Gravity 31, 224002 (2014). [36] Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, and H. Yamamoto, Phys. Rev. D 88, 043007 (2013). [37] The waveform shown is SXS:BBH:0305, available for download at http://www.black‑holes.org/waveforms. [38] A. H. Mroué et al., Phys. Rev. Lett. 111, 241104 (2013). [39] B. Abbott et al., arXiv:1602.03840. [40] N. J. Cornish and T. B. Littenberg, Classical Quantum Gravity 32, 135012 (2015). [41] B. Abbott et al., arXiv:1602.03843. [42] S. Chatterji, L. Blackburn, G. Martin, and E. Katsavounidis, Classical Quantum Gravity 21, S1809 (2004). [43] S. Klimenko et al., Phys. Rev. D 93, 042004 (2016). [44] B. Abbott et al., arXiv:1602.03839. [45] S. A. Usman et al., arXiv:1508.02357. [46] B. Abbott et al., https://dcc.ligo.org/LIGO‑P1500227/ public/main. [47] B. Abbott et al., arXiv:1602.03838. [48] R. W. P. Drever, The Detection of Gravitational Waves, edited by D. G. Blair (Cambridge University Press, Cambridge, England, 1991). [49] R. W. P. Drever et al., in Quantum Optics, Experimental Gravity, and Measurement Theory, edited by P. Meystre and M. O. Scully, NATO ASI, Ser. B, Vol. 94 (Plenum Press, New York, 1983), pp. 503–514. PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-9

PRL116,061102(2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 [50]R.Schilling (unpublished). [81]B.J.Owen and B.S.Sathyaprakash,Phys.Rev.D 60, [51]B.J.Meers,Phys.Rev.D 38.2317(1988). 022002(1999). [52]J.Mizuno,K.A.Strain,P.G.Nelson,J.M.Chen,R. [82]B.Allen,Phys.Rev.D71,062001(2005) Schilling.A.Ruidiger,W.Winkler,and K.Danzmann, [83]J.Abadie et al.,Phys.Rev.D 85,082002 (2012). Phys.Lett.A175,273(1993). [84]S.Babak et al.,Phys.Rev.D 87,024033 (2013). [53]P.Kwee et al.,Opt.Express 20,10617 (2012). [85]K.Cannon et al.,Astrophys.J.748,136 (2012) [54]C.L.Mueller et al.,Rev.Sci.Instrum.87,014502 [86]S.Privitera,S.R.P.Mohapatra,P.Ajith,K.Cannon,N. (2016. Fotopoulos,M.A.Frei,C.Hanna,A.J.Weinstein,and [55]T.T.Fricke et al.,Classical Quantum Gravity 29,065005 J.T.Whelan,Phys.Rev.D 89,024003 (2014). (2012). [87]M.Hannam,P.Schmidt,A.Bohe,L.Haegel,S.Husa,F. [56]S.M.Aston et al.,Classical Quantum Gravity 29,235004 Ohme,G.Pratten,and M.Puirrer,Phys.Rev.Lett.113. (2012). 151101(2014). [57]F.Matichard et al.,Classical Quantum Gravity 32,185003 [88]S.Khan,S.Husa,M.Hannam,F.Ohme,M.Purrer,X. (2015). Jimenez Forteza,and A.Bohe,Phys.Rev.D 93,044007 [58]G.M.Harry et al.,Classical Quantum Gravity 24,405 (2016). (2007). [89]J.Veitch et al..Phys.Rev.D 91,042003 (2015). [59]M.Granata et al..Phys.Rev.D 93.012007 (2016). [90]A.Krolak and B.F.Schutz.Gen.Relativ.Gravit.19.1163 [60]A.V.Cumming et al.,Classical Quantum Gravity 29. (1987) 035003(2012). [91]P.A.R.Ade et al.,arXiv:1502.01589. [61]A.Staley et al,Classical Quantum Gravity 31,245010 [92]J.Healy,C.O.Lousto,and Y.Zlochower,Phys.Rev.D90, (2014). 104004(2014). 62]L.Barsotti,M.Evans,and P.Fritschel,Classical Quantum [93]S.Husa,S.Khan,M.Hannam,M.Puirrer,F.Ohme,X. Gravity27.084026(2010). Jimenez Forteza,and A.Bohe,Phys.Rev.D 93,044006 63]B.Abbott et al..arXiv:1602.03845 (2016). [64]E.Goetz et al.,in Gravitational Waves:Proceedings,of [94]B.Abbott et al.,arXiv:1602.03841. the 8th Edoardo Amaldi Conference,Amaldi,New York [95]C.K.Mishra,K.G.Arun,B.R.Iyer,and B.S. 2009;E.Goetz and R.L.Savage Jr.,Classical Quantum Sathyaprakash,Phys.Rev.D 82,064010(2010). Gravity27,084024(2010). [96]T.G.F.Li,W.Del Pozzo.S.Vitale.C.Van Den Broeck. [65]A.Effler,R.M.S.Schofield,V.V.Frolov,G.Gonzalez,K. M.Agathos,J.Veitch,K.Grover,T.Sidery,R.Sturani,and Kawabe,J.R.Smith,J.Birch,and R.McCarthy,Classical A.Vecchio,Phys.Rev.D 85,082003(2012) Quantum Gravity 32,035017 (2015). [97]C.M.Wi,Phys.Rev.D57,2061(1998). [66]I.Bartos,R.Bork,M.Factourovich,J.Heefner,S.Marka, [98]C.Talmadge,J.P.Berthias,R.W.Hellings,and E.M. Z.Marka,Z.Raics,P.Schwinberg,and D.Sigg,Classical Standish,Phys.Rev.Lett.61,1159 (1988). Quantum Gravity 27,084025 (2010). [99]L.S.Finn and P.J.Sutton,Phys.Rev.D 65,044022 [67]J.Aasi et al.,Classical Quantum Gravity 32,115012 (2002). (2015) [100]A.S.Goldhaber and M.M.Nieto,Phys.Rev.D 9.1119 [68]J.Aasi et al.,Phys.Rev.D 87,022002 (2013). (1974). [69]B.Abbott et al.,arXiv:1602.03844. [101]S.Choudhury and S.SenGupta,Eur.Phys.J.C74.3159 [70]L.Nuttall et al.,Classical Quantum Gravity 32.245005 (2014). (2015). [102]A.Tutukov and L.Yungelson,Nauchnye Informatsii 27, [71]L.Lyons,Ann.Appl.Stat.2.887(2008). 70(1973). [72]S.Klimenko,I.Yakushin,A.Mercer,and G.Mitselmakher, [103]V.M.Lipunov,K.A.Postnov,and M.E.Prokhorov,Mon Classical Quantum Gravity 25,114029 (2008). Not.R.Astron.Soc.288.245 (1997). [73]R.Lynch,S.Vitale,R.Essick,E.Katsavounidis,and F. [104]K.Belczynski,S.Repetto,D.Holz,R.O'Shaughnessy,T. Robinet,arXiv:1511.05955. Bulik,E.Berti,C.Fryer,M.Dominik,arXiv:1510.04615 [74]J.Kanner,T.B.Littenberg,N.Cornish,M.Millhouse, [Astrophys.J.(to be published)]. E.Xhakaj,F.Salemi,M.Drago,G.Vedovato,and S. [105]S.Sigurdsson and L.Hernquist,Nature (London)364,423 Klimenko,Phys.Rev.D 93,022002 (2016). (1993). 75]A.Buonanno and T.Damour,Phys.Rev.D 62,064015 [106]S.F.Portegies Zwart and S.L.W.McMillan,Astrophys.J. (2000). Lett.528.L17(2000). [76]L.Blanchet,T.Damour,G.Esposito-Farese,and B.R. [107]C.L.Rodriguez,M.Morscher,B.Pattabiraman,S Iyer,Phys.Rev.Lett.93,091101 (2004). Chatterjee,C.-J.Haster,and F.A.Rasio,Phys.Rev.Lett. [77]A.Taracchini et al.,Phys.Rev.D 89,061502 115,051101(2015), 2014). [108]K.Belczynski,T.Bulik,C.L.Fryer,A.Ruiter,F.Valsecchi, [78]M.Puirrer,Classical Quantum Gravity 31,195010 J.S.Vink,and J.R.Hurley,Astrophys.J.714,1217 (2014). (2010). [79]B.Allen,W.G.Anderson,P.R.Brady,D.A.Brown,and [109]M.Spera,M.Mapelli,and A.Bressan,Mon.Not.R. J.D.E.Creighton,Phys.Rev.D 85,122006(2012). Astron..Soc.451,4086(2015). [80]B.S.Sathyaprakash and S.V.Dhurandhar,Phys.Rev.D [110]B.Abbott et al.,Astrophys.J.818,L22 (2016). 44,3819(1991). [111]B.Abbott et al.,arXiv:1602.03842. 061102-10

[50] R. Schilling (unpublished). [51] B. J. Meers, Phys. Rev. D 38, 2317 (1988). [52] J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, Phys. Lett. A 175, 273 (1993). [53] P. Kwee et al., Opt. Express 20, 10617 (2012). [54] C. L. Mueller et al., Rev. Sci. Instrum. 87, 014502 (2016). [55] T. T. Fricke et al., Classical Quantum Gravity 29, 065005 (2012). [56] S. M. Aston et al., Classical Quantum Gravity 29, 235004 (2012). [57] F. Matichard et al., Classical Quantum Gravity 32, 185003 (2015). [58] G. M. Harry et al., Classical Quantum Gravity 24, 405 (2007). [59] M. Granata et al., Phys. Rev. D 93, 012007 (2016). [60] A. V. Cumming et al., Classical Quantum Gravity 29, 035003 (2012). [61] A. Staley et al., Classical Quantum Gravity 31, 245010 (2014). [62] L. Barsotti, M. Evans, and P. Fritschel, Classical Quantum Gravity 27, 084026 (2010). [63] B. Abbott et al., arXiv:1602.03845. [64] E. Goetz et al., in Gravitational Waves: Proceedings, of the 8th Edoardo Amaldi Conference, Amaldi, New York, 2009; E. Goetz and R. L. Savage Jr., Classical Quantum Gravity 27, 084024 (2010). [65] A. Effler, R. M. S. Schofield, V. V. Frolov, G. González, K. Kawabe, J. R. Smith, J. Birch, and R. McCarthy, Classical Quantum Gravity 32, 035017 (2015). [66] I. Bartos, R. Bork, M. Factourovich, J. Heefner, S. Márka, Z. Márka, Z. Raics, P. Schwinberg, and D. Sigg, Classical Quantum Gravity 27, 084025 (2010). [67] J. Aasi et al., Classical Quantum Gravity 32, 115012 (2015). [68] J. Aasi et al., Phys. Rev. D 87, 022002 (2013). [69] B. Abbott et al., arXiv:1602.03844. [70] L. Nuttall et al., Classical Quantum Gravity 32, 245005 (2015). [71] L. Lyons, Ann. Appl. Stat. 2, 887 (2008). [72] S. Klimenko, I. Yakushin, A. Mercer, and G. Mitselmakher, Classical Quantum Gravity 25, 114029 (2008). [73] R. Lynch, S. Vitale, R. Essick, E. Katsavounidis, and F. Robinet, arXiv:1511.05955. [74] J. Kanner, T. B. Littenberg, N. Cornish, M. Millhouse, E. Xhakaj, F. Salemi, M. Drago, G. Vedovato, and S. Klimenko, Phys. Rev. D 93, 022002 (2016). [75] A. Buonanno and T. Damour, Phys. Rev. D 62, 064015 (2000). [76] L. Blanchet, T. Damour, G. Esposito-Farèse, and B. R. Iyer, Phys. Rev. Lett. 93, 091101 (2004). [77] A. Taracchini et al., Phys. Rev. D 89, 061502 (2014). [78] M. Pürrer, Classical Quantum Gravity 31, 195010 (2014). [79] B. Allen, W. G. Anderson, P. R. Brady, D. A. Brown, and J. D. E. Creighton, Phys. Rev. D 85, 122006 (2012). [80] B. S. Sathyaprakash and S. V. Dhurandhar, Phys. Rev. D 44, 3819 (1991). [81] B. J. Owen and B. S. Sathyaprakash, Phys. Rev. D 60, 022002 (1999). [82] B. Allen, Phys. Rev. D 71, 062001 (2005). [83] J. Abadie et al., Phys. Rev. D 85, 082002 (2012). [84] S. Babak et al., Phys. Rev. D 87, 024033 (2013). [85] K. Cannon et al., Astrophys. J. 748, 136 (2012). [86] S. Privitera, S. R. P. Mohapatra, P. Ajith, K. Cannon, N. Fotopoulos, M. A. Frei, C. Hanna, A. J. Weinstein, and J. T. Whelan, Phys. Rev. D 89, 024003 (2014), [87] M. Hannam, P. Schmidt, A. Bohé, L. Haegel, S. Husa, F. Ohme, G. Pratten, and M. Pürrer, Phys. Rev. Lett. 113, 151101 (2014). [88] S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. Jiménez Forteza, and A. Bohé, Phys. Rev. D 93, 044007 (2016). [89] J. Veitch et al., Phys. Rev. D 91, 042003 (2015). [90] A. Krolak and B. F. Schutz, Gen. Relativ. Gravit. 19, 1163 (1987). [91] P. A. R. Ade et al., arXiv:1502.01589. [92] J. Healy, C. O. Lousto, and Y. Zlochower, Phys. Rev. D 90, 104004 (2014). [93] S. Husa, S. Khan, M. Hannam, M. Pürrer, F. Ohme, X. Jiménez Forteza, and A. Bohé, Phys. Rev. D 93, 044006 (2016). [94] B. Abbott et al., arXiv:1602.03841. [95] C. K. Mishra, K. G. Arun, B. R. Iyer, and B. S. Sathyaprakash, Phys. Rev. D 82, 064010 (2010). [96] T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M. Agathos, J. Veitch, K. Grover, T. Sidery, R. Sturani, and A. Vecchio, Phys. Rev. D 85, 082003 (2012), [97] C. M. Will, Phys. Rev. D 57, 2061 (1998). [98] C. Talmadge, J. P. Berthias, R. W. Hellings, and E. M. Standish, Phys. Rev. Lett. 61, 1159 (1988). [99] L. S. Finn and P. J. Sutton, Phys. Rev. D 65, 044022 (2002). [100] A. S. Goldhaber and M. M. Nieto, Phys. Rev. D 9, 1119 (1974). [101] S. Choudhury and S. SenGupta, Eur. Phys. J. C 74, 3159 (2014). [102] A. Tutukov and L. Yungelson, Nauchnye Informatsii 27, 70 (1973). [103] V. M. Lipunov, K. A. Postnov, and M. E. Prokhorov, Mon. Not. R. Astron. Soc. 288, 245 (1997). [104] K. Belczynski, S. Repetto, D. Holz, R. O’Shaughnessy, T. Bulik, E. Berti, C. Fryer, M. Dominik, arXiv:1510.04615 [Astrophys. J. (to be published)]. [105] S. Sigurdsson and L. Hernquist, Nature (London) 364, 423 (1993). [106] S. F. Portegies Zwart and S. L. W. McMillan, Astrophys. J. Lett. 528, L17 (2000). [107] C. L. Rodriguez, M. Morscher, B. Pattabiraman, S. Chatterjee, C.-J. Haster, and F. A. Rasio, Phys. Rev. Lett. 115, 051101 (2015), [108] K. Belczynski, T. Bulik, C. L. Fryer, A. Ruiter, F. Valsecchi, J. S. Vink, and J. R. Hurley, Astrophys. J. 714, 1217 (2010). [109] M. Spera, M. Mapelli, and A. Bressan, Mon. Not. R. Astron. Soc. 451, 4086 (2015). [110] B. Abbott et al., Astrophys. J. 818, L22 (2016). [111] B. Abbott et al., arXiv:1602.03842. PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending 12 FEBRUARY 2016 061102-10