A new dawn: gravitational wave

observations from Earth and in space

Emanuele Berti, Johns Hopkins University

Emera Astronomy Center

Orono (ME), November 14 2019Planetarium show credits: Nicolas Yunes

School of Film, the Department of Physics and the Museum of the Rockies

A brief history of black holes

Black holes: the early storyNovember 1915:

✓ Einstein presents the equations of general relativity to the Prussian Academy of Science

1916:

✓ Karl Schwarzschild discovers black holes while in the German army during World War 1.

Schwarzschild dies of a disease developed on the Russian front

Einstein does not believe in the physical reality of the Schwarzschild solution…

1930:

✓ 19-year old Subramanyan Chandrasekhar wins a Scholarship to study in Cambridge.

On the boat to England, combining quantum mechanics and relativity,

he discovers that massive white dwarfs must collapse gravitationally.

Sir Arthur Eddington ridicules him: “stellar buffoonery”

1937:

✓ Chandra moves to Chicago

1983:

✓ Chandra receives the Nobel prize

Black holes: the early storySeptember 1939:

✓ World War 2 begins

✓ Oppenheimer & Snyder understand that collapse can lead to a black hole

1941:

✓ Oppenheimer stops working on relativity to lead the Manhattan Project

1939:

✓ John Wheeler & Niels Bohr study nuclear fission

✓ Wheeler’s brother dies in Italy;

he joins the Manhattan project

1950s:

✓ Wheeler and his students (including Kip Thorne)

return to the problem of gravitational collapse

1973:

✓ Misner-Thorne-Wheeler, “Gravitation”

Black holes: the Golden Age (1963-1970s)

Late 1960s and 1970s:

✓ “Golden age” of black hole physics

✓ Kip Thorne and students (including Saul Teukolsky)

prove stability and understand the dynamics of black holes

1963:

✓ Roy Kerr from New Zealand discovers a

mathematical solution describing rotating

black holes

✓ Maarten Schmidt at Caltech discovers the

first quasar, 3C273 at z=0.15

✓ Must be compact and outshines the

brightest galaxies!

✓ First supermassive black hole

Singularity theorems, the Big Bang, and Hawking radiation✓ Roger Penrose proves that gravitational collapse inevitably leads to singularities

✓ Stephen Hawking proves that the Universe must have been born out of a singularity…

unless quantum mechanics comes into play

✓ Hawking radiation: connection between general relativity and quantum mechanics?

Black holes: truth and beauty

“In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe.

This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.”

(S. Chandrasekhar)

How do black holes form? The life and death of stars

Life:✓ Gravity vs. pressure from nuclear burning

✓ Nuclear fusion produces heavy elements

✓ Iron is too stable, the star runs out of fuel

Death:✓ Gravity wins! Supernova

✓ Atoms heavier than iron formed in a supernova or neutron star

merger

✓ Crab nebula (1054): seen by Chinese astronomers for 23 days

during the day, and 2 years at night

✓ Crab left behind a neutron star

The stellar graveyard (or: the life of stars after death)

M<3Msun

3Msun<M< ~10Msun

http://essayweb.net/astronomy/blackhole.shtml

Visualizing gravity: curvature and “embedding diagrams”

Thorne’s “parable of the ants”6 intelligent ants live on a membrane

and communicate by rolling balls at constant speed (as measured locally).

5 ants gather at the center: the membrane collapses and drags things inward.

An “astronomer ant” keeps observing the balls, that arrive slower and slower. To her, the collapse

seems to freeze.

At t=15s, the astronomer ant stops receiving signals: the membrane is collapsing at the same

speed as the balls move.

However the collapsing star is not frozen! The five ants and the balls are all crushed into a central

singularity.

This is exactly what happens when a star collapses to a black hole.

How can we see a black hole?

How can we “see” a black hole?Sgr A*

(Movie: Reinhard Genzel)

Andromeda (M31): 2.6 million lyrs away, 108Msun black hole

Radio Microwave Infrared

Visible Ultraviolet X-Rays

Gravity: Newton vs. EinsteinEinstein (1915):✓ Gravity is spacetime curvature✓ “Spacetime tells mass how to move,

mass tells spacetime how to curve”

Newton (1687):✓ Action at a distance✓ Describes effect of gravity,

but does not explain it

Extreme light bending: EHT and M87’s light ring

55 million lyrs away, 6.5x109Msun black hole

Gravitational waves

Illustrations from Kip Thorne’s “Black holes and Time Warps: Einstein’s Outrageous Legacy”

2 m

1 ton

frot=1 kHz, h~(2.6 x 10-33 m)/rr > ~3x105 m: h < 9 x 10-39

M~1033 g, v=c, r~15 Mpc,h~10-21

Gravitational waves as tidal forces

Interferometric detectors

Interferometers ideal for the quadrupolar nature of gravitational waves:

send laser beams in perpendicular directions

and combine them on return to construct interference patterns.

Building new ears

Virgo

VIEWPOINT

The First Sounds of Merging BlackHolesGravitational waves emitted by the merger of two black holes have been detected, setting the

course for a new era of observational astrophysics.

by Emanuele Berti⇤,†

For decades, scientists have hoped they could “ lis-ten in” on violent astrophysical events by detectingtheir emission of gravitational waves. The waves,which can be described as oscillating distortions in

the geometry of spacetime, were first predicted to exist byEinstein in 1916, but they have never been observed di-rectly. Now, in an extraordinary paper, scientists report thatthey have detected the waves at the Laser InterferometerGravitational-wave Observatory (LIGO) [1]. From an analy-sis of the signal, researchers from LIGO in the US, and theircollaborators from theVirgo interferometer in Italy, infer thatthe gravitational waves were produced by the inspiral andmerger of two black holes (Fig. 1), each with a mass that ismore than 25 times greater than that of our Sun. Their find-ing provides the first observational evidence that black holebinary systems can form and merge in the Universe.

Gravitational waves are produced by moving masses, andlike electromagnetic waves, they travel at the speed of light.As they travel, thewavessquash and stretch spacetime in theplane perpendicular to their direction of propagation (seeinset, Video 1). Detecting them, however, is exceptionallyhard because they induce very small distortions: even thestrongest gravitational waves from astrophysical events areonly expected to produce relative length variations of order

10− 21.

“ Advanced” LIGO, as the recently upgraded version ofthe experiment is called, consists of two detectors, one inHanford, Washington, and one in Livingston, Louisiana.Each detector is a Michelson interferometer, consisting oftwo 4-km-long optical cavities, or “ arms,” that are arrangedin an L shape. The interferometer is designed so that, inthe absence of gravitational waves, laser beams traveling inthe two arms arrive at a photodetector exactly 180◦ out of

⇤Department of Physics and Astronomy, The University of Missis-

sippi, University, Mississippi 38677, USA†CENTRA, Departamento de Física, Instituto Superior Técnico,

Universidade de Lisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Por-

tugal

Figure 1: Numerical simulations of the gravitational waves emittedby the inspiral and merger of two black holes. The coloredcontours around each black hole represent the amplitude of thegravitational radiation; the blue lines represent the orbits of theblack holes and the green arrows represent their spins. (C.Henze/NASA Ames Research Center)

phase, yielding no signal. A gravitational wave propagat-ing perpendicular to the detector plane disrupts this perfectdestructive interference. During its first half-cycle, the wavewill lengthen one arm and shorten the other; during its sec-ond half-cycle, these changes are reversed (see Video 1).These length variations alter the phase difference betweenthe laser beams, allowing optical power—a signal—to reachthe photodetector. With two such interferometers, LIGO canrule out spurious signals (from, say, a local seismic wave)that appear in one detector but not in the other.

LIGO’s sensitiv ity is exceptional: it can detect length dif-ferences between the arms that are smaller than the sizeof an atomic nucleus. The biggest challenge for LIGO isdetector noise, primarily from seismic waves, thermal mo-tion, and photon shot noise. These disturbances can easilymask the small signal expected from gravitational waves.

physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17

GW150914: a new astronomy

The sound of black holes

LIGO/Virgo: O1, O2

• O1: 9/12/2015-1/19/2016: 3 BH-BH• O2: 11/30/2016-8/25/2017: 7 BH-BH + 1 NS-NS

https://gracedb.ligo.org/latest/https://www.gw-openscience.org/detector_status/

3

FIG. 1. Left: BNS range for each instrument during O2. The break at week 3 was for the 2016 end-of-year holidays. There was an additionalbreak in the run at week 23 to make improvements to instrument sensitivity. The Montana earthquake’s impact on the LHO instrument

sensitivity can be seen at week 31. Virgo joined O2 in week 34. Right: Amplitude spectral density of the total strain noise of the Virgo, LHOand LLO detectors. The curves are representative of the best performance of each detector during O2.

first-generation detector in 2011. The main modifications in-clude a new optical design, heavier mirrors, and suspendedoptical benches, including photodiodes in vacuum. Specialcare was also taken to improve the decoupling of the instru-ment from environmental disturbances. Oneof themain limit-ing noisesources below 100 Hz is the thermal Brownian exci-tation of thewiresused for suspending themirrors. A first testperformed on theVirgo configuration showed that silicafiberswould reduce this contribution. A vacuum contamination is-sue, which has since been corrected, led to failures of thesesilica suspension fibers, so metal wires were used to avoiddelaying Virgo’sparticipation in O2. Unlike the LIGO instru-ments, Virgo has not yet implemented signal-recycling. Thiswill be installed in a later upgrade of the instrument.

After several monthsof commissioning Virgo joined O2 onAugust 1st 2017 with a BNS range of ⇠25 Mpc. The perfor-mance experienced a temporary degradation on August 11th

and 12th, when the microseismic activity on site was highlyelevated and it was difficult to keep the interferometer in itslow-noise operating mode.

C. Data

Figure 1 shows the BNS ranges of the LIGO and Virgo in-struments over the course of O2, and the representative am-plitude spectral density plots of the total strain noise for eachdetector.

We subtracted several independent contributions to the in-strumental noise from the data at both LIGO detectors [50].For all of O2, theaverage increase in theBNSrange from thisnoise subtraction process at LHO was ⇡ 18% [50]. At LLOthenoisesubtraction process targeted narrow line features, re-sulting in a negligible increase in BNS range.

Calibrated strain data from each interferometer was pro-duced online for use in low-latency searches. Following therun, afinal frequency-dependent calibration wasgenerated foreach interferometer.

For the LIGO instruments this final calibration benefittedfrom theuseof post-run measurements and removal of instru-mental lines. The calibration uncertainties are 3.8% in ampli-tudeand 2.1 degrees in phasefor LLO; 2.6% in amplitude and2.4 degrees in phase for LHO. The results cited in this paperuse the full frequency-dependent calibration uncertainties de-scribed in [62, 63]. The LIGO timing uncertainty of < 1 s[64] is included in the phase correction factor.

Thecalibration of strain data produced online by Virgo hadlarge uncertainties due to the short time available for mea-surements. The data was reprocessed to reduce the errors bytaking into account better calibration models obtained frompost-run measurements and subtraction of frequency noise.The reprocessing included a time dependence for the noisesubtraction and for thedetermination of thefinesseof thecav-ities. The final uncertainties are 5.1% in amplitude and 2.3degrees in phase [65]. TheVirgo calibration has an additionaluncertainty of 20 soriginating from the timestamping of thedata.

During O2 the individual LIGO detectors had duty factorsof ⇠60% with a LIGO network duty factor of ⇠45%. Timeswith significant instrumental disturbances are flagged and re-moved, resulting in 118 days of data suitable for coincidentanalysis [66]. Of this data 15 days were collected in coin-cident operation with Virgo, which after joining O2 operatedwith a duty factor of ⇠80%. Times with excess instrumen-tal noise, which is not expected to render the data unusableare also flagged [66]. Individual searches may then decide toinclude or not include such times in their final results.

I I I . SEARCHES

The search results presented in the next section were ob-tained by two di↵erent, largely independent matched-filtersearches, PyCBC and GstLAL, and the burst search cWB.Because of the sensitivity imbalance between the AdvancedVirgo detector as compared to the two Advanced LIGO de-

Antenna pattern and sky localization

[Schutz, 1102.5421] [LVC, 1304.6670]

DL=40 MpcSNR=33

DW=16 deg2

H0 with GW170817…and all the black holes in O1/O2 (mostly GW170814)

[LVC, 1908.06060]

LIGO/Virgo: O1, O2, O3

• O1: 9/12/2015-1/19/2016: 3 BH-BH• O2: 11/30/2016-8/25/2017: 7 BH-BH + 1 NS-NS (with EM counterparts)• O3: started 4/1/2019 31 events: mostly BH-BH, 2/3 NS-NS, 2/3 NS-BH

https://gracedb.ligo.org/latest/https://www.gw-openscience.org/detector_status/

3

FIG. 1. Left: BNS range for each instrument during O2. The break at week 3 was for the 2016 end-of-year holidays. There was an additionalbreak in the run at week 23 to make improvements to instrument sensitivity. The Montana earthquake’s impact on the LHO instrument

sensitivity can be seen at week 31. Virgo joined O2 in week 34. Right: Amplitude spectral density of the total strain noise of the Virgo, LHOand LLO detectors. The curves are representative of the best performance of each detector during O2.

first-generation detector in 2011. The main modifications in-clude a new optical design, heavier mirrors, and suspendedoptical benches, including photodiodes in vacuum. Specialcare was also taken to improve the decoupling of the instru-ment from environmental disturbances. Oneof themain limit-ing noisesources below 100 Hz is the thermal Brownian exci-tation of thewiresused for suspending themirrors. A first testperformed on theVirgo configuration showed that silicafiberswould reduce this contribution. A vacuum contamination is-sue, which has since been corrected, led to failures of thesesilica suspension fibers, so metal wires were used to avoiddelaying Virgo’sparticipation in O2. Unlike the LIGO instru-ments, Virgo has not yet implemented signal-recycling. Thiswill be installed in a later upgrade of the instrument.

After several monthsof commissioning Virgo joined O2 onAugust 1st 2017 with a BNS range of ⇠25 Mpc. The perfor-mance experienced a temporary degradation on August 11th

and 12th, when the microseismic activity on site was highlyelevated and it was difficult to keep the interferometer in itslow-noise operating mode.

C. Data

Figure 1 shows the BNS ranges of the LIGO and Virgo in-struments over the course of O2, and the representative am-plitude spectral density plots of the total strain noise for eachdetector.

We subtracted several independent contributions to the in-strumental noise from the data at both LIGO detectors [50].For all of O2, theaverage increase in theBNSrange from thisnoise subtraction process at LHO was ⇡ 18% [50]. At LLOthenoisesubtraction process targeted narrow line features, re-sulting in a negligible increase in BNS range.

Calibrated strain data from each interferometer was pro-duced online for use in low-latency searches. Following therun, afinal frequency-dependent calibration wasgenerated foreach interferometer.

For the LIGO instruments this final calibration benefittedfrom theuseof post-run measurements and removal of instru-mental lines. The calibration uncertainties are 3.8% in ampli-tudeand 2.1 degrees in phasefor LLO; 2.6% in amplitude and2.4 degrees in phase for LHO. The results cited in this paperuse the full frequency-dependent calibration uncertainties de-scribed in [62, 63]. The LIGO timing uncertainty of < 1 s[64] is included in the phase correction factor.

Thecalibration of strain data produced online by Virgo hadlarge uncertainties due to the short time available for mea-surements. The data was reprocessed to reduce the errors bytaking into account better calibration models obtained frompost-run measurements and subtraction of frequency noise.The reprocessing included a time dependence for the noisesubtraction and for thedetermination of thefinesseof thecav-ities. The final uncertainties are 5.1% in amplitude and 2.3degrees in phase [65]. TheVirgo calibration has an additionaluncertainty of 20 soriginating from the timestamping of thedata.

During O2 the individual LIGO detectors had duty factorsof ⇠60% with a LIGO network duty factor of ⇠45%. Timeswith significant instrumental disturbances are flagged and re-moved, resulting in 118 days of data suitable for coincidentanalysis [66]. Of this data 15 days were collected in coin-cident operation with Virgo, which after joining O2 operatedwith a duty factor of ⇠80%. Times with excess instrumen-tal noise, which is not expected to render the data unusableare also flagged [66]. Individual searches may then decide toinclude or not include such times in their final results.

I I I . SEARCHES

The search results presented in the next section were ob-tained by two di↵erent, largely independent matched-filtersearches, PyCBC and GstLAL, and the burst search cWB.Because of the sensitivity imbalance between the AdvancedVirgo detector as compared to the two Advanced LIGO de-

What is next? More detectors on Earth

KAGRA first lock: August 23! Third-generation (3G) detectors: Einstein Telescope, Cosmic Explorer

The hunt goes on…

O1/O2 black holes:

rates, masses, spins

15

Mass Model Rate Parameters Spin Parameters

Model λ ↵a βa E[a] Var[a]

Fixed Parameter (power-law)A, with ↵ = 2.3,

0 1 1 N/ A N/ Amm ax = 50M

Fixed Parameter (flat -in-log) Equat ion 16 0 1 1 N/ A N/ A

Non-Evolving A, B, C 0 N/ A N/ A [0,1] [0, 0.25]

Evolvinga A [-25, 25] N/ A N/ A 0 0

aT his model assumes the black holes have zero spin.

Table 4. Summary of models in Sect ion 4, with prior ranges for the populat ion parameters determining the rate models. The

fixed parameter models are drawn from Abbot t et al. (2018). The fixed parameters are in bold. Each of these dist ribut ions

is uniform over the stated range; as previously, we require ↵a , βa ≥ 1. Details of the mass models listed here are described in

Table 2.

a strong correlat ion between the mass power-law slope

and the redshift evolut ion parameter, although the max-

imum mass parameter remains well-const rained. As in

Sect ion 3, we carry out a leave-one-out analysis, ex-

cluding the most massive and distant BBH, GW170729

from the sample (red curves in Figure 6). Without

GW170729, the marginalized mass-dist ribut ion poste-

riors become ↵ = 0.8+ 1.7− 2.2, mmax = 38+ 10

− 4 M .

Marginalizing over the two mass dist ribut ion param-

eters and the redshift -evolut ion parameter, the merger

rate density is consistent with being constant in red-

shift (λ = 0), and in part icular, it is consistent with

the rate est imates for the two fixed-parameter models

in Abbot t et al. (2018), as shown in Figure 5. How-

ever, we find a preference for a merger rate density

that increases at higher redshift (λ ≥ 0) at 0.88 cred-

ibility. This preference becomes less significant when

F igur e 5. Const raints on evolut ion of the BBH merger

rate density as a funct ion of redshift . Including the 10 BBHs

from O1 and O2 in our analysis, we find a preference for a

merger rate that increases with increasing redshift . The solid

blue line gives the posterior median merger rate density and

dark and light bands give 50% and 90% credible intervals.

In green and red, the solid line and shaded region shows the

median and 90% credible interval of the rate inferred for each

of the fixed-parameter models.

GW170729 is excluded from the analysis, because this

event likely merged at redshift z & 0.5, close to the O1-

O2 detect ion horizon. Although GW170729 shifts the

posterior towards larger values of λ , implying a stronger

redshift evolut ion of the merger rate, the posterior re-

mains well within the uncertaint ies inferred from the re-

maining nine BBHs. When including GW170729 in the

analysis, we find λ = 6.5+ 9.1− 9.3 at 90% credibility, com-

pared to λ = 0.9+ 9.8− 10.8 when excluding GW170729 from

the analysis. With only 10 BBH detect ions so far, the

wide range of possible values for λ is consistent with

most ast rophysical format ion channels. The precision of

this measurement will improve as we accumulate more

detect ions in future observing runs and may enable us to

discriminate between di↵erent format ion rate histories

or t ime-delay dist ribut ions (Sathyaprakash et al. 2012;

Van Den Broeck 2014; Fishbach et al. 2018).

5. THE SPIN DISTRIBUTION

The GW signal depends on spins in a complicated

way, but at leading order, and in the regime we are in-

terested in here, some combinat ions of parameters have

more impact on our inferences than others, and thus are

measurable. One such parameter is χe↵ . For binaries

which are near equal mass, we can see from Equat ion 1

that only when black hole spins are high and aligned

with the orbital angular momentum χe↵ will be measur-

ably greater than zero. Figure 5 in Abbot t et al. (2018)

illust rates the inferred χe↵ spin dist ribut ions for all of

the BBHs ident ified in our GW surveys in O1 and O2.

With a few except ions, current observat ionsof BBH spin

are not consistent with large, aligned black hole spins.

Only GW170729 and GW151226 show significant evi-

dence for posit ive χe↵ ; the rest of the posteriors cluster

around χe↵ = 0.

Despite these degeneracies, several tests have been

proposed to use spins to const rain BBH format ion chan-

nels (Vitale et al. 2017; Farr et al. 2017, 2018; Steven-

son et al. 2017a; Talbot & Thrane 2017; Wysocki et al.

Rates: better constraints, evidence of growth with z

24

proportional to R−1/ 2i

, for BNS and BBH, while for NSBH weuse a prior uniform in Ri which yields a conservative upperlimit bound.

A. Event Classification

To determine the probability that a given candidate origi-nated in one of the four categories, the models are marginal-ized over the counts with the ranking statistic distributionsfixed at the value of the ranking statistic of the candidate. Thedistribution that ismarginalized is theratio of thecategory un-der consideration versus all categories (including terrestrial):

pAi(xµ|{x}) =

Z

p({R},⇤T , {hVT i }|{x})RihVT i i p(xµ|Ai)

⇤T p(xµ|T) +P

j RjhVT i j p(xµ|A j)d{R}d⇤Td{hVT i } . (10)

Thus, we obtain pterrestrial , pBBH, pBNS, pNSBH, which are mu-tually exclusive categorizations. The overall probability ofastrophysical origin sums theexpression over all categories in{A}.

We expect di↵erent values of pA ito be assigned to any

given event by di↵erent search pipelines. This is due to dif-ferences in the averaged efficiency of various methods to dis-criminate signal from noise events, and also to the e↵ects ofrandom noisefluctuations on the ranking statistics assigned toa specific event. We also expect systematic uncertainties inthe quoted probabilities due to our lack of knowledge of thetrue event populations, for instance the mass distribution ofBNS and NSBH mergers.

Parameter estimation is not performed on all candidatesused to obtain rate estimates, so only the search masses andrankingsareused to derivetheastrophysical probabilities. Ta-ble IV shows the per-pipeline assigned probability values foreach of the relevant categories. The cWB search does nothave a specific event type corresponding to NSBH or BNS,thus we treat all cWB search events as BBH candidates. Py-CBC astrophysical probabilities are estimated by applyingsimple chirp mass cuts to the set of events with ranking statis-tic ⇢> 8: events with M < 2.1 are considered as candidateBNS, thosewith M > 4.35 ascandidate BBH, and all remain-ing events as potential NSBH.

B. Binary Black Hole Event Rates

After the detection of GW170104, the event rate ofBBH mergers had been measured to lie between 12-213Gpc−3 y−1 [14]. This included the four events identified atthat time. The hVT i , and hence the rates, are derived from aset of assumed BBH populations. In O1, two distributions ofthe primary mass— one uniform in the log and one a powerlaw p(m1) / m−↵

1with an index of ↵ = 2.3 — were used

as representative extremes. In both populations shown here,the mass distribution cuts o↵ at a lower mass of 5 M . Themass distributions cut o↵ at a maximum mass of 50 M . Thenew cuto↵ ismotivated both by more sophisticated modellingof the mass spectrum [54] preferring maximum BH massesmuch smaller than theprevious limit of 100 M , aswell asas-

FIG. 12. This figure shows the posterior distribution — combinedfrom theresultsof PyCBC and GstLAL— on theBBH event rate for

theflat in log (blue) and power-law (orange) mass distributions. Thesymmetric 90% confidence intervalsare indicated with vertical lines

beneath theposterior distribution. Theunion of intervals is indicatedin black.

trophysical processes which are expected to truncate the dis-tribution [130]. The BH spin distribution has magnitude uni-form in [0, 1]. The PyCBC search uses a spin tilt distributionwhich is isotropic over the unit sphere, and GstLAL uses adistribution that aligns BH spins to the orbital angular mo-mentum.

Theposteriorson theratedistributionsareshown in Fig. 12.Including all events, the event rate is now measured to be R =56+44

−27Gpc−3 y−1(GstLAL) and R = 57+47

−29Gpc−3 y−1(PyCBC)

for the power law distribution. For the uniform in log dis-tribution, we obtain R = 18.1+13.9

−8.7Gpc−3 y−1(GstLAL) and

R = 19.5+15.2−9.7

Gpc−3 y−1(PyCBC). Thedi↵erence in hVT i andrate distributions between the two spin populations is smallerthan the uncertainty from calibration. Therefore, we presenta distribution for both populations, combined over searches,in Fig 12 as an averaging over the spin configurations. Theunion of the intervals combined over both populations lies in

20 60

BH-BH NS-NS NS-BH

26

FIG. 13. This figure shows the posterior distributions of the BNSevent rate for the GstLAL and PyCBC searches. The uniform mass

distribution corresponds to theorangecurvesand Gaussian massdis-tributions corresponds to thebluecurves. Thesymmetric 90% confi-dence intervalsare indicated with vertical lines beneath theposterior

distributions.

tic threshold applied to either. PyCBC measures a smallerhVT i because its fiducial threshold is higher than GstLAL.Despite the threshold di↵erence, the two searches find similarvalues for ⇤BNS, and hence the rate for GstLAL is lower thanfor PyCBC. For the uniform mass set, we obtain an intervalat 90% confidence of R = 800+1970

−680Gpc−3 y−1(PyCBC) and

R = 662+1609−565

Gpc−3 y−1(GstLAL), and for theGaussian set we

obtain R = 1210+3230−1040

Gpc−3 y−1(PyCBC) and R = 920+2220−790

Gpc−3 y−1(GstLAL). These values are consistent with previ-ous observational values (both GW and radio pulsar) as wellas more recent investigations [199].

D. Neutron Star Black Hole Event Rates

The NSBH space is a unique challenge both to model as-trophysically and for which to produce accurate waveforms.Astrophysical models span a wide range of potential mass ra-tios and spin configurations, and there are no electromagneticobservational examples. Hence, we take an approach similarto previous analyses [192] and examine specific points in themass space while considering two component spin configu-rations: isotropic and orbital angular momentum aligned asdescribed in Sec. VII B.

Since there were no confident detection candidates in theNSBH category, we update the upper limit at 90% confidencein this category in Fig. 14. All upper limits are below 610Gpc−3 y−1. Those results are obtained using a uniform priorover R. The Je↵reys prior (which also appeared in [192])suppresses larger R values. This prior choice would obtain aless conservative upper limit. This limit is now stronger at allmasses than the “high” rate prediction [200] (103 Gpc−3 y−1)

FIG. 14. This figure shows the 90% rate upper limit for the NSBHcategory, measured at a set of three discrete BH masses (5, 10, 30

M ) with the fiducial NS mass fixed to 1.4 M . The upper limitis evaluated for both matched-filter search pipelines, with GstLAL

corresponding to red curves and PyCBC to blue. We also show twochoices of spin distributions: isotropic (dashed lines) and aligned

spin (solid lines).

for NSBH sources.

VII I . CONCLUSIONS

We have reported the results from GW searches for com-pact mergersduring thefirst and second observing runsby theAdvanced GW detector network. Advanced LIGO and Ad-vanced Virgo have confidently detected gravitational wavesfrom ten stellar-mass binary black hole mergers and one bi-nary neutron star inspiral. The signals were discovered usingthree independent analyses: twomatched-filter searches [8, 9]and one weakly modeled burst search [11]. We have re-ported four previously unpublished BBH signals discoveredduring O2, as well as updated FARs and parameter estimatesfor all previously reported GW detections. The reanalysis ofO1 data did not reveal any new GW events, but improve-ments to the various detection pipelines have resulted in anincrease of the significance of GW151012. Including thesefour new BBH mergers, theobserved BBHsspan awiderangeof component masses, from 7.7+2.2

−2.6M to 50.6+16.6

−10.2M . One

of the new events, GW170729, is found to be the highest-mass BBH observed to date, with GW170608 still being thelightest BBH [16]. Similar to previous results, we find thatthe spins of the individual black holes are only weakly con-strained, though for GW151226 and also for GW170729 wefind that χe↵ ispositiveand thuscan ruleout two non-spinningblack holes as their constituents at greater than the 90% cred-ible level. The binary mergers observed during O1 and O2range in distance between 40+10

−10Mpc for the binary neutron

star inspiral GW170817 to 2750+1350−1320

Mpc for GW170729,making it not only the heaviest BBH but also the most dis-

Masses, remnant mass/spin

GW170729 is special: (50.6 + 34.3) Msun, at edge of PISN/PPISN gap; 80.3 Msun remnantFarthest: DL~3Gpc, largest spin, low SNR. Princeton group: similar candidates

Where are the heavy BHs?

9

Mass Parameters Spin Parameters

Model ↵ mm ax mm i n βq λm µm σm δm E[a] Var[a] ⇣ σi

A [-4, 12] [30, 100] 5 0 0 N/ A N/ A N/ A [0, 1] [0, 0.25] 1 [0, 10]

B [-4, 12] [30, 100] [5, 10] [-4, 12] 0 N/ A N/ A N/ A [0, 1] [0, 0.25] 1 [0, 10]

C [-4, 12] [30, 100] [5, 10] [-4, 12] [0, 1] [20, 50] (0, 10] [0, 10] [0, 1] [0, 0.25] [0, 1] [0, 4]

Table 2. Summary of models used in Sect ions 3, 4, and 5, with the prior ranges for the populat ion parameters. The fixed

parameters are in bold. Each of these dist ribut ions is uniform over the stated range. All models in this Sect ion assume rates

which are uniform in the comoving volume (λ = 0). The lower limit on mm i n is chosen to be consistent with Abbot t et al.

(2018).

F igur e 1. Inferred di↵erent ial merger rate as a funct ion of primary mass, m1 , and mass rat io, q, for three di↵erent assumpt ions.

For each of the three increasingly complex assumpt ions A, B, C described in the text we show the PPD (dashed) and median

(solid), plus 50% and 90% symmet ric credible intervals (shaded regions), for the di↵erent ial rate. The results shown marginalize

over the spin dist ribut ion model. The fallo↵ at small masses in models B and C is driven by our choice of the prior limits on

the mm in parameter (see Table 2). All three models give consistent mass dist ribut ions within their 90% credible intervals over

a broad range of masses, consistent with their near-unity evidence rat ios (Table 3); in part icular, the peaks and t rough seen in

Model C, while suggest ive, are not ident ified at high credibility in the mass dist ribut ion.

mergers . 1. Thus, we are unable to place meaningful

const raints on the presence or absence of a mass gap at

low black hole mass.

Models B and C also allow the dist ribut ion of mass ra-

t ios to vary according to βq. In these cases the inferred

mass-rat io dist ribut ion favors comparable-mass binaries

(i.e., dist ribut ions with most support near q ' 1), see

panel two of Figure 1. Within the context of our pa-

rameterizat ion, we find βq = 6.7+ 4.8− 5.9 for Model B and

βq = 5.8+ 5.5− 5.8 for Model C. These values are consistent

with each other and are bounded above zero at 95% con-

fidence, thus implying that the mass rat io dist ribut ion

is nearly flat or declining with more ext reme mass ra-

t ios. The posterior on βq returns the prior for βq & 4.

Thus, we cannot say much about the relat ive likelihood

of asymmetric binaries, beyond their overall rarity.

The dist ribut ion of the parameter controlling the frac-

t ion of the power law versus the Gaussian component in

Model C is λm = 0.4+ 0.3− 0.3, which peaks away from zero,

implying that this model prefers a cont ribut ion to the

Evidence for the second mass gap?

Collapse or previous mergers?2

1g BH 1g BH

1g BH 1g BH

2g BH

1g BH 1g BH

2g BH

1g BH 1g BH

2g BH

1g+ 2g event1g+ 1g event 2g+ 2g event

1g BH

redshift z

redshift z

redshift z

redshift z̃

redshift z̃1

redshift z̃2

FIG. 1. Cartoon sketch of the three possible scenarios for the merger of two BHs. First generat ion (1g) BHs result ing fromstellar collapse can form second generat ion (2g) BHs via mergers. Imprints of these format ion channels are left in the stat ist ical

dist ribut ion of masses, spins and redshift of the detected events.

(i) 2g BHs should be more massive than BHs bornfrom stellar collapse;

(ii) quite independent ly of thedist ribut ion of spin mag-nitudes following core collapse (which is highly un-certain [39]), the spin magnitudes of 2g BHs shouldcluster (on average) around the dimensionless spin⇠ 0.7 result ing from the merger of nonspinningBHs [40];

(iii) stat ist ically, the merger of BH binaries including2g components should occur later (i.e., at smallerredshift or luminosity distance from GW detectors)because of the delay t ime between BH format ionand merger.

In this paper we make these arguments more quant ita-t ive and rigorous by developing a simple but physicallymot ivated model to describe the bulk theoret ical prop-ert ies of 1g and 2g binary BH mergers (Sec. I I). Thenwe consider a set of present and future GW detectors,and we simulate observable distr ibutions by select ing de-tectable binaries and est imat ing the expected measure-ment errors on their parameters (Sec. I I I). Finally we setup a Bayesian model select ion framework (Sec. IV) to ad-dress what can be done with current observat ions, and toquant ify thecapabilit iesof futuredetectors to dist inguishbetween di↵erent models (Sec. V). We conclude by sum-marizing our results and point ing out possible extensions(Sec. VI).

I I . T H EOR ET I CA L D I ST R I B U T I ON S

Our goal in this sect ion is to develop a simple prescrip-t ion to build populat ions of binary BHs. Our great lyoversimplified model is not meant to capture the com-plexity of binary evolut ion in an ast rophysical set t ing,but just the main features dist inguishing 1g and 2g BHs.

As illust rated by the cartoon in Fig. 1, we con-st ruct three theoretical distr ibutions, labeled by “ 1g+ 1g,”“ 1g+ 2g” and “ 2g+ 2g” . In this context , “ 1g” means thatone of the binary components is a first -generat ion BHproduced by stellar collapse, whereas “ 2g” means thatit is a second-generat ion BH produced by a previousmerger.

A . T he 1g+ 1g p opulat ion

Following the LIGO-Virgo Scient ific Collaborat ion [3],for the 1g+ 1g populat ion, we adopt three di↵erent pre-script ions for the dist ribut ion of source-frame masses:

(i) M odel “ flat ” : we assume uniformly dist ributedsource-frame masses m1 and m2 in the range m i 2[5M , 50M ] (i = 1, 2), where hereafter m1 > m2.

(ii) M odel “ log” : we take the logarithm of thesource-frame masses to be uniformly dist ributed in the

[Gültekin-Miller-Hamilton, astro-ph/0402532, astro-ph/0509885]

[Gerosa+EB,1703.06223; Fishbach+, 1703.06869]

Precession and effective spins

GW151226: ceff=0.18GW170729: ceff=0.36

Black hole spectroscopy

LIGO “testing GR” paper [arXiv:1602.03841]:

“According to the burst analysis, the GW150914 residual is not statistically distinguishable from the instrumental noiserecorded in the vicinity of the detection, suggesting that all of the measured power is well represented by the GR prediction for the signal from a BBH merger. […]We compute the 95% upper bound on the coherent network residual SNR. This upper bound is ≤ 7.3 at 95% confidence, independently of the maximum a posteriori waveform used.”

Is there any modification to GR in the (small) residual?

Superradiance: growing and decaying modes

Quasinormal modes:

❑ Ingoing waves at the horizon,outgoing waves at infinity

❑ Spectrum of damped modes (“ringdown”) [EB+, 0905.2975]

Massive scalar field:

❑ Superradiance: black hole bomb when[Press-Teukolsky 1972]

❑ Hydrogen-like, unstable bound states [Detweiler 1980, Zouros+Eardley, Dolan…]

[Arvanitaki+Dubovsky, 1004.3558]

Schwarzschild and Kerr quasinormal mode spectrum

[Berti-Cardoso-Will, gr-qc/0512160; EB+, gr-qc/0707.1202]

• One mode fixes mass and spin – and the whole spectrum!• N modes: N tests of GR dynamics…if they can be measured• Needs SNR>50 or so for a comparable mass, nonspinning binary merger

Beyond O3:

3G detectors

and LISA

A Gravity Center at Ole Miss – Why?