Direct Observa1on of Gravita1onal Waves from the Merger and Inspiral of Two Black Holes

Direct observa1on of gravita1onal waves from the merger and inspiral of two black holes

Bruce Allen Max Planck Ins1tute for Gravita1onal Physics (Albert Einstein Ins1tute, AEI) February 12, 2016

Gravita1onal waves: the discovery which shows that Einstein was right

Avignon 24.4.2017 2 Outline • Brief introduc7on to gravita7onal waves • On 14 September 2015, 4 days before star7ng its ﬁrst observa7onal run O1, Advanced LIGO recorded a strong gravita7onal wave burst • Source unambiguous. In source frame: merger of a 29 and 36 solar mass BH • What did we see? How do we know it is two black holes? How can we be sure it is real? What was going on “behind the scenes”? What do we learn? Other discoveries from O1 • Status of O2, prospects for the future

References: PRL 116, 061102 (2016); PRX 6, 041015 (2016); Annalen der Physik, 529, 1600209 (2017).

Avignon 24.4.2017 3 Discovery Paper

Selected for a Viewpoint in Physics week ending PRL 116, 061102 (2016) PHYSICAL REVIEW LETTERS 12 FEBRUARY 2016 “In the ﬁrst 24 hours, not Observation of Gravitational Waves from a Binary Black Hole Merger B. P. Abbott et al.* (LIGO Scientific Collaboration and Virgo Collaboration) only was the page for (Received 21 January 2016; published 11 February 2016) On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10−21. It matches the waveform your PRL abstract hit predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater 160 0.03 380,000 @mes, but the than 5.1σ. The source lies at a luminosity distance of 410þ Mpc corresponding to a redshift z 0.09þ . −180 −0.04 5 4 ¼ In the source frame, the initial black hole masses are 36−þ4 M and 29−þ4 M , and the final black hole mass is 4 0.5 2 ⊙ ⊙ 62−þ4 M , with 3.0−þ0.5 M c radiated in gravitational waves. All uncertainties define 90% credible intervals. PDF of the paper was 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. downloaded 230,000 DOI: 10.1103/PhysRevLett.116.061102

I. INTRODUCTION The discovery of the binary pulsar system PSR B1913 16 þ @mes. This is far more hits In 1916, the year after the final formulation of the field by Hulse and Taylor [20] and subsequent observations of equations of general relativity, Albert Einstein predicted its energy loss by Taylor and Weisberg [21] demonstrated the existence of gravitational waves. He found that the existence of gravitational waves. This discovery, than any PRL ever, and the linearized weak-field equations had wave solutions: along with emerging astrophysical understanding [22], transverse waves of spatial strain that travel at the speed of led to the recognition that direct observations of the light, generated by time variations of the mass quadrupole amplitude and phase of gravitational waves would enable the frac@on of @mes that moment of the source [1,2].Einsteinunderstoodthat studies of additional relativistic systems and provide new gravitational-wave amplitudes would be remarkably tests of general relativity, especially in the dynamic small; moreover, until the Chapel Hill conference in strong-field regime. 1957 there was significant debate about the physical Experiments to detect gravitational waves began with it resulted in a download reality of gravitational waves [3]. Weber and his resonant mass detectors in the 1960s [23], Also in 1916, Schwarzschild published a solution for the followed by an international network of cryogenic reso- field equations [4] that was later understood to describe a nant detectors [24]. Interferometric detectors were first was unusually high. black hole [5,6], and in 1963 Kerr generalized the solution suggested in the early 1960s [25] and the 1970s [26].A to rotating black holes [7]. Starting in the 1970s theoretical study of the noise and performance of such detectors [27], work led to the understanding of black hole quasinormal and further concepts to improve them [28],ledto proposals for long-baseline broadband laser interferome- Hundreds of thousands of modes [8–10], and in the 1990s higher-order post- Newtonian calculations [11] preceded extensive analytical ters with the potential for significantly increased sensi- studies of relativistic two-body dynamics [12,13]. These tivity [29–32]. By the early 2000s, a set of initial detectors advances, together with numerical relativity breakthroughs was completed, including TAMA 300 in Japan, GEO 600 in Germany, the Laser Interferometer Gravitational-Wave people actually wanted to in the past decade [14–16], have enabled modeling of binary black hole mergers and accurate predictions of Observatory (LIGO) in the United States, and Virgo in their gravitational waveforms. While numerous black hole Italy. Combinations of these detectors made joint obser- candidates have now been identified through electromag- vations from 2002 through 2011, setting upper limits on a read the whole paper!” variety of gravitational-wave sources while evolving into netic observations [17–19], black hole mergers have not previously been observed. a global network. In 2015, Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations [33–36]. *Full author list given at the end of the article. A century after the fundamental predictions of Einstein and Schwarzschild, we report the first direct detection of Published by the American Physical Society under the terms of Robert Garistro the Creative Commons Attribution 3.0 License. Further distri- gravitational waves and the first direct observation of a bution of this work must maintain attribution to the author(s) and binary black hole system merging to form a single black PRL editor the published article’s title, journal citation, and DOI. hole. Our observations provide unique access to the 0031-9007=16=116(6)=061102(16) 061102-1 Published by the American Physical Society

Avignon 24.4.2017 4 Gravita1onal Waves

⇤˙ /June 1916 ⇤ << ⇤ It follows that the gravita@onal ﬁeld propagates at the speed out light. We will inves@gate these gravita@onal wave solu@ons and the sources that give rise ⇤˙ /⇤ >> ⇤ to them. H2H2 df d⇥ =¯h 0 inﬂation • Spin 2 massless, propagate at c gw 42c3 f • For v<

Avignon 24.4.2017 5

0-1 b) Test Mass Advanced LIGO Detectors

H1 Livingston & 10 ms light travel time

Hanford = 4 km y L 3000 km aparta) L1 ΔL/L b) Test Mass Test Mass Sensi7ve from 30 to 2000 Hz Power• Beam Recycling Lx = 4 km H1 • Strain h=SplitterΔL/L 10 ms light travel time • In 100 Hz band at

= 4 km -22

y Laser 20 W 100 kW Circulating Power

L minimum, r.m.s. noise h~10 a) L1 Source Test Test O1 noise a factor ~3 above Mass Mass Signal• Recyclingdesign sensi7vity

Test Photodetector Mass Avignon 24.4.2017 6 Power Beam L = 4 km Recycling Splitter x

Laser 20 W 100 kW Circulating Power Source Test Test Mass Mass Signal Recycling Photodetector Copyright: Caltech/MIT LIGO Lab, 2016

Avignon 24.4.2017 7 GW150914 • Engineering run had begun 17 August 2015, for tuning, calibra7on, injec7on tests, and noise characterisa7on studies. • First observing run O1 (“science opera7ons mode”) scheduled to start on 18 September 2015 • VIRGO not opera7ng (under construc7on) GEO-600 lost lock 10 minutes before (AND not suﬃciently sensi7ve at low frequencies) • Event at 09:50 UTC on 14 September 2015, four days before planned O1 start 02:50 at LIGO Hanford, WA 04:50 at LIGO Livingston, LA 11:50 in Germany

Avignon 24.4.2017 8 AEI Hannover, September 14, 2015

Marco Drago Andrew Lundgren • Monday morning 11:50 • At 12:54, Marco sent an email to the • Coherent waveburst pipeline running collabora7on, asking for confirma7on at Caltech, event database had ~1000 that it’s not a hidden test signal entries (hardware injec7on) • Marco and Andy checked injec7on • Next hours: flurry of emails, decision flags and logbooks, data quality, made to lock down sites, freeze instrument Qscans of LHO/LLO data. state • Called LIGO operators: “everyone’s gone home”

Avignon 24.4.2017 9 Black hole separation (R ) 4 3 2 1 0.5 S

Inspiral Merger Ringdown 0 2 residuals -0.5 The Chirp

1 ) 1 -21 ) -21 0 ΔL/L 0 Strain (10 Strain (10

-1 H1 measured strain, bandpassed -1 H1 estimated strain incident L1 measured strain, bandpassed H1 estimated strain, bandpassed

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 Time (seconds) Time (seconds) • Bandpass ﬁltered 35-350 Hz, • Signal visible to the naked eye: some instrumental and ~200 ms calibra7on lines removed • “Instantaneous” SNR ~5, • Hanford inverted, shioed 7.1 op7mal ﬁlter SNR ~ 24 ms earlier

Avignon 24.4.2017 10 What could it be?

Copyright: Salford University Avignon 24.4.2017 11 Gravita1onal waves from orbi1ng masses 1m Equations orbital angular Gm2 r 2Gm Newton : frequency = m!2 ⍵ r3 = 1 Equations1 Equationsm r2 2 ) !2 r Gm2 r 2Gm 1 EquationsNewton : =Gmm!22 r3 =r 2Gm r2 2 ) 2 !2 23 2 2/3 5/3 1 !r 2 2 1 = m!!r 2 Gmr = Gm2 G m E =Gmm2 r+ rm 2 2)Gm = ! = !2/3 mechanicalNewton : 2 =2m!2 2 2r3 = r 2r 24/3 2 2 2 2 2/3 5/3 1 !r r2 1 !r 2 Gm2 ) Gm ! G m E = m + m = = !2/3 mechanical 2 2 2 2 r 2r 2 24/3 2 2/3 5/3 1 !r 2 1 !r 2 Gm Gm G m 2/3 Emechanical = m + m = = 4/3 ! 2 2 22 G 2 d32 r d3 2/3 2r5/3 8G 2 213/3G7/3m10/3 Einstein1 !r GW2 1 Luminosity!r 2 Gm = GmQ G Q m = 2/3m2r4!6 = !10/3 Emechanical = m + m G d3 =d53 3 ab8=G 3 ab 213/!3G57/3m10/3 5 Einstein2 GW2 Luminosity2 =2 Qr 5c Qdt2r= mdt2r4!264/=3 5c !10/3 5c 5c5 dt3 ab dt3 ab 5c5 5c5 3 3 13/3 7/3 10/3 G d d 8G 2 4 6 2 G m 10/3 Qab Qab = m r ! = ! 5c5 dt3 dt3 5c5 52/c35 5/3 3 3 13d/3 2/73/35/310/3 G m d! G d d 8G d2 4 6 2 GG m m 1/3 d10!/3 1/3 EinsteinQ Einstein GW LuminosityQ GW= Luminosity = m rE ! = = Emechanical! =! ! 5c5 dt3 ab dt3 ab 5c5 dt mechanicaldt 3 52c15/3 dt 3 21/3 dt · · 2/3 5/3 14/3 5/3 5/d3 G m 1/3 d! GWd! Luminosity3 2 G = m 14E11/mechanical3/3 5/3 5=/3 ! get mass from = · d! 3dt2 ! G m 311/231/3 dt dt 5c=5 · 2/3 5/3 ! frequency and its d dt G 5mc5 1/3 d·! GW Luminosity = Emechanical = ! 14/3 1/53/3 5/3 rate of change! dt d0-0! 3 23 2G m dt 12 = · ·Avignon 24.4.2017 !11/3 dt 0-05c5 d! 3 214/3G5/3m5/3 = · !11/3 dt 5c5 0-0

0-0 Each orbit makes two gravita1onal wave cycles

ΔL/L = gravita7onal wave strain

t 1 orbit

Avignon 24.4.2017 13 Black hole separation (R ) 4 3 2 1 0.5 S

Inspiral Merger Ringdown 0 2 residuals The Chirp -0.5 1 ORBIT 1 ORBIT 1 1 ORBIT ) 1 1 ORBIT -21 ) -21 0 0 Strain (10 Strain (10

-1 H1 measured strain, bandpassed -1 H1 estimated strain incident L1 measured strain, bandpassed H1 estimated strain, bandpassed

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 Time (seconds) Time (seconds)

Avignon 24.4.2017 14 LIGO-P150914-v12

an orbital frequency of 75 Hz without contact. Further- more, 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 multi- ple, widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise, to provide source sky localization from relative arrival times, and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector [32], a modi- fied Michelson interferometer (see Fig. 3) that measures gravitational-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 Lx = Ly = L =4km. 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 differ- ential length variation alters the phase difference between FIG. 2. Top: Estimated gravitational-wave strain amplitude from GW150914 projected onto H1. This shows the full band- the two light fields returning to the beamsplitter, transmit- width of the waveforms, without the filtering used for Fig. 1. ting an optical signal proportional to the gravitational-wave The inset images show numerical-relativity models of the black strain to the output photodetector. hole horizons as the black holes coalesce. Bottom: The Kep- To achieve sufficient sensitivity to measure gravitational lerian effective black hole separation in units of Schwarzschild waves the detectors include several enhancements to the 2 radii (RS =2GM/c ) and the effective relative velocity given basic Michelson interferometer. First, each arm contains by the post-Newtonian parameter v/c =(GM⇡f/c3)1/3, where a resonant optical cavity, formed by its two test mass mir- f is the gravitational-wave frequency calculated with numerical rors, that multiplies the effect of a gravitational wave on relativity and M is the total mass (value from Table I). the light phase by a factor of 300 [48]. Second, a partially transmissive power-recycling mirror at the input provides additional resonant buildup of the laser light in the interfer- At the lower frequencies, such evolution is characterized ometer as a whole [49, 50]: 20 W of laser input is increased by theMasses from the rate of frequency increase chirp mass [46] to 700 W incident on the beamsplitter, which is further in-

3/5 3 3/5 creased to 100 kW circulating in each arm cavity. Third, (m1m2) c 5 8/3 11/3 ˙ a partially transmissive signal-recycling mirror at the out- = 1/5 = ⇡ f f = 30 M, ⦿ M (m1 + m2) G 96 put optimizes the gravitational-wave signal extraction by  broadening the bandwidth of the arm cavities [51, 52]. where f and f˙ are the observed frequency and its time The interferometer is illuminated with a 1064-nm wave- derivative and G and c are the gravitational constant and length Nd:YAG laser, stabilized in amplitude, frequency, speed of light. Estimating f and f˙ from the data in Fig. 1 and beam geometry [53, 54]. The gravitational-wave sig- we obtain a chirp mass of 30 M , implying that the nal is extracted at the output port using homodyne read- M '> total mass M = m1 + m2 is 70 M in the detector out [55]. frame. This bounds the sum of the⇠ Schwarzschild radii of These interferometry techniques are designed to maxi- the binary components to 2GM/c2 > 210 km. To reach mize the conversion of strain to optical signal, thereby min- an orbital frequency of 75 Hz (half the⇠ gravitational-wave imizing the impact of photon shot noise (the principal noise frequency) the objects must have been very close and very at high frequencies). High strain sensitivity also requires compact; equal Newtonian point masses orbiting at this fre- that the test masses have low displacement noise, which quency would be only 350 km apart. A pair of neutron is achieved by isolating them from seismic noise (low fre- ' stars, while compact, wouldAvignon 24.4.201 not have7 the required mass, quencies)15 and designing them to have low thermal noise while a black hole-neutron star binary with the deduced (mid frequencies). Each test mass is suspended as the ﬁnal chirp mass would have a very large total mass, and would stage of a quadruple pendulum system [56], supported by thus merge at much lower frequency. This leaves black an active seismic isolation platform [57]. These systems holes as the only known objects compact enough to reach collectively provide more than 10 orders of magnitude of

3 LIGO-P150914-v12

Detectors — Gravitational-wave astronomy exploits multi- ple, widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise, to provide source sky localization from relative arrival times, and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector [32], a modi- fied Michelson interferometer (see Fig. 3) that measures gravitational-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 Lx = Ly = L =4km. 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 differ- ential length variation alters the phase difference between FIG. 2. Top: Estimated gravitational-wave strain amplitude from GW150914 projected onto H1. This shows the full band- the two light fields returning to the beamsplitter, transmit- width of the waveforms, without the filtering used for Fig. 1. ting an optical signal proportional to the gravitational-wave The inset images show numerical-relativity models of the black strain to the output photodetector. hole horizons as the black holes coalesce. Bottom: The Kep- To achieve sufficient sensitivity to measure gravitational lerian effective black hole separation in units of Schwarzschild waves the detectors include several enhancements to the 2 radii (RS =2GM/c ) and the effective relative velocity given basic Michelson interferometer. First, each arm contains by the post-Newtonian parameter v/c =(GM⇡f/c3)1/3, where a resonant optical cavity, formed by its two test mass mir- f is the gravitational-wave frequency calculated with numerical rors, that multiplies the effect of a gravitational wave on relativity and M is the total mass (value from Table I). the light phase by a factor of 300 [48]. Second, a partially transmissive power-recycling mirror at the input provides additional resonant buildup of the laser light in the interfer- At the lower frequencies, such evolution is characterized Black hole separation (R ) 4 3 2 1 0.5 ometer as a whole [49, 50]: 20 WS of laser input is increased Can only be two black holes!by the chirp mass [46] to 700 W incident on the beamsplitter, which is further in-

3/5 3 3/5 creased to 100Inspiral kW circulating in each arm cavity.Merger Third, Ringdown 0 (m1m2) c 5 8/3 11/3 ⦿ ˙ a2 partially transmissive signal-recycling mirror at the out- • Chirp mass M ~ 30 M => = 1/5 = ⇡ f f , M (m1 + m2) G 96 put optimizes the gravitational-wave signal extraction by residuals  Sum of Schwarzschild radii -0.5 ≥206km broadening the bandwidth of the arm cavities [51, 52]. where f and f˙ are the observed frequency and its time The interferometer is illuminated with a 1064-nm wave- derivative and G and c are the gravitational constant and length Nd:YAG laser, stabilized in amplitude, frequency,

At peak f = 150 Hz, orbital ) • GW 1 speed of light. Estimating f and f˙ from the data in Fig. 1 and1 beam geometry [53, 54]. The gravitational-wave sig- frequency = 75 Hz separa7on of we obtain a chirp mass of 30 M , implying that the -21 nal is extracted at the output port using homodyne read- M '> ) total mass M = m1 + m2 is 70 M in the detector out [55]. Newtonian point masses 346 km -21 frame. This bounds the sum of the⇠ Schwarzschild radii of These interferometry techniques are designed to maxi- 6 the binary components to 2GM/c2 > 210 km. To reach mize the conversion of strain to optical signal, thereby min- 0 • Ordinary stars are 10 0 km in size an orbital frequency of 75 Hz (half the⇠ gravitational-wave Strain (10 imizing the impact of photon shot noise (the principal noise 4 (merge at mHz). White dwarfs are 10frequency) the objects must have been very close and very at high frequencies). High strain sensitivity also requires compact; equal Newtonian point masses orbiting at this fre- that the test masses have low displacement noise, which Strain (10 km (merge at 1 Hz). They are too big quency would be only 350 km apart. A pair of neutron is achieved by isolating them from seismic noise (low fre- ' to explain this! -1 H1 measuredstars, strain, while bandpassed compact, would not have the required mass, -1quencies)H1 and estimated designing strain them incident to have low thermal noise L1 measuredwhile strain, a black bandpassed hole-neutron star binary with the deduced (mid frequencies).H1 estimated Each strain, test mass bandpassed is suspended as the ﬁnal chirp mass would have a very large total mass, and would stage of a quadruple pendulum system [56], supported by • Neutron stars are also not possible:thus merge at much lower frequency. This leaves black an active seismic isolation platform [57]. These systems 0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 m1 = 4 M⦿ => m2=600 M⦿ holes as theTime only known(seconds) objects compact enough to reach collectively provide more thanTime 10 orders (seconds) of magnitude of

=>Schwarzschild radius 1800km => too 3 big! Only black holes are heavy enough and small enough! Avignon 24.4.2017 16 Real? Or a detector ar1fact? • Instruments in normal opera7on and stable since September 12th, 2015 (apart from deliberate interven7on) • aLIGO can see such sources at 6 7mes the distance => 6x6x6 ~ 200 7mes the rate at ini7al LIGO instruments • Last scien7sts leo sites 2 hours (LHO) and 15 minutes (LLO) before the event. Operators only. Stefan Ballmer and Evan Hall, departed the LHO site soon aoer • Waveform does not resemble instrumental midnight, 2 hours before the event glitches or artefacts • Suscep7bility to radio, acous7c, magne7c, seismic and other external disturbances measured. These external disturbances are monitored: can not explain more than 6% of the observed GW amplitude

• Was not an accidental or malicious hardware Robert Schoﬁeld and Anamaria Eﬄer, injec7on: recorded control loop signals permit departed the LLO site at 04:35am reconstruc7on of the actuators: no fake signal 15 minutes before the event was added

Avignon 24.4.2017 17 Random Noise?

Much longer than 200,000 years before noise in the detector would mimic this signal, or a similar signal of the types that we search for.

Avignon 24.4.2017 18 The Movie

• Alessandra Buonanno and postdocs Sergei Ossokine and Roland Haas, with the SXS Collabora7on Avignon 24.4.2017 19 Luminosity Distance Es1mate

• Schwarzschild radius ~ 200 km • Metric strain h is order h~0.1 at Schwarzschild radius • Strain h fall oﬀ like inverse of distance d • At detector, maximum metric perturba7on h ~ 10-21 • This implies a distance d ~ 1020 x 200 km ~ 2 x 1025 m ~ 2 x 109 light years (correct to factor of two)

Avignon 24.4.2017 20 LIGO-P150914-v12 LIGO-P150914-v12 nonetheless effectivelynonetheless recover systems effectively with recover misaligned systems with misaligned TABLE I. Source parametersTABLE for I. Source GW150914. parameters We report for GW150914. me- We report me- spins in the parameterspins region in of the GW150914 parameter region [44]. Approx- of GW150914 [44]. Approx- dian values with 90% credibledian values intervals with 90% that includecredible statistical intervals that include statistical imately 250,000 templateimately waveforms 250,000 are template used to waveforms cover this are usederrors, to and cover systematic this errorserrors, from and systematic averaging the errors results from of averaging dif- the results of dif- parameter space. parameter space. ferent waveform models.ferent Masses waveform are given models. in the Masses source are frame, given in the source frame, The search calculatesThe the search matched-filter calculates signal-to-noise the matched-filterto signal-to-noise convert to the detectorto frameconvert multiply to the detector by (1 + framez) [87]. multiply The by (1 + z) [87]. The ratio ⇢(t) for each templateratio ⇢(t in) for each each detector template and in identi- each detectorsource and redshift identi- assumessource standardParameters from ficng (in source frame) redshift cosmology assumes [88]. standard cosmology [88]. fies maxima of ⇢(t)fieswith maxima respect of to⇢ the(t) timewith of respect arrival to the time of arrival +5 +5 of the signal [79–81].of the For signal each maximum[79–81]. For we calcu- each maximumPrimary we black calcu- hole massPrimary black hole mass 36 4 M 36 4 M late a chi-squared statisticlate a chi-squared2 to test whether statistic the2 datato test in whether the data in +4 • Radiated+4 energy: 3M⦿ (±0.5) r r Secondary black hole massSecondary black hole mass 29 4 M 29 4 M several different frequencyseveral bands different are frequency consistent bands with the are consistent with the +4 +4 56 2 2 Final black hole mass Final black hole mass 62 4 M Peak62 luminosity:4 M 3.6 x 10 erg/s matching template [82].matching Values template of r near [82]. unity Values indicate of r near unity indicate • 2 2 +0.05 +0.05 that the signal is consistentthat the with signal a coalescence. is consistent with If r ais coalescence.Final black If holer is spin Final black hole spin 0.67 0.07 0.67 0.07 (±15%): 200 solar masses per greater than unity, ⇢(greatert) is re-weighted than unity, as⇢(t⇢ˆ) is= re-weighted⇢/[(1 + as ⇢ˆ = ⇢/[(1 + +160 +160 Luminosity distance Luminosity distance 410 180 Mpc 410 180 Mpc 2 3 1/6 2 3 1/6 2 (r) )/2] [83, 84].( Ther) ) final/2] step[83, enforces 84]. The coincidence final step enforces coincidence +0.03 second!+0.03 (About 1µW/cm at between detectors by selectingbetween detectors event pairs by that selecting occur eventwithin pairs thatSource occur redshift, withinz Source redshift, z 0.09 0.04 0.09 0.04 12 a 15 ms window anda come15 ms from window the same and come template. from The the same template. The detector, ~10 millicrab!) 15 ms window is determined15 ms window by the 10 is determinedms inter-site by propa- the 10 ms inter-site propa- • Spins s1 and s2 only weakly gation time plus 5 msgation for uncertainty time plus in5 arrivalms for time uncertainty of weak in arrivalof the time source of weak parametersof the [91]. source The parameters initial and final [91]. masses, The initial and final masses, signals. We rank coincidentsignals. events We rank based coincident on the quadrature events based on the quadrature final spin, distance andfinal redshift spin, distanceof the source and redshift are shown of the in sourceconstrained: are shown in not extreme. sum ⇢ˆc of the ⇢ˆ fromsum both⇢ˆ detectorsc of the ⇢ˆ [43].from both detectors [43]. Table I. The spin of theTable primary I. The black spin hole of the is constrainedprimary black to hole is constrained to To produce backgroundTo produce data for background this search datathe SNR for thisbe search< 0. the7 (90% SNR crediblebe < interval)0.7 (90% indicating credible it interval) is not max- indicatingConsistent it is not max- with merger of two non- maxima of one detectormaxima are time-shifted of one detector and a are new time-shifted set of imally and a new spinning, set of whileimally the spin spinning, of the while secondary the spin is only of the secondary is only spinning black holes. coincident events is computed.coincident events Repeating is computed. this procedure Repeatingweakly this procedure constrained. Theseweakly source constrained. parameters These are source discussed parameters are discussed 107 times produces a10 noise7 times background produces analysis a noise background time analysis time ⇠ ⇠ in detail in [38]. Thein parameter detail in [38].uncertainties The parameter include uncertainties sta- • Final include spin of sta- 0.67 is about 6000 rpm equivalent to 608 000equivalentyears. to 608 000 years. tistical errors, and systematictistical errors, errors and from systematic averaging errors the re- from averaging the re- To account for the searchTo account background for the noise search varying backgroundsults noise of different varying waveformsults of models. different waveform models. across the target signalacross space, the candidate target signal and space, background candidate and background Using the fits to numericalUsing thesimulations fits to numerical of binary simulations black Avignon 24.4.201 of binary7 black 21 events are divided intoevents three are search divided classes into based three onsearch tem- classes based on tem- hole mergers in [92, 93],hole we mergers provide in estimates [92, 93], we of the provide mass estimates of the mass plate length. The rightplate panel length. of Fig. The 4 right shows panel the ofback- Fig. 4 shows the back- and spin of the final blackand spin hole, of the the total final energy black hole, radiated the in total energy radiated in ground for the searchground class of for GW150914. the search The class GW150914 of GW150914. The GW150914 gravitational waves, andgravitational the peak gravitational-wave waves, and the peak lumi- gravitational-wave lumi- detection-statistic valuedetection-statistic of ⇢ˆ = 23.6 valueis larger of ⇢ˆ than= any 23.6 is larger than any c c nosity [38]. The estimatednosity total [38]. energy The estimated radiated in total gravita- energy radiated in gravita- background event, sobackground only an upper event, bound so only can be an placed upper bound can be placed +0.5 2 +0.5 2 tional waves is 3.0 0tional.5 M c waves. The is system3.0 0.5 reachedM c . a The peak system reached a peak on its false alarm rate.on Across its false the alarm three rate. search Across classes the this three search classes this +0.5 56 +0.5 56 gravitational-wave luminositygravitational-wave of 3.6 0. luminosity4 10 erg of/3s,.6 0.4 10 erg/s, bound is 1 in 203 000boundyrs. This is 1 in translates203 000 toyrs. a false This alarm translates to a false alarm 7 7 +30 2 +30 ⇥ 2 ⇥ < 2 10 < 2 105.1 equivalent5.1 to 200 20 Mequivalentc /s. to 200 20 M c /s. probability probability, corresponding to , corresponding. to . A second, independent⇥ A matched-filtersecond, independent⇥ analysis matched-filter that uses analysisSeveral that analyses uses haveSeveral been analyses performed have to beendetermine performed to determine a different method fora different estimating method the significance for estimating of its the significancewhether or not of its GW150914whether is consistent or not GW150914 with a binary is consistent black with a binary black events [85, 86], alsoevents detected [85, GW150914 86], also detected with identical GW150914hole with system identical in generalhole relativity system [94]. in general A first relativity consistency [94]. A first consistency signal parameters andsignal consistent parameters significance. and consistent significance.check involves the masscheck and involves spin of the the mass final and black spin hole. of the final black hole. When an event is confidentlyWhen an identified event is confidently as a real grav- identifiedIn as general a real relativity, grav- theIn general end product relativity, of a black the end hole product binary of a black hole binary itational wave signal,itational as for GW150914, wave signal, the as background for GW150914,coalescence the background is a Kerrcoalescence black hole, is which a Kerr is fully black described hole, which is fully described used to determine theused significance to determine of other the significance events is re- of otherby its events mass is and re- spin.by For its quasicircular mass and spin. inspirals, For quasicircular these are inspirals, these are estimated without theestimated contribution without of this the event. contribution This is of thispredicted event. uniquelyThis is bypredicted Einstein’s uniquely equations by as Einstein’s a function equations of as a function of the background distributionthe background shown as distribution a purple line shown in the as a purplethe masses line andin the spins ofthe the masses two progenitor and spins ofblack the holes. two progenitor Us- black holes. Us- right panel of Fig. 4.right Based panel on this, of Fig. the 4. second Based most on this, sig- the seconding fitting most formulae sig- calibrateding fitting to formulae numerical calibrated relativity to sim- numerical relativity sim- nificant event has a falsenificant alarm event rate has of 1 a per false 2.3 alarm years rate and of 1 perulations 2.3 years [92], and we verifiedulations that [92], the remnant we verified mass that and the spin remnant mass and spin corresponding Poissoniancorresponding false alarm Poissonian probability false of 0.02. alarm probabilitydeduced from of 0.02. the earlydeduced stage of from the the coalescence early stage and of those the coalescence and those Waveform analysis ofWaveform this event analysis indicates of that this if event it is astro- indicatesinferred that if it independently is astro- inferred from the independently late stage are from consistent the late stage are consistent physical in origin it isphysical also a binary in origin black it is hole also [44]. a binary blackwith hole [44].each other, withwith no evidence each other, for with disagreement no evidence from for disagreement from general relativity. general relativity. Source discussion —Source The matched discussion filter— search The matched is opti- filter searchWithin is the opti- Post-NewtonianWithin the formalism, Post-Newtonian the phase formalism, of the phase of mized for detecting signals,mized for but detecting it provides signals, only approxi- but it providesthe only gravitational approxi- waveformthe gravitational during the waveform inspiral can during be ex- the inspiral can be ex- mate estimates of themate source estimates parameters. of the To source refine parameters. them we Topressed refine as them a power-series we pressed in f as1/ a3. power-series The coefficients in f 1 of/3. this The coefficients of this use general relativity-baseduse general models relativity-based that include precessing models that includeexpansion precessing can be computedexpansion in general can be relativity.computed Thus in general we relativity. Thus we spins [77, 78, 89, 90],spins and [77, for each 78, 89, model 90], perform and for eacha co- modelcan perform test for aconsistency co- can with test general for consistency relativity with [95, general 96] by relativity [95, 96] by herent Bayesian analysisherent to Bayesian derive posterior analysis distributions to derive posteriorallowing distributions the coefficientsallowing to deviate the coefficients from the nominal to deviate val- from the nominal val-

7 7 1 Equations 1 Equations

Gm2 r 2Gm Gm2 r 2Gm = m!2 r3 = = m!2 r3 = r2 2 ) !2 r2 2 ) !2 Es1mate of Radiated Energy in GWs 2 2 2/3 5/3 2 2 2/3 5/3 1 !r 2 1 !r 2 Gm 1 Gm!r 2 1G !mr 2 Gm Gm G m E = m + m E == m =+ m !2/3 = = !2/3 mechanical 2 2 2 2 mechanical r 2 2r2 2 24/23 r 2r 24/3 2 Set m = 35 M ⦿ and r=346 km, obtain Emechanical ~ 3 M ⦿c

G d3 d3 8G G d3 213/3Gd73/3m10/3 8G 213/3G7/3m10/3 Q Q = m2r4!6 = Q Q =!10/3m2r4!6 = !10/3 5c5 dt3 ab dt3 ab 5c5 5c5 dt3 ab dt5c35 ab 5c5 5c5

2/3 5/3 2/3 5/3 d G m 1/3 d! G m 1/3 d! GW Luminosity = E GW= Luminosity! = E = ! dt mechanical 3 21/3 dtdt mechanical 3 21/3 dt · · 14/3 5/3 5/3 14/3 5/3 5/3 d! 3 2 G m 11/3 d! 3 2 G m 11/3 = · Avignon 24.4.201!7 = · 22 ! dt 5c5 dt 5c5

0-0 0-0 Electromagne1c Follow-ups

Initial GW Initial Updated GCN Circular Final Burst Recovery GCN Circular (identiﬁed as BBH candidate) sky map

Fermi GBM, LAT, MAXI, Swift Swift Fermi LAT, IPN, INTEGRAL (archival) XRT XRT MAXI

Swift UVOT, SkyMapper, MASTER, TOROS, TAROT, VST, iPTF, , Pan-STARRS1 BOOTES-3 MASTER Keck TOROS Pan-STARRS1, KWFC, QUEST, DECam, LT, P200, Pi of the Sky, PESSTO, UH VST

VISTA ASKAP, ASKAP, , , MWA VLA VLA LOFAR MWA LOFAR LOFAR VLA

100 101 102 t t (days) merger

Execu1ve Summary: no electromagne1c emission

Avignon 24.4.2017 23 Binary Black Holes in O1 3

29 + 35 M⦿, SNR 24

13 + 23 M⦿, SNR 10

8 + 15 M⦿, SNR 13

Avignon 24.4.2017 24 FIG. 1. Left: Amplitude spectral density of the total strain noise of the H1 and L1 detectors, S( f ), in units of strain per pHz, and the recovered signals of GW150914, GW151226 and LVT151012 plotted so that the relative amplitudes can be related to the SNR of the signal p (as described in the text). Right: Time evolution of the recovered signals from when they enter the detectors’ sensitive band at 30 Hz. Both ﬁgures show the 90% credible regions of the LIGO Hanford signal reconstructions from a coherent Bayesian analysis using a non-precessing spin waveform model [46].

The gravitational-wave signal from a BBH merger takes the form. However, shorter duration artifacts can pollute the noise form of a chirp, increasing in frequency and amplitude as the background distribution of CBC searches. Many of these arti- black holes spiral inwards. The amplitude of the signal is facts have distinct signatures [49] visible in the auxiliary data maximum at the merger, after which it decays rapidly as the fi- channels from the large number of sensors used to monitor in- nal black hole rings down to equilibrium. In the frequency do- strumental or environmental disturbances at each observatory main, the amplitude decreases with frequency during inspiral, site [50]. When a significant noise source is identified, con- as the signal spends a greater number of cycles at lower fre- taminated data are removed from the analysis data set. After quencies. This is followed by a slower falloff during merger applying this data quality process, detailed in [51], the remain- and then a steep decrease during the ringdown. The amplitude ing coincident analysis time in O1 is 48.6 days. The analyses of GW150914 is significantly larger than the other two events search only stretches of data longer than a minimum duration, and at the time of the merger the gravitational-wave signal to ensure that the detectors are operating stably. The choice is lies well above the noise. GW151226 has lower amplitude but different in the two analyses and reduces the available data to sweeps across the whole detector’s sensitive band up to nearly 46.1 days for the PyCBC analysis and 48.3 days for the Gst- 800 Hz. The corresponding time series of the three wave- LAL analysis. forms are plotted in the right panel of Figure 1 to better vi- sualize the difference in duration within the Advanced LIGO band: GW150914 lasts only a few cycles while LVT151012 III. SEARCH RESULTS and GW151226 have lower amplitude but last longer. The analysis presented in this paper includes the total set of Two different, largely independent, analyses have been im- O1 data from September 12, 2015 to January 19, 2016, which plemented to search for stellar-mass BBH signals in the data contains a total coincident analysis time of 51.5 days accu- of O1: PyCBC [2–4] and GstLAL [5–7]. Both these analyses mulated when both detectors were operating in their normal employ matched filtering [52–60] with waveforms given by state. As discussed in [13] with regard to the first 16 days models based on general relativity [8, 9] to search for gravi- of O1 data, the output data of both detectors typically con- tational waves from binary neutron stars, BBHs, and neutron tain non-stationary and non-Gaussian features, in the form of star–black hole binaries. In this paper, we focus on the results transient noise artifacts of varying durations. Longer duration of the matched filter search for BBHs. Results of the searches artifacts, such as non-stationary behavior in the interferom- for binary neutron stars and neutron star–black hole binaries eter noise, are not very detrimental to CBC searches as they are reported in [61]. These matched-filter searches are com- occur on a time-scale that is much longer than any CBC wave- plemented by generic transient searches which are sensitive to VOLUME 26, NUMBER 21 PHYSICAL REVIEW LETTERS 24 Mwv 1971

0 Permanent address: Institute for Atomic Physics, tion from the obsemed neutron-capture 2+-level den- Bucharest, Rumania. sity at 7.6-MeV excitation. ~See, e.g., G. A. Keyworth, G. C. Kyker, Jr., E. G. ~N. Williams, T. H. Kruse, M. E. Williams, J. A. Bilpuch, and H. W. Newson, Nucl. Phys. 89, 590 (1966). Fenton, and G. L. Miller, to be published. M. Maruyama, K. Tsukada, K. Ozawa, F. Fujimoto, H. Feshbach, A. K. Kerman, and R. H. Lemmer, K. Komaki, M. Mannami, and T. Sakurai, Nucl. Phys. Ann. Phys. (New York) 41, 280 (1967); R. A. Ferrell A145, 581 (1970). and W. M. MacDonald, Phys. Rev. Lett. 16, 187 (1966). W. M. Gibson, M. Maruyama, D. W. Mingay, J. P. Intermediate St~cthe in Nuclear Reactions, edited F. Sellschop, G. M. Temmer, and R. Van Bree, Bull. by H. P. Kennedy and R. Schrils (University of Kentucky Amer. Phys. Soc. 16, 557 (1971). Press, Lexington, Ky. , 1968). G. M. Temmer, M. Maruyama, D. W. Mingay, J. D. Moses, thesis, Duke University, 1970 (unpub- M. Petrascu, and R. Van Bree, Bull. Amer. Phys. Soc. lished). 16, 182 (1971). ~3D. P. Lindstrom, H. W. Newson, E. G. Bilpuch, and L. H. Goldman, Phys. Rev. 165, 1203 (1968). G. E. Mitchell, to be published. W. Darcey, J. Fenton, T. H. Kruse, and M. E. Will- J. C. Browne, H. W. Newson, E. G. Bilpuch, and iams, unpublished. G. E. Mitchell, Nucl. Phys. A153, 481 (1970). R. Van Bree, unpublished computer program based ~5J. D. Mosey, private communication. in part on B. Teitelman and G. M. Temmer, Phys. Rev. L. Meyer-Schutzmeister, Z. Vager, R. E. Segel, 177, 1656 (1969), Appendix. This program does nof; and P. P. Singh, Nucl. Phys. A108, 180 (1968). allow for identical spins and parities, and the fit is ~YJ. A. Farrell, G. C. Kyker, Jr., E. G. Bilpuch, and therefore very tentative. H. W. Newson, Phys. Lett. 17, 286 (1965). J. R. Huizenga, private communication. This re- J. E. Monahan and A. J. Elwyn, Phys. Rev. Lett. 20, Hawking’s Area Theorem PRL 21, 1344 (1971)presents the best estimate, using a slight extrapola- 1119 (1968).

Gravitational Radiation from Colliding Black Holes

S. W. Hawking Institute of Theoretical Astronomy, University of Cambridge, Cambridge, England • Plug in m1, m2, mf and sf: it’s (Received 11 March 1971)

It is shown that there is an upper bound to the energy of the gravitational radiation sa7sﬁed! emitted when one collapsed object captures another. In the case of two objects with equal masses m and zero intrinsic angular momenta, this upper bound is (2-W2) m. ' • Problem: most of the SNR is before Weber' has recently reported coinciding mea- collapsed objects.2Up⇡iftto now no limits on the ef- surements of short bursts of gravitational radia-x(f)ficiencyh⇤(offthe)eprocesses have been known. The tion at a frequency⇢(oft1660)=Hz. These occurdf at a object of this Letter is to show that there is a the merger, so only values of m1, rate of about one per day and the bursts appear limit for the second process. For the case of to be coming from the center of the galaxy. It twoScollidingh(fcollapsed) objects, each of mass m seems likely'4 that the probabilityZof a burst and zero angular momentum, the amount of ener- m2 are determined independently. causing a coincidence between %eber's detectors gy that can be carried away by gravitational or is less than, . If one allows for this and assumes any other form of radiation is less than (2-v 2)m. that the radiation is broadband, one finds that the I assume the validity of the Carter-Israel con- The value of mf and sf are energy flux in gravitational radiation must be at jucture'' that the metric outside a collapsed ob- least 10'c erg/cm' day. 4 This would imply a ject settles down to that of one of the Kerr family determined by numerical rela7vity mass loss from2 the center of the galaxy of about2 of solutions' with positive mass m and angular 20 000Mmo/yr.f It is1+therefore possible1 that sthef >momentum a per unit mass less than or equal to am which G=c =1. mass of the galaxy might have been considerably m. (I using units in ) Each of 4 3 2 1 in the than it is now. ' This makes it these solutions contains a nonsingular event hori- Black hole separation (R ) (which gives the matching higher 0.5past S important to estimate✓ the efficiencyq with which ◆ zon, two-dimensional sections of which are topo- rest-mass energy can be converted into gravita- graphically spheres with area' tional radiation.2 Clearly nuclear reactions are 2 waveforms). GUARANTEED to 0 2 8wm[m+(m a) ' ]. - 2 Inspiral Merger Ringdown insufficientm1since 1+they release only1about 1%s1of + m2 1+ 1 s2 2 the rest mass. The efficiency might be higher The event horizon is the boundary ofthe region sa7sfy the area theorem, because in either the nonsphericalresidualsgravitational collapse of space-time from which particles or photons of a star -0.5or the✓collision andqcoalescence of two◆ can escape to✓infinity. I shallqconsider only ◆

the numerical solu7on sa7sﬁes 1344 1 ) 1

Einstein's equa7ons. -21 )

For this event, the area theorem is -21 0 being tested by the code that's 0 Strain (10 solving Einstein equa1ons, not by Strain (10 -1 H1 measured strain, bandpassed -1 H1 estimated strain incident Nature. L1 measured strain, bandpassed H1 estimated strain, bandpassed

0.2 0.25 0.3 0.35 0.4 0.45 0.2 0.25 0.3 0.35 0.4 0.45 Time (seconds) Time (seconds) Avignon 24.4.2017 25

0-1 Second Observing Run O2 Underway

• Began November 30th, 2016, with break over the holidays • Already more than 48 days of coincident data. • Increasing sensi7vity from O1 was more challenging than an7cipated. Instruments more sensi7ve to angular jiwer in the laser than predicted; can’t increase laser power as expected. Diﬃcult to control signal recycling cavity at Hanford. • Hanford O2 sensi7vity similar to O1. Livingston 30% more sensi7ve. • Overall 30% strain sensi7vity improvement would increase observable volume by a factor of 2.4. Expect ~10 events total • VIRGO hopes to join O2 later this year, adding bewer poin7ng and polarisa7on informa7on. All degrees of freedom locked in December; locked on dark fringe in March, but not yet in a low- noise conﬁgura7on.

Avignon 24.4.2017 26 LIGO Collabora1on statement (April 6) on status of O2

The second Advanced LIGO run began on November 30, 2016 and is currently in progress. As of March 23 approximately 48 days of Hanford-Livingston coincident science data have been collected, with a scheduled break between December 22, 2016 and January 4, 2017. The average reach of the LIGO network for binary merger events has been around 70 Mpc for 1.4+1.4 Msun, 300 Mpc for 10+10 Msun and 700 Mpc for 30+30 Msun mergers, with relative variations in time of the order of 10%.

As of March 23, 6 triggers, identified by online analysis using a loose false-alarm-rate threshold of one per month, have been identified and shared with astronomers who have signed memoranda of understanding with LIGO and Virgo for electromagnetic followup. A thorough investigation of the data and offline analysis are in progress; results will be shared when available.

Avignon 24.4.2017 27 Things I didn’t talk about

• Tes7ng GR: everything consistent. New ability to test GR in the strong ﬁeld dynamic regime. • Astrophysical implica7ons: metallicity during star forma7on that led to these BH could not have been too large. • Broad limit of 9-240 events per cubic Gpc/year on binary black hole merger rate. • Stochas7c “background” from more distant weaker sources: poten7ally detectable when we reach design sensi7vity • Other poten7al LIGO sources of gravita7onal waves • Other instruments: VIRGO, KAGRA, LIGO India, … • Searches for gravita7onal waves in other frequency bands with LISA, Pulsar Timing Arrays, CMB, …

Avignon 24.4.2017 28 20016-19: a “Golden Age” of GW astronomy

• Expect O3 run to start in 2018. At design sensi7vity: one event every few days for a year: ~100 events total • Within 2-3 years, we will know the mass and spin distribu7on of these binary black hole sources • Hope for at least one event close enough to directly determine the ﬁnal mass and spin and test the area theorem • Perhaps learn more about physics of black holes, for example the informa7on-loss paradox, ﬁrewalls, quantum proper7es, ???

Avignon 24.4.2017 29 Conclusions • We can detect gravita7onal waves directly (tracking amplitude and phase) • Existence of stellar mass black hole binaries established (not visible any other way!). Will be our dominant source. • A golden age for GW astronomy is coming. We will go from 2 detec7ons to 10 to 100 in the next few years. • Other signal sources (NS/NS, NS/BH, CW, or the unexpected. Please sign up for Einstein@Home

Avignon 24.4.2017 30