Institut d'astrophysique de Paris€¦ · Something about myself •Worked on gravitaIonal wave...

BruceAllenMaxPlanckIns1tuteforGravita1onalPhysics

(AlbertEinsteinIns1tute,AEI)

TheLIGOdiscoveries:howtoreadthebasicphysicsoffthedata

Topics

• SimplephysicalargumentthatGW150914

is2xBHs

•Whywebesureitwasnoterror/accident/

malicious

•Whatisthefalsealarmrate?(“5σ” boundisoFenmisunderstood)

•Whyaresomeparameters(distance)

muchmorepoorlydetermined?

•Whyaren’twetesIngtheareatheorem?

2Paris27.6.2017

References:PRL116,061102(2016);PRX6,041015(2016);Ann.Phys.529,

1600209(2017);PRL118,221101(2017)

Somethingaboutmyself•WorkedongravitaIonalwavedata

analysismethodsandproducIon

compuIngsincemid-1990s

• Groupof~30peopleatAEI• Atlasisthelargestresourceworld-wideintheLIGO/VIRGO

collaboraIon:36,000CPUcores,

2,500GPUs,10PB,1MW

• DirecttheEinstein@Home

volunteercompuIngproject(fewx

Atlas)

•Methodsandtechnologyalsoused

forconvenIonal(electromagneIc)

astronomy:~100radioandgamma-

raypulsarsdiscoveredsofar.

3Paris27.6.2017

FirstDetec1on

4Paris27.6.2017

14September2015:

AdvancedLIGO

recordedastrong

gravitaIonalwave

burst:mergerofa29and36solarmassBH.

DiscoveryPaper

5Paris27.6.2017

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-WaveObservatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards infrequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10−21. It matches the waveformpredicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of theresulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and afalse alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greaterthan 5.1σ. The source lies at a luminosity distance of 410þ160

−180 Mpc corresponding to a redshift z ¼ 0.09þ0.03−0.04 .

In the source frame, the initial black hole masses are 36þ5−4M⊙ and 29þ4

−4M⊙, and the final black hole mass is62þ4

−4M⊙, with 3.0þ0.5−0.5M⊙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 directdetection 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 fieldequations of general relativity, Albert Einstein predictedthe existence of gravitational waves. He found thatthe linearized weak-field equations had wave solutions:transverse waves of spatial strain that travel at the speed oflight, generated by time variations of the mass quadrupolemoment of the source [1,2]. Einstein understood thatgravitational-wave amplitudes would be remarkablysmall; moreover, until the Chapel Hill conference in1957 there was significant debate about the physicalreality of gravitational waves [3].Also in 1916, Schwarzschild published a solution for the

field equations [4] that was later understood to describe ablack hole [5,6], and in 1963 Kerr generalized the solutionto rotating black holes [7]. Starting in the 1970s theoreticalwork led to the understanding of black hole quasinormalmodes [8–10], and in the 1990s higher-order post-Newtonian calculations [11] preceded extensive analyticalstudies of relativistic two-body dynamics [12,13]. Theseadvances, together with numerical relativity breakthroughsin the past decade [14–16], have enabled modeling ofbinary black hole mergers and accurate predictions oftheir gravitational waveforms. While numerous black holecandidates have now been identified through electromag-netic observations [17–19], black hole mergers have notpreviously been observed.

The discovery of the binary pulsar systemPSR B1913þ16by Hulse and Taylor [20] and subsequent observations ofits energy loss by Taylor and Weisberg [21] demonstratedthe existence of gravitational waves. This discovery,along with emerging astrophysical understanding [22],led to the recognition that direct observations of theamplitude and phase of gravitational waves would enablestudies of additional relativistic systems and provide newtests of general relativity, especially in the dynamicstrong-field regime.Experiments to detect gravitational waves began with

Weber and his resonant mass detectors in the 1960s [23],followed by an international network of cryogenic reso-nant detectors [24]. Interferometric detectors were firstsuggested in the early 1960s [25] and the 1970s [26]. Astudy of the noise and performance of such detectors [27],and further concepts to improve them [28], led toproposals for long-baseline broadband laser interferome-ters with the potential for significantly increased sensi-tivity [29–32]. By the early 2000s, a set of initial detectorswas completed, including TAMA 300 in Japan, GEO 600in Germany, the Laser Interferometer Gravitational-WaveObservatory (LIGO) in the United States, and Virgo inItaly. Combinations of these detectors made joint obser-vations from 2002 through 2011, setting upper limits on avariety of gravitational-wave sources while evolving intoa global network. In 2015, Advanced LIGO became thefirst of a significantly more sensitive network of advanceddetectors to begin observations [33–36].A century after the fundamental predictions of Einstein

and Schwarzschild, we report the first direct detection ofgravitational waves and the first direct observation of abinary black hole system merging to form a single blackhole. 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 ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

PRL 116, 061102 (2016)Selected for a Viewpoint in Physics

PHY S I CA L R EV I EW LE T T ER Sweek ending

12 FEBRUARY 2016

0031-9007=16=116(6)=061102(16) 061102-1 Published by the American Physical Society

Photodetector

BeamSplitter

Power Recycling

Laser

Source100 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

L y =

4 k

m

AdvancedLIGODetectors

Livingston& Hanford 3000kmapart

6Paris27.6.2017

• SensiIveband:30to2000Hz

• Strainh=ΔL/L• In100Hzbandatminimum,r.m.s.noise

h~10-22

Photodetector

BeamSplitter

Power Recycling

Laser

Source100 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

L y =

4 k

m

L1

GW150914

• Firstobservingrun(O1,scienceoperaIons)startscheduled18September2015

• Eventat09:50UTCon14September2015,fourdaysbeforeO1start

7Paris27.6.2017

AEIHannover,September14,2015

•Mondaymorning11:50inGermany

(02:50inHanford,04:50inLivingston)

• CoherentwaveburstpipelinerunningatCaltech,eventdatabasehad~1000

entries

•MarcoandAndycheckedinjecIon

flagsandlogbooks,dataquality,made

QscansofLHO/LLOdata.

• ContactedLIGOoperators:“everyone’sgonehome”

• At12:54,Marcosentanemailtothe

collaboraIon,askingforconfirmaIon

thatit’snotahiddentestsignal

(hardwareinjecIon)

• Nexthours:flurryofemails,decision

tolockdownsites,freezeinstrument

state

8Paris27.6.2017

AndrewLundgrenMarcoDrago

TheChirp

• Bandpassfiltered35-350Hz,someinstrumentaland

calibraIonlinesremovedwithnotchfilters

• Hanfordinverted,shiFed7.1msearlier

• Signalvisibletothenakedeye:~200ms

• “Instantaneous”SNR~5,opImalfilterSNR~249

Paris27.6.2017

-0.5

0

0.5

residuals

0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

Stra

in (1

0-21 )

H1 measured strain, bandpassedL1 measured strain, bandpassed

Black hole separation (RS)

0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

2

Stra

in (1

0-21 )

H1 estimated strain incidentH1 estimated strain, bandpassed

4 3 2 1

Inspiral Merger Ringdown

ΔL/L

Whatcoulditbe?

10Paris27.6.2017

Copyright:SalfordUniversity

Gravita1onalwavesfromorbi1ngmasses

11Paris27.6.2017

r

orbitalangular

frequency⍵

m

m

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

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2

�2+1

2m

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2

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2

r

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dt

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dt

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m

5/3

5c5!

11/3

0-0


12Paris27.6.2017

r

orbitalangular

frequency⍵

m

m

1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

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2m

�!r

2

�2+1

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r

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3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

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6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

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2

�2+1

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�!r

2

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2

r

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dt

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3

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2r

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6 =213/3G7/3

m

10/3

5c5!

10/3


dt

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2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0


13Paris27.6.2017

r

orbitalangular

frequency⍵

m

m1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

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2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

NOdipolegravita1onalradia1ond=Σ mi xi

ḋ =Σ mi vi = pḋ =0(Note:forequalmasses,d=0) .


14Paris27.6.2017

r

orbitalangular

frequency⍵

m

m1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

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2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

Einstein GW Luminosity =G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3

Einstein GW Luminosity = � d

dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0


15Paris27.6.2017

r

orbitalangular

frequency⍵

m

m

nowrand⍵ changewithIme!

1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3


5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3


5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0


16Paris27.6.2017

r

orbitalangular

frequency⍵

m

m

getmassfrom

frequencyandits

rateofchange!

1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3


5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Newton :Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3


5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

Eachorbitmakestwogravita1onalwavecycles

17Paris27.6.2017

CopyrightS.Larson

.

1orbit

t

ΔL/L=gravitaIonalwavestrain

TheChirp

• Lastfourbinaryorbitsfollowedbymerger

andringdown

• Nosignofeccentricityinrawdata18

Paris27.6.2017

-0.5

0

0.5

residuals

0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

Stra

in (1

0-21 )



0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

2

Stra

in (1

0-21 )


4 3 2 1


ΔL/L

1ORBIT1ORBIT

1ORBIT1ORBIT

ChirpMass

19Paris27.6.2017

LIGO-P150914-v12

FIG. 2. Top: Estimated gravitational-wave strain amplitudefrom GW150914 projected onto H1. This shows the full band-width of the waveforms, without the filtering used for Fig. 1.The inset images show numerical-relativity models of the blackhole horizons as the black holes coalesce. Bottom: The Kep-lerian effective black hole separation in units of Schwarzschildradii (R

S

= 2GM/c2) and the effective relative velocity givenby the post-Newtonian parameter v/c = (GM⇡f/c3)1/3, wheref is the gravitational-wave frequency calculated with numericalrelativity and M is the total mass (value from Table I).

At the lower frequencies, such evolution is characterizedby the chirp mass [46]

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 timederivative and G and c are the gravitational constant andspeed of light. Estimating f and f from the data in Fig. 1we obtain a chirp mass of M ' 30M�, implying that thetotal mass M = m1 + m2 is >⇠ 70M� in the detectorframe. This bounds the sum of the Schwarzschild radii ofthe binary components to 2GM/c2 >⇠ 210 km. To reachan orbital frequency of 75 Hz (half the gravitational-wavefrequency) the objects must have been very close and verycompact; equal Newtonian point masses orbiting at this fre-quency would be only ' 350 km apart. A pair of neutronstars, while compact, would not have the required mass,while a black hole-neutron star binary with the deducedchirp mass would have a very large total mass, and wouldthus merge at much lower frequency. This leaves blackholes as the only known objects compact enough to reach

an orbital frequency of 75 Hz without contact. Further-more, the decay of the waveform after it peaks is consis-tent with the damped oscillations of a black hole relaxingto a final stationary Kerr configuration. Below, we presenta general-relativistic analysis of GW150914; Fig. 2 showsthe calculated waveform using the resulting source param-eters.

Detectors — Gravitational-wave astronomy exploits multi-ple, widely separated detectors to distinguish gravitationalwaves from local instrumental and environmental noise, toprovide source sky localization from relative arrival times,and to measure wave polarizations. The LIGO sites eachoperate a single Advanced LIGO detector [32], a modi-fied Michelson interferometer (see Fig. 3) that measuresgravitational-wave strain as a difference in length of its or-thogonal arms. Each arm is formed by two mirrors, act-ing as test masses, separated by L

x

= Ly

= L = 4 km.A passing gravitational wave effectively alters the armlengths such that the measured difference is �L(t) =�L

x

� �Ly

= h(t)L, where h is the gravitational-wavestrain amplitude projected onto the detector. This differ-ential length variation alters the phase difference betweenthe two light fields returning to the beamsplitter, transmit-ting an optical signal proportional to the gravitational-wavestrain to the output photodetector.

To achieve sufficient sensitivity to measure gravitationalwaves the detectors include several enhancements to thebasic Michelson interferometer. First, each arm containsa resonant optical cavity, formed by its two test mass mir-rors, that multiplies the effect of a gravitational wave onthe light phase by a factor of 300 [48]. Second, a partiallytransmissive power-recycling mirror at the input providesadditional resonant buildup of the laser light in the interfer-ometer as a whole [49, 50]: 20 W of laser input is increasedto 700 W incident on the beamsplitter, which is further in-creased to 100 kW circulating in each arm cavity. Third,a partially transmissive signal-recycling mirror at the out-put optimizes the gravitational-wave signal extraction bybroadening the bandwidth of the arm cavities [51, 52].The interferometer is illuminated with a 1064-nm wave-length Nd:YAG laser, stabilized in amplitude, frequency,and beam geometry [53, 54]. The gravitational-wave sig-nal is extracted at the output port using homodyne read-out [55].

These interferometry techniques are designed to maxi-mize the conversion of strain to optical signal, thereby min-imizing the impact of photon shot noise (the principal noiseat high frequencies). High strain sensitivity also requiresthat the test masses have low displacement noise, whichis achieved by isolating them from seismic noise (low fre-quencies) and designing them to have low thermal noise(mid frequencies). Each test mass is suspended as the finalstage of a quadruple pendulum system [56], supported byan active seismic isolation platform [57]. These systemscollectively provide more than 10 orders of magnitude of

3

=30M⦿

Canonlybetwoblackholes!• ChirpmassM ~30M⦿

=>m1,m2~35M⦿=> SumofSchwarzschildradii≥206km

• AtpeakfGW=150Hz,orbitalfrequency=75HzseparaIonofNewtonianpoint

masses346km

• Ordinarystarsare106kminsize(merge

atmHz).Whitedwarfsare104

km

(mergeat1Hz).Theyaretoobigto

explaindata!

• Neutronstarsarealsonotpossible:m1=4M⦿ =>m2=600M⦿

=>Schwarzschildradius1800km=>too

big!

20Paris27.6.2017

Onlyblackholesareheavyenoughandsmallenough!

-0.5

0

0.5

residuals

0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

Stra

in (1

0-21 )



0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

2

Stra

in (1

0-21 )


4 3 2 1


Real?Detectorar1fact?Fraud?

• Instrumentsstablesince

September12th,2015

• LastscienIstsleFsites2hours(LHO)and15minutes(LLO)

beforetheevent.Operators

only.

•Waveformdoesnotresemble

instrumentalglitchesorartefacts

• SuscepIbilitytoenvironment

(radio,acousIc,magneIc,

seismic,…)measured.Cannot

explainmorethan6%ofthe

observedGWamplitude

21Paris27.6.2017

RobertSchofieldandAnamariaEffler,departedtheLLOsiteat04:35am15minutesbeforetheevent

StefanBallmerandEvanHall,departedtheLHOsitesoonaFer

midnight,2hoursbeforetheevent

23September2015

22Paris27.6.2017

BA

BA

BA

BA

AP

AP

AP

CONTROLLOOPRECONSTRUCTION

23Paris27.6.2017

• Photodiode(PD)signalsfromfringes

• Signals:recordedatyellowstars• InjecIons:addintoEndTestMass(ETMX)controller

• So:compareL2/L3DACstoexpecta1onfromDARMinput

• ExaminaIonoftheserecordedvaluesand(consistent)

reconstrucIonofthefilteroperaIonprovesnoinjecIonsignal

(Evans,LIGO-T1500536-v3)

RandomNoise?

24Paris27.6.2017

Muchlongerthan200,000yearsbeforenoiseinthedetectorwouldmimicthissignal,orasimilarsignalof

thetypesthatwesearchfor.

Op1malFiltering• FilterdatathroughmodelSEOB

waveforms

•Waveformsgroupedbymassinto3

classes,relevantoneisblue.Gridof

templatewaveformsinparameterspace.

• ComputeopImalstaIsIcsignal-to-noise

raIo(SNR)ρ• Normalisedsotheexpected/average

valueofρ2 is 2.

• Large ρ2=> strong signal present

• ρ2 is divided by a !2 factor which

reduces it if signal does not resemble template • Triggers at two sites must be in

the same template, within 15 msec• Final ranking statistic is

quadrature sum of SNR at both sites

25Paris27.6.2017

9

transient search is used in this analysis.Of the 17.5 days of data that are used as input to the anal-

ysis, the PyCBC analysis discards times for which either ofthe LIGO detectors is in their observation state for less than2064 s; shorter intervals are considered to be unstable detec-tor operation by this analysis and are removed from the ob-servation time. After discarding time removed by data-qualityvetoes and periods when detector operation is considered un-stable the observation time remaining is 16 days.

For each template h(t) and for the strain data from a sin-gle detector s(t), the analysis calculates the square of thematched-filter SNR defined by [12]

r

2(t) ⌘ 1hh|hi

⇥hs|hci2(t)+ hs|hsi2(t)

⇤, (1)

where the correlation is defined by

hs|hi(t) = 4Z •

0

s( f )h⇤( f )Sn( f )

e2pi f t d f , (2)

where hc and hs are the orthogonal sine and cosine parts of thetemplate and s( f ) is the Fourier transform of the time domainquantity s(t) given by

s( f ) =Z •

�•s(t)e�2pi f t dt. (3)

The quantity Sn(| f |) is the one-sided average power spec-tral density of the detector noise, which is re-calculated ev-ery 2048 s (in contrast to the fixed spectrum used in templatebank construction). Calculation of the matched-filter SNR inthe frequency domain allows the use of the computationallyefficient Fast Fourier Transform [79, 80]. The square of thematched-filter SNR in Eq. (1) is normalized by

hh|hi = 4Z •

0

h( f )h⇤( f )Sn( f )

d f , (4)

so that its mean value is 2, if s(t) contains only stationarynoise [81].

Non-Gaussian noise transients in the detector can produceextended periods of elevated matched-filter SNR that increasethe search background [4]. To mitigate this, a time-frequencyexcess power (burst) search [82] is used to identify high-amplitude, short-duration transients that are not flagged bydata-quality vetoes. If the burst search generates a trigger witha burst SNR exceeding 300, the PyCBC analysis vetoes thesedata by zeroing out 0.5s of s(t) centered on the time of thetrigger. The data is smoothly rolled off using a Tukey windowduring the 0.25 s before and after the vetoed data. The thresh-old of 300 is chosen to be significantly higher than the burstSNR obtained from plausible binary signals. For comparison,the burst SNR of GW150914 in the excess power search is⇠ 10. A total of 450 burst-transient vetoes are produced inthe two detectors, resulting in 225 s of data removed from thesearch. A time-frequency spectrogram of the data at the timeof each burst-transient veto was inspected to ensure that noneof these windows contained the signature of an extremely loudbinary coalescence.

(a) H1, 16 c

2 bins (b) H1, optimized c

2 bins

(c) L1, 16 c

2 bins (d) L1, optimized c

2 bins

FIG. 4. Distributions of noise triggers over re-weighted SNR r ,for Advanced LIGO engineering run data taken between September2 and September 9, 2015. Each line shows triggers from templateswithin a given range of gravitational-wave frequency at maximumstrain amplitude, fpeak. Left: Triggers obtained from H1, L1 data re-spectively, using a fixed number of p = 16 frequency bands for the c

2

test. Right: Triggers obtained with the number of frequency bandsdetermined by the function p = d0.4( fpeak/Hz)2/3e. Note that whilenoise distributions are suppressed over the whole template bank withthe optimized choice of p, the suppression is strongest for templateswith lower fpeak values. Templates that have a fpeak < 220Hz pro-duce a large tail of noise triggers with high re-weighted SNR evenwith the improved c

2-squared test tuning, thus we separate thesetemplates from the rest of the bank when calculating the noise back-ground.

The analysis places a threshold of 5.5 on the single-detectormatched-filter SNR and identifies maxima of r(t) with respectto the time of arrival of the signal. For each maximum wecalculate a chi-squared statistic to determine whether the datain several different frequency bands are consistent with thematching template [15]. Given a specific number of frequencybands p, the value of the reduced c

2r is given by

c

2r =

p2p�2

p

Âi=1

✓ri �

r

p

◆2, (5)

where ri is the matched-filter SNR of the template in the i-th frequency band. Values of c

2r near unity indicate that the

9




r

2(t) ⌘ 1hh|hi


⇤, (1)


hs|hi(t) = 4Z •

0

s( f )h⇤( f )Sn( f )

e2pi f t d f , (2)


s( f ) =Z •

�•s(t)e�2pi f t dt. (3)


hh|hi = 4Z •

0

h( f )h⇤( f )Sn( f )

d f , (4)



(a) H1, 16 c


2 bins

(c) L1, 16 c


2 bins


2




2r is given by

c

2r =

p2p�2

p

Âi=1

✓ri �

r

p

◆2, (5)



9




r

2(t) ⌘ 1hh|hi


⇤, (1)


hs|hi(t) = 4Z •

0

s( f )h⇤( f )Sn( f )

e2pi f t d f , (2)


s( f ) =Z •

�•s(t)e�2pi f t dt. (3)


hh|hi = 4Z •

0

h( f )h⇤( f )Sn( f )

d f , (4)



(a) H1, 16 c


2 bins

(c) L1, 16 c


2 bins


2




2r is given by

c

2r =

p2p�2

p

Âi=1

✓ri �

r

p

◆2, (5)



9




r

2(t) ⌘ 1hh|hi


⇤, (1)


hs|hi(t) = 4Z •

0

s( f )h⇤( f )Sn( f )

e2pi f t d f , (2)


s( f ) =Z •

�•s(t)e�2pi f t dt. (3)


hh|hi = 4Z •

0

h( f )h⇤( f )Sn( f )

d f , (4)



(a) H1, 16 c


2 bins

(c) L1, 16 c


2 bins


2




2r is given by

c

2r =

p2p�2

p

Âi=1

✓ri �

r

p

◆2, (5)



6

tion period (referred to as LVT151012) was reported on Oc-tober 12, 2015 at 09:54:43 UTC with a combined matched-filter SNR of 9.6. The search reported a false alarm rate of 1per 2.3 years and a corresponding false alarm probability of0.02 for this candidate event. Detector characterization stud-ies have not identified an instrumental or environmental arti-fact as causing this candidate event [14]. However, its falsealarm probability is not sufficiently low to confidently claimthis candidate event as a signal. Detailed waveform analysis ofthis candidate event indicates that it is also a binary black holemerger with source frame masses 23+18

�5 M� and 13+4�5 M�, if

it is of astrophysical origin.This paper is organized as follows: Sec. II gives an

overview of the compact binary coalescence search and themethods used. Sec. III and Sec. IV describe the constructionand tuning of the two independently implemented analysesused in the search. Sec. V presents the results of the search,and follow-up of the two most significant candidate events,GW150914 and LVT151012.

II. SEARCH DESCRIPTION

The binary coalescence search [19–26] reported here tar-gets gravitational waves from binary neutron stars, binaryblack holes, and neutron star–black hole binaries, usingmatched filtering [27] with waveforms predicted by generalrelativity. Both the PyCBC and GstLAL analyses correlatethe detector data with template waveforms that model the ex-pected signal. The analyses identify candidate events that aredetected at both observatories consistent with the 10 ms inter-site propagation time. Events are assigned a detection-statisticvalue that ranks their likelihood of being a gravitational-wavesignal. This detection statistic is compared to the estimateddetector noise background to determine the probability that acandidate event is due to detector noise.

We report on a search using coincident observations be-tween the two Advanced LIGO detectors [28] in Hanford, WA(H1) and in Livingston, LA (L1) from September 12 to Octo-ber 20, 2015. During these 38.6 days, the detectors were incoincident operation for a total of 18.4 days. Unstable instru-mental operation and hardware failures affected 20.7 hoursof these coincident observations. These data are discardedand the remaining 17.5 days are used as input to the analy-ses [14]. The analyses reduce this time further by imposinga minimum length over which the detectors must be operat-ing stably; this is different between the two analysis, as de-scribed in Sec. III and Sec. IV. After applying this cut, thePyCBC analysis searched 16 days of coincident data and theGstLAL analysis searched 17 days of coincident data. To pre-vent bias in the results, the configuration and tuning of theanalyses were determined using data taken prior to September12, 2015.

A gravitational-wave signal incident on an interferometeralters its arm lengths by dLx and dLy, such that their mea-sured difference is DL(t) = dLx � dLy = h(t)L, where h(t) isthe gravitational-wave metric perturbation projected onto thedetector, and L is the unperturbed arm length [29]. The strain

100 101 102

Mass 1 [M�]

100

101

Mas

s2

[M�

]

|�1| < 0.9895, |�2| < 0.05

|�1,2| < 0.05

|�1,2| < 0.9895

FIG. 1. The four-dimensional search parameter space covered bythe template bank shown projected into the component-mass plane,using the convention m1 > m2. The lines bound mass regions withdifferent limits on the dimensionless aligned-spin parameters c1 andc2. Each point indicates the position of a template in the bank. Thecircle highlights the template that best matches GW150914. Thisdoes not coincide with the best-fit parameters due to the discrete na-ture of the template bank.

is calibrated by measuring the detector’s response to test massmotion induced by photon pressure from a modulated calibra-tion laser beam [30]. Changes in the detector’s thermal andalignment state cause small, time-dependent systematic errorsin the calibration [30]. The calibration used for this searchdoes not include these time-dependent factors. Appendix Ademonstrates that neglecting the time-dependent calibrationfactors does not affect the result of this search.

The gravitational waveform h(t) depends on the chirpmass of the binary, M = (m1m2)3/5/(m1 + m2)1/5 [31, 32],the symmetric mass ratio h = (m1m2)/(m1 + m2)2 [33],and the angular momentum of the compact objects c1,2 =cS1,2/Gm2

1,2 [34, 35] (the compact object’s dimensionlessspin), where S1,2 is the angular momentum of the compactobjects. The effect of spin on the waveform depends also onthe ratio between the component objects’ masses. Parameterswhich affect the overall amplitude and phase of the signal asobserved in the detector are maximized over in the matched-filter search, but can be recovered through full parameter esti-mation analysis [18]. The search parameter space is thereforedefined by the limits placed on the compact objects’ massesand spins. The minimum component masses of the search aredetermined by the lowest expected neutron star mass, whichwe assume to be 1M� [36]. There is no known maximumblack hole mass [37], however we limit this search to bina-ries with a total mass less than M = m1 + m2 100M�. TheLIGO detectors are sensitive to higher mass binaries, how-ever; the results of searches for binaries that lie outside thissearch space will be reported in future publications.

For binary component objects with masses less than 2M�,we limit the magnitude of the component object’s spin to 0.05,the spin of the fastest known pulsar in a double neutron star

FourierTransform

SNR

Innerproduct

Normalisa1on

B.Allenetal.,Phys.Rev.D85,122006(2012) B.Allen,Phys.Rev.D71,062001(2005)

Whatisthefalsealarmprobability?• Orangesquares:highestSNReventsinthefirst16daysof

datacollected(12Sept-20Oct)

• EsImatebackgroundbyshiFing

instrumentaldatainImeatone

sitein0.1secondincrements

(>>10mseclight-travelIme)

approximately2x106

Imes.

• Generate608,000yearsof“arIficial”data,searchfor

events

• Includingtrialsfactor,falsealarmrate<1in203,000years

• ForaGaussianprocess,thisis>5.1σ

26Paris27.6.2017

2� 3� 4� 5.1� > 5.1�2� 3� 4� 5.1� > 5.1�

8 10 12 14 16 18 20 22 24Detection statistic �c

10�8

10�7

10�6

10�5

10�4

10�3

10�2

10�1

100

101

102

Num

ber

ofev

ents

GW150914

Binary coalescence search

Search ResultSearch BackgroundBackground excluding GW150914

Whatisthefalsealarmprobability?• Orangesquares:highestSNReventsinthefirst16daysofdata

collected(12Sept-20Oct)

• EsImatebackgroundbyshiFing

instrumentaldatainImeatone

sitein0.1secondincrements(>>

10mseclight-travelIme)

approximately2x106

Imes.

• Generate608,000yearsof“arIficial”data,searchforevents

• Includingtrialsfactor,falsealarm

rate<1in203,000years

• ForaGaussianprocess,thisis>5.1σ• Realfalsealarmratemuchmuch

less!Wegotlucky,couldhaveconfidentlydetectedit70%fartheraway.

27Paris27.6.2017

2� 3� 4� 5.1� > 5.1�2� 3� 4� 5.1� > 5.1�

8 10 12 14 16 18 20 22 24Detection statistic �c

10�8

10�7

10�6

10�5

10�4

10�3

10�2

10�1

100

101

102

Num

ber

ofev

ents

GW150914

Binary coalescence search

Search ResultSearch BackgroundBackground excluding GW150914

Onceeventevery1021years.Thisis 10111mestheageoftheuniverse!

10orders

ofm

agnitude

15orders

ofm

agnitude

Parameters:skyposi1on

28Paris27.6.2017

• 7-msec time delay gives a CIRCLE on the sky. Why an arc?

• Bayesian analysis: most likely source direction is directly above or below plane of detector.

• Intersect these, get only a portion of circle

Crudest(Luminosity)DistanceEs1mate

• Schwarzschildradius~200km

•Metricstrainhisorderh~0.1atSchwarzschildradius

• Strainhfallsofflikeinverseofdistanced• Atdetector,maximummetricperturbaIonh~10-21

• Thisimpliesadistanced~1020x200km~2x1025m~2x109lightyears(correcttofactoroftwo)

29Paris27.6.2017

Parameters:massesanddistance

30

LIGO-P150914-v12

nonetheless effectively recover systems with misalignedspins in the parameter region of GW150914 [44]. Approx-imately 250,000 template waveforms are used to cover thisparameter space.

The search calculates the matched-filter signal-to-noiseratio ⇢(t) for each template in each detector and identi-fies maxima of ⇢(t) with respect to the time of arrivalof the signal [79–81]. For each maximum we calcu-late a chi-squared statistic �2

r

to test whether the data inseveral different frequency bands are consistent with thematching template [82]. Values of �2

r

near unity indicatethat the signal is consistent with a coalescence. If �2

r

isgreater than unity, ⇢(t) is re-weighted as ⇢ = ⇢/[(1 +(�2

r

)3)/2]1/6 [83, 84]. The final step enforces coincidencebetween detectors by selecting event pairs that occur withina 15ms window and come from the same template. The15ms window is determined by the 10ms inter-site propa-gation time plus 5ms for uncertainty in arrival time of weaksignals. We rank coincident events based on the quadraturesum ⇢

c

of the ⇢ from both detectors [43].To produce background data for this search the SNR

maxima of one detector are time-shifted and a new set ofcoincident events is computed. Repeating this procedure⇠ 107 times produces a noise background analysis timeequivalent to 608 000 years.

To account for the search background noise varyingacross the target signal space, candidate and backgroundevents are divided into three search classes based on tem-plate length. The right panel of Fig. 4 shows the back-ground for the search class of GW150914. The GW150914detection-statistic value of ⇢

c

= 23.6 is larger than anybackground event, so only an upper bound can be placedon its false alarm rate. Across the three search classes thisbound is 1 in 203 000 yrs. This translates to a false alarmprobability < 2⇥ 10�7, corresponding to 5.1�.

A second, independent matched-filter analysis that usesa different method for estimating the significance of itsevents [85, 86], also detected GW150914 with identicalsignal parameters and consistent significance.

When an event is confidently identified as a real grav-itational wave signal, as for GW150914, the backgroundused to determine the significance of other events is re-estimated without the contribution of this event. This isthe background distribution shown as a purple line in theright panel of Fig. 4. Based on this, the second most sig-nificant event has a false alarm rate of 1 per 2.3 years andcorresponding Poissonian false alarm probability of 0.02.Waveform analysis of this event indicates that if it is astro-physical in origin it is also a binary black hole [44].

Source discussion — The matched filter search is opti-mized for detecting signals, but it provides only approxi-mate estimates of the source parameters. To refine them weuse general relativity-based models that include precessingspins [77, 78, 89, 90], and for each model perform a co-herent Bayesian analysis to derive posterior distributions

TABLE I. Source parameters for GW150914. We report me-dian values with 90% credible intervals that include statisticalerrors, and systematic errors from averaging the results of dif-ferent waveform models. Masses are given in the source frame,to convert to the detector frame multiply by (1 + z) [87]. Thesource redshift assumes standard cosmology [88].

Primary black hole mass 36+5�4 M�

Secondary black hole mass 29+4�4 M�

Final black hole mass 62+4�4 M�

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

of the source parameters [91]. The initial and final masses,final spin, distance and redshift of the source are shown inTable I. The spin of the primary black hole is constrained tobe < 0.7 (90% credible interval) indicating it is not max-imally spinning, while the spin of the secondary is onlyweakly constrained. These source parameters are discussedin detail in [38]. The parameter uncertainties include sta-tistical errors, and systematic errors from averaging the re-sults of different waveform models.

Using the fits to numerical simulations of binary blackhole mergers in [92, 93], we provide estimates of the massand spin of the final black hole, the total energy radiated ingravitational waves, and the peak gravitational-wave lumi-nosity [38]. The estimated total energy radiated in gravita-tional waves is 3.0+0.5

�0.5 M�c2. The system reached a peakgravitational-wave luminosity of 3.6+0.5

�0.4 ⇥ 1056 erg/s,equivalent to 200+30

�20 M�c2/s.Several analyses have been performed to determine

whether or not GW150914 is consistent with a binary blackhole system in general relativity [94]. A first consistencycheck involves the mass and spin of the final black hole.In general relativity, the end product of a black hole binarycoalescence is a Kerr black hole, which is fully describedby its mass and spin. For quasicircular inspirals, these arepredicted uniquely by Einstein’s equations as a function ofthe masses and spins of the two progenitor black holes. Us-ing fitting formulae calibrated to numerical relativity sim-ulations [92], we verified that the remnant mass and spindeduced from the early stage of the coalescence and thoseinferred independently from the late stage are consistentwith each other, with no evidence for disagreement fromgeneral relativity.

Within the Post-Newtonian formalism, the phase ofthe gravitational waveform during the inspiral can be ex-pressed as a power-series in f1/3. The coefficients of thisexpansion can be computed in general relativity. Thus wecan test for consistency with general relativity [95, 96] byallowing the coefficients to deviate from the nominal val-

7

LIGO-P150914-v12



r


r


r


r


c




c



















7

• Instrument calibration accurate 3% percent.

•Waveform models accurate to 1%

• SNR high enough that noise should give errors of ~5%

• Errors in masses and spins at ±10% level

•Why are distance uncertainties ±40% ?

Paris27.6.2017

Whyisdistancesouncertain?

• Edge-on:onlyonepolarisaIon,bothdetectorswouldseethis,butwithprojecIoncosinefactor,dependinguponorientaIon

• Face-on/face-offorientaIon:twopolarisaIons,detectorsseedifferentlinearcombinaIons(butsametotalamplitude)

• Onaverageface-on/offorientaIonismorevisiblethanedge-on:face-on/off,

becauseithasunitprojecIonontodetectorarms=>strongersignal.(NB:this

statementisindependentofthedata!)31

Paris27.6.2017

Orbitalplaneface-on

GWshavecircularpolarisa1onOrbitalplaneedge-on

GWshavelinearpolarisa1on

⍳ ⍳=90°⍳=0

Inferenceaboutorbitalinclina1on

32

−1 −0.5 0 0.5 1cos(inclination angle)

0

1

2

3

"Detected" Posterior (data free!)

−1 −0.5 0 0.5 1cos(inclination angle)

0

0.5

1

1.5

2

Astrophysical Prior Probability Distribution

⍳

Prior(astrophysical)

probabilitydistribuIonfor

cos(⍳)

Posteriorprobability

distribuIonforcos(⍳),usingonlytheinformaIon

thatwehavedetected

somethingwithSNR=24

(butwithnoother

informaIonfromthedata)

Paris27.6.2017

Howwouldcircularpolarisa1onlook?

• IfdetectorsareseeingdisInctpolarisaIons,phaseinonedetectorleadstheotherdetectorby90degrees

• AFer“liningup”arrivalImes,wouldlooklikeabove

• Edge-on:onepolarisaIon,signalsalwaysinphase• Face-on:twopolarisaIons,phaseshiFpossible

33Paris27.6.2017

Hanford

Livingston

Ime

strain

Weakevidenceforface-off

• TheslightphaseshiFsuggestsface-offismorelikely(79%)than

face-on(21%)

• Edge-onunlikelybecauseexpectedsignalwouldbe

weaker,NOTbasedondata.

34Paris27.6.2017

face-onface-off

Massesanddistance•Waveform models and

Instrument calibration: ± 3% percent errors

• Detector noise: ± 5% errors

• Reasonable: errors in masses and spins at ±10% level

• But distance uncertainties are ±40% . Because we don’t know how orbital plane of binary was oriented.

35Paris27.6.2017

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RadiatedEnergy

36Paris27.6.2017

1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

1 Equations

Gm

2

r

2= m!

2�r

2

�) r

3 =2Gm

!

2

Emechanical =1

2m

�!r

2

�2+1

2m

�!r

2

�2�Gm

2

r

= �Gm

2

2r= �G

2/3m

5/3

24/3!

2/3

G

5c5�d

3

dt

3Qab

��d

3

dt

3Qab

�=

8G

5c5m

2r

4!

6 =213/3G7/3

m

10/3

5c5!

10/3


dt

Emechanical =G

2/3m

5/3

3 · 21/3!

�1/3 d!

dt

d!

dt

=3 · 214/3G5/3

m

5/3

5c5!

11/3

0-0

m=35M⦿,r=346km,getEmechanical~3M⦿c2

Energylost,powerradiated• Radiated energy:

3M⦿ (±0.5)

• Peak luminosity: 3.6 x 1056 erg/s (±15%)= 200 M⦿//s

• Flux about 1µW/cm2 at detector, ~1012 millicrab

• Cell phone at 1 meter!37

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7

1m

3solarmassesingravita1onalwaves

•Mostoftheenergyemiwedin~40msec

• 10msecaFermerger,expandingshellof

GWenergy15,000kminradius.Energy

densityinGW:~60kg/cm3

• 1secaFermerger,shell300,000kmradius,

energydensityinshell~100g/cm3.You

couldsafelyobservefromthisdistanceinaspace-suit:strainwouldchangeyourbodylengthby~1mm

• 10saFermerger,shellhasexpandedto

3,000,000kmradius.Energydensityin

GW:~1g/cm3

38Paris27.6.2017

r

r~t

⍴ ~r-2~t-2

VOLUME 26, NUMBER 21 PHYSICAL REVIEW LETTERS 24 Mwv 1971

0 Permanent address: Institute for Atomic Physics,Bucharest, Rumania.~See, e.g. , G. A. Keyworth, G. C. Kyker, Jr. , E. G.

Bilpuch, and H. W. Newson, Nucl. Phys. 89, 590 (1966).M. Maruyama, K. Tsukada, K. Ozawa, F. Fujimoto,

K. Komaki, M. Mannami, and T. Sakurai, Nucl. Phys.A145, 581 (1970).W. M. Gibson, M. Maruyama, D. W. Mingay, J. P.

F. Sellschop, G. M. Temmer, and R. Van Bree, Bull.Amer. Phys. Soc. 16, 557 (1971).G. M. Temmer, M. Maruyama, D. W. Mingay,

M. Petrascu, and R. Van Bree, Bull. Amer. Phys. Soc.16, 182 (1971).L. H. Goldman, Phys. Rev. 165, 1203 (1968).W. Darcey, J. Fenton, T. H. Kruse, and M. E. Will-

iams, unpublished.R. Van Bree, unpublished computer program based

in part on B.Teitelman and G. M. Temmer, Phys. Rev.177, 1656 (1969), Appendix. This program does nof;allow for identical spins and parities, and the fit istherefore very tentative.J. R. Huizenga, private communication. This re-

presents the best estimate, using a slight extrapola-

tion from the obsemed neutron-capture 2+-level den-sity at 7.6-MeV excitation.~N. Williams, T. H. Kruse, M. E. Williams, J. A.

Fenton, and G. L. Miller, to be published.H. Feshbach, A. K. Kerman, and R. H. Lemmer,

Ann. Phys. (New York) 41, 280 (1967); R. A. Ferrelland W. M. MacDonald, Phys. Rev. Lett. 16, 187 (1966).Intermediate St~cthe in Nuclear Reactions, edited

by H. P. Kennedy and R. Schrils (University of KentuckyPress, Lexington, Ky. , 1968).J. D. Moses, thesis, Duke University, 1970 (unpub-

lished).~3D. P. Lindstrom, H. W. Newson, E. G. Bilpuch, andG. E. Mitchell, to be published.J. C. Browne, H. W. Newson, E. G. Bilpuch, and

G. E. Mitchell, Nucl. Phys. A153, 481 (1970).~5J. D. Mosey, private communication.L. Meyer-Schutzmeister, Z. Vager, R. E. Segel,

and P. P. Singh, Nucl. Phys. A108, 180 (1968).~YJ. A. Farrell, G. C. Kyker, Jr., E. G. Bilpuch, andH. W. Newson, Phys. Lett. 17, 286 (1965).J. E. Monahan and A. J. Elwyn, Phys. Rev. Lett. 20,

1119 (1968).

Gravitational Radiation from Colliding Black Holes

S. W. HawkingInstitute of Theoretical Astronomy, University of Cambridge, Cambridge, England

(Received 11 March 1971)

It is shown that there is an upper bound to the energy of the gravitational radiationemitted when one collapsed object captures another. In the case of two objects withequal masses m and zero intrinsic angular momenta, this upper bound is (2-W2) m.

Weber' ' has recently reported coinciding mea-surements of short bursts of gravitational radia-tion at a frequency of 1660 Hz. These occur at arate of about one per day and the bursts appearto be coming from the center of the galaxy. Itseems likely'4 that the probability of a burstcausing a coincidence between %eber's detectorsis less than, . If one allows for this and assumesthat the radiation is broadband, one finds that theenergy flux in gravitational radiation must be atleast 10'c erg/cm' day. 4 This would imply amass loss from the center of the galaxy of about20 000M o/yr. It is therefore possible that themass of the galaxy might have been considerablyhigher in the past than it is now. ' This makes itimportant to estimate the efficiency with whichrest-mass energy can be converted into gravita-tional radiation. Clearly nuclear reactions areinsufficient since they release only about 1% ofthe rest mass. The efficiency might be higherin either the nonspherical gravitational collapseof a star or the collision and coalescence of two

collapsed objects. Up to now no limits on the ef-ficiency of the processes have been known. Theobject of this Letter is to show that there is alimit for the second process. For the case oftwo colliding collapsed objects, each of mass mand zero angular momentum, the amount of ener-gy that can be carried away by gravitational orany other form of radiation is less than (2-v 2)m.I assume the validity of the Carter-Israel con-

jucture'' that the metric outside a collapsed ob-ject settles down to that of one of the Kerr familyof solutions' with positive mass m and angularmomentum a per unit mass less than or equal tom. (I am using units in which G=c =1.) Each ofthese solutions contains a nonsingular event hori-zon, two-dimensional sections of which are topo-graphically spheres with area'

8wm[m+(m a) ' ]. -The event horizon is the boundary of the regionof space-time from which particles or photonscan escape to infinity. I shall consider only

1344

Hawking’sAreaTheoremPRL21,1344(1971)

39

⇢(t) =

Zdf

x(f)h⇤(f)e2⇡ift

Sh(f)

m

2f

✓1 +

q1� s

2f

◆>

m

21

✓1 +

q1� s

21

◆+m

22

✓1 +

q1� s

22

◆

0-1

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7

✓

-0.5

0

0.5

residuals

0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

Stra

in (1

0-21 )



0.2 0.25 0.3 0.35 0.4 0.45Time (seconds)

-1

0

1

2

Stra

in (1

0-21 )


4 3 2 1

Inspiral Merger RingdownGW150914testareatheorem?No!

40

•MostSNRbeforemerger:only

valuesofm1,m2aredetermined

independently.

•mfandsfdeterminedby

numericalrelaIvity(whichgives

thematchingwaveforms)

• IfareatheoremwereNOT

saIsfied,thenthenumerical

relaIvitycodesolvingtheEinstein

equaIonsmustbefaulty

Paris27.6.2017

M=340μs(indetectorframe)

NumericalsimulaIons:QNMdominates

starIng~10MaFerpeak10M=3.4ms(indetectorframe)

PRL116(22),221101

BinaryBlackHolesinO1/O2

41Paris27.6.2017

29+35M⦿,SNR24

8+15M⦿,SNR13

13+23M⦿,SNR10

31+19M⦿,SNR13

1

-1

1

-1

1

-1

(Strainh)x1021

1

-1

GW170104:firstDetec1oninO2•Mergerof31and19M⦿ blackholes

• 2M⦿lostinGWs

• Distance:redshiF0.18correspondingto880Mpc

• LikefirstdetecIonGW150914,

onlyattwicethedistance!

• “GW170104wasfirstiden;fied

byinspec;onoflowlatency

triggersfromLivingstondata.

Anautomatedno;fica;onwas

notgeneratedastheHanford

detector’scalibra;onstatewas

temporarilysetincorrectlyin

thelow-latencysystem.”

42Paris27.6.2017

Phys.Rev.Lew.118,221101(2017)

AlexNitz,AEIHannover

Inferenceaboutblackholespins

•Mightprovideevidenceabout

theoriginsofthebinaryblack

holesystems

• “Smokinggun”:precessionofthe

orbitalplane

• Hardtodetect:effectsonwaveformstrongestwhenorbital

planeviewededge-on;hidden

whenviewedface-on/off.

• AnetworkofdetectorswithdifferentorientaIonswillmake

usmorelikelytodetectsystems

thatarenotface-on/off

• Comparepriorsandposteriors

43Paris27.6.2017 GW170104

Summary• InferencefromtheaLIGOdataisverydirect.But

cansomeImesbemisleading

• Dataanalysisisverycomputeintensive,butthe

humanelementissIllimportant

• Ifthefalsealarmrate/probabilityisabound

ratherthananumber,don’tmisinterpretit

• Solarmassesradiatedintensofmillisecondsis

dramaIc,butneverthelessineffectual

•Whenlookingatposteriorprobability

distribuIonsforparameters,besuretocompare

thiswithpriors.Whatcomesfromthedataitself?

44Paris27.6.2017

Conclusions•WecandetectgravitaIonalwaves

directly(trackingamplitudeand

phase)

• Existenceofstellarmassblackhole

binariesestablished(notvisibleany

otherway!).Willbeourdominant

source.

• AgoldenageforGWastronomyis

coming.Wewillgofrom2

detecIonsto10to100inthenext

fewyears.

• Othersignalsources(NS/NS,NS/BH,CW,ortheunexpected.Pleasesign

upforEinstein@Home

45Paris27.6.2017

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