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Observation of Gravitational Waves from a Binary Black Hole Merger

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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[superscript -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[+160 over -180] Mpc corresponding to a redshift z = 0.09[+0.03 over -0.04]. In the source frame, the initial black hole masses are 36[+5 over -4]M[subscript ⊙] and 29[+4 over -4]M[subscript ⊙], and the final black hole mass is 62[+4 over -4]M[subscript ⊙], with 3.0[+0.5 over -0.5]M[subscript ⊙]c[superscript 2] 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.
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 6.9−0.4+0.5  ms later at H1; for a visual comparison, the H1 data are also shown, shifted in time by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [37, 38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show 90% credible regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms [39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets [40, 41]. These reconstructions have a 94% overlap, as shown in [39]. Third row: Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series. Bottom row:A time-frequency representation [42] of the strain data, showing the signal frequency increasing over time.
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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 1.0×1021. It matches the waveform
predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the
resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a
false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater
than 5.1σ. The source lies at a luminosity distance of 410þ160
180 Mpc corresponding to a redshift z¼0.09þ0.03
0.04 .
In the source frame, the initial black hole masses are 36þ5
4Mand 29þ4
4M, and the final black hole mass is
62þ4
4M,with3.0þ0.5
0.5Mc2radiated in gravitational waves. All uncertainties define 90% credible intervals.
These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct
detection of gravitational waves and the first observation of a binary black hole merger.
DOI: 10.1103/PhysRevLett.116.061102
I. INTRODUCTION
In 1916, the year after the final formulation of the field
equations of general relativity, Albert Einstein predicted
the existence of gravitational waves. He found that
the linearized weak-field equations had wave solutions:
transverse waves of spatial strain that travel at the speed of
light, generated by time variations of the mass quadrupole
moment of the source [1,2]. Einstein understood that
gravitational-wave amplitudes would be remarkably
small; moreover, until the Chapel Hill conference in
1957 there was significant debate about the physical
reality of gravitational waves [3].
Also in 1916, Schwarzschild published a solution for the
field equations [4] that was later understood to describe a
black hole [5,6], and in 1963 Kerr generalized the solution
to rotating black holes [7]. Starting in the 1970s theoretical
work led to the understanding of black hole quasinormal
modes [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. This discovery,
along with emerging astrophysical understanding [22],
led to the recognition that direct observations of the
amplitude and phase of gravitational waves would enable
studies of additional relativistic systems and provide new
tests of general relativity, especially in the dynamic
strong-field regime.
Experiments to detect gravitational waves began with
Weber and his resonant mass detectors in the 1960s [23],
followed by an international network of cryogenic reso-
nant detectors [24]. Interferometric detectors were first
suggested in the early 1960s [25] and the 1970s [26].A
study of the noise and performance of such detectors [27],
and further concepts to improve them [28],ledto
proposals for long-baseline broadband laser interferome-
ters with the potential for significantly increased sensi-
tivity [2932]. By the early 2000s, a set of initial detectors
was completed, including TAMA 300 in Japan, GEO 600
in Germany, the Laser Interferometer Gravitational-Wave
Observatory (LIGO) in the United States, and Virgo in
Italy. Combinations of these detectors made joint obser-
vations from 2002 through 2011, setting upper limits on a
variety of gravitational-wave sources while evolving into
a global network. In 2015, Advanced LIGO became the
first of a significantly more sensitive network of advanced
detectors to begin observations [3336].
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.
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properties of space-time in the strong-field, high-velocity
regime and confirm predictions of general relativity for the
nonlinear dynamics of highly disturbed black holes.
II. OBSERVATION
On September 14, 2015 at 09:50:45 UTC, the LIGO
Hanford, WA, and Livingston, LA, observatories detected
the coincident signal GW150914 shown in Fig. 1. The initial
detection was made by low-latency searches for generic
gravitational-wave transients [41] and was reported within
three minutes of data acquisition [43]. Subsequently,
matched-filter analyses that use relativistic models of com-
pact binary waveforms [44] recovered GW150914 as the
most significant event from each detector for the observa-
tions reported here. Occurring within the 10-ms intersite
FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right
column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filtered
with a 35350 Hz bandpass filter to suppress large fluctuations outside the detectorsmost sensitive frequency band, and band-reject
filters to remove the strong instrumental spectral lines seen in the Fig. 3spectra. Top row, left: H1 strain. Top row, right: L1 strain.
GW150914 arrived first at L1 and 6.9þ0.5
0.4ms 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 detectorsrelative 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% credible
regions for two independent waveform reconstructions. One (dark gray) models the signal using binary black hole template waveforms
[39]. The other (light gray) does not use an astrophysical model, but instead calculates the strain signal as a linear combination of
sine-Gaussian wavelets [40,41]. These reconstructions have a 94% overlap, as shown in [39].Third row: Residuals after subtracting the
filtered numerical relativity waveform from the filtered detector time series. Bottom row:A time-frequency representation [42] of the
strain data, showing the signal frequency increasing over time.
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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 observational
mode. With only two detectors the source position is
primarily determined by the relative arrival time and
localized to an area of approximately 600 deg2(90%
credible region) [39,46].
The basic features of GW150914 point to it being
produced by the coalescence of two black 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, m1and m2, due to gravitational-wave emission. At
the lower frequencies, such evolution is characterized by
the chirp mass [11]
M¼ðm1m2Þ3=5
ðm1þm2Þ1=5¼c3
G5
96 π8=3f11=3_
f3=5
;
where fand _
fare the observed frequency and its time
derivative and Gand care the gravitational constant and
speed of light. Estimating fand _
ffrom the data in Fig. 1,
we obtain a chirp mass of M30M, implying that the
total mass M¼m1þm2is 70Min the detector frame.
This bounds the sum of the Schwarzschild radii of the
binary components to 2GM=c2210 km. To reach an
orbital frequency of 75 Hz (half the gravitational-wave
frequency) the objects must have been very close and very
compact; equal Newtonian point masses orbiting at this
frequency would be only 350 km apart. A pair of
neutron stars, while compact, would not have the required
mass, while a black hole neutron star binary with the
deduced chirp mass would have a very large total mass,
and would thus merge at much lower frequency. This
leaves black holes as the only known objects compact
enough to reach an orbital frequency of 75 Hz without
contact. Furthermore, the decay of the waveform after it
peaks is consistent with the damped oscillations of a black
hole relaxing to a final stationary Kerr configuration.
Below, we present a general-relativistic analysis of
GW150914; Fig. 2shows the calculated waveform using
the resulting source parameters.
III. DETECTORS
Gravitational-wave astronomy exploits multiple, widely
separated detectors to distinguish gravitational waves from
local instrumental and environmental noise, to provide
source sky localization, and to measure wave polarizations.
The LIGO sites each operate a single Advanced LIGO
detector [33], a modified Michelson interferometer (see
Fig. 3) that measures gravitational-wave strain as a differ-
ence in length of its orthogonal arms. Each arm is formed
by two mirrors, acting as test masses, separated by
Lx¼Ly¼L¼4km. A passing gravitational wave effec-
tively alters the arm lengths such that the measured
difference is ΔLðtÞ¼δLxδLy¼hðtÞL, where his 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 Wof 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
(RS¼2GM=c2) and the effective relative velocity given by the
post-Newtonian parameter v=c ¼ðGMπf=c3Þ1=3, where fis the
gravitational-wave frequency calculated with numerical relativity
and Mis 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:YAG laser,
stabilized in amplitude, frequency, and beam geometry
[53,54]. The gravitational-wave signal is extracted at the
output port using a homodyne readout [55].
These interferometry techniques are designed to maxi-
mize the conversion of strain to optical signal, thereby
minimizing the impact of photon shot noise (the principal
noise at high frequencies). High strain sensitivity also
requires that the test masses have low displacement noise,
which is achieved by isolating them from seismic noise (low
frequencies) and designing them to have low thermal noise
(intermediate frequencies). Each test mass is suspended as
the final stage of a quadruple-pendulum system [56],
supported by an active seismic isolation platform [57].
These systems collectively provide more than 10 orders
of magnitude of isolation from ground motion for frequen-
cies above 10 Hz. Thermal noise is minimized by using
low-mechanical-loss materials in the test masses and their
suspensions: the test masses are 40-kg fused silica substrates
with low-loss dielectric optical coatings [58,59],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 1μPa.
Servo controls are used to hold the arm cavities on
resonance [61] and maintain proper alignment of the optical
components [62]. The detector output is calibrated in strain
by measuring its response to test mass motion induced by
photon pressure from a modulated calibration laser beam
[63]. The calibration is established to an uncertainty (1σ)of
less than 10% in amplitude and 10 degrees in phase, and is
continuously monitored with calibration laser excitations at
selected frequencies. Two alternative methods are used to
validate the absolute calibration, one referenced to the main
laser wavelength and the other to a radio-frequency oscillator
(a)
(b)
FIG. 3. Simplified diagram of an Advanced LIGO detector (not to scale). A gravitational wave propagating orthogonally to the
detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening
the other during one half-cycle of the wave; these length changes are reversed during the other half-cycle. The output photodetector
records these differential cavity length variations. While a 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 105channels 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].
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 detectorssusceptibility to environmental disturb-
ances was quantified by measuring their response to spe-
cially generated magnetic, radio-frequency, acoustic, and
vibration excitations. These tests indicated that any external
disturbance large enough to have caused the observed signal
would have been clearly recorded by the array of environ-
mental sensors. None of the environmental sensors recorded
any disturbances that evolved in time and frequency like
GW150914, and all environmental fluctuations during the
second that contained GW150914 were too small to account
for more than 6% of its strain amplitude. Special care was
taken to search for long-range correlated disturbances that
might produce nearly simultaneous signals at the two sites.
No significant disturbances were found.
The detector strain data exhibit non-Gaussian noise
transients that arise from a variety of instrumental mecha-
nisms. Many have distinct signatures, visible in auxiliary
data channels that are not sensitive to gravitational waves;
such instrumental transients are removed from our analyses
[69]. Any instrumental transients that remain in the data
are accounted for in the estimated detector backgrounds
described below. There is no evidence for instrumental
transients that are temporally correlated between the two
detectors.
V. SEARCHES
We present the analysis of 16 days of coincident
observations between the two LIGO detectors from
September 12 to October 20, 2015. This is a subset of
the data from Advanced 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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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
ηc¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2Ec=ð1þEn=EcÞ
p, where Ecis the dimensionless
coherent signal energy obtained by cross-correlating the
two reconstructed waveforms, and Enis the dimensionless
residual noise energy after the reconstructed signal is
subtracted from the data. The statistic ηcthus 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 ηc¼20.0, 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 <2×106of observing
one or more noise events as strong as GW150914 during
the analysis time, equivalent to 4.6σ. The left panel of
Fig. 4shows 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 (C2þC3).
In this two-class search the GW150914 event is found in
the C2þC3class. The left panel of Fig. 4shows the
C2þC3class results and background. In the background
of this class there are four events with ηc32.1, yielding a
false alarm rate for GW150914 of 1 in 8 400 years. This
corresponds to a false alarm probability of 5×106
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 5.1σand 4.6σfor 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 (C2þC3). 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
4M, we use the effective-one-body formalism [75], which
combines results from the post-Newtonian approach
[11,76] with results from black hole perturbation theory
and numerical relativity. The waveform model [77,78]
assumes that the spins of the merging objects are aligned
with the orbital angular momentum, but the resulting
templates can, nonetheless, effectively recover systems
with misaligned spins in the parameter region of
GW150914 [44]. Approximately 250 000 template wave-
forms are used to cover this parameter space.
The search calculates the matched-filter signal-to-noise
ratio ρðtÞfor each template in each detector and identifies
maxima of ρðtÞwith respect to the time of arrival of the signal
[7981]. For each maximum we calculate a chi-squared
statistic χ2
rto test whether the data in several different
frequency bands are consistent with the matching template
[82].Valuesofχ2
rnear unity indicate that the signal is
consistent with a coalescence. If χ2
ris greater than unity, ρðtÞ
is reweighted as ˆ
ρ¼ρ=1þðχ2
rÞ3=2g1=6[83,84]. The final
step enforces coincidence between detectors by selecting
event pairs that occur within a 15-ms window and come from
the same template. The 15-ms window is determined by the
10-ms intersite propagation time plus 5 ms for uncertainty in
arrival time of weak signals. We rank coincident events based
on the quadrature sum ˆ
ρcof the ˆ
ρfrom 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
107times 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. 4shows the background for the
search class of GW150914. The GW150914 detection-
statistic value of ˆ
ρc¼23.6is larger than any background
event, so only an upper bound can be placed on its false
alarm rate. Across the three search classes this bound is 1 in
203 000 years. This translates to a false alarm probability
<2×107, corresponding to 5.1σ.
A second, independent matched-filter analysis that uses a
different method for estimating the significance of its
events [85,86], also detected GW150914 with identical
signal parameters and consistent significance.
When an event is confidently identified as a real
gravitational-wave signal, as for GW150914, the back-
ground used to determine the significance of other events is
reestimated without the contribution of this event. This is
the background distribution shown as a purple line in the
right panel of Fig. 4. Based on this, the second most
significant event has a false alarm rate of 1 per 2.3 years and
corresponding Poissonian false alarm probability of 0.02.
Waveform analysis of this event indicates that if it is
astrophysical in origin it is also a binary black hole
merger [44].
VI. SOURCE DISCUSSION
The matched-filter search is optimized for detecting
signals, but it provides only approximate estimates of
the source parameters. To refine them we use general
relativity-based models [77,78,87,88], some of which
include spin precession, and for each model perform a
coherent Bayesian analysis to derive posterior distributions
of the source parameters [89]. The initial and final masses,
final spin, distance, and redshift of the source are shown in
Table I. The spin of the primary black hole is constrained
to be <0.7(90% credible interval) indicating it is not
maximally spinning, while the spin of the secondary is only
weakly constrained. These source parameters are discussed
in detail in [39]. The parameter uncertainties include
statistical errors and systematic errors from averaging the
results of different waveform models.
Using the fits to numerical simulations of binary black
hole mergers in [92,93], we provide estimates of the mass
and spin of the final black hole, the total energy radiated
in gravitational waves, and the peak gravitational-wave
luminosity [39]. The estimated total energy radiated in
gravitational waves is 3.0þ0.5
0.5Mc2. The system reached a
peak gravitational-wave luminosity of 3.6þ0.5
0.4×1056 erg=s,
equivalent to 200þ30
20 Mc2=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 (1þz)
[90]. The source redshift assumes standard cosmology [91].
Primary black hole mass 36þ5
4M
Secondary black hole mass 29þ4
4M
Final black hole mass 62þ4
4M
Final black hole spin 0.67þ0.05
0.07
Luminosity distance 410þ160
180 Mpc
Source redshift z0.09þ0.03
0.04
PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending
12 FEBRUARY 2016
061102-7
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 Einsteins equations as a
function of the masses and spins of the two progenitor
black holes. Using fitting formulas calibrated to numerical
relativity simulations [92], we verified that the remnant
mass and spin deduced from the early stage of the
coalescence and those inferred independently from the late
stage are consistent with each other, with no evidence for
disagreement from general relativity.
Within the post-Newtonian formalism, the phase of the
gravitational waveform during the inspiral can be expressed
as a power series in f1=3. The coefficients of this expansion
can be computed in general relativity. Thus, we can test for
consistency with general relativity [95,96] by allowing the
coefficients to deviate from the nominal values, and seeing
if the resulting waveform is consistent with the data. In this
second check [94] we place constraints on these deviations,
finding no evidence for violations of general relativity.
Finally, assuming a modified dispersion relation for
gravitational waves [97], our observations constrain the
Compton wavelength of the graviton to be λg>1013 km,
which could be interpreted as a bound on the graviton mass
mg<1.2×1022 eV=c2. This improves on Solar System
and binary pulsar bounds [98,99] by factors of a few and a
thousand, respectively, but does not improve on the model-
dependent bounds derived from the dynamics of Galaxy
clusters [100] and weak lensing observations [101].In
summary, all three tests are consistent with the predictions
of general relativity in the strong-field regime of gravity.
GW150914 demonstrates the existence of stellar-mass
black holes more massive than 25M, and establishes that
binary black holes can form in nature and merge within a
Hubble time. Binary black holes have been predicted to form
both in isolated binaries [102104] and in dense environ-
ments by dynamical interactions [105107]. The formation
of such massive black holes from stellar evolution requires
weak massive-star winds, which are possible in stellar
environments with metallicity lower than 1=2the 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
2400 Gpc3yr1in the comoving frame [111113]. 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
LIGOandconstructionandoperationof theGEO 600detector.
Additional support for Advanced LIGO was provided by the
Australian ResearchCouncil. The authors 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
the Virgo detector, and forthe creation and support of the EGO
consortium. The authors also gratefully acknowledge research
support from these agencies as well as by the Council of
Scientific and Industrial Research of India, Department of
Science and Technology, India, Science & Engineering
Research Board (SERB), India, Ministry of Human
Resource Development, India, the Spanish Ministerio de
Economía y Competitividad, the Conselleria dEconomia i
Competitivitat and Conselleria dEducació, Cultura i
PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending
12 FEBRUARY 2016
061102-8
Universitats of the Govern de les Illes Balears, the National
Science Centre of Poland, the European Commission, the
Royal Society, the Scottish Funding Council, the Scottish
Universities Physics Alliance, the Hungarian Scientific
Research Fund (OTKA), the Lyon Institute of Origins
(LIO), the National Research Foundation of Korea,
Industry Canada and the Province of Ontario through the
Ministry of Economic Development and Innovation, the
Natural Sciences and Engineering Research Council of
Canada, Canadian Institute for Advanced Research, the
Brazilian Ministry of Science, Technology, and Innovation,
Russian Foundation for Basic Research, the Leverhulme
Trust, the Research Corporation, Ministry of Science and
Technology (MOST), Taiwan, and the Kavli Foundation.
The authors gratefully acknowledge the support of the NSF,
STFC, MPS, INFN, CNRS and the State of Niedersachsen,
Germany, for provision of computational resources. This
article has been assigned the document numbers LIGO-
P150914 and VIR-0015A-16.
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T. Chalermsongsak,1S. J. Chamberlin,72 M. Chan,36 S. Chao,73 P. Charlton,74 E. Chassande-Mottin,30 H. Y. Chen,75
Y. Chen,76 C. Cheng,73 A. Chincarini,47 A. Chiummo,34 H. S. Cho,77 M. Cho,62 J. H. Chow,20 N. Christensen,78 Q. Chu,51
S. Chua,60 S. Chung,51 G. Ciani,5F. Clara,37 J. A. Clark,63 F. Cleva,53 E. Coccia,25,12,13 P.-F. Cohadon,60 A. Colla,79,28
C. G. Collette,80 L. Cominsky,81 M. Constancio Jr.,11 A. Conte,79,28 L. Conti,42 D. Cook,37 T. R. Corbitt,2N. Cornish,31
A. Corsi,71 S. Cortese,34 C. A. Costa,11 M. W. Coughlin,78 S. B. Coughlin,82 J.-P. Coulon,53 S. T. Countryman,39
P. Couvares,1E. E. Cowan,63 D. M. Coward,51 M. J. Cowart,6D. C. Coyne,1R. Coyne,71 K. Craig,36 J. D. E. Creighton,16
T. D. Creighton,83 J. Cripe,2S. G. Crowder,84 A. M. Cruise,45 A. Cumming,36 L. Cunningham,36 E. Cuoco,34 T. Dal Canton,8
S. L. Danilishin,36 S. DAntonio,13 K. Danzmann,17,8 N. S. Darman,85 C. F. Da Silva Costa,5V. Dattilo,34 I. Dave,48
H. P. Daveloza,83 M. Davier,23 G. S. Davies,36 E. J. Daw,86 R. Day,34 S. De,35 D. DeBra,40 G. Debreczeni,38 J. Degallaix,65
M. De Laurentis,67,4 S. Deléglise,60 W. Del Pozzo,45 T. Denker,8,17 T. Dent,8H. Dereli,53 V. Dergachev,1R. T. DeRosa,6
R. De Rosa,67,4 R. DeSalvo,87 S. Dhurandhar,14 M. C. Díaz,83 L. Di Fiore,4M. Di Giovanni,79,28 A. Di Lieto,18,19
S. Di Pace,79,28 I. Di Palma,29,8 A. Di Virgilio,19 G. Dojcinoski,88 V. Dolique,65 F. Donovan,10 K. L. Dooley,21 S. Doravari,6,8
R. Douglas,36 T. P. Downes,16 M. Drago,8,89,90 R. W. P. Drever,1J. C. Driggers,37 Z. Du,70 M. Ducrot,7S. E. Dwyer,37
T. B. Edo,86 M. C. Edwards,78 A. Effler,6H.-B. Eggenstein,8P. Ehrens,1J. Eichholz,5S. S. Eikenberry,5W. Engels,76
R. C. Essick,10 T. Etzel,1M. Evans,10 T. M. Evans,6R. Everett,72 M. Factourovich,39 V. Fafone,25,13,12 H. Fair,35
S. Fairhurst,91 X. Fan,70 Q. Fang,51 S. Farinon,47 B. Farr,75 W. M. Farr,45 M. Favata,88 M. Fays,91 H. Fehrmann,8
M. M. Fejer,40 D. Feldbaum,5I. Ferrante,18,19 E. C. Ferreira,11 F. Ferrini,34 F. Fidecaro,18,19 L. S. Finn,72 I. Fiori,34
D. Fiorucci,30 R. P. Fisher,35 R. Flaminio,65,92 M. Fletcher,36 H. Fong,69 J.-D. Fournier,53 S. Franco,23 S. Frasca,79,28
F. Frasconi,19 M. Frede,8Z. Frei,54 A. Freise,45 R. Frey,59 V. Frey,23 T. T. Fricke,8P. Fritschel,10 V. V. Frolov,6P. Fulda,5
M. Fyffe,6H. A. G. Gabbard,21 J. R. Gair,93 L. Gammaitoni,32,33 S. G. Gaonkar,14 F. Garufi,67,4 A. Gatto,30 G. Gaur,94,95
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N. Gehrels,68 G. Gemme,47 B. Gendre,53 E. Genin,34 A. Gennai,19 J. George,48 L. Gergely,96 V. Germain,7Abhirup Ghosh,15
Archisman Ghosh,15 S. Ghosh,52,9 J. A. Giaime,2,6 K. D. Giardina,6A. Giazotto,19 K. Gill,97 A. Glaefke,36 J. R. Gleason,5
E. Goetz,98 R. Goetz,5L. Gondan,54 G. González,2J. M. Gonzalez Castro,18,19 A. Gopakumar,99 N. A. Gordon,36
M. L. Gorodetsky,49 S. E. Gossan,1M. Gosselin,34 R. Gouaty,7C. Graef,36 P. B. Graff,62 M. Granata,65 A. Grant,36 S. Gras,10
C. Gray,37 G. Greco,57,58 A. C. Green,45 R. J. S. Greenhalgh,100 P. Groot,52 H. Grote,8S. Grunewald,29 G. M. Guidi,57,58
X. Guo,70 A. Gupta,14 M. K. Gupta,95 K. E. Gushwa,1E. K. Gustafson,1R. Gustafson,98 J. J. Hacker,22 B. R. Hall,56
E. D. Hall,1G. Hammond,36 M. Haney,99 M. M. Hanke,8J. Hanks,37 C. Hanna,72 M. D. Hannam,91 J. Hanson,6
T. Hardwick,2J. Harms,57,58 G. M. Harry,101 I. W. Harry,29 M. J. Hart,36 M. T. Hartman,5C.-J. Haster,45 K. Haughian,36
J. Healy,102 J. Heefner,1,a A. Heidmann,60 M. C. Heintze,5,6 G. Heinzel,8H. Heitmann,53 P. Hello,23 G. Hemming,34
M. Hendry,36 I. S. Heng,36 J. Hennig,36 A. W. Heptonstall,1M. Heurs,8,17 S. Hild,36 D. Hoak,103 K. A. Hodge,1D. Hofman,65
S. E. Hollitt,104 K. Holt,6D. E. Holz,75 P. Hopkins,91 D. J. Hosken,104 J. Hough,36 E. A. Houston,36 E. J. Howell,51
Y. M. Hu,36 S. Huang,73 E. A. Huerta,105,82 D. Huet,23 B. Hughey,97 S. Husa,66 S. H. Huttner,36 T. Huynh-Dinh,6A. Idrisy,72
N. Indik,8D. R. Ingram,37 R. Inta,71 H. N. Isa,36 J.-M. Isac,60 M. Isi,1G. Islas,22 T. Isogai,10 B. R. Iyer,15 K. Izumi,37
M. B. Jacobson,1T. Jacqmin,60 H. Jang,77 K. Jani,63 P. Jaranowski,106 S. Jawahar,107 F. Jiménez-Forteza,66 W. W. Johnson,2
N. K. Johnson-McDaniel,15 D. I. Jones,26 R. Jones,36 R. J. G. Jonker,9L. Ju,51 K. Haris,108 C. V. Kalaghatgi,24,91
V. Kalogera,82 S. Kandhasamy,21 G. Kang,77 J. B. Kanner,1S. Karki,59 M. Kasprzack,2,23,34 E. Katsavounidis,10
W. Katzman,6S. Kaufer,17 T. Kaur,51 K. Kawabe,37 F. Kawazoe,8,17 F. Kéfélian,53 M. S. Kehl,69 D. Keitel,8,66 D. B. Kelley,35
W. Kells,1R. Kennedy,86 D. G. Keppel,8J. S. Key,83 A. Khalaidovski,8F. Y. Khalili,49 I. Khan,12 S. Khan,91 Z. Khan,95
E. A. Khazanov,109 N. Kijbunchoo,37 C. Kim,77 J. Kim,110 K. Kim,111 Nam-Gyu Kim,77 Namjun Kim,40 Y.-M. Kim,110
E. J. King,104 P. J. King,37 D. L. Kinzel,6J. S. Kissel,37 L. Kleybolte,27 S. Klimenko,5S. M. Koehlenbeck,8K. Kokeyama,2
S. Koley,9V. Kondrashov,1A. Kontos,10 S. Koranda,16 M. Korobko,27 W. Z. Korth,1I. Kowalska,44 D. B. Kozak,1
V. Kringel,8B. Krishnan,8A. Królak,112,113 C. Krueger,17 G. Kuehn,8P. Kumar,69 R. Kumar,36 L. Kuo,73 A. Kutynia,112
P. Kwee,8B. D. Lackey,35 M. Landry,37 J. Lange,102 B. Lantz,40 P. D. Lasky,114 A. Lazzarini,1C. Lazzaro,63,42 P. Leaci,29,79,28
S. Leavey,36 E. O. Lebigot,30,70 C. H. Lee,110 H. K. Lee,111 H. M. Lee,115 K. Lee,36 A. Lenon,35 M. Leonardi,89,90
J. R. Leong,8N. Leroy,23 N. Letendre,7Y. Levin,114 B. M. Levine,37 T. G. F. Li,1A. Libson,10 T. B. Littenberg,116
N. A. Lockerbie,107 J. Logue,36 A. L. Lombardi,103 L. T. London,91 J. E. Lord,35 M. Lorenzini,12,13 V. Loriette,117
M. Lormand,6G. Losurdo,58 J. D. Lough,8,17 C. O. Lousto,102 G. Lovelace,22 H. Lück,17,8 A. P. Lundgren,8J. Luo,78
R. Lynch,10 Y. Ma,51 T. MacDonald,40 B. Machenschalk,8M. MacInnis,10 D. M. Macleod,2F. Magaña-Sandoval,35
R. M. Magee,56 M. Mageswaran,1E. Majorana,28 I. Maksimovic,117 V. Malvezzi,25,13 N. Man,53 I. Mandel,45 V. Mandic,84
V. Mangano,36 G. L. Mansell,20 M. Manske,16 M. Mantovani,34 F. Marchesoni,118,33 F. Marion,7S. Márka,39 Z. Márka,39
A. S. Markosyan,40 E. Maros,1F. Martelli,57,58 L. Martellini,53 I. W. Martin,36 R. M. Martin,5D. V. Martynov,1J. N. Marx,1
K. Mason,10 A. Masserot,7T. J. Massinger,35 M. Masso-Reid,36 F. Matichard,10 L. Matone,39 N. Mavalvala,10
N. Mazumder,56 G. Mazzolo,8R. McCarthy,37 D. E. McClelland,20 S. McCormick,6S. C. McGuire,119 G. McIntyre,1
J. McIver,1D. J. McManus,20 S. T. McWilliams,105 D. Meacher,72 G. D. Meadors,29,8 J. Meidam,9A. Melatos,85
G. Mendell,37 D. Mendoza-Gandara,8R. A. Mercer,16 E. Merilh,37 M. Merzougui,53 S. Meshkov,1C. Messenger,36
C. Messick,72 P. M. Meyers,84 F. Mezzani,28,79 H. Miao,45 C. Michel,65 H. Middleton,45 E. E. Mikhailov,120 L. Milano,67,4
J. Miller,10 M. Millhouse,31 Y. Minenkov,13 J. Ming,29,8 S. Mirshekari,121 C. Mishra,15 S. Mitra,14 V. P. Mitrofanov,49
G. Mitselmakher,5R. Mittleman,10 A. Moggi,19 M. Mohan,34 S. R. P. Mohapatra,10 M. Montani,57,58 B. C. Moore,88
C. J. Moore,122 D. Moraru,37 G. Moreno,37 S. R. Morriss,83 K. Mossavi,8B. Mours,7C. M. Mow-Lowry,45 C. L. Mueller,5
G. Mueller,5A. W. Muir,91 Arunava Mukherjee,15 D. Mukherjee,16 S. Mukherjee,83 N. Mukund,14 A. Mullavey,6
J. Munch,104 D. J. Murphy,39 P. G. Murray,36 A. Mytidis,5I. Nardecchia,25,13 L. Naticchioni,79,28 R. K. Nayak,123 V. Necula,5
K. Nedkova,103 G. Nelemans,52,9 M. Neri,46,47 A. Neunzert,98 G. Newton,36 T. T. Nguyen,20 A. B. Nielsen,8S. Nissanke,52,9
A. Nitz,8F. Nocera,34 D. Nolting,6M. E. N. Normandin,83 L. K. Nuttall,35 J. Oberling,37 E. Ochsner,16 J. ODell,100
E. Oelker,10 G. H. Ogin,124 J. J. Oh,125 S. H. Oh,125 F. Ohme,91 M. Oliver,66 P. Oppermann,8Richard J. Oram,6B. OReilly,6
R. OShaughnessy,102 C. D. Ott,76 D. J. Ottaway,104 R. S. Ottens,5H. Overmier,6B. J. Owen,71 A. Pai,108 S. A. Pai,48
J. R. Palamos,59 O. Palashov,109 C. Palomba,28 A. Pal-Singh,27 H. Pan,73 Y. Pan,62 C. Pankow,82 F. Pannarale,91 B. C. Pant,48
F. Paoletti,34,19 A. Paoli,34 M. A. Papa,29,16,8 H. R. Paris,40 W. Parker,6D. Pascucci,36 A. Pasqualetti,34 R. Passaquieti,18,19
D. Passuello,19 B. Patricelli,18,19 Z. Patrick,40 B. L. Pearlstone,36 M. Pedraza,1R. Pedurand,65 L. Pekowsky,35 A. Pele,6
S. Penn,126 A. Perreca,1H. P. Pfeiffer,69,29 M. Phelps,36 O. Piccinni,79,28 M. Pichot,53 M. Pickenpack,8F. Piergiovanni,57,58
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V. Pierro,87 G. Pillant,34 L. Pinard,65 I. M. Pinto,87 M. Pitkin,36 J. H. Poeld,8R. Poggiani,18,19 P. Popolizio,34 A. Post,8
J. Powell,36 J. Prasad,14 V. Predoi,91 S. S. Premachandra,114 T. Prestegard,84 L. R. Price,1M. Prijatelj,34 M. Principe,87
S. Privitera,29 R. Prix,8G. A. Prodi,89,90 L. Prokhorov,49 O. Puncken,8M. Punturo,33 P. Puppo,28 M. Pürrer,29 H. Qi,16
J. Qin,51 V. Quetschke,83 E. A. Quintero,1R. Quitzow-James,59 F. J. Raab,37 D. S. Rabeling,20 H. Radkins,37 P. Raffai,54
S. Raja,48 M. Rakhmanov,83 C. R. Ramet,6P. Rapagnani,79,28 V. Raymond,29 M. Razzano,18,19 V. Re,25 J. Read,22
C. M. Reed,37 T. Regimbau,53 L. Rei,47 S. Reid,50 D. H. Reitze,1,5 H. Rew,120 S. D. Reyes,35 F. Ricci,79,28 K. Riles,98
N. A. Robertson,1,36 R. Robie,36 F. Robinet,23 A. Rocchi,13 L. Rolland,7J. G. Rollins,1V. J. Roma,59 J. D. Romano,83
R. Romano,3,4 G. Romanov,120 J. H. Romie,6D. Rosińska,127,43 S. Rowan,36 A. Rüdiger,8P. Ruggi,34 K. Ryan,37
S. Sachdev,1T. Sadecki,37 L. Sadeghian,16 L. Salconi,34 M. Saleem,108 F. Salemi,8A. Samajdar,123 L. Sammut,85,114
L. M. Sampson,82 E. J. Sanchez,1V. Sandberg,37 B. Sandeen,82 G. H. Sanders,1J. R. Sanders,98,35 B. Sassolas,65
B. S. Sathyaprakash,91 P. R. Saulson,35 O. Sauter,98 R. L. Savage,37 A. Sawadsky,17 P. Schale,59 R. Schilling,8,b J. Schmidt,8
P. Schmidt,1,76 R. Schnabel,27 R. M. S. Schofield,59 A. Schönbeck,27 E. Schreiber,8D. Schuette,8,17 B. F. Schutz,91,29
J. Scott,36 S. M. Scott,20 D. Sellers,6A. S. Sengupta,94 D. Sentenac,34 V. Sequino,25,13 A. Sergeev,109 G. Serna,22
Y. Setyawati,52,9 A. Sevigny,37 D. A. Shaddock,20 T. Shaffer,37 S. Shah,52,9 M. S. Shahriar,82 M. Shaltev,8Z. Shao,1
B. Shapiro,40 P. Shawhan,62 A. Sheperd,16 D. H. Shoemaker,10 D. M. Shoemaker,63 K. Siellez,53,63 X. Siemens,16 D. Sigg,37
A. D. Silva,11 D. Simakov,8A. Singer,1L. P. Singer,68 A. Singh,29,8 R. Singh,2A. Singhal,12 A. M. Sintes,66
B. J. J. Slagmolen,20 J. R. Smith,22 M. R. Smith,1N. D. Smith,1R. J. E. Smith,1E. J. Son,125 B. Sorazu,36 F. Sorrentino,47
T. Souradeep,14 A. K. Srivastava,95 A. Staley,39 M. Steinke,8J. Steinlechner,36 S. Steinlechner,36 D. Steinmeyer,8,17
B. C. Stephens,16 S. P. Stevenson,45 R. Stone,83 K. A. Strain,36 N. Straniero,65 G. Stratta,57,58 N. A. Strauss,78 S. Strigin,49
R. Sturani,121 A. L. Stuver,6T. Z. Summerscales,128 L. Sun,85 P. J. Sutton,91 B. L. Swinkels,34 M. J. Szczepańczyk,97
M. Tacca,30 D. Talukder,59 D. B. Tanner,5M. Tápai,96 S. P. Tarabrin,8A. Taracchini,29 R. Taylor,1T. Theeg,8
M. P. Thirugnanasambandam,1E. G. Thomas,45 M. Thomas,6P. Thomas,37 K. A. Thorne,6K. S. Thorne,76 E. Thrane,114
S. Tiwari,12 V. Tiwari,91 K. V. Tokmakov,107 C. Tomlinson,86 M. Tonelli,18,19 C. V. Torres,83,c C. I. Torrie,1D. Töyrä,45
F. Travasso,32,33 G. Traylor,6D. Trifirò,21 M. C. Tringali,89,90 L. Trozzo,129,19 M. Tse,10 M. Turconi,53 D. Tuyenbayev,83
D. Ugolini,130 C. S. Unnikrishnan,99 A. L. Urban,16 S. A. Usman,35 H. Vahlbruch,17 G. Vajente,1G. Valdes,83
M. Vallisneri,76 N. van Bakel,9M. van Beuzekom,9J. F. J. van den Brand,61,9 C. Van Den Broeck,9D. C. Vander-Hyde,35,22
L. van der Schaaf,9J. V. van Heijningen,9A. A. van Veggel,36 M. Vardaro,41,42 S. Vass,1M. Vasúth,38 R. Vaulin,10
A. Vecchio,45 G. Vedovato,42 J. Veitch,45 P. J. Veitch,104 K. Venkateswara,131 D. Verkindt,7F. Vetrano,57,58 A. Viceré,57,58
S. Vinciguerra,45 D. J. Vine,50 J.-Y. Vinet,53 S. Vitale,10 T. Vo,35 H. Vocca,32,33 C. Vorvick,37 D. Voss,5W. D. Vousden,45
S. P. Vyatchanin,49 A. R. Wade,20 L. E. Wade,132 M. Wade,132 S. J. Waldman,10 M. Walker,2L. Wallace,1S. Walsh,16,8,29
G. Wang,12 H. Wang,45 M. Wang,45 X. Wang,70 Y. Wang,51 H. Ward,36 R. L. Ward,20 J. Warner,37 M. Was,7B. Weaver,37
L.-W. Wei,53 M. Weinert,8A. J. Weinstein,1R. Weiss,10 T. Welborn,6L. Wen,51 P. Weßels,8T. Westphal,8K. Wette,8
J. T. Whelan,102,8 S. E. Whitcomb,1D. J. White,86 B. F. Whiting,5K. Wiesner,8C. Wilkinson,37 P. A. Willems,1L. Williams,5
R. D. Williams,1A. R. Williamson,91 J. L. Willis,133 B. Willke,17,8 M. H. Wimmer,8,17 L. Winkelmann,8W. Winkler,8
C. C. Wipf,1A. G. Wiseman,16 H. Wittel,8,17 G. Woan,36 J. Worden,37 J. L. Wright,36 G. Wu,6J. Yablon,82 I. Yakushin,6
W. Yam,10 H. Yamamoto,1C. C. Yancey,62 M. J. Yap,20 H. Yu,10 M. Yvert,7A. Zadrożny,112 L. Zangrando,42 M. Zanolin,97
J.-P. Zendri,42 M. Zevin,82 F. Zhang,10 L. Zhang,1M. Zhang,120 Y. Zhang,102 C. Zhao,51 M. Zhou,82 Z. Zhou,82 X. J. Zhu,51
M. E. Zucker,1,10 S. E. Zuraw103 and J. Zweizig1
(LIGO Scientific Collaboration and Virgo Collaboration)
1LIGO, California Institute of Technology, Pasadena, California 91125, USA
2Louisiana State University, Baton Rouge, Louisiana 70803, USA
3Università di Salerno, Fisciano, I-84084 Salerno, Italy
4INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
5University of Florida, Gainesville, Florida 32611, USA
6LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
7Laboratoire dAnnecy-le-Vieux de Physique des Particules (LAPP), Université Savoie Mont Blanc, CNRS/IN2P3,
F-74941 Annecy-le-Vieux, France
8Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167 Hannover, Germany
9Nikhef, Science Park, 1098 XG Amsterdam, Netherlands
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10LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
11Instituto Nacional de Pesquisas Espaciais, 12227-010 São José dos Campos, São Paulo, Brazil
12INFN, Gran Sasso Science Institute, I-67100 LAquila, Italy
13INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
14Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
15International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560012, India
16University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
17Leibniz Universität Hannover, D-30167 Hannover, Germany
18Università di Pisa, I-56127 Pisa, Italy
19INFN, Sezione di Pisa, I-56127 Pisa, Italy
20Australian National University, Canberra, Australian Capital Territory 0200, Australia
21The University of Mississippi, University, Mississippi 38677, USA
22California State University Fullerton, Fullerton, California 92831, USA
23LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
24Chennai Mathematical Institute, Chennai, India 603103
25Università di Roma Tor Vergata, I-00133 Roma, Italy
26University of Southampton, Southampton SO17 1BJ, United Kingdom
27Universität Hamburg, D-22761 Hamburg, Germany
28INFN, Sezione di Roma, I-00185 Roma, Italy
29Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-14476 Potsdam-Golm, Germany
30APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cité, F-75205 Paris Cedex 13, France
31Montana State University, Bozeman, Montana 59717, USA
32Università di Perugia, I-06123 Perugia, Italy
33INFN, Sezione di Perugia, I-06123 Perugia, Italy
34European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
35Syracuse University, Syracuse, New York 13244, USA
36SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
37LIGO Hanford Observatory, Richland, Washington 99352, USA
38Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
39Columbia University, New York, New York 10027, USA
40Stanford University, Stanford, California 94305, USA
41Università di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
42INFN, Sezione di Padova, I-35131 Padova, Italy
43CAMK-PAN, 00-716 Warsaw, Poland
44Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
45University of Birmingham, Birmingham B15 2TT, United Kingdom
46Università degli Studi di Genova, I-16146 Genova, Italy
47INFN, Sezione di Genova, I-16146 Genova, Italy
48RRCAT, Indore MP 452013, India
49Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
50SUPA, University of the West of Scotland, Paisley PA1 2BE, United Kingdom
51University of Western Australia, Crawley, Western Australia 6009, Australia
52Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, Netherlands
53Artemis, Université Côte dAzur, CNRS, Observatoire Côte dAzur, CS 34229, Nice cedex 4, France
54MTA Eötvös University, LenduletAstrophysics Research Group, Budapest 1117, Hungary
55Institut de Physique de Rennes, CNRS, Université de Rennes 1, F-35042 Rennes, France
56Washington State University, Pullman, Washington 99164, USA
57Università degli Studi di Urbino Carlo Bo,I-61029 Urbino, Italy
58INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
59University of Oregon, Eugene, Oregon 97403, USA
60Laboratoire Kastler Brossel, UPMC-Sorbonne Universités, CNRS, ENS-PSL Research University, Collège de France,
F-75005 Paris, France
61VU University Amsterdam, 1081 HV Amsterdam, Netherlands
62University of Maryland, College Park, Maryland 20742, USA
63Center for Relativistic Astrophysics and School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
64Institut Lumière Matière, Université de Lyon, Université Claude Bernard Lyon 1, UMR CNRS 5306, 69622 Villeurbanne, France
65Laboratoire des Matériaux Avancés (LMA), IN2P3/CNRS, Université de Lyon, F-69622 Villeurbanne, Lyon, France
66Universitat de les Illes Balears, IAC3IEEC, E-07122 Palma de Mallorca, Spain
67Università di Napoli Federico II,Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
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68NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
69Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario M5S 3H8, Canada
70Tsinghua University, Beijing 100084, China
71Texas Tech University, Lubbock, Texas 79409, USA
72The Pennsylvania State University, University Park, Pennsylvania 16802, USA
73National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
74Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
75University of Chicago, Chicago, Illinois 60637, USA
76Caltech CaRT, Pasadena, California 91125, USA
77Korea Institute of Science and Technology Information, Daejeon 305-806, Korea
78Carleton College, Northfield, Minnesota 55057, USA
79Università di Roma La Sapienza,I-00185 Roma, Italy
80University of Brussels, Brussels 1050, Belgium
81Sonoma State University, Rohnert Park, California 94928, USA
82Northwestern University, Evanston, Illinois 60208, USA
83The University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
84University of Minnesota, Minneapolis, Minnesota 55455, USA
85The University of Melbourne, Parkville, Victoria 3010, Australia
86The University of Sheffield, Sheffield S10 2TN, United Kingdom
87University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
88Montclair State University, Montclair, New Jersey 07043, USA
89Università di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
90INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
91Cardiff University, Cardiff CF24 3AA, United Kingdom
92National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
93School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
94Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
95Institute for Plasma Research, Bhat, Gandhinagar 382428, India
96University of Szeged, Dóm tér 9, Szeged 6720, Hungary
97Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA
98University of Michigan, Ann Arbor, Michigan 48109, USA
99Tata Institute of Fundamental Research, Mumbai 400005, India
100Rutherford Appleton Laboratory, HSIC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
101American University, Washington, D.C. 20016, USA
102Rochester Institute of Technology, Rochester, New York 14623, USA
103University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
104University of Adelaide, Adelaide, South Australia 5005, Australia
105West Virginia University, Morgantown, West Virginia 26506, USA
106University of Białystok, 15-424 Białystok, Poland
107SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
108IISER-TVM, CET Campus, Trivandrum Kerala 695016, India
109Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
110Pusan National University, Busan 609-735, Korea
111Hanyang University, Seoul 133-791, Korea
112NCBJ, 05-400 Świerk-Otwock, Poland
113IM-PAN, 00-956 Warsaw, Poland
114Monash University, Victoria 3800, Australia
115Seoul National University, Seoul 151-742, Korea
116University of Alabama in Huntsville, Huntsville, Alabama 35899, USA
117ESPCI, CNRS, F-75005 Paris, France
118Università di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
119Southern University and A&M College, Baton Rouge, Louisiana 70813, USA
120College of William and Mary, Williamsburg, Virginia 23187, USA
121Instituto de Física Teórica, University Estadual Paulista/ICTP South American Institute for Fundamental Research,
São Paulo SP 01140-070, Brazil
122University of Cambridge, Cambridge CB2 1TN, United Kingdom
123IISER-Kolkata, Mohanpur, West Bengal 741252, India
124Whitman College, 345 Boyer Avenue, Walla Walla, Washington 99362 USA
125National Institute for Mathematical Sciences, Daejeon 305-390, Korea
126Hobart and William Smith Colleges, Geneva, New York 14456, USA
PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending
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127Janusz Gil Institute of Astronomy, University of Zielona Góra, 65-265 Zielona Góra, Poland
128Andrews University, Berrien Springs, Michigan 49104, USA
129Università di Siena, I-53100 Siena, Italy
130Trinity University, San Antonio, Texas 78212, USA
131University of Washington, Seattle, Washington 98195, USA
132Kenyon College, Gambier, Ohio 43022, USA
133Abilene Christian University, Abilene, Texas 79699, USA
aDeceased, April 2012.
bDeceased, May 2015.
cDeceased, March 2015.
PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS week ending
12 FEBRUARY 2016
061102-16
... Gravitational wave detections (Abbott et al. 2016(Abbott et al. , 2019a(Abbott et al. , 2021 have led to new ways of constraining BH spin. Indeed, the gravitational wave signals contain information on the angular momentum of the BHs and their binary. ...
Preprint
Black hole (BH) spin can play an important role in galaxy evolution by controlling the amount of energy and momentum ejected from near the BH into the surroundings. We focus on the magnetically-arrested disk (MAD) state in the sub- and super-Eddington regimes, when the accretion disk is radiatively-inefficient and geometrically-thick, and the system launches strong BH-powered jets. Using a suite of 3D general relativistic magnetohydrodynamic (GRMHD) simulations, we find that for any initial spin, a MAD rapidly spins down the BH to the equilibrium spin of $0 < a_{\rm eq} \lesssim 0.1$, very low compared to $a_{\rm eq} = 1$ for the standard thin luminous (Novikov-Thorne) disks. This implies that rapidly accreting (super-Eddington) BHs fed by MADs tend to lose most of their rotational energy to magnetized relativistic outflows. In a MAD, a BH only needs to accrete $10\%$ of its own mass to spin down from $a=1$ to $a=0.2$. We construct a semi-analytic model of BH spin evolution in MADs by taking into account the torques on the BH due to both the hydrodynamic disk and electromagnetic jet components, and find that the low value of $a_{\rm eq}$ is due to both the jets slowing down the BH rotation and the disk losing a large fraction of its angular momentum to outflows. Our results have crucial implications on how BH spins evolve in active galaxies and other systems such as collapsars, where BH spin-down timescale can be short enough to significantly affect the evolution of BH-powered jets.
... With the completion of their third observing run, the catalogue of gravitational-wave (GW) signals detected by the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO; LIGO Scientific Collaboration et al. 2015) and Advanced Virgo (Acernese et al. 2015) is growing rapidly (The LIGO Scientific Collaboration et al. 2021). These sources include the mergers of binary black holes (BHs) (Abbott et al. 2016), a binary neutron star (NS) (Abbott et al. 2017c,e), and NS-BH binaries (Abbott et al. 2021b). However, compact-object mergers are not the only sources expected to produced detectable GW emission. ...
Article
Full-text available
Low-mass X-ray binaries have long been theorised as potential sources of continuous gravitational-wave radiation, yet there is no observational evidence from recent LIGO/Virgo observing runs. Even for the theoretically ‘loudest’ source, Sco X-1, the upper limit on gravitational-wave strain has been pushed ever lower. Such searches require precise measurements of the source properties for sufficient sensitivity and computational feasibility. Collating over 20 years of high-quality spectroscopic observations of the system, we present a precise and comprehensive ephemeris for Sco X-1 through radial velocity measurements, performing a full homogeneous reanalysis of all relevant datasets and correcting previous analyses. Our Bayesian approach accounts for observational systematics and maximises not only precision, but also the fidelity of uncertainty estimates — crucial for informing principled continuous-wave searches. Our extensive dataset and analysis also enables us to construct the highest signal-to-noise, highest resolution phase-averaged spectrum of a low-mass X-ray binary to date. Doppler tomography reveals intriguing transient structures present in the accretion disk and flow driven by modulation of the accretion rate, necessitating further characterisation of the system at high temporal and spectral resolution. Our ephemeris corrects and supersedes previous ephemerides, and provides a factor three reduction in the number of templates in the search space, facilitating precision searches for continuous gravitational-wave emission from Sco X-1 throughout the upcoming LIGO/Virgo/KAGRA O4 observing run and beyond.
... The dataset [31] we use to train this model is a timeseries dataset that contains gravitational-wave measurements (simulated) from 3 gravitational wave interferometers (LIGO Hanford, LIGO Livingston, and Virgo) in a network. Each time series data contains either of 2 things, detector noise or detector noise with a gravitational wave signal embedded in it. ...
Conference Paper
Full-text available
The recent detections of gravitational waves from merging binary black holes have opened the doors for a new era of multi-messenger astrophysics. Sensitive gravitational wave detectors such as the "Laser Interferometer Gravitational-wave Observatory" (LIGO) are able to observe these signals, therefore confirming the general theory of relativity by Einstein. However, detecting faint gravitational waves (GW) signals remains a major challenge, and quickly training a good model with an enormous training data set is an even bigger challenge. To overcome these challenges, we have proposed a system that uses a cross-system mirrored strategy (distributed learning) to train the model in minimal time. To detect the faintest of the signals, we used 2D CNNs where we converted the 1D time-series data to a 2D spectrum using Fourier Transforms. This was done to extract the maximum possible features. By using distributed learning, we were able to concurrently train local models on different devices and got the final local weights. Then we aggregate all these local weights in a single system and get the final solitary global model. By using this technique of training the model, we were not only able to comfortably manage very large datasets (100s of GBs) but we were also able to finish the model training 4.5 times faster than all the prior state-of-the-art models.
Article
This work presents a novel perfect reconstruction filterbank decomposition (PRFBD) method for nonlinear and non-stationary time-series and image data representation and analysis. The Fourier decomposition method (FDM), an adaptive approach based on Fourier representation (FR), is shown to be a special case of the proposed PRFBD. In addition, adaptive Fourier–Gauss decomposition (FGD) based on FR and Gaussian filters, and adaptive Fourier–Butterworth decomposition (FBD) based on Butterworth filters are developed as the other special cases of the proposed PRFBD method. The proposed theory of PRFBD can decompose any signal (time-series, image, or other data) into a set of desired number of Fourier intrinsic band functions (FIBFs) that follow the amplitude-modulation and frequency-modulation (AM-FM) representations. A generic filterbank representation, where perfect reconstruction can be ensured for any given set of lowpass or highpass filters, is also presented. We performed an extensive analysis on both simulated and real-life data (COVID-19 pandemic, Earthquake and Gravitational waves) to demonstrate the efficacy of the proposed method. The resolution results in the time-frequency representation demonstrate that the proposed method is more promising than the state-of-the-art approaches.
Article
This paper deals with gravitational thermodynamics. The first and second laws of thermodynamics are established in terms of energy density and pressure, which are defined in the scope of Teleparallelism Equivalent to General Relativity (TEGR). Such laws are applied to gravitational waves, in particular the PP-wave. A negative entropy variation for an isothermal process is obtained.
Thesis
The thesis focuses on the noise modelling in pulsar timing data and the search for very-low frequency (from nano-Hz to micro-Hz) gravitational waves with Pulsar Timing Array (PTA). The first chapter gives a general introduction of the subject where I present the scientific context and describethe data analysis methods. I start with the notion of pulsar timing, using a specific example: modelling the timimng data of pulsar J1909-3744, where I also present the updated timing parameters.Then I introduce methodology used in searching for gravitational waves at nano-Hertz with PTA, and conclude with the description of tools used in this thesis to perform data analysis within a Bayesian framework. The second chapter focuses on the single-pulsar noise modelling, applied to six pulsars of the EPTA Data Release 2. In particular, this work highlights the great complexity in the analysis of the PTA data which combine decades of observations of different pulsars from several radio telescopes. The third chapter presents results of the search for a stochastic gravitationalwave background (GWB) in the European Pulsar Timing Array (EPTA) and the International Pulsar Timing Array (IPTA) data with a focus on parts with my direct participation. In particular, I present the impact of the custom single-pulsar noise modelling (given in Chapter 2) on the GWB measurement. The recent results from three PTA collaborations are particularly interesting as they converge on the presence of a common red noise signal across considered pulsars with similar amplitude and spectral index, but without being able to confirm yet its gravitational nature and thus the desired GWB detection. Currently, PTAs are working on extending the data sets by adding the latest observations and including more pulsars into analysis to improve the accuracy and uncover the nature of the observed signal. The fourth and last chapter describes the uncertainties in the Solar System Ephemeris (SSE) and their impact on the PTA results, especially on the GWB measurement. We use SSE provided by Institut de mécanique céleste et de calcul des éphémérides(IMCCE) as a basis to construct the model called EphemGP. We demonstrate that this model is efficient at absorbing systematics in the SSE by introducing variations in the orbital parameters of the main planets of the Solar System. The ability to absorb dipolar correlations induced by SSE uncertainties is very import for the robust detection of the GWB. I compare performance of EphemGP to other existing models, and conclude with the application of this model to the recent EPTA data.
Article
In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of pointlike particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from general relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star–black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies ω≃10−13 eV, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.
Article
In a General Relativistic framework, Gravitational Waves (GW) and Electromagnetic (EM) waves are expected to respond in the same way to the effects of matter perturbations between the emitter and the observer. A different behaviour might be a signature of alternative theories of gravity. In this work we study the cross-correlation of resolved GW events (from compact objects mergers detected by the Einstein Telescope, either assuming or excluding the detection of an EM counterpart) and EM signals (coming both from the Intensity Mapping of the neutral hydrogen distribution and resolved galaxies from the SKA Observatory), considering weak lensing, angular clustering and their cross term (L × C) as observable probes. Cross-correlations of these effects are expected to provide promising information on the behaviour of these two observables, hopefully shedding light on beyond GR signatures. We perform a Fisher matrix analysis with the aim of constraining the { μ 0 , η 0 , Σ 0 } parameters, either opening or keeping fixed the background parameters { w 0 , w a }. We find that, although lensing-only forecasts provide significantly unconstrained results, the combination with angular clustering and the cross-correlation of all three considered tracers (GW, IM, resolved galaxies) leads to interesting and competitive constraints. This offers a novel and alternative path to both multi-tracing opportunities for Cosmology and the Modified Gravity sector.
Article
Pulsar timing offers an independent avenue to test general relativity and alternative gravity theories. This requires an understanding of how metric polarizations beyond the familiar transverse tensor ones imprint as a stochastic gravitational wave background and correlate the arrival time of radio pulses from a pair of millisecond pulsars. In this work, we focus on an isotropic stochastic gravitational wave background and present a straightforward, self-contained formalism for obtaining the power spectrum and the overlap reduction function, the relevant physical observable in a pulsar timing array, for generic gravitational degrees of freedom featuring both transverse and longitudinal modes off the light cone. We additionally highlight our consideration of finite pulsar distances, which we find significant in two ways: first, making all the modes well defined, and second, keeping the small-scale power that is contained by pulsars of subdegree separations in the sky. We discuss this for tensor, vector, and scalar polarizations, for each one focusing on the angular power spectrum and the overlap reduction function for an isotropic stochastic gravitational wave background. Our results pave the road for an efficient numerical method for examining the gravitational wave-induced spatial correlations across millisecond pulsars in a pulsar timing array.
Article
Full-text available
To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries -- binary star systems composed of neutron stars and/or black holes in their late stage of evolution -- require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries -- moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.
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Full-text available
The discovery of the gravitational-wave (GW) source GW150914 with the Advanced LIGO detectors provides the first observational evidence for the existence of binary black hole (BH) systems that inspiral and merge within the age of the universe. Such BH mergers have been predicted in two main types of formation models, involving isolated binaries in galactic fields or dynamical interactions in young and old dense stellar environments. The measured masses robustly demonstrate that relatively "heavy" BHs () can form in nature. This discovery implies relatively weak massive-star winds and thus the formation of GW150914 in an environment with a metallicity lower than about 1/2 of the solar value. The rate of binary-BH (BBH) mergers inferred from the observation of GW150914 is consistent with the higher end of rate predictions ( Gpc−3 yr−1) from both types of formation models. The low measured redshift () of GW150914 and the low inferred metallicity of the stellar progenitor imply either BBH formation in a low-mass galaxy in the local universe and a prompt merger, or formation at high redshift with a time delay between formation and merger of several Gyr. This discovery motivates further studies of binary-BH formation astrophysics. It also has implications for future detections and studies by Advanced LIGO and Advanced Virgo, and GW detectors in space.
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Full-text available
We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 to 20 square degrees will require at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.
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Full-text available
We present a method for detection and reconstruction of the gravitational wave (GW) transients with the networks of advanced detectors. Originally designed to search for the transients with the initial GW detectors, it uses significantly improved algorithms, which enable both the low-latency searches with rapid localization of GW events for the electro-magnetic followup and high confidence detection of a broad range of the transient GW sources. In the paper we present the analytic framework of the method. Following a short description of the core analysis algorithms, we introduce a novel approach to the reconstruction of the GW polarization from a pattern of detector responses to a GW signal. This polarization pattern is a unique signature of an arbitrary GW signal that can be measured independent from the other source parameters. The polarization measurements enable rapid reconstruction of the GW waveforms, sky localization and helps identification of the source origin.
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Full-text available
We present the results of mechanical characterizations of many different high-quality optical coatings made of ion-beam-sputtered titania-doped tantala and silica, developed originally for interferometric gravitational-wave detectors. Our data show that in multi-layer stacks (like high-reflection Bragg mirrors, for example) the measured coating dissipation is systematically higher than the expectation and is correlated with the stress condition in the sample. This has a particular relevance for the noise budget of current advanced gravitational-wave interferometers, and, more generally, for any experiment involving thermal-noise limited optical cavities.
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Full-text available
We compare evolutionary predictions of double compact object merger rate densities with initial and forthcoming LIGO/Virgo upper limits. We find that: (i) Due to the cosmological reach of advanced detectors, current conversion methods of population synthesis predictions into merger rate densities are insufficient. (ii) Our optimistic models are a factor of 18 below the initial LIGO/Virgo upper limits for BH-BH systems, indicating that a modest increase in observational sensitivity (by a factor of 2.5) may bring the first detections or first gravitational wave constraints on binary evolution. (iii) Stellar-origin massive BH-BH mergers should dominate event rates in advanced LIGO/Virgo and can be detected out to redshift z=2 with templates including inspiral, merger, and ringdown. Normal stars (<150 Msun) can produce such mergers with total redshifted mass up to 400 Msun. (iv) High black hole natal kicks can severely limit the formation of massive BH-BH systems (both in isolated binary and in dynamical dense cluster evolution), and thus would eliminate detection of these systems even at full advanced LIGO/Virgo sensitivity. We find that low and high black hole natal kicks are allowed by current observational electromagnetic constraints. (v) The majority of our models yield detections of all types of mergers with advanced detectors. Numerous massive BH-BH merger detections will indicate small (if any) natal kicks for massive BHs. These systems would also shed light on the merger origin, possibly distinguishing mergers arising from field binary evolution (aligned spins) and dense clusters (misaligned spins).
Article
Full-text available
The recent completion of Advanced LIGO suggests that gravitational waves (GWs) may soon be directly observed. Past searches for gravitational-wave transients have been impacted by transient noise artifacts, known as glitches, introduced into LIGO data due to instrumental and environmental effects. In this work, we explore how waveform complexity, instead of signal-to-noise ratio, can be used to rank event candidates and distinguish short duration astrophysical signals from glitches. We test this framework using a new hierarchical pipeline that directly compares the Bayesian evidence of explicit signal and glitch models. The hierarchical pipeline is shown to have strong performance, and in particular, allows high-confidence detections of a range of waveforms at realistic signal-to-noise ratio with a two detector network.
Article
The Advanced LIGO gravitational wave detectors are nearing their design sensitivity and should begin taking meaningful astrophysical data in the fall of 2015. These resonant optical interferometers will have unprecedented sensitivity to the strains caused by passing gravitational waves. The input optics play a significant part in allowing these devices to reach such sensitivities. Residing between the pre-stabilized laser and the main interferometer, the input optics is tasked with preparing the laser beam for interferometry at the sub-attometer level while operating at continuous wave input power levels ranging from 100 mW to 150 W. These extreme operating conditions required every major component to be custom designed. These designs draw heavily on the experience and understanding gained during the operation of Initial LIGO and Enhanced LIGO. In this article we report on how the components of the input optics were designed to meet their stringent requirements and present measurements showing how well they have lived up to their design.
Article
The advanced era of gravitational-wave astronomy, with data collected in part by the LIGO gravitational-wave interferometers, has begun as of fall 2015. One potential type of detectable gravitational waves is short-duration gravitational-wave bursts, whose waveforms can be difficult to predict. We present the framework for a new detection algorithm -- called \textit{oLIB} -- that can be used in relatively low-latency to turn calibrated strain data into a detection significance statement. This pipeline consists of 1) a sine-Gaussian matched-filter trigger generator based on the Q-transform -- known as \textit{Omicron} --, 2) incoherent down-selection of these triggers to the most signal-like set, and 3) a fully coherent analysis of this signal-like set using the Markov chain Monte Carlo (MCMC) Bayesian evidence calculator \textit{LALInferenceBurst} (LIB). These steps effectively compress the full data stream into a set of search statistics for the most signal-like events, and we use elements from information theory to minimize the amount of information regarding the signal-versus-noise hypothesis lost during this compression. We optimally extract this information by using a likelihood-ratio test (LRT) to map these search statistics into a significance statement. Using representative archival LIGO data, we show that the algorithm can detect gravitational-wave burst events of realistic strength in realistic instrumental noise with good detection efficiencies across different burst waveform morphologies. We also demonstrate that the combination of search statistics by means of an LRT can improve the detection efficiency of our search. Finally, we show that oLIB's performance is robust against the choice of gravitational-wave populations used to model the LRT likelihoods.
Article
In this paper we discuss the anatomy of frequency-domain gravitational-wave signals from non-precessing black-hole coalescences with the goal of constructing accurate phenomenological waveform models. We first present new numerical-relativity simulations for mass ratios up to 18 including spins. From a comparison of different post-Newtonian approximants with numerical-relativity data we select the uncalibrated SEOBNRv2 model as the most appropriate for the purpose of constructing hybrid post-Newtonian/numerical-relativity waveforms, and we discuss how we prepare time-domain and frequency-domain hybrid data sets. We then use our data together with results in the literature to calibrate simple explicit expressions for the final spin and radiated energy. Equipped with our prediction for the final state we then develop a simple and accurate merger-ringdown-model based on modified Lorentzians in the gravitational wave amplitude and phase, and we discuss a simple method to represent the low frequency signal augmenting the TaylorF2 post-Newtonian approximant with terms corresponding to higher orders in the post-Newtonian expansion. We finally discuss different options for modelling the small intermediate frequency regime between inspiral and merger-ringdown. A complete phenomenological model based on the present work is presented in a companion paper.