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Scanned, typewritten, or born digital, Cashmere rebuilds every PDF as structured content AI can read, cite, and credit.

How we got here

Your catalog was built for people to find. Now AI has to understand it.

Most publishers hold thousands, often millions, of PDFs, laid down in layers over thirty years. Each layer solved the problem of its day.

1990s

You went digital

The paper archive was scanned into PDFs, one picture per page. The pages survived. What was on them, to software, did not.

Old or new, your PDFs weren't made for AI.

A scan from 1960 and a PDF from last month fail in different ways, but both fail. Getting your corpus ready means more than better OCR: every page has to be rebuilt as a document an AI can navigate, quote, and credit. That is what Cashmere does, for every PDF you hold.

The problem

Not all PDFs are created equal

Whether software can read a PDF depends on how it was made, and the oldest files, often the most valuable in a catalog, are the hardest of all. Here is one equation from each kind, three ways.

1
Hard
Born digital
LIGO 2016 · Kakeya 2025 · Beilstein 2026
The text is real, but it is stored as letters placed on a page, in the font’s own private encoding. Fractions fall apart, = becomes ¼, and a two-column page reads straight across both columns.
The page
What the PDF's own text says
```
M ¼ ðm1m2Þ3=5 ðm1 þ m2Þ1=5 ¼ c3 G 5 96 π−8=3f−11=3 _f 3=5 ;
```
Text layer: present, scrambled
What the omnipub says
$M = \frac{( m _{1} m _{2} ) ^{3/5}}{( m _{1} + m _{2} ) ^{1/5}} = \frac{c ^{3}}{G} [\frac{5}{96} π^{- 8/3} f^{- 11/3} f ˙]^{3/5},$
LIGO, 2016, page 3
2
Harder
Scanned print
Einstein 1905 · NACA 1953
A photograph of a printed page. The only text is an OCR layer added later, which reads ordinary words and gives up on everything else: equations, tables, and symbols.
The page
What the PDF's own text says
```
= 
Ot 
Or 
9: 
oder 
let.
```
OCR layer: fragments
What the omnipub says
$\frac{1}{2} (\frac{1}{V - v} + \frac{1}{V + v}) \frac{\partial τ}{\partial t} = \frac{\partial τ}{\partial x ^{'}} + \frac{1}{V - v} \frac{\partial τ}{\partial t},$
$\frac{\partial τ}{\partial x ^{'}} + \frac{v}{V ^{2} - v ^{2}} \frac{\partial τ}{\partial t} = 0.$
Einstein, 1905, page 9
3
Hardest
Typewritten originals
NASA TN D-233, Katherine Johnson, 1960
Typed, copied, and scanned from the copy. Uneven strikes, stamps, and margin notes, and Greek letters the OCR never learned: every λ, ω, and θ below is lost or misread.
The page
What the PDF's own text says
```
2_i_2e = (h2 + r_oET) + _E[t(e2e) -t(el)] - h I
```
OCR layer: symbols lost
What the omnipub says
$Δ λ_{1 - 2 e} = (λ_{2} + n ω_{E} T) + ω_{E} [t (θ_{2 e}) - t (θ_{1})] - λ_{1}$
NASA TN D-233, 1960, page 20

Why it matters

AI can only use what it can read.

A paper that fails ingestion is invisible: it can’t be searched, retrieved, cited, or licensed.

Wrong is worse than missing.

A misread number in a table or a garbled equation doesn’t look broken to an AI. It gets quoted, confidently.

The back catalog is the hard part.

Decades of scanned journals, reports, and books hold a publisher’s most distinctive content, and they are the nastiest PDFs of all.

How it works

From a page of ink to a document AI can use

One page of Katherine Johnson’s 1960 NASA paper, all the way through Cashmere. Every picture below is the real page and the real output.

STEP 01
Start with a PDF
A PDF records where ink goes on a page. To software, this page is a picture: the equations aren't text at all, and its OCR layer reads them as noise.
STEP 02
Read the page like a person
The Pro parser finds the structure a reader sees: which marks are a heading, a paragraph, an equation, a table, or a figure, and the order they're read in.
heading26
paragraph235
equation84
table11
figure13
list item24
787 blocks in the whole paper
STEP 03
Make every piece a block
Each piece becomes an omnipub block with a type and a stable address, so it can be searched, quoted, cited, and licensed on its own. Equations become real math.
Contents
1. SUMMARY3
2. INTRODUCTION4
3. SYMBOLS102
4. SATELLITE POSITION RELATIONSHIPS5
5. EXPRESSION FOR PLACING A SATELLITE OVER A SELECTEDPOSITION27
6. APPENDIX B1
7. EQUATIONS FOR CALCULATING AZIMUTH ANGLE, OBLATENESS EFFECTS,AND SATELLITE POSITION AND ILLUSTRATIVE EXAMPLES1
8. Azimuth Angle9
9. Oblateness Effects6
10. Satellite Position
11. Illustrative Examples of Orbit Calculations
28 sections · 787 blocks · 7,545 words · 13,716 tokens
STEP 04
Assemble the whole paper
The blocks are put back together as the paper itself: sections inside sections, in reading order, each with its own address. The result is one document an AI can navigate and measure, from its table of contents down to a single equation.

{
  "path": "dete/expr/ab/equa/azim/m1",
  "type": "math",
  "alttext": "[t(\\theta_{2e}) - t(\\theta_1)] \\approx \\frac{T}{360} (\\lambda_{2e} - \\lambda_1)",
  "fingerprint": "sha256:a73139c4833c122…",
  "section": "Azimuth Angle",
  "origin": {
    "page": 20,
    "region": [
      235.5,
      491.4,
      368.8,
      510.1
    ]
  }
}

STEP 05

Keep the link to the page

Every block remembers where it sat on the original page. An answer can cite the exact equation it used, and anyone can check it against the source.

Pick a paper below to see every page and every block side by side.

Why Cashmere

Parsed isn’t the same as AI-ready

Plenty of tools can pull text out of a PDF. An AI needs more: what each piece is, where it belongs, where it came from, and what it may be used for. That is the work Cashmere does, on the files other pipelines give up on.

Right on the hard pages

Layout, text, math, and tables are read from the page image itself, not from the broken text layer, so a 1905 scan comes out as clean as a 2025 preprint.

Structured like the work

Headings, sections, and reading order are kept, and every block gets a stable address. An AI can find the right passage instead of guessing from a wall of text.

Traceable to the source

Every block keeps its place on the original page. An answer can cite the exact paragraph or equation it used, and anyone can check it.

Licensed and measured

Rights travel with the content, and use is counted block by block, so you know what AI systems read and you get paid for it.

6 papers, 335 pages, from a 1905 scan to a 2025 preprint, converted by one pipeline with no hand corrections. Bring us your hardest PDFs.

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See for yourself

Six real papers. Open any one.

Each opens full screen: the original PDF on the left, the omnipub beside it, and the data behind any block you click.

Converted by Cashmere’s Pro parser, November 2026, and shown without hand corrections.

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Observation of Gravitational Waves from a Binary Black Hole Merger

Scanned PDF

page 1 / 16

Page 1 of 16 of the scanned original of Observation of Gravitational Waves from a Binary Black Hole Merger

OmnipubClick any block to see its data

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 $1.0 \times 1 0^{- 21}$ . 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 $5.1 σ$ . The source lies at a luminosity distance of $41 0_{- 180}^{+ 160}$ Mpc corresponding to a redshift $z = 0.0 9_{- 0.04}^{+ 0.03}$ . In the source frame, the initial black hole masses are $3 6_{- 4}^{+ 5} M_{⊙}$ and $2 9_{- 4}^{+ 4} M_{⊙}$ , and the final black hole mass is $6 2_{- 4}^{+ 4} M_{⊙}$ , with $3. 0_{- 0.5}^{+ 0.5} M_{⊙} c^{2}$ 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.

DOI: 10.1103/PhysRevLett.116.061102

I. INTRODUCTION

In 1916, the year after the final formulation of the field equations of general relativity, Albert Einstein predicted the existence of gravitational waves. He found that the linearized weak-field equations had wave solutions: transverse waves of spatial strain that travel at the speed of light, generated by time variations of the mass quadrupole moment of the source [1,2]. Einstein understood that gravitational-wave amplitudes would be remarkably small; moreover, until the Chapel Hill conference in 1957 there was significant debate about the physical reality of gravitational waves [3].

Also in 1916, Schwarzschild published a solution for the field equations [4] that was later understood to describe a black hole [5,6], and in 1963 Kerr generalized the solution to rotating black holes [7]. Starting in the 1970s theoretical work led to the understanding of black hole quasinormal modes [8–10], and in the 1990s higher-order post-Newtonian calculations [11] preceded extensive analytical studies of relativistic two-body dynamics [12,13]. These advances, together with numerical relativity breakthroughs in the past decade [14–16], have enabled modeling of binary black hole mergers and accurate predictions of their gravitational waveforms. While numerous black hole candidates have now been identified through electromagnetic observations [17–19], black hole mergers have not previously been observed.

The discovery of the binary pulsar system PSR B1913+16 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 resonant detectors [24]. Interferometric detectors were first suggested in the early 1960s [25] and the 1970s [26]. A study of the noise and performance of such detectors [27], and further concepts to improve them [28], led to proposals for long-baseline broadband laser interferometers with the potential for significantly increased sensitivity [29–32]. By the early 2000s, a set of initial detectors was completed, including TAMA 300 in Japan, GEO 600 in Germany, the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States, and Virgo in Italy. Combinations of these detectors made joint observations from 2002 through 2011, setting upper limits on a variety of gravitational-wave sources while evolving into a global network. In 2015, Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations [33–36].

A century after the fundamental predictions of Einstein and Schwarzschild, we report the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging to form a single black hole. Our observations provide unique access to the

*Full author list given at the end of the article.

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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 compact binary waveforms [44] recovered GW150914 as the most significant event from each detector for the observations reported here. Occurring within the 10-ms intersite

A 3x2 grid of plots comparing H1 and L1 data. The top row shows observed strain, the middle row shows numerical relativity and wavelet/template reconstructions, and the bottom row shows residuals. The bottom row also includes a 2D heatmap of normalized amplitude vs frequency and time.

Hanford, Washington (H1)

Livingston, Louisiana (L1)

Strain ( $1 0^{- 21}$ )

Frequency (Hz)

Time (s)

Normalized amplitude

The figure displays strain data for two detectors, Hanford (H1) and Livingston (L1), over a time range of approximately 0.25 to 0.45 seconds. The top row shows the observed strain in red (H1) and blue (L1), with the L1 data also shown shifted and inverted in orange. The middle row shows the strain from numerical relativity (red) and its reconstructions using wavelet (light gray) and template (dark gray) methods. The bottom row shows the residual strain (red for H1, blue for L1). The bottom row also includes a 2D heatmap of normalized amplitude (0 to 8) as a function of frequency (32 to 512 Hz) and time (0.30 to 0.45 s). A color bar on the right indicates the normalized amplitude scale.

Legend:

H1 observed
L1 observed
H1 observed (shifted, inverted)
Numerical relativity
Reconstructed (wavelet)
Reconstructed (template)
Residual

Color Bar: Normalized amplitude, 0 to 8

Detector	Time (s)	Frequency (Hz)	Normalized Amplitude
H1	0.40	128	~6
L1	0.40	128	~4

A 3x2 grid of plots comparing H1 and L1 data. The top row shows observed strain, the middle row shows numerical relativity and wavelet/template reconstructions, and the bottom row shows residuals. The bottom row also includes a 2D heatmap of normalized amplitude vs frequency and time.

FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series are filtered with a 35–350 Hz bandpass filter to suppress large fluctuations outside the detectors’ most sensitive frequency band, and band-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 strain. GW150914 arrived first at L1 and $6. 9_{- 0.4}^{+ 0.5}$ 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.

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 $600 deg^{2}$ (90% credible region) [39,46].

The basic features of GW150914 point to it being produced by the coalescence of two black holes—i.e., their orbital inspiral and merger, and subsequent final black hole ringdown. Over 0.2 s, the signal increases in frequency and amplitude in about 8 cycles from 35 to 150 Hz, where the amplitude reaches a maximum. The most plausible explanation for this evolution is the inspiral of two orbiting masses, $m_{1}$ and $m_{2}$ , due to gravitational-wave emission. At the lower frequencies, such evolution is characterized by the chirp mass [11]

M = \frac{( m _{1} m _{2} ) ^{3/5}}{( m _{1} + m _{2} ) ^{1/5}} = \frac{c ^{3}}{G} [\frac{5}{96} π^{- 8/3} f^{- 11/3} f ˙]^{3/5},

where $f$ and $f ˙$ are the observed frequency and its time derivative and $G$ and $c$ are the gravitational constant and speed of light. Estimating $f$ and $f ˙$ from the data in Fig. 1, we obtain a chirp mass of $M ≃ 30 M_{⊙}$ , implying that the total mass $M = m_{1} + m_{2}$ is $≳ 70 M_{⊙}$ in the detector frame. This bounds the sum of the Schwarzschild radii of the binary components to $2 GM / c^{2} ≳ 210 km$ . To reach an orbital frequency of 75 Hz (half the gravitational-wave frequency) the objects must have been very close and very compact; equal Newtonian point masses orbiting at this frequency would be only $≃ 350 km$ apart. A pair of neutron stars, while compact, would not have the required mass, while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency. This leaves black holes as the only known objects compact enough to reach an orbital frequency of 75 Hz without contact. Furthermore, the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration. Below, we present a general-relativistic analysis of GW150914; Fig. 2 shows the calculated waveform using the resulting source parameters.

III. DETECTORS

Gravitational-wave astronomy exploits multiple, widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise, to provide source sky localization, and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO

Multi-panel chart: Gravitational wave strain and black hole separation/velocity over time.

The figure consists of two panels sharing a common x-axis representing Time (s) from 0.30 to 0.45.

Top Panel: Shows the Strain ( $1 0^{- 21}$ ) on the y-axis, ranging from -1.0 to 1.0. The strain oscillates with increasing amplitude during the inspiral and merger phases, and then damps out during the ring-down phase. Two curves are shown: a red line for 'Numerical relativity' and a grey line for 'Reconstructed (template)'. Above the plot, diagrams illustrate the orbital evolution of two black holes through the inspiral, merger, and ring-down stages.

Bottom Panel: Shows the Velocity ( $c$ ) on the left y-axis, ranging from 0.3 to 0.6, and the Separation ( $R_{S}$ ) on the right y-axis, ranging from 0 to 4. Two curves are shown: a black line for 'Black hole separation' and a green line for 'Black hole relative velocity'. The separation decreases while the relative velocity increases over time.

Approximate data points from the bottom panel

Time (s)	Black hole separation ( $R_{S}$ )	Black hole relative velocity ( $c$ )
0.30	~3.5	~0.33
0.35	~3.0	~0.35
0.40	~2.5	~1.5
0.42	~1.0	~2.5

Legend:

Numerical relativity
Reconstructed (template)
Black hole separation
Black hole relative velocity

Phases: Inspiral, Merger, Ring-down

Axes:

Top panel y: Strain ( $1 0^{- 21}$ )
Bottom panel left y: Velocity ( $c$ )
Bottom panel right y: Separation ( $R_{S}$ )

Multi-panel chart: Gravitational wave strain and black hole separation/velocity over time.

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 ( $R_{s} = 2 GM / c^{2}$ ) and the effective relative velocity given by the post-Newtonian parameter $v / c = (GM π f / c^{3})^{1/3}$ , where $f$ is the gravitational-wave frequency calculated with numerical relativity and $M$ is the total mass (value from Table I).

detector [33], a modified Michelson interferometer (see Fig. 3) that measures gravitational-wave strain as a difference in length of its orthogonal arms. Each arm is formed by two mirrors, acting as test masses, separated by $L_{x} = L_{y} = L = 4 km$ . A passing gravitational wave effectively alters the arm lengths such that the measured difference is $Δ L (t) = δ L_{x} - δ L_{y} = h (t) L$ , 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 transmissive power-recycling mirror at the input provides additional 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

Scientific illustration: Schematic of a gravitational wave detector setup and strain noise spectrum.

(a) Schematic of the detector setup. A laser source (20 W) is shown on the left. The beam is recycled and split into two paths. The vertical path ( $L_{y} = 4$ km) has two test masses. The horizontal path ( $L_{x} = 4$ km) has two test masses and circulates 100 kW of power. The signal is recycled and detected by a photodetector. An inset shows the location of the detector in the US with a 10 ms light travel time between H1 and L1.

(b) Strain noise ( $Hz^{- 1/2}$ ) vs Frequency (Hz) for H1 (red) and L1 (blue). The noise is lowest around 100 Hz and increases at higher frequencies.

Schematic Diagram:

Laser Source: 20 W
Power Recycling
Beam Splitter
Test Mass (Vertical Path)
Test Mass (Horizontal Path)
Signal Recycling
Photodetector
$L_{y} = 4$ km
$L_{x} = 4$ km
100 kW Circulating Power

Strain Noise Spectrum:

Frequency (Hz)	H1 ( $Hz^{- 1/2}$ )	L1 ( $Hz^{- 1/2}$ )
20	$1 0^{- 22}$	$1 0^{- 22}$
100	$1 0^{- 23}$	$1 0^{- 23}$
1000	$1 0^{- 22}$	$1 0^{- 22}$

Scientific illustration: Schematic of a gravitational wave detector setup and strain noise spectrum.

FIG. 3. Simplified diagram of an Advanced LIGO detector (not to scale). A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave; these length changes are reversed during the other half-cycle. The output photodetector records these differential cavity length variations. While a detector's directional response is maximal for this case, it is still significant for most other angles of incidence or polarizations (gravitational waves propagate freely through the Earth). Inset (a): Location and orientation of the LIGO detectors at Hanford, WA (H1) and Livingston, LA (L1). Inset (b): The instrument noise for each detector near the time of the signal detection; this is an amplitude spectral density, expressed in terms of equivalent gravitational-wave strain amplitude. The sensitivity is limited by photon shot noise at frequencies above 150 Hz, and by a superposition of other noise sources at lower frequencies [47]. Narrow-band features include calibration lines (33–38, 330, and 1080 Hz), vibrational modes of suspension fibers (500 Hz and harmonics), and 60 Hz electric power grid harmonics.

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 maximize 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 frequencies above 10 Hz. Thermal noise is minimized by using low-mechanical-loss materials in the test masses and their

suspensions: the test masses are 40-kg fused silica substrates with low-loss dielectric optical coatings [58,59], and are suspended with fused silica fibers from the stage above [60].

To minimize additional noise sources, all components other than the laser source are mounted on vibration isolation stages in ultrahigh vacuum. To reduce optical phase fluctuations caused by Rayleigh scattering, the pressure in the 1.2-m diameter tubes containing the arm-cavity beams is maintained below $1 μ Pa$ .

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 ( $1 σ$ ) 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

[64]. Additionally, the detector response to gravitational waves is tested by injecting simulated waveforms with the calibration laser.

To monitor environmental disturbances and their influence 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 $\sim 1 0^{5}$ channels record the interferometer's operating point and the state of the control systems. Data collection is synchronized to Global Positioning System (GPS) time to better than $10 μ s$ [66]. Timing accuracy is verified with an atomic clock and a secondary GPS receiver at each observatory site.

In their most sensitive band, 100–300 Hz, the current LIGO detectors are 3 to 5 times more sensitive to strain than initial LIGO [67]; at lower frequencies, the improvement is even greater, with more than ten times better sensitivity below 60 Hz. Because the detectors respond proportionally to gravitational-wave amplitude, at low redshift the volume of space to which they are sensitive increases as the cube of strain sensitivity. For binary black holes with masses similar to GW150914, the space-time volume surveyed by the observations reported here surpasses previous observations 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 environmental disturbances were performed, giving no evidence to suggest that GW150914 could be an instrumental artifact [69]. The detectors' susceptibility to environmental disturbances was quantified by measuring their response to specially 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 environmental 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 mechanisms. Many have distinct signatures, visible in auxiliary data channels that are not sensitive to gravitational waves; such instrumental transients are removed from our analyses [69]. Any instrumental transients that remain in the data are accounted for in the estimated detector backgrounds

described below. There is no evidence for instrumental transients that are temporally correlated between the two detectors.

V. SEARCHES

We present the analysis of 16 days of coincident observations between the two LIGO detectors from September 12 to October 20, 2015. This is a subset of the data from Advanced LIGO's first observational period that ended on January 12, 2016.

GW150914 is confidently detected by two different types of searches. One aims to recover signals from the coalescence of compact objects, using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals, with minimal assumptions about waveforms. These searches use independent methods, and their response to detector noise consists of different, uncorrelated, events. However, strong signals from binary black hole mergers are expected to be detected by both searches.

Each search identifies candidate events that are detected at both observatories consistent with the intersite propagation time. Events are assigned a detection-statistic value that ranks their likelihood of being a gravitational-wave signal. The significance of a candidate event is determined by the search background—the rate at which detector noise produces events with a detection-statistic value equal to or higher than the candidate event. Estimating this background is challenging for two reasons: the detector noise is nonstationary and non-Gaussian, so its properties must be empirically determined; and it is not possible to shield the detector from gravitational waves to directly measure a signal-free background. The specific procedure used to estimate the background is slightly different for the two searches, but both use a time-shift technique: the time stamps of one detector's data are artificially shifted by an offset that is large compared to the intersite propagation time, and a new set of events is produced based on this time-shifted data set. For instrumental noise that is uncorrelated 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 different 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

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 $η_{c} = 2 E_{c} / (1 + E_{n} / E_{c})$ , where $E_{c}$ is the dimensionless coherent signal energy obtained by cross-correlating the two reconstructed waveforms, and $E_{n}$ is the dimensionless residual noise energy after the reconstructed signal is subtracted from the data. The statistic $η_{c}$ thus quantifies the SNR of the event and the consistency of the data between the two detectors.

Based on their time-frequency morphology, the events are divided into three mutually exclusive search classes, as described in [41]: events with time-frequency morphology of known populations of noise transients (class C1), events with frequency that increases with time (class C3), and all remaining events (class C2).

Detected with $η_{c} = 20.0$ , GW150914 is the strongest event of the entire search. Consistent with its coalescence signal signature, it is found in the search class C3 of events with increasing time-frequency evolution. Measured on a background equivalent to over 67 400 years of data and including a trials factor of 3 to account for the search classes, its false alarm rate is lower than 1 in 22 500 years. This corresponds to a probability $< 2 \times 1 0^{- 6}$ of observing one or more noise events as strong as GW150914 during the analysis time, equivalent to $4.6 σ$ . The left panel of Fig. 4 shows the C3 class results and background.

The selection criteria that define the search class C3 reduce the background by introducing a constraint on the signal morphology. In order to illustrate the significance of GW150914 against a background of events with arbitrary shapes, we also show the results of a search that uses the same set of events as the one described above but without this constraint. Specifically, we use only two search classes: the C1 class and the union of C2 and C3 classes (C2 + C3). In this two-class search the GW150914 event is found in the C2 + C3 class. The left panel of Fig. 4 shows the C2 + C3 class results and background. In the background of this class there are four events with $η_{c} \geq 32.1$ , yielding a false alarm rate for GW150914 of 1 in 8 400 years. This corresponds to a false alarm probability of $5 \times 1 0^{- 6}$ equivalent to $4.4 σ$ .

Generic transient search

Binary coalescence search

Number of events

Detection statistic $η_{c}$

Detection statistic $ρ^_{c}$

Search Result (C3)

Search Background (C3)

Search Result (C2+C3)

Search Background (C2+C3)

Background excluding GW150914

GW150914

$2 σ$ $3 σ$ $4 σ$ $4.4 σ$ $4.4 σ$

$2 σ$ $3 σ$ $4 σ$ $4.6 σ$ $> 4.6 σ$

$2 σ$ $3 σ$ $4 σ$ $5.1 σ$ $> 5.1 σ$

The left panel shows the generic transient search results. The y-axis is logarithmic from $1 0^{- 8}$ to $1 0^{2}$ . The x-axis is the detection statistic $η_{c}$ from 8 to 32. The search result (C3) is shown as a red step line, and the search background (C3) is a black step line. The search result (C2+C3) is a green step line, and the search background (C2+C3) is a green step line. The background excluding GW150914 is a purple step line. GW150914 is marked at $η_{c} \approx 20$ .

The right panel shows the binary coalescence search results. The y-axis is logarithmic from $1 0^{- 8}$ to $1 0^{2}$ . The x-axis is the detection statistic $ρ^_{c}$ from 8 to 24. The search result is a red step line, and the search background is a black step line. The background excluding GW150914 is a purple step line. GW150914 is marked at $ρ^_{c} \approx 23.5$ .

Both panels show a significant decrease in the number of events as the detection statistic increases, with GW150914 being a notable outlier.

Multi-panel chart: Comparison of generic transient search and binary coalescence search detection statistics.

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 $5.1 σ$ and $4.6 σ$ for the binary coalescence and the generic transient searches, respectively. Left: Along with the primary search (C3) we also show the results (blue markers) and background (green curve) for an alternative search that treats events independently of their frequency evolution (C2 + C3). The classes C2 and C3 are defined in the text. Right: The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914 in one detector with noise in the other detector. (This type of event is practically absent in the generic transient search background because they do not pass the time-frequency consistency requirements used in that search.) The purple curve is the background excluding those coincidences, which is used to assess the significance of the second strongest event.

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 $99 M_{⊙}$ , total mass less than $100 M_{⊙}$ , and dimensionless spins up to 0.99 [44]. To model systems with total mass larger than $4 M_{⊙}$ , 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 waveforms are used to cover this parameter space.

The search calculates the matched-filter signal-to-noise ratio $ρ (t)$ for each template in each detector and identifies maxima of $ρ (t)$ with respect to the time of arrival of the signal [79–81]. For each maximum we calculate a chi-squared statistic $χ_{r}^{2}$ to test whether the data in several different frequency bands are consistent with the matching template [82]. Values of $χ_{r}^{2}$ near unity indicate that the signal is consistent with a coalescence. If $χ_{r}^{2}$ is greater than unity, $ρ (t)$ is reweighted as $ρ^= ρ / {[1 + (χ_{r}^{2})^{3}] /2}^{1/6}$ [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 $ρ^_{c}$ of the $ρ^$ from both detectors [45].

To produce background data for this search the SNR maxima of one detector are time shifted and a new set of coincident events is computed. Repeating this procedure $\sim 1 0^{7}$ times produces a noise background analysis time equivalent to 608 000 years.

To account for the search background noise varying across the target signal space, candidate and background events are divided into three search classes based on template length. The right panel of Fig. 4 shows the background for the search class of GW150914. The GW150914 detection-statistic value of $ρ^_{c} = 23.6$ is larger than any background event, so only an upper bound can be placed on its false alarm rate. Across the three search classes this bound is 1 in 203 000 years. This translates to a false alarm probability $< 2 \times 1 0^{- 7}$ , corresponding to $5.1 σ$ .

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.

TABLE I. Source parameters for GW150914. We report median values with 90% credible intervals that include statistical errors, and systematic errors from averaging the results of different waveform models. Masses are given in the source frame; to convert to the detector frame multiply by $(1 + z)$ [90]. The source redshift assumes standard cosmology [91].

Primary black hole mass	$3 6_{- 4}^{+ 5} M_{⊙}$
Secondary black hole mass	$2 9_{- 4}^{+ 4} M_{⊙}$
Final black hole mass	$6 2_{- 4}^{+ 4} M_{⊙}$
Final black hole spin	$0.6 7_{- 0.07}^{+ 0.05}$
Luminosity distance	$41 0_{- 180}^{+ 160}$ Mpc
Source redshift $z$	$0.0 9_{- 0.04}^{+ 0.03}$

When an event is confidently identified as a real gravitational-wave signal, as for GW150914, the background used to determine the significance of other events is reestimated without the contribution of this event. This is the background distribution shown as a purple line in the right panel of Fig. 4. Based on this, the second most significant event has a false alarm rate of 1 per 2.3 years and corresponding Poissonian false alarm probability of 0.02. Waveform analysis of this event indicates that if it is astrophysical in origin it is also a binary black hole merger [44].

VI. SOURCE DISCUSSION

The matched-filter search is optimized for detecting signals, but it provides only approximate estimates of the source parameters. To refine them we use general relativity-based models [77,78,87,88], some of which include spin precession, and for each model perform a coherent Bayesian analysis to derive posterior distributions of the source parameters [89]. The initial and final masses, final spin, distance, and redshift of the source are shown in Table I. The spin of the primary black hole is constrained to be $< 0.7$ (90% credible interval) indicating it is not maximally spinning, while the spin of the secondary is only weakly constrained. These source parameters are discussed in detail in [39]. The parameter uncertainties include statistical errors and systematic errors from averaging the results of different waveform models.

Using the fits to numerical simulations of binary black hole mergers in [92,93], we provide estimates of the mass and spin of the final black hole, the total energy radiated in gravitational waves, and the peak gravitational-wave luminosity [39]. The estimated total energy radiated in gravitational waves is $3. 0_{- 0.5}^{+ 0.5} M_{⊙} c^{2}$ . The system reached a peak gravitational-wave luminosity of $3. 6_{- 0.4}^{+ 0.5} \times 1 0^{56}$ erg/s, equivalent to $20 0_{- 20}^{+ 30} M_{⊙} c^{2} / s$ .

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

consistency check involves the mass and spin of the final black hole. In general relativity, the end product of a black hole binary coalescence is a Kerr black hole, which is fully described by its mass and spin. For quasicircular inspirals, these are predicted uniquely by Einstein's equations as a function of the masses and spins of the two progenitor black holes. Using fitting formulas calibrated to numerical relativity simulations [92], we verified that the remnant mass and spin deduced from the early stage of the coalescence and those inferred independently from the late stage are consistent with each other, with no evidence for disagreement from general relativity.

Within the post-Newtonian formalism, the phase of the gravitational waveform during the inspiral can be expressed as a power series in $f^{1/3}$ . The coefficients of this expansion can be computed in general relativity. Thus, we can test for consistency with general relativity [95,96] by allowing the coefficients to deviate from the nominal values, and seeing if the resulting waveform is consistent with the data. In this second check [94] we place constraints on these deviations, finding no evidence for violations of general relativity.

Finally, assuming a modified dispersion relation for gravitational waves [97], our observations constrain the Compton wavelength of the graviton to be $λ_{g} > 1 0^{13}$ km, which could be interpreted as a bound on the graviton mass $m_{g} < 1.2 \times 1 0^{- 22}$ eV/ $c^{2}$ . 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 $\approx 25 M_{⊙}$ , and establishes that binary black holes can form in nature and merge within a Hubble time. Binary black holes have been predicted to form both in isolated binaries [102–104] and in dense environments by dynamical interactions [105–107]. The formation of such massive black holes from stellar evolution requires weak massive-star winds, which are possible in stellar environments with metallicity lower than $\approx 1/2$ the solar value [108,109]. Further astrophysical implications of this binary black hole discovery are discussed in [110].

These observational results constrain the rate of stellar-mass binary black hole mergers in the local universe. Using several different models of the underlying binary black hole mass distribution, we obtain rate estimates ranging from $2 - 400$ Gpc^-3 yr^-1 in the comoving frame [111–113]. This is consistent with a broad range of rate predictions as reviewed in [114], with only the lowest event rates being excluded.

Binary black hole systems at larger distances contribute to a stochastic background of gravitational waves from the superposition of unresolved systems. Predictions for such a background are presented in [115]. If the signal from such a

population were detected, it would provide information about the evolution of such binary systems over the history of the universe.

VII. OUTLOOK

Further details about these results and associated data releases are available at [116]. Analysis results for the entire first observational period will be reported in future publications. Efforts are under way to enhance significantly the global gravitational-wave detector network [117]. These include further commissioning of the Advanced LIGO detectors to reach design sensitivity, which will allow detection of binaries like GW150914 with 3 times higher SNR. Additionally, Advanced Virgo, KAGRA, and a possible third LIGO detector in India [118] will extend the network and significantly improve the position reconstruction and parameter estimation of sources.

VIII. CONCLUSION

The LIGO detectors have observed gravitational waves from the merger of two stellar-mass black holes. The detected waveform matches the predictions of general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck Society (MPS), and the State of Niedersachsen, Germany, for support of the construction of Advanced LIGO and construction and operation of the GEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS), and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector, and for the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), India, Ministry of Human Resource Development, India, the Spanish Ministerio de Economía y Competitividad, the Conselleria d'Economia i Competitivitat and Conselleria d'Educació, Cultura i

Universitats of the Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Sciences and Engineering Research Council of Canada, Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Russian Foundation for Basic Research, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen, Germany, for provision of computational resources. This article has been assigned the document numbers LIGO-P150914 and VIR-0015A-16.

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Meadors,^29,8 J. Meidam,⁹ A. Melatos,⁸⁵ G. Mendell,³⁷ D. Mendoza-Gandara,⁸ R. A. Mercer,¹⁶ E. Merilh,³⁷ M. Merzougui,⁵³ S. Meshkov,¹ C. 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,⁵ R. 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,⁸ B. Mours,⁷ C. M. Mow-Lowry,⁴⁵ C. L. Mueller,⁵ G. Mueller,⁵ A. 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,⁵ I. 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,⁸ S. Nissanke,^52,9 A. Nitz,⁸ F. Nocera,³⁴ D. Nolting,⁶ M. E. N. Normandin,⁸³ L. K. Nuttall,³⁵ J. Oberling,³⁷ E. Ochsner,¹⁶ J. O'Dell,¹⁰⁰ E. Oelker,¹⁰ G. H. Ogin,¹²⁴ J. J. Oh,¹²⁵ S. H. Oh,¹²⁵ F. Ohme,⁹¹ M. Oliver,⁶⁶ P. Oppermann,⁸ Richard J. Oram,⁶ B. O'Reilly,⁶ R. O'Shaughnessy,¹⁰² C. D. Ott,⁷⁶ D. J. Ottaway,¹⁰⁴ R. S. Ottens,⁵ H. Overmier,⁶ B. 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,⁶ D. Pascucci,³⁶ A. Pasqualetti,³⁴ R. Passaquietti,^18,19 D. Passuello,¹⁹ B. Patricelli,^18,19 Z. Patrick,⁴⁰ B. L. Pearlstone,³⁶ M. Pedraza,¹ R. Pedurand,⁶⁵ L. Pekowsky,³⁵ A. Pele,⁶ S. Penn,¹²⁶ A. Perreca,¹ H. P. Pfeiffer,^69,29 M. Phelps,³⁶ O. Piccinni,^79,28 M. Pichot,⁵³ M. Pickenpack,⁸ F. Piergiovanni,^57,58

V. Pierro,⁸⁷ G. Pillant,³⁴ L. Pinard,⁶⁵ I. M. Pinto,⁸⁷ M. Pitkin,³⁶ J. H. Poeld,⁸ R. 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,¹ M. Prijatelj,³⁴ M. Principe,⁸⁷ S. Privitera,²⁹ R. Prix,⁸ G. A. Prodi,^89,90 L. Prokhorov,⁴⁹ O. Puncken,⁸ M. Punturo,³³ P. Puppo,²⁸ M. Pürrer,²⁹ H. Qi,¹⁶ J. Qin,⁵¹ V. Quetschke,⁸³ E. A. Quintero,¹ R. 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,⁶ P. 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,⁷ J. G. Rollins,¹ V. J. Roma,⁵⁹ J. D. Romano,⁸³ R. Romano,^3,4 G. Romanov,¹²⁰ J. H. Romie,⁶ D. Rosińska,^127,43 S. Rowan,³⁶ A. Rüdiger,⁸ P. Ruggi,³⁴ K. Ryan,³⁷ S. Sachdev,¹ T. Sadecki,³⁷ L. Sadeghian,¹⁶ L. Salconi,³⁴ M. Saleem,¹⁰⁸ F. Salemi,⁸ A. Samajdar,¹²³ L. Sammut,^85,114 L. M. Sampson,⁸² E. J. Sanchez,¹ V. Sandberg,³⁷ B. Sandeen,⁸² G. H. Sanders,¹ J. 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,⁸ D. Schuette,^8,17 B. F. Schutz,^91,29 J. Scott,³⁶ S. M. Scott,²⁰ D. Sellers,⁶ A. 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,⁸ Z. 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,⁸ A. Singer,¹ L. P. Singer,⁶⁸ A. Singh,^29,8 R. Singh,² A. Singhal,¹² A. M. Sintes,⁶⁶ B. J. J. Slagmolen,²⁰ J. R. Smith,²² M. R. Smith,¹ N. D. Smith,¹ R. J. E. Smith,¹ E. J. Son,¹²⁵ B. Sorazu,³⁶ F. Sorrentino,⁴⁷ T. Souradeep,¹⁴ A. K. Srivastava,⁹⁵ A. Staley,³⁹ M. Steinke,⁸ J. 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,⁶ T. 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,⁵ M. Tápai,⁹⁶ S. P. Tarabrin,⁸ A. Taracchini,²⁹ R. Taylor,¹ T. Theeg,⁸ M. P. Thirugnanasambandam,¹ E. G. Thomas,⁴⁵ M. Thomas,⁶ P. Thomas,³⁷ K. A. Thorne,⁶ K. 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,¹ D. Töyrä,⁴⁵ F. Travasso,^32,33 G. Traylor,⁶ D. 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,¹ G. Valdes,⁸³ M. Vallisneri,⁷⁶ N. van Bakel,⁹ M. van Beuzekom,⁹ J. F. J. van den Brand,^61,9 C. Van Den Broeck,⁹ D. C. Vander-Hyde,^35,22 L. van der Schaaf,⁹ J. V. van Heijningen,⁹ A. A. van Veggel,³⁶ M. Vardaro,^41,42 S. Vass,¹ M. Vasúth,³⁸ R. Vaulin,¹⁰ A. Vecchio,⁴⁵ G. Vedovato,⁴² J. Veitch,⁴⁵ P. J. Veitch,¹⁰⁴ K. Venkateswara,¹³¹ D. Verkindt,⁷ F. 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,⁵ W. D. Vousden,⁴⁵ S. P. Vyatchanin,⁴⁹ A. R. Wade,²⁰ L. E. Wade,¹³² M. Wade,¹³² S. J. Waldman,¹⁰ M. Walker,² L. Wallace,¹ S. 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,⁷ B. Weaver,³⁷ L.-W. Wei,⁵³ M. Weinert,⁸ A. J. Weinstein,¹ R. Weiss,¹⁰ T. Welborn,⁶ L. Wen,⁵¹ P. Weßels,⁸ T. Westphal,⁸ K. Wette,⁸ J. T. Whelan,^102,8 S. E. Whitcomb,¹ D. J. White,⁸⁶ B. F. Whiting,⁵ K. Wiesner,⁸ C. Wilkinson,³⁷ P. A. Willems,¹ L. Williams,⁵ R. D. Williams,¹ A. R. Williamson,⁹¹ J. L. Willis,¹³³ B. Willke,^17,8 M. H. Wimmer,^8,17 L. Winkelmann,⁸ W. Winkler,⁸ C. C. Wipf,¹ A. G. Wiseman,¹⁶ H. Wittel,^8,17 G. Woan,³⁶ J. Worden,³⁷ J. L. Wright,³⁶ G. Wu,⁶ J. Yablon,⁸² I. Yakushin,⁶ W. Yam,¹⁰ H. Yamamoto,¹ C. C. Yancey,⁶² M. J. Yap,²⁰ H. Yu,¹⁰ M. Yvert,⁷ A. Zadrožny,¹¹² L. Zangrando,⁴² M. Zanolin,⁹⁷ J.-P. Zendri,⁴² M. Zevin,⁸² F. Zhang,¹⁰ L. Zhang,¹ M. 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. Zuraw,¹⁰³ 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 d'Annecy-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

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 L'Aquila, 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 d'Azur, CNRS, Observatoire Côte d'Azur, CS 34229, Nice cedex 4, France
⁵⁴MTA Eötvös University, "Lendulet" Astrophysics 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, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
⁶⁷Università di Napoli "Federico II," Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy

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 Biał ystok, 15-424 Biał ystok, 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

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.

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