Observation of GravitationalWaves from a Binary Black Hole Merger

The LIGO Scientific Collaboration and The Virgo Collaboration

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitationalwave

Observatory (LIGO) simultaneously observed a transient gravitational-wave signal. The signal

sweeps upwards in frequency from 35 Hz to 250 Hz with a peak gravitational-wave strain of 1:0 _ 10���21.

It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes

and the ringdown of the resulting single black hole. The signal was observed with a matched filter signalto-

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 _. The source lies at a luminosity distance of 410+160

���180 Mpc corresponding

to a redshift z = 0:09+0:03

���0:04. In the source frame, the initial black hole masses are 36+5

���4M_ and 29+4

���4M_,

and the final black hole mass is 62+4

���4M_, with 3:0+0:5

���0:5M_c2 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.

PACS numbers: 04.80.Nn, 04.25.dg, 95.85.Sz, 97.80.-d

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

从一个黑洞的合并gravitationalwaves观察

LIGO科学合作和处女座的合作

在09:50:45 UTC两探测器的激光干涉引力波2015年9月14日

 

天文台（LIGO）同时观察到一个短暂的引力波信号。信号

把以上的频率从35赫兹到250赫兹以1:0 _ 10���21峰引力波应变。

 

它与波形的灵感和一对广义相对论所预言的黑洞合并

 

和由此产生的单一黑洞的响铃。一个匹配滤波器的信号，观察信号—

 

噪音之比为24和假警报率估计为小于1事件每000 203年，相当于

 

一个意义大于5:1 _。源位于160 + 410的亮度距离

���180 MPC相应

一个红移z = + 0:03 0:09

���0:04。在源框架，初始黑洞群众36 + 5

���4m_和29 + 4

���4m_，

而最终黑洞质量为62±4

���4m_，以3:0 + 0:5

���0:5m_c2辐射引力波。所有不确定因素

定义90%可信区间。这些观察表明存在的二进制恒星质量

黑洞系统。这是第一个直接探测引力波和第一个观察的

 

二元黑洞合并。

PACS编号：04.80.nn，04.25.dg，95.85.sz，D 97.80。

介绍-在1916，年后的最后制定

广义相对论的场方程，爱因斯坦艾伯特

预测引力波的存在。他

发现线性化的弱场方程有波

解决方案：横向波的空间应变，旅行

光的速度，所产生的时间变化的质量

四极矩的来源[ 1，2 ]。爱因斯坦明白

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]. In the

past decade these analytical advances, together with breakthroughs

in numerical relativity [14–16], have enabled accurate

simulations of binary black hole mergers. 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],

这种引力波的振幅将非常明显

小；而且，直到教堂山会议在

1957关于物理现实的重大辩论

引力波[ 3 ]。

在1916出版的，史瓦西解

场方程[ 4 ]，后来被理解为描述

黑洞[ 5，6 ]，并在1963克尔广义的解决方案

旋转黑洞[ 7 ]。从20世纪70年代开始的理论

工作导致黑洞似的理解

模式[ 8，10 ]，并在20世纪90年代高阶—

牛顿计算[ 11 ]之前广泛的分析

相对论双体动力学研究[ 12，13 ]。在

过去的十年中，这些分析的进步，与突破

在数值相对论[ 14，16 ]，使精确

二元黑洞合并的模拟。而

现在已经确定了许多黑洞候选

通过电磁观测[ 17，19 ]，黑洞

合并以前没有被观察到。

双星系统的发现

PSR b1913 + 16哈尔斯和泰勒[ 20 ]和随后的

泰勒对其能量损失的观测

韦斯伯格[ 21 ]证明引力的存在

波。这一发现，随着新兴天体物理学

理解[ 22 ]，导致认识到直接观察

引力波的振幅和相位

将使额外的相对论系统的研究和

提供新的广义相对论，特别是在

动力强场。

探测引力波的实验开始了

在20世纪60年代，韦伯和他的共振质谱检测器[ 23 ]，

其次是一个国际低温共振网络

探测器[ 24 ]。干涉探测器

建议在20世纪60年代初[ 25 ]和20世纪70年代[ 26 ]。一

这种探测器的噪声和性能的研究[ 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 TAMA300 in Japan, GEO600 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 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.

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, 45] recovered

GW150914 as the most significant event from each detector

for the observations reported here. Occuring within the

10 ms inter-site propagation time, the events have a combined

signal-to-noise ratio (SNR) of 24.

LIGO-P150914-v13

和进一步的概念，以提高他们[ 28 ]，导致建议

长基线宽带激光干涉仪

潜在的显着增加的敏感性[ 29，32 ]。

在本世纪初，一组初始探测器完成，

包括在日本的TAMA300，GEO600在德国，

激光干涉引力波天文台

（LIGO）在美国，意大利和处女座。

这些探测器的组合进行联合观测

从2002到2011，设定上限

引力波的来源，同时发展成为一个全球性的

网络。2015高级LIGO成为第一

先进探测器的更灵敏的网络

开始观察[ 33，36 ]。

一个世纪后，爱因斯坦的基本预测

和史瓦西，我们报告的第一个直接的检测

引力波和二元的直接观测

黑洞系统合并形成一个黑洞。

我们的观察提供了独特的访问属性

在强场，高速度的制度和

确定非线性广义相对论的预测

高度不安的黑洞动力学。

在09:50:45 UTC 2015年9月14日观测

LIGO汉福德，WA，和利文斯顿，La，天文台

检测到的信号gw150914表现一致

图1。初始检测是由低延迟

搜索一般的引力波瞬变[ 41 ]和

据报道，三分钟内的数据采集[ 43 ]。

随后，匹配滤波器的分析，使用相对论

紧凑的二进制波形模型[ 44，45 ]恢复

gw150914从每个探测器的最重大的事件

这里的观测报告。发生在

10毫秒站点间的传播时间，事件有一个组合

信噪比（信噪比）为24。

ligo-p150914-v13

-1.0

-0.5

0.0

0.5

1.0

H1 observed

L1 observed

H1 observed (shifted, inverted)

Hanford, Washington (H1) Livingston, Louisiana (L1)

-1.0

-0.5

0.0

0.5

1.0

Strain (10 21)

Numerical relativity

Reconstructed (wavelet)

Reconstructed (template)

Numerical relativity

Reconstructed (wavelet)

Reconstructed (template)

-0.5

0.0

0.5

Residual Residual

0.30 0.35 0.40 0.45

Time (s)

32

64

128

256

512

Frequency (Hz)

0.30 0.35 0.40 0.45

•1

•0.5

零

零点五

一

H1的观察

L1观察

H1观察（移，倒）

恒福利文斯顿，华盛顿（H1），路易斯安那（L1）

•1

•0.5

零

零点五

一

应变（21 - 10）

数值相对论

重构（小波）

重构（模板）

数值相对论

重构（小波）

重构（模板）

•0.5

零

零点五

残留残留

0.35 0.40 0.45 0.30

时间（秒）

三十二

六十四

一百二十八

二百五十六

五百一十二

频率（赫兹）

0.35 0.40 0.45 0.30

Time (s)

0

2

4

6

8

Normalized amplitude

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 band-pass 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+0:5

���0:4 ms later at H1; for a visual comparison the H1 data are also shown, shifted in

time by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected

onto each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent

with those recovered from GW150914 [37, 38] confirmed to 99.9% by an independent calculation based on [15]. Shaded areas show

90% 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.

Only the LIGO detectors were observing at the time of

GW150914. The Virgo detector was being upgraded, and

时间（秒）

零

二

四

六

八

归一化振幅

图1。通过LIGO汉福德观测引力波事件gw150914（H1，左柱板）和利文斯顿（L1，

右栏面板）探测器。时间是相对于2015年9月14日在09:50:45 UTC。用于可视化，所有时间序列

被过滤的35个350赫兹的带通滤波器，以抑制大的波动以外的探测器的最敏感的频段，和

带阻滤波器，以消除在图3谱图中所见的强谱线。后排，左：H1菌株。顶排，右边：

L1菌株。gw150914先到达了L1和9 + 0:5

���0:4 MS后来在H1；一个视觉比较的数据也显示，在转移

时间通过这个量和反转（以帐户的探测器的相对方向）。第二行：引力波应变投影

在35至350赫兹波段上的每个探测器。固体线显示一个参数一致的系统的数值相对性波形

与那些从gw150914 [ 38 ] 37恢复，证实99.9%基于[ 15 ]独立计算。阴影区域显示

独立波形重建的90%个可信区域。一个（暗灰色）模型的信号，使用二进制黑洞

模板波形[ 39 ]。其他（浅灰色）不使用物理模型，而计算应变信号为线性

正弦-高斯小波的组合[ 40，41 ]。这些重建有94%个重叠，如图39所示。第三行：残差

减去滤波后的数值相对论波形的滤波检测器的时间序列。底部行：时频

表示[ 42 ]的应变数据，示出的信号频率随着时间的推移而增加。

只有LIGO探测器观测时

gw150914。处女座的探测器正在升级

 

GEO600, though not sensitive enough to have detected 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 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

2

LIGO-P150914-v13

0.30 0.35 0.40 0.45

Time (s)

0.3

0.4

0.5

0.6

Velocity (c)

Black hole separation

Black hole relative velocity

0

1

2

3

4

Separation (RS)

-1.0

-0.5

0.0

0.5

1.0

GEO600，虽然没有检测到足够的敏感

事件，正在运行，但不是在观察模式。随着

只有2个探测器的源位置主要是确定

相对到达时间和局部区域

约600 deg2（90%可信区间）[ 39，46 ]。

对gw150914点的基本特征，它产生

由两个黑洞���即聚结，他们

轨道inspiral和合并，以及随后的最后的黑洞

振铃。在0:2的频率信号的增加

和幅度在约8个周期从35到150赫兹的地方

振幅达到最大值。最可信的解释

这种演变是两轨道的灵感

二

ligo-p150914-v13

0.35 0.40 0.45 0.30

时间（秒）

零点三

零点四

零点五

零点六

速度（丙）

黑洞分离

黑洞相对速度

零

一

二

三

四

分离（卢比）

•1

•0.5

零

零点五

一

Strain (10 21)

Inspiral Merger Ringdown

Numerical relativity

Reconstructed (template)

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 (RS = 2GM=c2) and the effective relative velocity given

by the post-Newtonian parameter v=c = (GM_f=c3)1=3, where

f is the gravitational-wave frequency calculated with numerical

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

masses, m1 and m2, due to gravitational-wave emission.

At the lower frequencies, such evolution is characterized

by the chirp mass [47]

M=

(m1m2)3=5

(m1 + m2)1=5 =

c3

G

_

5

96

_���8=3f���11=3f_

_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 ofM' 30M_, implying that the

total mass M = m1 + m2 is >_

70M_ in the detector

应变（21 - 10）

灵感合并振铃

数值相对论

重构（模板）

图2。顶：估计引力波振幅

从gw150914投射到H1。这显示了全带宽

的波形，没有用于图1的过滤。

嵌入图像显示黑色的数值相对论模型

孔的视野为黑洞合并。底部：开普勒

在史瓦西黑洞的单位有效分离

半径（RS = 2GM = C2）和有效相对速度给定

采用后牛顿参数V = C =（gm_f = 1 = 3，其中C3）

用数值计算的引力波频率

相对和我是总的质量（从表我的价值）。

群众，M1和M2，由于引力波辐射。

在较低的频率，这样的演变特征

由线性调频质量[ 47 ]

米=

（m2）3 = 5

（M1 + M2）1 = 5 =

C3

G

_

五

九十六

_���8 = 11 = 3f_ 3F���

_3 = 5

；

其中F和f_是所观察到的频率和时间

衍生工具和克和碳是引力常数和

光的速度。从图1中的数据估计F和f_

我们得到一个线性调频质量间的30m_，暗示

总质量M = M1 + M2 > _

在探测器70m_

frame. This bounds the sum of the Schwarzschild radii of

the binary components to 2GM=c2 >_

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.

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

difference in length of its orthogonal arms. Each arm is

formed by two mirrors, acting as test masses, separated by

Lx = Ly = L = 4 km. A passing gravitational wave effectively

alters the arm lengths such that the measured difference

is _L(t) = _Lx ��� _Ly = 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 beamsplitter,

transmitting an optical signal proportional to the

帧。这个边界的史瓦西半径的总和

以绿肥= C2＞_二进制组件

210公里。到达

75赫兹（半引力波的一半的轨道频率

频率）的对象必须是非常接近和非常

在这个频率下绕轨道运行的紧凑型

将只“350公里外。一对中子

星星，虽然致密，不会有所需的质量，

黑洞中子星双星与推导出

线性调频质量将有一个非常大的总质量，并将

因此，合并在低得多的频率。这片树叶黑色

孔作为唯一已知的对象，结构紧凑，足以达到

没有接触的75赫兹的轨道频率。此外，

波形峰后的衰减是一致的

随着阻尼振荡的黑洞放松

到最后静止的克尔配置。下面，我们提出

一个gw150914广义相对论分析；如图2所示。

使用所得的源参数计算出的波形。

探测引力波天文学利用多个，

广泛分离的探测器来区分引力

波从当地的仪器和环境噪声，到

天空提供源定位，并测量波的极化。

LIGO网站每运行一个单一的先进

LIGO探测器[ 33 ]，一种改进的迈克尔逊干涉仪

（见图3），测量引力波的应变

正交臂长度差。每只手臂

由双反射镜形成的，作为测试群众，由

LX =，= L = 4公里。有效地传递引力波

改变臂的长度，使得测量的差异

是_l（t）= _lx���_ly = h（t），其中h是

将引力波应变振幅投射到探测器上。

这种差分长度的变化，改变相位差

两光场回到分束器之间，

发送光信号与所

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 [49]. Second, a partially

transmissive power-recycling mirror at the input provides

additional resonant buildup of the laser light in the interferometer

as a whole [50, 51]: 20Wof laser input is increased

to 700W incident on the beamsplitter, which is further increased

to 100kW circulating in each arm cavity. Third,

a partially transmissive signal-recycling mirror at the output

optimizes the gravitational-wave signal extraction by

broadening the bandwidth of the arm cavities [52, 53].

The interferometer is illuminated with a 1064-nm wavelength

Nd:YAG laser, stabilized in amplitude, frequency,

and beam geometry [54, 55]. The gravitational-wave signal

is extracted at the output port using homodyne readout

[56].

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

(mid frequencies). Each test mass is suspended as the final

stage of a quadruple pendulum system [57], supported by

an active seismic isolation platform [58]. These systems

collectively provide more than 10 orders of magnitude of

isolation from ground motion for frequencies above 10 Hz.

3

LIGO-P150914-v13

引力波对输出光探测器的应变。

要达到足够的灵敏度来测量重力

波的探测器包括几个增强功能

基本迈克尔逊干涉仪。首先，每个手臂包含

由其双测试质量反射镜形成的谐振腔，

乘一个引力波的影响

光相位由300个因子[ 49 ]。其次，部分

透射功率回收镜在输入提供

干涉仪中激光的附加共振积累

作为一个整体的[ 50，51 ]：20wof激光输入增加

到700W事件的分束器，这是进一步增加

100kW级臂各腔循环。第三，

一部分透射镜在输出信号的循环

优化了引力波信号的提取

扩大臂腔的带宽[ 52，53 ]。

该干涉仪被照亮的1064纳米的波长

Nd：YAG激光，稳定的幅度、频率，

和梁几何[ 54，55 ]。引力波信号

在使用零差读出输出端口提取

[ 56 ]。

这些干涉技术的设计，以最大限度地提高

应变对光信号的转换，从而最大限度地减少

光子散粒噪声的影响（主要噪声

在高频率）。高应变灵敏度也要求

测试质量低的位移噪声，这

是通过将它们与地震噪声隔离（低频率）来实现的

设计低噪声的热噪声

（中频）。每一个测试质量被作为最终的中止

一个四级倒立摆系统的阶段[ 57 ]，支持

一种主动隔震平台[ 58 ]。这些系统

集体提供超过10个数量级

从地面运动的频率超过10赫兹的隔离。

三

ligo-p150914-v13

Photodetector

Beam

Splitter

Power

Recycling

Laser

Source

100 kW Circulating Power

b)

a)

Signal

Recycling

Test

Mass

Test

Mass

Test

Mass

Test

Mass

Lx = 4 km

20 W

H1

L1

10 ms light

travel time

Ly = 4 km

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

光电探测器

梁

分束器

功率

回收

激光

源

100千瓦循环发电

乙）

一）

信号

回收

测试

质量

测试

质量

测试

质量

测试

质量

LX = 4公里

20瓦特

H1

L1

10毫秒的光

旅行时间

= 4公里

图3。一种先进的LIGO探测器简化图（不按比例）。引力波垂直于探测器

平行于4公里的光学谐振腔平面和线性偏振的效果会有延长和缩短4公里的手臂

在一个周期的一半周期的波，这些长度的变化是相反的，在另一个半周期。输出光探测器记录

这些差分腔长度的变化。而检测器的定向响应是最大的

 

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 [48]. Narrowband features include calibration lines (33 – 38 Hz, 330 Hz, and 1080 Hz), vibrational modes of suspension

fibers (500 Hz and harmonics), and 60 Hz electric power grid harmonics.

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 [59, 60], and are suspended with

fused silica fibers from the stage above [61].

To minimize additional noise sources, all components

other than the laser source are mounted on vibration isolation

stages in ultra-high 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 _Pa.

Servo controls are used to hold the arm cavities on resonance

[62] and maintain proper alignment of the optical

components [63]. 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 [64]. The calibration is established to an uncertainty

(1_) 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

这种情况下，它仍然是最重要的

入射偏振角或其他（引力波的传播自由通过地球）。插图：位置和方向

在汉福德LIGO探测器，洼（H1）和利文斯顿，La（L1）。插入B：每个探测器附近的时候仪器噪声

的信号检测；这是一个幅度谱密度，表示在等效的引力波振幅。

的灵敏度是有限的光子散粒噪声在150赫兹以上的频率，并通过在较低的其他噪声源的叠加

频率[ 48 ]。窄带功能包括校准线（33至38赫兹，330赫兹，1080赫兹），振动模式的悬挂

光纤（500赫兹和谐波），和60赫兹电力网谐波。

热噪声最小化，使用低机械损耗

在试验质量和悬浮物中的材料：试验

质量为40千克的低损耗介电石英基片

光学薄膜[ 59，60 ]，并被暂停

熔融石英纤维从舞台上[ 61 ]。

为了减少额外的噪声源，所有组件

除了激光光源被安装在隔振

超高真空期。减少光学相位

由瑞利散射引起的波动，压力

光束包含臂腔1.2米直径的管

保持在1 _pa。

伺服控制是用来保持手臂上的谐振腔

[ 62 ]并保持适当的光学对准

组件[ 63 ]。检测器输出被校准

应变测量其响应测试质量运动引起的

由调校的光子压力

激光束[ 64 ]。校准是建立的不确定性

（1_）小于10%的振幅和10度

在相，并连续监测与校准

在选定频率的激光激发。替代

方法用于验证绝对校准，一

引用到主激光波长和另一个

radio-frequency oscillator [65]. 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

[66]. Another _ 105 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 _s [67]. Timing accuracy

is verified with an atomic clock and a secondary GPS receiver

at each observatory site.

4

LIGO-P150914-v13

In their most sensitive band, 100 – 300 Hz, the current

LIGO detectors are 3 to 5 times more sensitive to strain

than initial LIGO [68]; 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 [69].

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 [70].

Exhaustive investigations of instrumental and environmental

disturbances were performed, giving no evidence

射频振荡器[ 65 ]。此外，检测器

模拟引力波的响应进行了测试

校准激光波形。

监测环境干扰及其影响

在探测器上，每个天文台的网站都配备了

一系列的传感器：地震仪、加速度计，

麦克风、磁强计、收音机、天气

传感器，交流电源线监测，和一个宇宙射线探测器

[ 66 ]。另一个_ 105通道记录干涉仪

操作点和控制系统的状态。

数据采集是同步的全球定位系统

（GPS）的时间比10 _s [ 67 ]。定时精度

用原子钟和一个二级全球定位系统验证

在每个天文台的网站。

四

ligo-p150914-v13

在他们最敏感的波段，100，300赫兹，电流

LIGO探测器是3至5倍，更敏感的应变

比初始LIGO [ 68 ]；在较低的频率，改善

甚至更大，具有十倍以上的敏感性

低于60赫兹。因为探测器按比例响应

引力波振幅，在低红移

他们敏感的空间体积增大

作为应变灵敏度的多维数据集。对于二进制黑洞

群众类似gw150914，时空量调查

据报道，这里的观测结果超过了以前的

观测的数量级[ 69 ]。

探测器验证-这两个探测器处于稳定状态

在gw150914几小时的手术。所有性能

措施，特别是他们的平均敏感性和

瞬态噪声特性，是典型的全分析

期[ 70 ]。

仪器和环境的详尽调查

干扰进行，没有证据

to suggest that GW150914 could be an instrumental artifact

[70]. 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 [70]. 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.

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

建议gw150914可以辅助器

[ 70 ]。探测器对环境的敏感性

通过测量其响应的干扰进行量化

特别是产生磁性，射频，声学，

振动激励。这些测试表明，任何

外部干扰大，足以引起所观察到的

信号将被清楚地记录在阵列

环境传感器。没有环境

传感器记录任何干扰，发展的时间和

像gw150914频率，和所有的环境波动

包含gw150914进行中的第二

过小的帐户超过6%的应变幅度。

特别小心被带到寻找远程

相关的干扰，可能产生几乎同时

在这两家网站的信号。无重大干扰

被发现。

检测器应变数据表现出非高斯噪声瞬变

从各种各样的工具机制中出现。

许多有明显的签名，可见于辅助

对引力不敏感的数据通道

波；这样的仪器瞬变从我们的

分析[ 70 ]。任何保持在

数据是在估计的检测器的背景

下面描述。没有任何证据的工具

时间相关的瞬态

双检测器。

搜索-我们提出了16天的分析一致

观察两个LIGO探测器之间

9月12日至2015年10月20日。这是一个子集

从先进的LIGO的第一观察期数据

2016年1月12日结束。

gw150914是由两个不同的自信的检测

搜索类型。一个目标，以恢复信号从

紧致对象的聚结，利用最佳匹配滤波

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 inter-site 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 non-stationary 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 timestamps

of one detector’s data are artificially shifted by an

offset that is large compared to the inter-site 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

用广义相对论预测的波形。这个

其他搜索目标是一个广泛的通用瞬态信号，

关于波形的最小假设。这些

搜索使用独立的方法，以及它们的响应

检测器噪声由不同的，不相关的，事件。

然而，强大的信号，从二进制黑洞合并

预计将检测到这两个搜索。

每个搜索标识被检测到的候选事件

在观测站点间传输的一致性

时间。事件被分配一个检测统计值

这一行列的可能性是一个引力波信号。

一个候选事件的意义是由

搜索背景，在该速率的检测器噪声

产生事件的检测统计值等于

或高于候选人的事件。估计这个背景

是具有挑战性的两点原因：探测器噪声

是非平稳和非高斯，所以它的属性必须

凭经验确定，这是不可能的

引力波探测器直接测量

无信号背景。具体的程序

估计的背景是稍微不同的

搜索，但使用时移技术：时间戳

一个探测器的数据被人为地改变了

偏移量大的相比，站点间的传播

时间，和一组新的事件产生的基础上，这

时间偏移数据集。对于仪器噪声是不相关的

这是一种有效的方法来估计

背景。在这个过程中，一个引力波

在一个检测器的信号可能与时间偏移噪声

在其他检测器中的瞬变，从而有助于

背景估计。这会导致高估

噪音背景，因此更保守的评估

候选事件的意义。

非高斯噪声的特性各不相同

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].

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 multi-detector maximum likelihood method.

Each event is ranked according to the detection statistic

_c =

p

2Ec=(1 + En=Ec), where Ec is the dimensionless

coherent signal energy obtained by cross-correlating

the two reconstructed waveforms, and En is the dimensionless

residual noise energy after the reconstructed signal is

5

LIGO-P150914-v13

2x 3x 4x 4.4x 4.4x

2x 3x 4x 4.6x > 4.6x

8 10 12 14 16 18 20 >32

Detection statistic mc

10−8

10−7

10−6

不同时频区域。这意味着

在信号的空间中搜索背景并不一致

被搜查。为了最大限度地提高灵敏度和提供

更好地估计事件的意义，搜索排序两个

他们的背景估计和他们的事件候选人

不同类别的时频形态。

一个候选事件的意义

反对其阶级的背景。为有

搜索多个类，这个意义是减少了

一个实验因子等于71的数目。

通用的瞬态搜索-设计为操作而不

一个特定的波形模型，该搜索确定重合

在时频表示中的多余的功率

检测器应变数据[ 72，43 ]，用于信号频率

1千赫和持续时间长达几秒钟。

搜索重建信号波形一致

用一个共同的引力波信号在两个探测器

使用多检测器最大似然法。

每一个事件都是按检测统计排名

_c =

P

2ec =（1 + EN = EC，EC）是无量纲

交叉相关的相干信号能量

重建的波形，以及连接是无量纲的

重建后的信号是残余噪声能量

五

ligo-p150914-v13

2X 3X 4X 4.4x 4.4倍

2X 3X 4X 4.6倍> 4.6倍

10 12 14 16 18 20 32

检测统计

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

102

Number of events

−/ /

GW150914

Generic transient search

Search Result (C3)

Search Background (C3)

Search Result (C2+C3)

Search Background (C2+C3)

2x 3x 4x 5.1x > 5.1x

2x 3x 4x 5.1x > 5.1x

8 10 12 14 16 18 20 22 24

Detection statistic ˆvc

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

100

101

102

Number of events

GW150914

Binary coalescence search

10−5

10−4

10−3

10−2

10−1

一百

一百零一

一百零二

事件数

−/ /

gw150914

通用暂态搜索

搜索结果（C3）

研究背景（C3）

搜索结果（C2 + C3）

研究背景（C2 + C3）

2X 3X 4X 5.1倍> 5.1倍

2X 3X 4X 5.1倍> 5.1倍

10 12 14 16 18 20 22 24 8

检测统计ˆVC

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

一百

一百零一

一百零二

事件数

gw150914

二元聚结

Search Result

Search Background

Background excluding GW150914

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 _ and 4:6 _ 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 blackline

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.

subtracted from the data. The statistic _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 _c = 20:0, GW150914 is the strongest

搜索结果

搜索背景

背景gw150914除外

图4。搜索结果从通用的瞬态搜索（左）和二元聚结搜索（右）。这些直方图显示

在搜索类中的候选事件（橙色标记）和背景事件的平均数（黑线）

 

gw150914发现作为一个搜索检测统计功能以0:2 bin宽度。上面的鳞片给了

一种基于相应噪声背景的高斯标准偏差事件的意义。gw150914的意义

 

大于5:1 _和4:6 _为二进制聚结和一般的瞬时搜索，分别。左：随着

 

元搜索引擎（C3）我们也显示结果（蓝色标记）和背景（绿色曲线）寻找替代治疗事件

独立的频率演变（C2 + C3）。类C2和C3在文本的定义。右：在黑色的尾巴

的二进制搜索的背景是一个检测器，并对gw150914随机的巧合由于与其他噪声

探测器。（这种类型的事件实际上是不存在的，在一般的瞬态搜索背景，因为他们不通过时频

一致性要求用于搜索。）紫色曲线的背景排除巧合，这是用来评估

 

第二个最强事件的意义。

从数据中减去。统计_c从而量化

事件信噪比与数据的一致性

双检测器。

基于它们的时频形态学特征

分为三个相互排斥的搜索类，作为

描述在[ 41 ]：事件与时间-频率形态

已知的瞬态噪声的人群（C1类）；事件

频率随时间增加（C3）；和

剩余的事件（C2类）。

与_c = 20:0的检测，gw150914是最强的

event of the entire search. Consistent with its coalescence

signal signature, it is found in the search class C3 of events

with increasing time-frequency evolution. Measured on a

background equivalent to over 67 400 years of data and including

a trials factor of 3 to account for the search classes,

its false alarm rate is lower than 1 in 22 500 years. This

corresponds to a probability < 2 _ 10���6 of observing one

or more noise events as strong as GW150914 during the

analysis time, equivalent to 4:6 _. 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 _c _ 32:1, yielding a false

alarm rate for GW150914 of 1 in 8 400 years. This corresponds

to a false alarm probability of 5 _ 10���6 equivalent

to 4:4 _.

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.

Binary coalescence search — This search targets

gravitational-wave emission from binary systems with individual

masses from 1M_ to 99M_, total mass less than

100M_ and dimensionless spins up to 0.99 [45]. To

model systems with total mass larger than 4M_, we use

事件的整个搜索。与它的合并

信号，它是在事件的搜索类C3发现

随着时频演化。测量的

背景相当于400年以上67年的数据

一个3到搜索类的实验因子，

其误报率低于22，500年1。这

对应于概率小于2 _ 10���6观察

以上的噪声事件gw150914强在

分析时间，相当于6 _。图4左面板

显示C3类结果和背景。

定义搜索类C3的选择标准降低

背景通过引入一个约束的信号

形态。为了说明的意义

对一个事件的gw150914任意背景

形状，我们也显示搜索的结果，使用

同一组事件，正如上面所描述的那样

这个约束。具体地说，我们只使用2个搜索类：

C1级和C2和C3类联盟（C2 + C3）。

在这两类搜索发现是gw150914事件

C2 + C3类。图4左面板显示C2 + C3

班级成绩及背景。在此背景下

班上有四个事件与_c _ 32:1，产生一个错误

在8个400年的1 gw150914报警率。这相当于

到5 _ 10���6等效虚警概率

来4:4 _。

对于鲁棒性和验证，我们也使用其他通用

瞬态搜索算法[ 41 ]。不同的搜索

[ 73 ]和一个参数估计后续行动[ 74 ]

gw150914一致的意义和信号参数。

二进制合并搜索-搜索目标

二元系统的引力波发射

从1m_到99m_群众，总质量小于

100m_和无量纲转动了0.99 [ 45 ]。以

总质量大于4m_模型系统，我们使用

the effective-one-body (EOB) 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

6

LIGO-P150914-v13

nonetheless effectively recover systems with misaligned

spins in the parameter region of GW150914 [45]. Approximately

250,000 template waveforms are used to cover this

parameter space.

The search calculates the matched-filter signal-to-noise

ratio _(t) for each template in each detector and identifies

maxima of _(t) with respect to the time of arrival

of the signal [79–81]. For each maximum we calculate

a chi-squared statistic _2r

to test whether the data in

several different frequency bands are consistent with the

matching template [82]. Values of _2r

near unity indicate

that the signal is consistent with a coalescence. If _2r

is

greater than unity, _(t) is re-weighted as ^_ = _=[(1 +

(_2r

)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 inter-site propagation

time plus 5 ms for uncertainty in arrival time of weak

signals. We rank coincident events based on the quadrature

sum ^_c of the ^_ from both detectors [44].

To produce background data for this search the SNR

maxima of one detector are time-shifted and a new set of

有效单体（EOB）形式[ 75 ]，它结合

后牛顿法的结果[ 76，11 ]

从黑洞的扰动理论和数值计算结果

相对论。波形模型[ 77，78 ]假设

合并对象的旋转与该

轨道角动量，但由此产生的模板可以

六

ligo-p150914-v13

尽管如此，有效恢复系统的失调

旋转在gw150914 [ 45 ]参数区域。约

250000个模板波形被用来覆盖此

参数空间。

搜索计算匹配滤波器的信号-噪声

比_（t）为每个模板在各检测和识别

最大的_（T）的到达时间

信号[ 79，81 ]。对于每一个最大的我们计算

卡方统计_2r

检验数据是否在

几个不同的频段是一致的

匹配模板[ 82 ]。值_2r

近统一指示

与聚结的信号是一致的。如果_2r

是

大于1，_（T）重新加权作为^ _ = _ = [（1 +

（_2r

）3）2）= 1 = 6 [ 83，84 ]。最后一步执行重合

在检测器之间选择事件对发生在

一个15毫秒的窗口，来自同一个模板。这个

15毫秒的窗口是由10个相互间的网站传播

时间加5毫秒的不确定性在到达时间的薄弱

信号。我们在正交的基础上进行重合的事件

和^ _c的^ _从探测器[ 44 ]。

为了产生背景数据，该搜索信噪比

最大的一个检测器的时间转移和一组新的

coincident events is computed. Repeating this procedure

_ 107 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 ^_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 yrs. This translates to a false alarm

probability < 2 _ 10���7, corresponding to 5:1 _.

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 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 [45].

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, 89, 90], some

of which include spin precession, and for each model perform

a coherent Bayesian analysis to derive posterior dis-

TABLE I. Source parameters for GW150914. We report median

计算重合事件。重复这个过程

_ 107次产生的背景噪声分析

相当于000年608年。

为搜索背景噪声变化

在目标信号空间，候选人和背景

事件被分为三个搜索类基于模板

长度。图4的右边面板显示了背景

为gw150914搜索类。的gw150914

对^ _c = 23:6检测统计值大于任何

背景事件，所以只能放置一个上限

关于它的误报率。跨越三个搜索类

下限是1 203 000年这就是一场虚惊

概率小于2 _ 10���7，对应_ 5:1。

二、独立匹配滤波器的分析方法

估计其意义的不同方法

事件[ 85，86 ]，也发现gw150914相同

信号参数和一致的意义。

当一个事件被自信地认定为真正的引力

波信号，作为gw150914，背景

用于确定其他事件的意义的重新估计

没有这个事件的贡献。这是

背景分布显示为紫色线在

图4右面板。基于此，二最重要

事件的误报率为1每2.3年和

相应的泊松虚警概率0.02。

这一事件波形的分析表明，如果是天体物理学

它也是一个二进制黑洞[ 45 ]。

源讨论-匹配滤波器搜索优化

用于检测信号，但它仅提供近似

源参数估计。来完善他们

使用广义相对论为基础的模型[ 77，78，89，90 ]，一些

其中包括旋进，并为每个模型执行

一个连贯的贝叶斯分析，以获得后验分布—

表一gw150914源参数。我们报告中位

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) [87]. The

source redshift assumes standard cosmology [88].

Primary black hole mass 36+5

���4M_

Secondary black hole mass 29+4

���4M_

Final black hole mass 62+4

���4M_

Final black hole spin 0:67+0:05

���0:07

Luminosity distance 410+160

���180 Mpc

Source redshift, z 0:09+0:03

���0:04

tributions of the source parameters [91]. 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

���0:5M_c2. The system reached a peak

gravitational-wave luminosity of 3:6+0:5

值与90%可信区间，包括统计

错误，和系统误差从平均不同的结果

波形模型。群众在源框架，

转换为检测器帧乘（1 + 87）[ ]。这个

源红移假设标准宇宙学[ 88 ]。

原生黑洞质量36±5

���4m_

二次黑洞质量29±4

���4m_

最终黑洞质量62±4

���4m_

最后的黑洞自旋0:67 + 0:05

���0:07

光度距离410±160

���180 MPC

源红移，Z + 0:03 0:09

���0:04

的源参数[ 91 ]性。最初的

最终质量，最终旋转，距离和红移的源

在表一，一次黑洞的旋转

约束将<< 0:7（90%可信区间）指示

它不是最大限度地旋转，而旋转的

二是弱约束。这些源参数

在[ 39 ]中详细讨论。参数不确定

包括统计误差，系统误差

从平均不同波形模型的结果。

使用适合的二进制黑色的数值模拟

在[ 93，92 ]，我们提供的质量估计的洞

和旋转的最后黑洞，辐射总能量

引力波，峰值引力波亮度

[ 39 ]。引力辐射的估计总能量

波是3:0 + 0:5

���0:5m_c2。系统达到峰值

6 + 0:5的引力波的亮度

���0:4 _ 1056 erg=s,

equivalent to 200+30

���20M_c2=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 formulae 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 val-

7

LIGO-P150914-v13

ues, 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 _g > 1013 km,

which could be interpreted as a bound on the graviton mass

���0:4 _ 1056尔格= S，

相当于200 + 30

���20m_c2 =美国

已经进行了一些分析，以确定

是否gw150914与二进制黑色一致

广义相对论中的孔系[ 94 ]。第一个一致性

检查涉及最终黑洞的质量和旋转。

在广义相对论中，黑洞二元的最终产物

聚结是一个克尔黑洞，这是充分描述

通过它的质量和旋转。对于quasicircular inspirals，这些

爱因斯坦方程组作为函数的预测

双祖黑洞的质量和自旋。使用

数值相对论模拟的拟合公式

[ 92 ]，我们证实了这些残余的质量和旋转

从早期的聚结和那些推导出

推断出独立的后期阶段是一致的

与对方，没有任何证据的意见分歧

广义相对论。

在后牛顿形式主义，阶段

在灵感的引力波可以表示

作为F1 = 3的幂级数。这个系数

广义相对论可以计算扩展。因此，我们

可以测试的一致性与广义相对论[ 96，95 ]

允许系数偏离标称值—

七

ligo-p150914-v13

用，和看得到的波形是一致的

数据。在这94次检查中，我们所处的约束

对这些偏差，没有发现任何违反的证据

广义相对论。

最后，假设一个修改的色散关系

引力波[ 97 ]，我们的观测限制

康普顿波长的引力子是_g > 1013公里，

这可以理解为一种束缚的引力质量

mg < 1:2_10���22 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 modeldependent

bounds derived from dynamics of galaxy clusters

[100] and weak lensing observations [101]. In summary,

all three tests are consistent with the predictions of

general relativity in the strong-field regime of gravity.

GW150914 demonstrates the existence of stellar-mass

black holes more massive than ' 25M_, and establishes

that binary black holes can form in nature and merge within

a Hubble time. Binary black holes have been predicted to

form both in isolated binaries [102–104] and in dense environments

by dynamical interactions [105–107]. 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=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 stellarmass

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 2–400Gpc���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.

Outlook — Further details about these results and associated

Mg＜1:2_10���22 EV = C2。太阳系的改善

和二进制脉冲星界[ 98，99 ]由几个和一个因素

千年，分别，但不完善的模型依赖

星系团簇的动力学

[ 100 ]和[ 101 ]弱引力透镜观测。总之，

所有这三个测试是一致的预测

重力强场条件下的广义相对论。

gw150914表明恒星质量的存在

黑洞的质量比的25m_，建立

这个二进制黑洞可以在自然中形成并在内部合并

哈勃时间。二进制黑洞已经预测

在孤立的二进制文件中的形式[ 102，104 ]和在密集的环境中

通过动态相互作用[ 105，107 ]。形成

从恒星演化的巨大黑洞需要

弱大质量恒星风，这是可能的在恒星环境

与金属丰度低于1 = 2的太阳

值[ 108，109 ]。这进一步的天体物理学的影响

二进制黑洞发现在[ 110 ]中讨论。

这些观察结果约束stellarmass率

本地宇宙中的二元黑洞合并。使用

几种不同型号的底层二进制黑色

孔的质量分布，我们得到的速度估计范围

从随动架[ 111–2–400gpc���3年���1

113 ]。这与广泛的速度预测是一致的

正如在[ 114 ]，只有最低事件

排除率。

较大距离的二元黑洞系统

从引力波的随机背景

未解决的系统叠加。这样一个预测

背景介绍[ 115 ]。如果从这样的信号

一个人口被检测到，它将提供信息

关于历史上这样的二元制度的演变

宇宙的。

展望-关于这些结果和相关的进一步细节

data releases are available at http://dx.doi.

org/10.7935/K5MW2F23. Analysis results for the entire

first observational period will be reported in future publications.

Efforts are underway to enhance significantly the

global gravitational wave detector network [116]. 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 [117] will extend the network

and significantly improve the position reconstruction and

parameter estimation of sources.

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

GEO600 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

数据显示，在http://dx.doi可用。

org / 10.7935/k5mw2f23。整个分析结果

首次观察期将在未来的出版物中报告。

努力正在进行中，以提高显着

全球引力波探测器网络[ 116 ]。这些

包括进一步调试的先进LIGO探测器

达到设计灵敏度，这将允许检测

像gw150914双星3倍更高的信噪比。

此外，先进的处女座，kagra，和可能的

LIGO探测器第三印度[ 117 ]将网络延伸

并显着提高了位置重建和

源参数估计。

结论：LIGO探测器所观察到的引力

从合并的2个恒星质量黑波

孔。检测到的波形匹配的预测

的灵感和一对合并广义相对论

黑洞和由此产生的单黑响铃

孔。这些观察表明二进制的存在

恒星质量黑洞系统。这是第一个直接

引力波的探测和第一观测

二元黑洞合并。

致谢：作者感谢

美国国家科学基金会的支持

（NSF）的LIGO的建设和运行

实验室和先进的LIGO以及科学

和技术设施理事会（STFC）美国

王国，最大普朗克社会（国会议员），和国家

德国的下萨克森州的建设支持

先进的LIGO和施工操作的

GEO600探测器。高级LIGO的额外支持

由澳大利亚研究委员会提供。作者

感谢意大利Istituto Nazionale

第二Fisica Nucleare（INFN）、法国国家中心去

la Recherche Scientifique（CNRS）的基础

Fundamental Research on Matter supported by the Netherlands

Organisation for Scientific Research, for the construction

and operation of the Virgo detector and 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 Econom´ıa y Competitividad,

the Conselleria d’Economia i Competitivitat and Conselleria

d’Educaci´o, 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 National Science and Engineering Research

Council 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-16.8

 

 

 

 

荷兰的物质基础研究

科学研究组织，为建设

和操作的处女座探测器和创造

以及自我联盟的支持。作者

也非常感谢这些研究支持

机构以及科学和工业理事会

印度科学研究部

技术，印度，科学与工程研究委员会

（塞尔维亚），印度人力资源发展部，

印度、西班牙Ministerio de经济´ıY competitividad，

我的conselleria d'economia competitivitat和conselleria

d'educaci´阿，我的universitats文化治理

de les巴利阿里群岛，波兰国家科学中心，

欧洲委员会，英国皇家学会，苏格兰

资助委员会，苏格兰大学物理联盟，

匈牙利科学研究基金（otka），

里昂大学的起源（狮子），国家研究

韩国，加拿大，工业和全省的基础

安大略经济发展部

与创新，国家科学与工程研究

加拿大加拿大省高级研究所

研究，巴西科技部，

和创新，俄罗斯基础研究基金会，

该信托，研究公司，部

科学技术（大部分）、台湾科维

基础。作者非常感谢支持

美国国家科学基金会，STFC，MPS，INFN，法国国家科学研究中心和国家

德国的下萨克森州提供的计算

资源。这篇文章已被分配的文件

数字ligo-p150914和vir-0015a-16.8