Fermat's Library | Observation of Gravitational Waves from a Binary Black Hole Merger annotated/explained version.

Gravitational waves were predicted by Einstein's theory of General ...

A very well executed video explanation about Gravitational waves an...

Links to Einstein's Original papers (in German): * [Einstein, Al...

If you want to learn more about General Relativity, Linearized Grav...

This plot shows the gravitational wave event as observed by the two...

Signal-to-noise ratio (abbreviated SNR or S/N) is a simple measure ...

In 2014 Virgo and LIGO signed the [Memorandum of Understanding Betw...

These plots show the evolution with time of: 1. top red: gravitati...

The chirp mass of a binary system of two black holes respective mas...

This animation shows the effect a gravitational wave would have on ...

Gravitational waves are very hard to detect however the detection p...

The precision needed to detect a gravitational wave is incredible. ...

Plots comparing the number of candidate events and the mean number ...

Two initial black holes with 36 solar masses and 29 solar masses me...

A Kerr black hole also called rotating black hole is a black hole t...

Two major scientific breakthroughs: 1. the first direct observat...

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.

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

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.

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-2

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).

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-3

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.

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-4

[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

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBRUARY 2016

061102-5

Comments