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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...
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Gravitational waves are very hard to detect however the detection p...
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Two initial black holes with 36 solar masses and 29 solar masses me...
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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
. 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
Mpc corresponding to a redshift z ¼ 0.09
In the source frame, the initial black hole masses are 36
and 29
, and the final black hole mass is
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
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 [810], 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 [1416], 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 [1719], 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 articles title, journal citation, and DOI.
PRL 116, 061102 (2016)
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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.
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 35350 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
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 35350 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
credible region) [39,46].
The basic features of GW150914 point to it being
produced by the coalescence of two black holesi.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
þ m
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.
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
, 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
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 detectors 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 (3338, 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 interferometers
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, 100300 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].
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
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 LIGOs 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 backgroundthe 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 detectors 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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