consistency check inv olves the mass and spin of the final

black hole. In general relativity , the end product of a black

hole binary coalescence is a Kerr black hole, which is fully

described by its mass and spin. For quasicircular inspirals,

these are predicted uniquely by Einstein ’ s equations as a

function of the masses and spins of the two progenitor

black holes. Using fitting formulas calibrated to numerical

relati vity simulations [92] , we verifi ed 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 .

W ithin the post-Newtonian formalism, the phase of the

gravitational waveform during the inspiral can be expressed

as a po wer series in f

1 = 3

. The coefficients of this expansion

can be computed in general relativity . Thus, we can test for

consistency with general relati vity [95,96] by allowing the

coeff icients to deviate from the nominal values, and seeing

if the resulting waveform is consistent with the data. In this

second check [94] we place constraints on these deviations,

finding no evidence for violations of general relativity .

Finally , assuming a modified dispersion relation for

gravitational waves [97] , our observ ations constrain the

Compton wavelength of the graviton to be λ

g

> 10

13

km,

which could be interpreted as a bound on the graviton mass

m

g

< 1 . 2 × 10

− 22

eV =c

2

. This improves on Solar System

and binary pulsar bounds [98,99] by factors of a fe w and a

thousand, respectively , but does not improve on the model-

dependent bounds derived from the dynamics of Galaxy

clusters [100] and weak lensing observ ations [101] .I n

summary , all three tests are consistent with the predictions

of general relati vity in the strong-field regime of gravity .

GW150914 demonst rates the existence of stellar-mass

bla ck hole s more mas si v e than ≃ 25 M

⊙

, and establ ishes t hat

bin ary blac k hole s can form in nat ure and mer ge wit hin a

Hu bble time . Bina ry blac k hole s hav e been pred icte d to for m

bot h in isol at ed bina rie s [102 – 104] and in d ense environ-

me nts by dyna mic al inte rac tion s [105 – 10 7] . The form at ion

of such m assive bl ack ho les fro m st ell ar evoluti on r equ ires

wea k mas si v e-sta r wind s, whic h are pos sib le in st ella r

en vironments with metall icity lower th an ≃ 1 = 2 the s olar

val u e [10 8,10 9] . Fu rther as trophysical im plications of this

bin ary black hole disc ov ery are disc uss ed in [110] .

These observational results constrain the rate of stellar-

mass binary black hole mergers in the local universe. Using

seve ral different models of the underlying binary black hole

mass distribution, we obtain rate estimates ranging from

2 – 400 Gpc

− 3

yr

− 1

in the comoving frame [111 – 113] . This

is consistent with a broad range of rate predictions as

re viewed in [114] , with only the lowest event rates being

excluded.

Binary black hole systems at larger distances contribute

to a stochastic background of gravitational wav es 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 evo lution of such binary systems over the history

of the univ erse.

VII. OUTLOOK

Further details about these results and associated data

releases are available at [116] . Analysis results for the

entire first observ ational period will be reported in future

publications. Efforts are under way to enhance significantly

the global gravitational-w ave detector network [117] .

These include further commissioning of the Advanced

LIGO detectors to reach design sensitivity , which will

allo w detection of binaries like GW150914 with 3 times

higher SNR. Additionally , Adv anced V irgo, KA GRA, and

a possible third LIGO detector in India [118] will extend

the network and significantly improve the position

reconstruction and parameter estimation of sources.

VIII. CONCLUSION

The LIGO detectors hav e observed gravitational waves

from the merger of two stellar-mass black holes. The

detected waveform matches the predictions of general

relati vity 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

Th e autho rs grat efu lly ackn o wle dge the suppo rt of the

United States National Science Foundatio n (NSF) for the

co nstru ct ion and opera ti on of the LIGO Labor ator y and

Advanced LIGO as well as th e Science an d T echnology

Facilities Co uncil (STFC) o f th e Un ited Kin gdom, th e M ax-

Planck Society (MPS), and the State of Ni edersachsen,

Germ an y , for supp ort of the cons truc tion of Ad v ance d

LI GO and c onst ru ctio n and ope rat ion of the GEO 600 dete ctor .

Ad diti ona l supp or t for Adv anc ed LIGO was pro vide d by th e

Au stra lia n R esea rc h Co unc il. The aut hor s grate full y ackno wl-

ed ge the Itali an Istit uto Nazio nal e di Fisi ca Nuc lea re (INFN ),

the French Centre National de la Recher che Scien tifique

(CN RS), and the Fou nd ati on for Fun da ment al Res earc h on

Mat ter sup po rte d by the Ne therl an ds Or gani sa tion fo r

Sci ent if ic Rese arc h, for the const ru cti on and opera tio n of

the V irgo det ect or , and for t he c rea tion and supp ort of the E GO

co nsor tium . The autho rs als o grate ful ly ackn o wle dge res earc h

support f rom these agencies as well as by the Co uncil o f

Sci ent if ic and Indus tri al Rese arch of Indi a, Depar tme nt of

Science and T ech nology , India, Science & Engineering

Res earc h Board (SERB ), Ind ia, Mini st ry of Human

Res our ce De v elop me nt, In dia , the Spa nish Mini ste rio de

Economía y C ompetiti vidad, the Consell eria d ’ Ec onom ia i

Competitivitat and Co nselleria d ’ Educació, Cultura i

PRL 116, 061102 (2016)

PHYSICAL REVIEW LETTERS

week ending

12 FEBR U AR Y 2016

061102-8