Gravitational Wave Observations from Earth and in Space

Home , Black hole bomb, Maarten Schmidt, Reinhard Genzel, Roy Kerr

A new dawn: gravitational wave observations from Earth and in space

Emanuele Berti, Johns Hopkins University Emera Astronomy Center Orono (ME), November 14 2019 Planetarium 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 story November 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 story September 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

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) 8 Andromeda (M31): 2.6 million lyrs away, 10 Msun black hole

Radio Microwave Infrared

Visible Ultraviolet X-Rays Gravity: Newton vs. Einstein Newton (1687): Einstein (1915): ✓ Action at a distance ✓ Gravity is spacetime curvature ✓ Describes effect of gravity, ✓ “Spacetime tells mass how to move, but does not explain it mass tells spacetime how to curve” Extreme light bending: EHT and M87’s light ring

9 55 million lyrs away, 6.5x10 Msun black hole Gravitational waves

Gravitational waves as tidal forces

1 ton

2 m

frot=1 kHz, h~(2.6 x 10-33 m)/r r > ~3x105 m: h < 9 x 10-39 M~1033 g, v=c, r~15 Mpc, Illustrations from Kip Thorne’s h~10-21 “Black holes and Time Warps: Einstein’s Outrageous Legacy” 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 GW150914: a new astronomy

VIEWPOINT The First Sounds of Merging Black Holes Gravitational 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⇤,†

or decades, scientists have hoped they could “ lis- ten in” on violent astrophysical events by detecting their emission of gravitational waves. The waves, Fwhich can be described as oscillating distortions in the geometry of spacetime, were first predicted to exist by Einstein in 1916, but they have never been observed di- rectly. Now, in an extraordinary paper, scientists report that they have detected the waves at the Laser Interferometer Gravitational-wave Observatory (LIGO) [1]. From an analysis of the signal, researchers from LIGO in the US, and their collaborators from theVirgo interferometer in Italy, infer that the gravitational waves were produced by the inspiral and merger of two black holes (Fig. 1), each with a mass that is more than 25 times greater than that of our Sun. Their find- ing provides the first observational evidence that black hole binary systems can form and merge in the Universe. Gravitational waves are produced by moving masses, and Figure 1: Numerical simulations of the gravitational waves emitted like electromagnetic waves, they travel at the speed of light. by the inspiral and merger of two black holes. The colored Asthey travel, thewaves squash and stretch spacetime in the contours around each black hole represent the amplitude of the plane perpendicular to their direction of propagation (see gravitational radiation; the blue lines represent the orbits of the black holes and the green arrows represent their spins. (C. inset, Video 1). Detecting them, however, is exceptionally Henze/NASA Ames Research Center) hard because they induce very small distortions: even the strongest gravitational waves from astrophysical events are only expected to produce relative length variations of order 10− 21. phase, yielding no signal. A gravitational wave propagat- ing perpendicular to the detector plane disrupts this perfect “ Advanced” LIGO, as the recently upgraded version of destructive interference. During its first half-cycle, the wave the experiment is called, consists of two detectors, one in will lengthen one arm and shorten the other; during its sec- Hanford, Washington, and one in Livingston, Louisiana. ond half-cycle, these changes are reversed (see Video 1). Each detector is a Michelson interferometer, consisting of These length variations alter the phase difference between two 4-km-long optical cavities, or “ arms,” that are arranged the laser beams, allowing optical power—a signal—to reach in an L shape. The interferometer is designed so that, in the photodetector. With two such interferometers, LIGO can the absence of gravitational waves, laser beams traveling in rule out spurious signals (from, say, a local seismic wave) ◦ the two arms arrive at a photodetector exactly 180 out of that appear in one detector but not in the other. LIGO’s sensitivity is exceptional: it can detect length dif- ⇤Department of Physics and Astronomy, The University of Missis- ferences between the arms that are smaller than the size sippi, University, Mississippi 38677, USA of an atomic nucleus. The biggest challenge for LIGO is †CENTRA, Departamento de Física, Instituto Superior Técnico, detector noise, primarily from seismic waves, thermal mo- Universidade de Lisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Por- tion, and photon shot noise. These disturbances can easily tugal mask the small signal expected from gravitational waves.

physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17 The sound of black holes

3 LIGO/Virgo: O1, O2

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 additional break in the run at week• O1:23 to 9/12/2015make improvements-1/19/2016:to instrument sensiti3 vityBH. -TheBHMontana earthquake’ s impact on the LHO instrument sensitivity can be seen• at weekO2: 31.11/30/2016Virgo joined O2-8/25/2017:in week 34. Right: Amplitude7 BH-BHspectral + 1 densityNS-NSof the total strain noise of the Virgo, LHO and LLO detectors. The curves are representative of the best performance of each detector during O2.

first-generation detector in 2011. The main modifications in- For the LIGO instruments this final calibration benefitted clude a new opticalhttps://gracedb.ligo.org/latest/design, heavier mirrors, and suspended from the use of post-run measurements and removal of instru- optical benches, includinghttps://www.gwphotodiodes in-openscience.org/detector_status/vacuum. Special mental lines. The calibration uncertainties are 3.8% in ampli- care was also taken to improve the decoupling of the instru- tudeand 2.1 degreesinphasefor LLO; 2.6% inamplitude and ment from environmental disturbances. Oneof themain limit- 2.4 degrees in phase for LHO. The results cited in this paper ing noisesources below 100 Hz isthe thermal Brownian exci- use the full frequency-dependent calibration uncertainties de- tation of thewires used for suspending themirrors. A first test scribed in [62, 63]. The LIGO timing uncertainty of < 1 s performed on theVirgo configuration showed that silica fibers [64] isincluded in the phase correction factor. would reduce this contribution. A vacuum contamination is- The calibration of strain data produced online by Virgo had sue, which has since been corrected, led to failures of these large uncertainties due to the short time available for mea- silica suspension fibers, so metal wires were used to avoid surements. The data was reprocessed to reduce the errors by delaying Virgo’sparticipation in O2. Unlike the LIGO instru- taking into account better calibration models obtained from ments, Virgo has not yet implemented signal-recycling. This post-run measurements and subtraction of frequency noise. will be installed in a later upgrade of the instrument. The reprocessing included a time dependence for the noise After several months of commissioning Virgo joined O2 on subtraction and for thedetermination of thefinesse of thecav- August 1st 2017 with a BNS range of ⇠25 Mpc. The perfor- ities. The final uncertainties are 5.1% in amplitude and 2.3 mance experienced a temporary degradation on August 11th degrees in phase [65]. The Virgo calibration has an additional and 12th, when the microseismic activity on site was highly uncertainty of 20 soriginating from the time stamping of the elevated and it was difficult to keep the interferometer in its data. low-noise operating mode. During O2 the individual LIGO detectors had duty factors of ⇠60% with a LIGO network duty factor of ⇠45%. Times with significant instrumental disturbances are flagged and re- C. Data moved, resulting in 118 days of data suitable for coincident analysis [66]. Of this data 15 days were collected in coincident operation with Virgo, which after joining O2 operated Figure 1 shows the BNS ranges of the LIGO and Virgo in- with a duty factor of ⇠80%. Times with excess instrumen- struments over the course of O2, and the representative am- tal noise, which is not expected to render the data unusable plitude spectral density plots of the total strain noise for each are also flagged [66]. Individual searches may then decide to detector. include or not include such times in their final results. We subtracted several independent contributions to the instrumental noise from the data at both LIGO detectors [50]. For all of O2, the average increase in the BNS range from this noise subtraction process at LHO was ⇡ 18% [50]. At LLO III. SEARCHES thenoisesubtraction process targeted narrow line features, resulting in a negligible increase in BNS range. The search results presented in the next section were ob- Calibrated strain data from each interferometer was pro- tained by two di↵erent, largely independent matched-filter duced online for use in low-latency searches. Following the searches, PyCBC and GstLAL, and the burst search cWB. run, afinal frequency-dependent calibration was generated for Because of the sensitivity imbalance between the Advanced each interferometer. Virgo detector as compared to the two Advanced LIGO de-

Antenna pattern and sky localization

[Schutz, 1102.5421] [LVC, 1304.6670] DL=40 Mpc SNR=33 DW=16 deg2 H0 with GW170817…and all the black holes in O1/O2 (mostly GW170814)

[LVC, 1908.06060] 3 LIGO/Virgo: O1, O2, O3

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 additional break in the run at week• O1:23 to 9/12/2015make improvements-1/19/2016:to instrument sensiti3 vityBH. -TheBHMontana earthquake’ s impact on the LHO instrument sensitivity can be seen• at weekO2: 31.11/30/2016Virgo joined O2-8/25/2017:in week 34. Right: Amplitude7 BH-BHspectral + 1 densityNS-NSof the(withtotal strain EM noisecounterparts)of the Virgo, LHO and LLO detectors. The curves are representative of the best performance of each detector during O2. • O3: started 4/1/2019 31 events: mostly BH-BH, 2/3 NS-NS, 2/3 NS-BH

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] A, with ↵ =2.3, Fixed Parameter (power-law) 0 11N/A N/A mmax =50M Fixed Parameter (flat-in-log) Equation 16 0 11N/A N/A 24 Non-Evolving A, B, C 0 N/A N/A [0,1] [0, 0.25] a −1/ 2 Evolving A [-25, 25] N/A N/A 00 proportional to Ri , for BNS and BBH, while for NSBH we A. Event Classification a use a prior uniform in Ri which yields a conservative upper T his model assumes the black holes have zero spin. limit bound. To determine the probability that a given candidate origi- Table 4. Summary of models in Section 4, with prior ranges for the population parameters determining the rate models. T he nated in one of the four categories, the models are marginalized over the counts with the ranking statistic distributionsfixed parameter models are drawn from Abbot t et al. (2018). T he fixed parameters are in bold. Each of these distributions fixed at the value of the ranking statistic of the candidate.isTheuniform over the stated range; as previously, we require ↵ a , βa ≥ 1. Details of the mass models listed here are described in distribution that ismarginalized istheratio of thecategoryTaun-ble 2. der consideration versus all categories (including terrestrial): a strong correlat ion between the mass power-law slope GW170729 is excluded from the analysis, because this Z and the redshift evolution parameter, although the max- event likely merged at redshift z & 0.5, close to the O1- RihVTi i p(xµ|Ai) pAi (xµ|{x}) = p({R}, ⇤T , {hVTi }|{x}) P d{R}d⇤T d{hVTi } . im(10)um mass parameter remains well-constrained. As in O2 detection horizon. Although GW170729 shifts the ⇤T p(xµ|T) + j Rj hVTi j p(xµ|Aj ) Section 3, we carry out a leave-one-out analysis, ex- posterior towards larger values of λ, implying a stronger Rates: better constraints, evidence of growth with z 26 20 60 cluding the most massive and distant BBH, GW170729 redshift evolution of the merger rat e, the posterior re- Thus, we obtain pterrestrial , pBBH, pBNS, pNSBH, which are mu- from the sample (red curves in Figure 6). Without mains well within the uncertainties inferred from the re- tually exclusive categorizations. The overall probability of GW170729, the marginalized mass-distribution poste- maining nine BBHs. When including GW170729 in the astrophysical origin sums the expression over all categories in +1.7 +10 +9.1 {A}. riors become ↵ =0.8− 2.2, mmax = 38− 4 M . analysis, we find λ =6.5− 9.3 at 90% credibility, com- Marginalizing over the two mass distribution param- pared to λ =0.9+9.8 when excluding GW170729 from We expect di↵erent values of pAi to be assigned to any − 10.8 given event by di↵erent search pipelines. This is due to dif- eters and the redshift-evolution parameter, the merger the analysis. With only 10 BBH detections so far, the ferences in the averaged efficiency of various methods to dis- criminate signal from noise events, and also to the e↵ects of rat e density is consistent with being constant in red- wide range of possible values for λ is consistent with random noise fluctuations on the ranking statistics assigned to shift (λ = 0), and in particular, it is consistent with most astrophysical format ion channels. The precision of a specific event. We also expect systematic uncertainties in the rat e estimat es for the two fixed-parameter models this measurement will improve as we accumulat e more the quoted probabilities due to our lack of knowledge of the true event populations, for instance the mass distribution of in Abbot t et al. (2018), as shown in Figure 5. How- detections in future observing runs and may enable us to BNS and NSBH mergers. ever, we find a preference for a merger rat e density discriminat e between di↵erent format ion rat e histories Parameter estimation is not performed on all candidates that increases at higher redshift (λ ≥ 0) at 0.88 cred- or time-delay distributions (Sat hyaprakash et al. 2012; used to obtain rate estimates, so only the search masses and rankings areused to derivetheastrophysical probabilities. Ta- ibility. This preference becomes less significant when Van Den Broeck 2014; Fishbach et al. 2018). ble IV shows the per-pipeline assigned probability values for FIG. 14. This figure shows the 90% rate upper limit for the NSBH each of the relevant categories. The cWB search does not BH-BH NS-NS NS-BH FIG. 12. This figure shows the posterior distribution — combined FIG. 13. This figure shows the posterior distributions of the BNS category, measured at a set of three5. TdiscreteHE SBHPImassesN DIS(5,T10,RI30BUTION have a specific event type corresponding to NSBH or BNS, from theresults of PyCBC and GstLAL— on theBBH event ratefor event rate for the GstLAL and PyCBC searches. The uniform mass M ) with the fiducial NS mass fixed to 1.4 M . The upper limit thus we treat all cWB search events as BBH candidates. Py- the flat in log (blue) and power-law (orange) mass distributions. The distribution corresponds to theorange curves and Gaussian massdis- is evaluated for bothThematched-filterGW signsearchal dpipelines,ependswithonGstLALspins in a complicat ed CBC astrophysical probabilities are estimated by applying symmetric 90% confidence intervals are indicated with vertical lines tributions corresponds to thebluecurves. The symmetric 90% confi- corresponding to red curves and PyCBC to blue. We also show two simple chirp mass cuts to the set of events with ranking statis- beneath the posterior distribution. The union of intervalsisindicated dence intervals are indicated with vertical lines beneath the posterior choices of spinwadistriby, butions:ut at isotropicleadin(dashedg ordelines)r, anandd alignedin the regime we are in- tic ⇢> 8: events with M < 2.1 are considered as candidate in black. distributions. spin (solid lines).terested in here, some combinat ions of parameters have BNS, thosewith M > 4.35 as candidate BBH, and all remain- ing events as potential NSBH. more impact on our inferences than ot hers, and thus are trophysical processes which are expected to truncate the dis- measurable. One such parameter is χe↵ . For binaries tic threshold applied to either. PyCBC measures a smaller for NSBH sources. tribution [130]. The BH spin distribution has magnitude uni- hVTi because its fiducial threshold is higher than GstLAL. which are near equal mass, we can see from Equat ion 1 B. Binary Black Hole Event Rates form in [0, 1]. The PyCBC search uses a spin tilt distribution Despite the threshold di↵erence, the two searches find similar that only when black hole spins are high and aligned which is isotropic over the unit sphere, and GstLAL uses a values for ⇤ , and hence the rate for GstLAL islower than BNS with VIII.the orCONCLUSIONSbital angular momentum χe↵ will be measur- After the detection of GW170104, the event rate of distribution that aligns BH spins to the orbital angular mo- for PyCBC. For the uniform mass set, we obtain an interval BBH mergers had been measured to lie between 12-213 mentum. at 90% confidence of R = 800+1970 Gpc−3 y−1(PyCBC) and ably great er than zero. Figure 5 in Abbot t et al. (2018) −3 −680 −1 Theposteriors on theratedistributionsareshown inFig. 12. +1609 −3 −1 We have reported the results from GW searches for com- Gpc y [14]. This included the four events identified at R = 662 Gpc y (GstLAL), and for theGaussian set we illustrat es the inferred χe↵ spin distributions for all of that time. The hVTi , and hence the rates, are derived from a Including all events, the event rate isnow measured to be R = −565 pact mergersduring thefirst and second observing runsby the obtain R = 1210+3230 Gpc−3 y−1(PyCBC) and R = 920+2220 set of assumed BBH populations. In O1, two distributions of 56+44 Gpc−3 y−1(GstLAL) and R = 57+47 Gpc−3 y−1(PyCBC) −1040 −790 Advanced GWthedetectorBBHsnetwideork.ntifiAdvedancedin ouLIGOr GWandsAd-urveys in O1 and O2. −27 −29 Gpc−3 y−1(GstLAL). These values are consistent with previ- the primary mass — one uniform in the log and one a power for the power law distribution. For the uniform in logFigurdis- e 5. Constraints on evolution of the BBH mergvanceder VirgoWhaitvhe confidentlya few excedetectedptionsgra, cvitationalurrent obwasveesrvat ions of BBH spin law p(m ) / m−↵ with an index of = 2.3 — were used tribution, we obtain R = 18.1+13.9 Gpc−3 y−1(GstLAL) and ous observational values (both GW and radio pulsar) as well from ten stellar-mass binary black hole mergers and one bi- 1 1 ↵ −8.7 rate density as a function of redshift. Including the 10 BBHs are not consistent with large, aligned black hole spins. as representative extremes. In both populations shown here, R = 19.5+15.2 Gpc−3 y−1(PyCBC). Thedi↵erence inhVTi and as more recent investigations [199]. nary neutron star inspiral. The signals were discovered using −9.7 from O1 and O2 in our analysis, we find a preference for a the mass distribution cuts o↵ at a lower mass of 5 M . The rate distributions between the two spin populations issmaller three independentOnlyanalyses:GW170729two matched-filterand GWsearches151226[8, 9s]how significant evi- merger rate that increases with increasing redshift. T he solid mass distributions cut o↵ at a maximum mass of 50 M . The than the uncertainty from calibration. Therefore, we present and one weaklydencmodelede for pbosurstitivsearche χe↵[11; t].heWreshat vofe re-the posteriors cluster new cuto↵ ismotivated both by more sophisticated modelling a distribution for both populations, combined over searches,blue line giveDs.thNeutre poonsteStarriorBlackmedHoleian EvmentergRateser rate density aportednd four previously unpublished BBH signals discovered around χe↵ = 0. of the mass spectrum [54] preferring maximum BH masses in Fig 12 as an averaging over the spin configurations.dTheark and light bands give 50% and 90% credible intervaduringls. O2, as well as updated FARs and parameter estimates Despite these degeneracies, several tests have been much smaller than theprevious limit of 100 M , as well as as- union of the intervals combined over both populations liesIn ingreeThen anNSBHd redspace, theissoaliuniqued linechallengeand shadbothed reto gmodelion shas-ows tforheall previously reported GW detections. The reanalysis of O1 data did not reveal any new GW events, but improve- meditrophan aysicallynd 90%andcrefordibwhichle inttoervproduceal of thaccuratee rate iwnafeveforms.rred for each proposed to use spins to constrain BBH format ion chan- Astrophysical models span a wide range of potential mass ra- ments to thenelsvarious(Videtectiontale etpipelinesal. 2017ha;veFresultedarr et inalan. 2017, 2018; Steven- of thtiose fixanded-spinparaconfigurations,meter modeandls. there are no electromagnetic increase of the significance of GW151012. Including these observational examples. Hence, we take an approach similar four new BBHsonmeregers,t althe. 2017aobserv;edTBBHsalbotspan& aTwidehranrangee 2017; Wysocki et al. +2.2 +16.6 to previous analyses [192] and examine specific points in the of component masses, from 7.7−2.6 M to 50.6−10.2 M . One mass space while considering two component spin configu- of the new events, GW170729, is found to be the highest- rations: isotropic and orbital angular momentum aligned as mass BBH observed to date, with GW170608 still being the described in Sec. VII B. lightest BBH [16]. Similar to previous results, we find that Since there were no confident detection candidates in the the spins of the individual black holes are only weakly con- NSBH category, we update the upper limit at 90% confidence strained, though for GW151226 and also for GW170729 we in this category in Fig. 14. All upper limits are below 610 find that χe↵ ispositiveand thuscan ruleout two non-spinning Gpc−3 y−1. Those results are obtained using a uniform prior black holes as their constituents at greater than the 90% cred- over R. The Je↵reys prior (which also appeared in [192]) ible level. The binary mergers observed during O1 and O2 +10 suppresses larger R values. This prior choice would obtain a range in distance between 40−10 Mpc for the binary neutron +1350 less conservative upper limit. This limit isnow stronger at all star inspiral GW170817 to 2750−1320 Mpc for GW170729, masses than the “high” rate prediction [200] (103 Gpc−3 y−1) 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 remnant Farthest: DL~3Gpc, largest spin, low SNR. Princeton group: similar candidates 9

Mass Parameters Spin Parameters

Model ↵ mmax mmin βq λ m µm σm δm E[a] Var[a] ⇣ σi A [-4, 12] [30, 100] 500 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 Sections 3, 4,and 5, with the prior ranges for the population parameters. T he ﬁxed parameters are in bold. Each of these distributions is uniform over the stated range. All models in this Section assume rates which are uniform in the comoving volume (λ =0). T he lower limit on mmin is chosen to be consistent with Abbott et al. (2018). Where are the heavy BHs?

Figur e 1. Inferred di↵erential merger rate as a function of primary mass, m1 , and mass ratio, q, for three di↵erent assumptions. For each of the three increasingly complex assumptions A, B, C described in the text we show the PPD (dashed) and median (solid), plus 50% and 90% symmetric credible intervals (shaded regions), for the di↵erential rate. T he results shown marginalize over the spin distribution model. T he fallo↵ at small masses in models B and C is driven by our choice of the prior limits on the mmin parameter (see Table 2). All three models give consistent mass distributions within their 90% credible intervals over a broad range of masses, consistent with their near-unity evidence ratios (Table 3); in particular, the peaks and trough seen in Model C, while suggestive, are not identified at high credibility in the mass distribution. mergers . 1. Thus, we are unable to place meaningful with each ot her and are bounded above zero at 95% con- constraints on the presence or absence of a mass gap at fidence, thus implying that the mass rat io distribution low black hole mass. is nearly flat or declining with more extreme mass ra- Models B and C also allow the distribution of mass ratios. The posterior on βq returns the prior for βq & 4. tios to vary according to βq. In these cases the inferred Thus, we cannot say much about the relat ive likelihood mass-rat io distribution favors comparable-mass binaries of asymmetric binaries, beyond their overall rarity. (i.e., distributions with most support near q ' 1), see The distribution of the parameter controlling the frac- panel two of Figure 1. Within the context of our pa- tion of the power law versus the Gaussian component in +4.8 +0.3 rameterizat ion, we find βq =6.7− 5.9 for Model B and Model C is λ m =0.4− 0.3, which peaks away from zero, +5.5 βq =5.8− 5.8 for Model C. These values are consistent implying that this model prefers a contribution to the Evidence for the second mass gap? Collapse or previous mergers? 2

1g BH 1g BH

1g BH 1g BH 1g BH 1g BH redshift z˜1

2g BH

redshift z˜2 redshift z˜ 2g BH 2g BH 1g BH

1g BH 1g BH

redshift z redshift z

redshift z

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

FIG. 1. Cartoon[Gültekinsketch of th-eMillerthree p-oHamilton,ssible scenari oastros for th-ephm/0402532,erger of two B Hastros. Firs-pht ge/0509885]neration (1g) BHs resulting from stellar collapse can form seco[Gerosa+EB,1703.06223;nd generation (2g) BHs via merge rsFishbach. Imprints+,of t1703.06869]hese formation channels areleft in the statistical distribution of masses, spins and redshift of the detected events.

(i) 2g BHs should be more massive than BHs born II. T H EOR ET I C A L D I ST R I B U T I ON S from stellar collapse; (ii) quite independently of the distribution of spin mag- Our goal in this section is to develop a simple prescrip- nitudes following core collapse (which is highly un- tion to build populat ions of binary BHs. Our great ly certain [39]), the spin magnitudes of 2g BHs should oversimplified model is not meant to capture the com- cluster (on average) around the dimensionless spin plexity of binary evolution in an astrophysical setting, ⇠ 0.7 resulting from the merger of nonspinning but just the main feat ures distinguishing 1g and 2g BHs. BHs [40]; As illustrat ed by the cartoon in Fig. 1, we con- st ruct three theoret ical distributions, labeled by “ 1g+ 1g,” (iii) stat istically, the merger of BH binaries including “ 1g+ 2g” and “ 2g+ 2g” . In this context, “ 1g” means that 2g components should occur lat er (i.e., at smaller one of the binary components is a first-generat ion BH redshift or luminosity distance from GW detectors) produced by stellar collapse, whereas “ 2g” means that because of the delay time between BH format ion it is a second-generat ion BH produced by a previous and merger. merger. In this paper we make these arguments more quantita- tive and rigorous by developing a simple but physically mot ivat ed model to describe the bulk theoretical prop- A. T he 1g+ 1g p opulat ion erties of 1g and 2g binary BH mergers (Sec. II). Then we consider a set of present and future GW detectors, Following the LIGO-Virgo Scientific Collaborat ion [3], and we simulat e obser vable distributions by selecting de- for the 1g+ 1g populat ion, we adopt three di↵erent pre- tectable binaries and estimat ing the expected measure- scriptions for the distribution of source-frame masses: ment errors on their parameters (Sec. III). Finally we set up a Bayesian model selection framework (Sec. IV) to ad- (i) M odel “ fl at ” : we assume uniformly distributed dress what can be done with current observat ions, and to source-frame masses m1 and m2 in the range mi 2 quantify the capabilities of future detectors to distinguish [5M , 50M ](i =1, 2), where hereafter m1 >m2. between di↵erent models (Sec. V). We conclude by sum- marizing our results and pointing out possible extensions (ii) M odel “ log” : we takethelogarithm of the source- (Sec. VI). frame masses to be uniformly distributed in the Precession and effective spins

GW151226: ceff=0.18 GW170729: 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 noise recorded 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

[Arvanitaki+Dubovsky, 1004.3558] Quasinormal modes: Massive scalar field: ❑ Ingoing waves at the horizon, ❑ Superradiance: black hole bomb when outgoing waves at infinity [Press-Teukolsky 1972] ❑ Spectrum of damped modes (“ringdown”) ❑ Hydrogen-like, unstable bound states [EB+, 0905.2975] [Detweiler 1980, Zouros+Eardley, Dolan…] Schwarzschild and Kerr quasinormal mode spectrum

• 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

[Berti-Cardoso-Will, gr-qc/0512160; EB+, gr-qc/0707.1202] Beyond O3: 3G detectors and LISA A Gravity Center at Ole Miss – Why?