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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 410

þ160

−180

Mpc corresponding to a redshift z ¼ 0.09

þ0.03

−0.04

In the source frame, the initial black hole masses are 36

þ5

−4

⊙

and 29

þ4

−4

⊙

, and the final black hole mass is

þ4

−4

⊙

,with3.0

þ0.5

−0.5

⊙

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 y ear 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 o f

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 ther e 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. T his discovery,

along with emerging astrophy sical 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 b y 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 furth er concepts to improve them [28],ledto

proposals for long-b aseline broadband laser interferome-

ters with the potential for significantly increased sensi-

tivity [29– 32]. By t he 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. Comb inations 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 networ k. I n 2015, Advanced LIGO became the

first of a significantly mor e sensitive network of advanced

detectors to begin obser vations [3 3– 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.

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0031-9007=16=116(6)=061102(16) 061102-1 Published by the American Physical Society

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 relati vistic models of com-

pact binary waveforms [44] recovered GW150914 as the

most significant ev ent 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 6.9

þ0.5

−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% credi ble

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.

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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 observationa l

mode. With only two detectors the source position is

primar ily determined by the relative arrival time and

localized to an area of ap proximately 600 deg

(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, m

and m

, due to gravitational-wave emission. At

the lower frequencies, such evolution is characterized by

the chirp mass [11]

M ¼

ðm

3=5

ðm

þ m

1=5



−8=3

−11=3



3=5

;

where f and

f are the observed f requency a nd its time

derivative and G and c are the gravitational co nstant 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 m

þ m

is ≳70M

⊙

in the detector frame.

This boun ds the sum of the Schwarzschild radii of t he

binary components to 2GM=c

≳ 210 km. To reach an

orbital f requency of 75 Hz (half the gravitational-wave

frequency) th e 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, w ould not have the r equired

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 ob jects compact

enough to r each an orbital frequency of 75 Hz without

contact. Furthermore , the decay of the waveform after it

peaks i s 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 s hows the calculate d 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

¼ L

¼ L ¼ 4 km. A passing gravitational wave effec-

tively alters the arm lengths such that the measured

difference is ΔLðtÞ¼δL

− δ L

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

¼ 2GM=c

) and the effective relative velocity given by the

post-Newtonian parameter v=c ¼ðGMπf=c

1=3

, where f is the

gravitational-wave frequency calculated with numerical relativity

and M is the total mass (value from Table I).

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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:YA G 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 (lo w

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],andare

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 alternati ve 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.

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[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 ∼10

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 an y 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 sensiti v e 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

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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

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

=ð1 þ E

, where E

is the dimensionless

coherent signal energy obtained by cross-correlating the

two reconstructed waveforms, and E

is the dimensionless

residual noise energy after the reconstructed signal is

subtracted from the data. The statistic η

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 η

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 η

≥ 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.

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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

⊙

, 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 χ

to test whether the data in several different

frequency bands are consistent with the matching template

[82].Valuesofχ

near unity indicate that the signal is

consistent with a coalescence. If χ

is greater than unity, ρðtÞ

is reweighted as

ρ ¼ ρ=f½1 þðχ

=2g

1=6

[83,84]. The final

step enforces coincidence between detectors by selecting

ev ent 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

arriv al time of weak signals. We rank coincident events based

on the quadrature sum

of the

ρ 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

∼10

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

¼ 23.6 is larger than any background

ev ent, 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 3.0

þ0.5

−0.5

⊙

. The system reached a

peak gravitational-wave luminosity of 3.6

þ0.5

−0.4

× 10

erg=s,

equivalent to 200

þ30

−20

⊙

=s.

Several analyses have been performed to determine

whether or not GW150914 is consistent with a binary

black hole system in general relativity [94]. A first

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

þ5

−4

⊙

Secondary black hole mass

þ4

−4

⊙

Final black hole mass

þ4

−4

⊙

Final black hole spin

0.67

þ0.05

−0.07

Luminosity distance

410

þ160

−180

Mpc

Source redshift z

0.09

þ0.03

−0.04

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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 f

1=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 λ

> 10

km,

which could be interpreted as a bound on the graviton mass

< 1.2 × 10

−22

eV=c

. 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

en vironments 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

−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

LIGOandconstructionandoperationoftheGEO600detector.

Additional support for Advanced LIGO was provided by the

Australian Research Council.Theauthors gratefully acknowl-

edge 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

theVirgodetector, and for the creationand supportof the EGO

consortium. The authorsalso gratefully acknowledge research

support from these agencies as well as by the Council of

Scientific and Industrial Research of India, Department of

Science and Technology, India, Science & Engineering

Research Board (SERB), India, Ministry of Human

Resource Development, India, the Spanish Ministerio de

Economía y Competiti vidad, the Conselleria d’Economia i

Competitivitat and Conselleria d’Educació, Cultura i

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061102-8

Univ ersitats 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

Univ ersities 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 computational resources. This

article has been assigned the document numbers LIGO-

P150914 and VIR-0015A-16.

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B. P. Abbott,

R. Abbott,

T. D. Abbott,

M. R. Abernathy,

F. Acernese,

3,4

K. Ackley,

C. Adams,

T. Adams,

P. Addesso,

R. X. Adhikari,

V. B. Adya,

C. Affeldt,

M. Agathos,

K. Agatsuma,

N. Aggarwal,

O. D. Aguiar,

L. Aiello,

12,13

A. Ain,

P. Ajith,

B. Allen,

8,16,17

A. Allocca,

18,19

P. A. Altin,

S. B. Anderson,

W. G. Anderson,

K. Arai,

M. A. Arain,

M. C. Araya,

C. C. Arceneaux,

J. S. Areeda,

N. Arnaud,

K. G. Arun,

S. Ascenzi,

25,13

G. Ashton,

M. Ast,

S. M. Aston,

P. Astone,

P. Aufmuth,

C. Aulbert,

S. Babak,

P. Bacon,

M. K. M. Bader,

P. T. Baker,

F. Baldaccini,

32,33

G. Ballardin,

S. W. Ballmer,

J. C. Barayoga,

S. E. Barclay,

B. C. Barish,

D. Barker,

F. Barone,

3,4

B. Barr,

L. Barsotti,

M. Barsuglia,

D. Barta,

J. Bartlett,

M. A. Barton,

I. Bartos,

R. Bassiri,

A. Basti,

18,19

J. C. Batch,

C. Baune,

V. Bavigadda,

M. Bazzan,

41,42

B. Behnke,

M. Bejger,

C. Belczynski,

A. S. Bell,

C. J. Bell,

B. K. Berger,

J. Bergman,

G. Bergmann,

C. P. L. Berry,

D. Bersanetti,

46,47

A. Bertolini,

J. Betzwieser,

S. Bhagwat,

R. Bhandare,

I. A. Bilenko,

G. Billingsley,

J. Birch,

R. Birney,

O. Birnholtz,

S. Biscans,

A. Bisht,

8,17

M. Bitossi,

C. Biwer,

M. A. Bizouard,

J. K. Blackburn,

C. D. Blair,

D. G. Blair,

R. M. Blair,

S. Bloemen,

O. Bock,

T. P. Bodiya,

M. Boer,

G. Bogaert,

C. Bogan,

A. Bohe,

P. Bojtos,

C. Bond,

F. Bondu,

R. Bonnand,

B. A. Boom,

R. Bork,

V. Boschi,

18,19

S. Bose,

56,14

Y. Bouffanais,

A. Bozzi,

C. Bradaschia,

P. R. Brady,

V. B. Braginsky,

M. Branchesi,

57,58

J. E. Brau,

T. Briant,

A. Brillet,

M. Brinkmann,

V. Brisson,

P. Brockill,

A. F. Brooks,

D. A. Brown,

D. D. Brown,

N. M. Brown,

C. C. Buchanan,

A. Buikema,

T. Bulik,

H. J. Bulten,

61,9

A. Buonanno,

29,62

D. Buskulic,

C. Buy,

R. L. Byer,

M. Cabero,

L. Cadonati,

G. Cagnoli,

64,65

C. Cahillane,

J. Calderón Bustillo,

66,63

T. Callister,

E. Calloni,

67,4

J. B. Camp,

K. C. Cannon,

J. Cao,

C. D. Capano,

E. Capocasa,

F. Carbognani,

S. Caride,

J. Casanueva Diaz,

C. Casentini,

25,13

S. Caudill,

M. Cavaglià,

F. Cavalier,

R. Cavalieri,

G. Cella,

C. B. Cepeda,

L. Cerboni Baiardi,

57,58

G. Cerretani,

18,19

E. Cesarini,

25,13

R. Chakraborty,

T. Chalermsongsak,

S. J. Chamberlin,

M. Chan,

S. Chao,

P. Charlton,

E. Chassande-Mottin,

H. Y. Chen,

Y. Chen,

C. Cheng,

A. Chincarini,

A. Chiummo,

H. S. Cho,

M. Cho,

J. H. Chow,

N. Christensen,

Q. Chu,

S. Chua,

S. Chung,

G. Ciani,

F. Clara,

J. A. Clark,

F. Cleva,

E. Coccia,

25,12,13

P.-F. Cohadon,

A. Colla,

79,28

C. G. Collette,

L. Cominsky,

M. Constancio Jr.,

A. Conte,

79,28

L. Conti,

D. Cook,

T. R. Corbitt,

N. Cornish,

A. Corsi,

S. Cortese,

C. A. Costa,

M. W. Coughlin,

S. B. Coughlin,

J.-P. Coulon,

S. T. Countryman,

P. Couvares,

E. E. Cowan,

D. M. Coward,

M. J. Cowart,

D. C. Coyne,

R. Coyne,

K. Craig,

J. D. E. Creighton,

T. D. Creighton,

J. Cripe,

S. G. Crowder,

A. M. Cruise,

A. Cumming,

L. Cunningham,

E. Cuoco,

T. Dal Canton,

S. L. Danilishin,

S. D’Antonio,

K. Danzmann,

17,8

N. S. Darman,

C. F. Da Silva Costa,

V. Dattilo,

I. Dave,

H. P. Daveloza,

M. Davier,

G. S. Davies,

E. J. Daw,

R. Day,

S. De,

D. DeBra,

G. Debreczeni,

J. Degallaix,

M. De Laurentis,

67,4

S. Deléglise,

W. Del Pozzo,

T. Denker,

8,17

T. Dent,

H. Dereli,

V. Dergachev,

R. T. DeRosa,

R. De Rosa,

67,4

R. DeSalvo,

S. Dhurandhar,

M. C. Díaz,

L. Di Fiore,

M. Di Giovanni,

79,28

A. Di Lieto,

18,19

S. Di Pace,

79,28

I. Di Palma,

29,8

A. Di Virgilio,

G. Dojcinoski,

V. Dolique,

F. Donovan,

K. L. Dooley,

S. Doravari,

6,8

R. Douglas,

T. P. Downes,

M. Drago,

8,89,90

R. W. P. Drever,

J. C. Driggers,

Z. Du,

M. Ducrot,

S. E. Dwyer,

T. B. Edo,

M. C. Edwards,

A. Effler,

H.-B. Eggenstein,

P. Ehrens,

J. Eichholz,

S. S. Eikenberry,

W. Engels,

R. C. Essick,

T. Etzel,

M. Evans,

T. M. Evans,

R. Everett,

M. Factourovich,

V. Fafone,

25,13,12

H. Fair,

S. Fairhurst,

X. Fan,

Q. Fang,

S. Farinon,

B. Farr,

W. M. Farr,

M. Favata,

M. Fays,

H. Fehrmann,

M. M. Fejer,

D. Feldbaum,

I. Ferrante,

18,19

E. C. Ferreira,

F. Ferrini,

F. Fidecaro,

18,19

L. S. Finn,

I. Fiori,

D. Fiorucci,

R. P. Fisher,

R. Flaminio,

65,92

M. Fletcher,

H. Fong,

J.-D. Fournier,

S. Franco,

S. Frasca,

79,28

F. Frasconi,

M. Frede,

Z. Frei,

A. Freise,

R. Frey,

V. Frey,

T. T. Fricke,

P. Fritschel,

V. V. Frolov,

P. Fulda,

M. Fyffe,

H. A. G. Gabbard,

J. R. Gair,

L. Gammaitoni,

32,33

S. G. Gaonkar,

F. Garufi,

67,4

A. Gatto,

G. Gaur,

94,95

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-11

N. Gehrels,

G. Gemme,

B. Gendre,

E. Genin,

A. Gennai,

J. George,

L. Gergely,

V. Germain,

Abhirup Ghosh,

Archisman Ghosh,

S. Ghosh,

52,9

J. A. Giaime,

2,6

K. D. Giardina,

A. Giazotto,

K. Gill,

A. Glaefke,

J. R. Gleason,

E. Goetz,

R. Goetz,

L. Gondan,

G. González,

J. M. Gonzalez Castro,

18,19

A. Gopakumar,

N. A. Gordon,

M. L. Gorodetsky,

S. E. Gossan,

M. Gosselin,

R. Gouaty,

C. Graef,

P. B. Graff,

M. Granata,

A. Grant,

S. Gras,

C. Gray,

G. Greco,

57,58

A. C. Green,

R. J. S. Greenhalgh,

100

P. Groot,

H. Grote,

S. Grunewald,

G. M. Guidi,

57,58

X. Guo,

A. Gupta,

M. K. Gupta,

K. E. Gushwa,

E. K. Gustafson,

R. Gustafson,

J. J. Hacker,

B. R. Hall,

E. D. Hall,

G. Hammond,

M. Haney,

M. M. Hanke,

J. Hanks,

C. Hanna,

M. D. Hannam,

J. Hanson,

T. Hardwick,

J. Harms,

57,58

G. M. Harry,

101

I. W. Harry,

M. J. Hart,

M. T. Hartman,

C.-J. Haster,

K. Haughian,

J. Healy,

102

J. Heefner,

1,a

A. Heidmann,

M. C. Heintze,

5,6

G. Heinzel,

H. Heitmann,

P. Hello,

G. Hemming,

M. Hendry,

I. S. Heng,

J. Hennig,

A. W. Heptonstall,

M. Heurs,

8,17

S. Hild,

D. Hoak,

103

K. A. Hodge,

D. Hofman,

S. E. Hollitt,

104

K. Holt,

D. E. Holz,

P. Hopkins,

D. J. Hosken,

104

J. Hough,

E. A. Houston,

E. J. Howell,

Y. M. Hu,

S. Huang,

E. A. Huerta,

105,82

D. Huet,

B. Hughey,

S. Husa,

S. H. Huttner,

T. Huynh-Dinh,

A. Idrisy,

N. Indik,

D. R. Ingram,

R. Inta,

H. N. Isa,

J.-M. Isac,

M. Isi,

G. Islas,

T. Isogai,

B. R. Iyer,

K. Izumi,

M. B. Jacobson,

T. Jacqmin,

H. Jang,

K. Jani,

P. Jaranowski,

106

S. Jawahar,

107

F. Jiménez-Forteza,

W. W. Johnson,

N. K. Johnson-McDaniel,

D. I. Jones,

R. Jones,

R. J. G. Jonker,

L. Ju,

K. Haris,

108

C. V. Kalaghatgi,

24,91

V. Kalogera,

S. Kandhasamy,

G. Kang,

J. B. Kanner,

S. Karki,

M. Kasprzack,

2,23,34

E. Katsavounidis,

W. Katzman,

S. Kaufer,

T. Kaur,

K. Kawabe,

F. Kawazoe,

8,17

F. Kéfélian,

M. S. Kehl,

D. Keitel,

8,66

D. B. Kelley,

W. Kells,

R. Kennedy,

D. G. Keppel,

J. S. Key,

A. Khalaidovski,

F. Y. Khalili,

I. Khan,

S. Khan,

Z. Khan,

E. A. Khazanov,

109

N. Kijbunchoo,

C. Kim,

J. Kim,

110

K. Kim,

111

Nam-Gyu Kim,

Namjun Kim,

Y.-M. Kim,

110

E. J. King,

104

P. J. King,

D. L. Kinzel,

J. S. Kissel,

L. Kleybolte,

S. Klimenko,

S. M. Koehlenbeck,

K. Kokeyama,

S. Koley,

V. Kondrashov,

A. Kontos,

S. Koranda,

M. Korobko,

W. Z. Korth,

I. Kowalska,

D. B. Kozak,

V. Kringel,

B. Krishnan,

A. Królak,

112,113

C. Krueger,

G. Kuehn,

P. Ku m a r,

R. Kumar,

L. Kuo,

A. Kutynia,

112

P. Kwee,

B. D. Lackey,

M. Landry,

J. Lange,

102

B. Lantz,

P. D. Lasky,

114

A. Lazzarini,

C. Lazzaro,

63,42

P. Leaci,

29,79,28

S. Leavey,

E. O. Lebigot,

30,70

C. H. Lee,

110

H. K. Lee,

111

H. M. Lee,

115

K. Lee,

A. Lenon,

M. Leonardi,

89,90

J. R. Leong,

N. Leroy,

N. Letendre,

Y. Levin,

114

B. M. Levine,

T. G. F. Li,

A. Libson,

T. B. Littenberg,

116

N. A. Lockerbie,

107

J. Logue,

A. L. Lombardi,

103

L. T. London,

J. E. Lord,

M. Lorenzini,

12,13

V. Loriette,

117

M. Lormand,

G. Losurdo,

J. D. Lough,

8,17

C. O. Lousto,

102

G. Lovelace,

H. Lück,

17,8

A. P. Lundgren,

J. Luo,

R. Lynch,

Y. M a,

T. MacDonald,

B. Machenschalk,

M. MacInnis,

D. M. Macleod,

F. Magaña-Sandoval,

R. M. Magee,

M. Mageswaran,

E. Majorana,

I. Maksimovic,

117

V. Malvezzi,

25,13

N. Man,

I. Mandel,

V. Mandic,

V. Mangano,

G. L. Mansell,

M. Manske,

M. Mantovani,

F. Marchesoni,

118,33

F. Marion,

S. Márka,

Z. Márka,

A. S. Markosyan,

E. Maros,

F. Martelli,

57,58

L. Martellini,

I. W. Martin,

R. M. Martin,

D. V. Martynov,

J. N. Marx,

K. Mason,

A. Masserot,

T. J. Massinger,

M. Masso-Reid,

F. Matichard,

L. Matone,

N. Mavalvala,

N. Mazumder,

G. Mazzolo,

R. McCarthy,

D. E. McClelland,

S. McCormick,

S. C. McGuire,

119

G. McIntyre,

J. McIver,

D. J. McManus,

S. T. McWilliams,

105

D. Meacher,

G. D. Meadors,

29,8

J. Meidam,

A. Melatos,

G. Mendell,

D. Mendoza-Gandara,

R. A. Mercer,

E. Merilh,

M. Merzougui,

S. Meshkov,

C. Messenger,

C. Messick,

P. M. Meyers,

F. Mezzani,

28,79

H. Miao,

C. Michel,

H. Middleton,

E. E. Mikhailov,

120

L. Milano,

67,4

J. Miller,

M. Millhouse,

Y. Minenkov,

J. Ming,

29,8

S. Mirshekari,

121

C. Mishra,

S. Mitra,

V. P. Mitrofanov,

G. Mitselmakher,

R. Mittleman,

A. Moggi,

M. Mohan,

S. R. P. Mohapatra,

M. Montani,

57,58

B. C. Moore,

C. J. Moore,

122

D. Moraru,

G. Moreno,

S. R. Morriss,

K. Mossavi,

B. Mours,

C. M. Mow-Lowry,

C. L. Mueller,

G. Mueller,

A. W. Muir,

Arunava Mukherjee,

D. Mukherjee,

S. Mukherjee,

N. Mukund,

A. Mullavey,

J. Munch,

104

D. J. Murphy,

P. G. Murray,

A. Mytidis,

I. Nardecchia,

25,13

L. Naticchioni,

79,28

R. K. Nayak,

123

V. Necula,

K. Nedkova,

103

G. Nelemans,

52,9

M. Neri,

46,47

A. Neunzert,

G. Newton,

T. T. Nguyen,

A. B. Nielsen,

S. Nissanke,

52,9

A. Nitz,

F. Nocera,

D. Nolting,

M. E. N. Normandin,

L. K. Nuttall,

J. Oberling,

E. Ochsner,

J. O’Dell,

100

E. Oelker,

G. H. Ogin,

124

J. J. Oh,

125

S. H. Oh,

125

F. Ohme,

M. Oliver,

P. Oppermann,

Richard J. Oram,

B. O’Reilly,

R. O’Shaughnessy,

102

C. D. Ott,

D. J. Ottaway,

104

R. S. Ottens,

H. Overmier,

B. J. Owen,

A. Pai,

108

S. A. Pai,

J. R. Palamos,

O. Palashov,

109

C. Palomba,

A. Pal-Singh,

H. Pan,

Y. Pan,

C. Pankow,

F. Pannarale,

B. C. Pant,

F. Paoletti,

34,19

A. Paoli,

M. A. Papa,

29,16,8

H. R. Paris,

W. Parker,

D. Pascucci,

A. Pasqualetti,

R. Passaquieti,

18,19

D. Passuello,

B. Patricelli,

18,19

Z. Patrick,

B. L. Pearlstone,

M. Pedraza,

R. Pedurand,

L. Pekowsky,

A. Pele,

S. Penn,

126

A. Perreca,

H. P. Pfeiffer,

69,29

M. Phelps,

O. Piccinni,

79,28

M. Pichot,

M. Pickenpack,

F. Piergiovanni,

57,58

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-12

V. Pierro,

G. Pillant,

L. Pinard,

I. M. Pinto,

M. Pitkin,

J. H. Poeld,

R. Poggiani,

18,19

P. Popolizio,

A. Post,

J. Powell,

J. Prasad,

V. Predoi,

S. S. Premachandra,

114

T. Prestegard,

L. R. Price,

M. Prijatelj,

M. Principe,

S. Privitera,

R. Prix,

G. A. Prodi,

89,90

L. Prokhorov,

O. Puncken,

M. Punturo,

P. Puppo,

M. Pürrer,

H. Qi,

J. Qin,

V. Quetschke,

E. A. Quintero,

R. Quitzow-James,

F. J. Raab,

D. S. Rabeling,

H. Radkins,

P. Raffai,

S. Raja,

M. Rakhmanov,

C. R. Ramet,

P. Rapagnani,

79,28

V. Raymond,

M. Razzano,

18,19

V. R e,

J. Read,

C. M. Reed,

T. Regimbau,

L. Rei,

S. Reid,

D. H. Reitze,

1,5

H. Rew,

120

S. D. Reyes,

F. Ricci,

79,28

K. Riles,

N. A. Robertson,

1,36

R. Robie,

F. Robinet,

A. Rocchi,

L. Rolland,

J. G. Rollins,

V. J. Roma,

J. D. Romano,

R. Romano,

3,4

G. Romanov,

120

J. H. Romie,

D. Rosińska,

127,43

S. Rowan,

A. Rüdiger,

P. Ruggi,

K. Ryan,

S. Sachdev,

T. Sadecki,

L. Sadeghian,

L. Salconi,

M. Saleem,

108

F. Salemi,

A. Samajdar,

123

L. Sammut,

85,114

L. M. Sampson,

E. J. Sanchez,

V. Sandberg,

B. Sandeen,

G. H. Sanders,

J. R. Sanders,

98,35

B. Sassolas,

B. S. Sathyaprakash,

P. R. Saulson,

O. Sauter,

R. L. Savage,

A. Sawadsky,

P. Schale,

R. Schilling,

8,b

J. Schmidt,

P. Schmidt,

1,76

R. Schnabel,

R. M. S. Schofield,

A. Schönbeck,

E. Schreiber,

D. Schuette,

8,17

B. F. Schutz,

91,29

J. Scott,

S. M. Scott,

D. Sellers,

A. S. Sengupta,

D. Sentenac,

V. Sequino,

25,13

A. Sergeev,

109

G. Serna,

Y. Setyawati,

52,9

A. Sevigny,

D. A. Shaddock,

T. Shaffer,

S. Shah,

52,9

M. S. Shahriar,

M. Shaltev,

Z. Shao,

B. Shapiro,

P. Shawhan,

A. Sheperd,

D. H. Shoemaker,

D. M. Shoemaker,

K. Siellez,

53,63

X. Siemens,

D. Sigg,

A. D. Silva,

D. Simakov,

A. Singer,

L. P. Singer,

A. Singh,

29,8

R. Singh,

A. Singhal,

A. M. Sintes,

B. J. J. Slagmolen,

J. R. Smith,

M. R. Smith,

N. D. Smith,

R. J. E. Smith,

E. J. Son,

125

B. Sorazu,

F. Sorrentino,

T. Souradeep,

A. K. Srivastava,

A. Staley,

M. Steinke,

J. Steinlechner,

S. Steinlechner,

D. Steinmeyer,

8,17

B. C. Stephens,

S. P. Stevenson,

R. Stone,

K. A. Strain,

N. Straniero,

G. Stratta,

57,58

N. A. Strauss,

S. Strigin,

R. Sturani,

121

A. L. Stuver,

T. Z. Summerscales,

128

L. Sun,

P. J. Sutton,

B. L. Swinkels,

M. J. Szczepańczyk,

M. Tacca,

D. Talukder,

D. B. Tanner,

M. Tápai,

S. P. Tarabrin,

A. Taracchini,

R. Taylor,

T. Theeg,

M. P. Thirugnanasambandam,

E. G. Thomas,

M. Thomas,

P. Thomas,

K. A. Thorne,

K. S. Thorne,

E. Thrane,

114

S. Tiwari,

V. Tiwari,

K. V. Tokmakov,

107

C. Tomlinson,

M. Tonelli,

18,19

C. V. Torres,

83,c

C. I. Torrie,

D. Töyrä,

F. Travasso,

32,33

G. Traylor,

D. Trifirò,

M. C. Tringali,

89,90

L. Trozzo,

129,19

M. Tse,

M. Turconi,

D. Tuyenbayev,

D. Ugolini,

130

C. S. Unnikrishnan,

A. L. Urban,

S. A. Usman,

H. Vahlbruch,

G. Vajente,

G. Valdes,

M. Vallisneri,

N. van Bakel,

M. van Beuzekom,

J. F. J. van den Brand,

61,9

C. Van Den Broeck,

D. C. Vander-Hyde,

35,22

L. van der Schaaf,

J. V. van Heijningen,

A. A. van Veggel,

M. Vardaro,

41,42

S. Vass,

M. Vasúth,

R. Vaulin,

A. Vecchio,

G. Vedovato,

J. Veitch,

P. J. Veitch,

104

K. Venkateswara,

131

D. Verkindt,

F. Vetrano,

57,58

A. Viceré,

57,58

S. Vinciguerra,

D. J. Vine,

J.-Y. Vinet,

S. Vitale,

T. Vo,

H. Vocca,

32,33

C. Vorvick,

D. Voss,

W. D. Vousden,

S. P. Vyatchanin,

A. R. Wade,

L. E. Wade,

132

M. Wade,

132

S. J. Waldman,

M. Walker,

L. Wallace,

S. Walsh,

16,8,29

G. Wang,

H. Wang,

M. Wang,

X. Wang,

Y. Wang,

H. Ward,

R. L. Ward,

J. Warner,

M. Was,

B. Weaver,

L.-W. Wei,

M. Weinert,

A. J. Weinstein,

R. Weiss,

T. Welborn,

L. Wen,

P. Weßels,

T. Westphal,

K. Wette,

J. T. Whelan,

102,8

S. E. Whitcomb,

D. J. White,

B. F. Whiting,

K. Wiesner,

C. Wilkinson,

P. A. Willems,

L. Williams,

R. D. Williams,

A. R. Williamson,

J. L. Willis,

133

B. Willke,

17,8

M. H. Wimmer,

8,17

L. Winkelmann,

W. Winkler,

C. C. Wipf,

A. G. Wiseman,

H. Wittel,

8,17

G. Woan,

J. Worden,

J. L. Wright,

G. Wu,

J. Yablon,

I. Yakushin,

W. Yam,

H. Yamamoto,

C. C. Yancey,

M. J. Yap,

H. Yu,

M. Yvert,

A. Zadrożny,

112

L. Zangrando,

M. Zanolin,

J.-P. Zendri,

M. Zevin,

F. Zhang,

L. Zhang,

M. Zhang,

120

Y. Zhang,

102

C. Zhao,

M. Zhou,

Z. Zhou,

X. J. Zhu,

M. E. Zucker,

1,10

S. E. Zuraw,

103

and J. Zweizig

(LIGO Scientific Collaboration and Virgo Collaboration)

LIGO, California Institute of Technology, Pasadena, California 91125, USA

Louisiana State University, Baton Rouge, Louisiana 70803, USA

Università di Salerno, Fisciano, I-84084 Salerno, Italy

INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

University of Florida, Gainesville, Florida 32611 , USA

LIGO Livingston Observatory, Livingston, Louisiana 70754, USA

Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3,

F-74941 Annecy-le-Vieux, France

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany

Nikhef, Science Park, 1098 XG Amsterdam, Netherlands

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-13

LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil

INFN, Gran Sasso Science Institute, I-67100 L’Aquila, Italy

INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy

Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India

International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India

University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA

Leibniz Universität Hannover, D-30167 Hannover, Germany

Università di Pisa, I-56127 Pisa, Italy

INFN, Sezione di Pisa, I-56127 Pisa, Italy

Australian National University, Canberra, Australian Capital Territory 0200, Australia

The University of Mississippi, University, Mississippi 38677 , USA

California State University Fullerton, Fullerton, California 92831, USA

LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

Chennai Mathematical Institute, Chennai, India 60310 3

Università di Roma Tor Vergata, I-00133 Roma, Italy

University of Southampton, Southampton SO17 1BJ, United Kingdom

Universität Hamburg, D-22761 Hamburg, Germany

INFN, Sezione di Roma, I-00185 Roma, Italy

Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany

APC, AstroParticule et Cosmologie, Université Pari s Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,

Sorbonne Paris Cité, F-75205 Paris Cedex 13, France

Montana State University, Bozeman, Montana 59717, USA

Università di Perugia, I-06123 Perugia, Italy

INFN, Sezione di Perugia, I-06123 Perugia, Italy

European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy

Syracuse University, Syracuse, New York 13244, USA

SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom

LIGO Hanford Observatory, Richland, Washington 99352, USA

Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary

Columbia University, New York, New York 10027, USA

Stanford University, Stanford, California 94305, USA

Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy

INFN, Sezione di Padova, I-35131 Padova, Italy

CAMK-PAN, 00-716 Warsaw, Poland

Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland

University of Birmingham, Birmingham B15 2TT, United Kingdom

Università degli Studi di Genova, I-16146 Genova, Italy

INFN, Sezione di Genova, I-16146 Genova, Italy

RRCAT, Indore MP 452013, India

Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom

University of Western Australia, Crawley, Western Australia 6009, Australia

Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, Netherlands

Artemis, Université Côte d’Azur, CNRS, Observatoire Côte d’Azur, CS 34229, Nice cedex 4, France

MTA Eötvös University, “Lendulet” Astrophysics Research Group, Budapest 1117, Hungary

Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France

Washington State University, Pullman, Washington 99164, USA

Università degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy

University of Oregon, Eugene, Oregon 97403, USA

Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France,

F-75005 Paris, France

VU University Amsterdam, 1081 HV Amsterdam, Netherlands

University of Maryland, College Park, Maryland 20742, USA

Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, UMR CNRS 5306, 69622 Villeurbanne, France

Laboratoire des Matériaux Avancés (LMA), IN2P3/CNRS, Université de Lyon, F-69622 Villeurbanne, Lyon, France

Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain

Università di Napoli “Federico II,” Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

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NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA

Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada

Tsinghua University, Beijing 100084, China

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University of Chicago, Chicago, Illinois 60637, USA

Caltech CaRT, Pasadena, California 91125, USA

Korea Institute of Science and Technology Information, Daejeon 305-806, Korea

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Università di Roma “La Sapienza,” I-00185 Roma, Italy

University of Brussels, Brussels 1050, Belgium

Sonoma State University, Rohnert Park, California 94928, USA

Northwestern University, Evanston, Illinois 60208, USA

The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA

University of Minnesota, Minneapolis, Minnesota 55455, USA

The University of Melbourne, Parkville, Victoria 3010, Australia

The University of Sheffield, Sheffield S10 2TN, United Kingdom

University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy

Montclair State University, Montclair, New Jersey 07043 , USA

Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy

INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy

Cardiff University, Cardiff CF24 3AA, United Kingdom

National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India

Institute for Plasma Research, Bhat, Gandhinagar 382428, India

University of Szeged, Dóm tér 9, Szeged 6720, Hungary

Embry-Riddle Aeronautical Univer sity, Prescott, Arizona 86301, USA

University of Michigan, Ann Arbor, Michigan 48109, USA

Tata Institute of Fundamental Research, Mumbai 400005, India

100

Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom

101

American University, Washington, D.C. 20016, USA

102

Rochester Institute of Technology, Rochester, New York 14623, USA

103

University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA

104

University of Adelaide, Adelaide, South Australia 5005, Australia

105

West Virginia University, Morgantown, West Virginia 26506, USA

106

University of Biał ystok, 15-424 Biał ystok, Poland

107

SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom

108

IISER-TVM, CET Campus, Trivandrum Kerala 695016, India

109

Institute of Applied Physics, Nizhny Novgorod, 603950, Russia

110

Pusan National University, Busan 609-735, Korea

111

Hanyang University, Seoul 133-791, Korea

112

NCBJ, 05-400 Świerk-Otwock, Poland

113

IM-PAN, 00-956 Warsaw, Poland

114

Monash University, Victoria 3800, Australia

115

Seoul National University, Seoul 151-742, Korea

116

University of Alabama in Huntsville, Huntsville, Alabama 35899, USA

117

ESPCI, CNRS, F-75005 Paris, France

118

Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy

119

Southern University and A&M College, Baton Rouge, Louisiana 70813, USA

120

College of William and Mary, Williamsburg, Virginia 23187, USA

121

Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research,

São Paulo SP 01140-070, Brazil

122

University of Cambridge, Cambridge CB2 1TN, United Kingdom

123

IISER-Kolkata, Mohanpur, West Bengal 741252, India

124

Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA

125

National Institute for Mathematical Sciences, Daejeon 305-390, Korea

126

Hobart and William Smith Colleges, Geneva, New York 14456, USA

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Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland

128

Andrews University, Berrien Springs, Michigan 49104, USA

129

Università di Siena, I-53100 Siena, Italy

130

Trinity University, San Antonio, Texas 78212, USA

131

University of Washington, Seattle, Washington 98195, USA

132

Kenyon College, Gambier, Ohio 43022, USA

133

Abilene Christian University, Abilene, Texas 79699, USA

Deceased, April 2012.

Deceased, May 2015.

Deceased, March 2015.

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-16

Discussion

Hello Micael. Thank you for annotating this paper for us! Could you elaborate on what you mean by "strain" here? I tried looking this up myself, but was unable to follow the links that I found. These plots show the evolution with time of: 1. top red: gravitational-wave strain 2. bottom green: black hole relative velocity 3. bottom black: black hole separation as observed by LIGO before and when the two black holes merged. Two initial black holes with 36 solar masses and 29 solar masses merged into a final black hole that is 62 solar masses while radiating away 3 solar masses worth of energy in the form of gravitational waves. The chirp mass of a binary system of two black holes respective masses $m_{1}$ and $m_{2}$ is given by $$\mathcal{M}=\frac{(m_{1}m_{2})^{3/5}}{(m_{1}+m_{2})^{1/5}}.$$ In general relativity, the chirp mass determines the leading-order amplitude and frequency evolution of the gravitational-wave signal emitted by the binary system during its inspiral. Two major scientific breakthroughs: 1. the first direct observation of gravitational waves after Einstein's prediction a century ago. 2. the first observation of the collision and merger of a pair of black holes. This plot shows the gravitational wave event as observed by the two LIGO sites: - Left: corresponds to Hanford, Washington - Right: corresponds Livingston, Louisiana On the top plots one can see the gravitational wave strain as a function of time. On the bottom, one can see the signal frequency of event GW150914 increasing over time. The amplitude of a gravitational wave is called strain, and can be expressed as a dimensionless quantity h: $$h \simeq \frac{dL}{L} $$ If two masses are separated by characteristic scale L, then the change in the scale dL is of order the gravitational wave amplitude h. In the case of LIGO this gives a fractional change in length, or equivalently light travel time, across a detector. As you can see the strain is extremely small, making gravitational waves hard to detect. The strain represents the expansion of space caused by gravitational waves? Links to Einstein's Original papers (in German): * [Einstein, Albert, Näherungsweise Integration der Feldgleichungen der Gravitation, 1916](http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/BGG54UCY/index.meta&pn=1) * [Einstein, Albert, Über Gravitationswellen, 1918](http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/W7ZU8V1E/index.meta) And here is a link to the English version: * [Approximate Integration of the Field Equations of Gravitation](http://einsteinpapers.press.princeton.edu/vol6-trans/213) ![Einstein paper thumbnail](http://i.imgur.com/DhALCiD.jpg "Einstein paper thumbnail") A very well executed video explanation about Gravitational waves and this discovery by the New York times: [LIGO Hears Gravitational Waves Einstein Predicted](http://www.nytimes.com/video/science/100000004200661/what-are-gravitational-waves-ligo-black-holes.html?action=click&gtype=vhs&version=vhs-heading&module=vhs&region=title-area) Here is a link to a didactic explanation of gravitational waves by the folks at PhD Comics: [Gravitational Waves Explained ](https://www.youtube.com/watch?v=4GbWfNHtHRg) Signal-to-noise ratio (abbreviated SNR or S/N) is a simple measure used in science that compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal power to the noise power and is usually expressed in decibels: $$SNR = \frac{P_{signal}}{P_{noise}}.$$ The event detected by LIGO had a $SNR = 24$ (an excellent SNR would lie within $20-28$). If you want to learn more about General Relativity, Linearized Gravity and take a closer look at the theoretical prediction of gravitational waves here are some lectures worth taking a look at: * [Linearized Gravity, Caltech](http://www.tapir.caltech.edu/~chirata/ph236/lec08.pdf) * [Lectures by Kip Thorne](http://www.its.caltech.edu/~kip/scripts/lectures.html) In 2014 Virgo and LIGO signed the [Memorandum of Understanding Between VIRGO and LIGO](https://dcc.ligo.org/LIGO-M060038/public) where they agree to share and jointly analyze the data recorded by their detectors and jointly publish their results. The giant interferometric detectors are looking for signals which are weak, infrequent and buried into instrumental noises of various origins. In order to claim a **discovery of gravitational wave scientists need a simultaneous detection in a number of instruments**. Unfortunately, Virgo was not collecting data because it was undergoing an upgrade at the time of this event. You can learn more about Virgo:[European Gravitational Observatory](https://www.ego-gw.it/public/about/whatIs.aspx) Plots comparing the number of candidate events and the mean number of background events. The observation of event GW150914 has a significance of 5.1$\sigma$ in the binary coalescence search and a significance of 4.6$\sigma$ in the generic transient search. In physics a discovery is made if an observation has a significance of 5$\sigma$ or more. Another simple explanation of the detection principle: **Figure 1:** A beamsplitter splits coherent light into two beams which reflect off the mirrors. In the absence of gravitational waves the reflected beams recombine and no interference pattern is detected. **Figure 2:** A gravitational wave passing over the left arm (yellow) changes its length and the reflected beams cannot cancel each other and an interference pattern is observed in the photodetector. ![illustration of the effect of a gw](http://i.imgur.com/nqGRuDQ.png "illustration of the effect of a gw") Gravitational waves are very hard to detect however the detection principle is fairly simple to understand. The principle used by LIGO is to measure changes induced by gravitational waves on the distances between freely-moving test masses using coherent trains of electromagnetic waves. The LIGO interferometer is designed so that, in the absence of gravitational waves, laser beams traveling in the two arms arrive at a photodetector exactly 180° out of phase, yielding no signal. A gravitational wave propagating perpendicular to the detector plane disrupts this perfect destructive interference. During its first half-cycle, the wave will lengthen one arm and shorten the other; during its second half-cycle, these changes are reversed. These length variations alter the phase difference between the laser beams, allowing optical power—a signal—to reach the photodetector. See this video to get a better grasp of how the detection works: [LIGO detection video](http://physics.aps.org/assets/12484057-b7a4-4f38-afdc-cf16b3768180/video1.mp4 "LIGO detection video") Gravitational waves were predicted by Einstein's theory of General Relativity, published in 1916. Gravitational waves correspond to oscillations of the curvature of space-time caused by the interaction of supermassive objects like black holes. These waves propagate outwards of the source and transport energy as gravitational radiation. This paper describes two major scientific breakthroughs: 1. the first direct detection of gravitational waves 2. the first observation of the collision and merger of a pair of black holes The image below illustrates the resulting gravitational waves caused by the interaction of two black holes. ![Gravitational Waves](http://www.extremetech.com/wp-content/uploads/2016/02/Gravitational-Waves.jpg "Gravitational Waves") The precision needed to detect a gravitational wave is incredible. In a recent [Reddit AMA](https://np.reddit.com/r/IAmA/comments/45g8qu/we_are_the_ligo_scientific_collaboration_and_we/) someone from the LIGO instrumentation team said: *"We say we measure the variation in mirror displacement with this enormous accuracy, but what we measure is the variation in the reflection phase from the highly reflective mirror coatings. If you look at it microscopically, the wavefronts of the laser beam scatter off of each individual atom in the coating, and the total superposition of these elementary waves results in the back-reflected beam. This means that the reflected wavefronts varry an 'average' reflection phase from the individual elementary waves that scatter off the $~10^{20}$ atoms in the mirror coating that interact with the laser field. This means that we basically average over about $~10^{20}$ atoms, and hence achieve this level of precision."* This animation shows the effect a gravitational wave would have on a ring of particles. As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles, the particles will follow the distortion in space-time as shown in the animation below. The area enclosed by these particles does not change. ![Effect of gravitational waves](https://upload.wikimedia.org/wikipedia/commons/b/b8/GravitationalWave_PlusPolarization.gif) A Kerr black hole also called rotating black hole is a black hole that has angular momentum, i.e. it rotates along one of its axis. The image below depicts a Kerr black hole with its rotation axis and boundaries![Kerr BH](http://nrumiano.free.fr/Images/tn_kerr_E.png "Kerr BH")

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