Gravitational wave observations of binary

black hole mergers

Miami 2017

James A. Clark

December 15, 2017

The story so far. . .

In two observing runs (“O1”, “O2”) we have so observed:

• O1: GW150914, LVT1510121, GW151226

• O2: GW170104, GW170608, GW170814

1“LVT”: LIGO-Virgo transient, lower significance 1 / 21

Masses

GW150914: spectacular discovery of unknown class of black hole,

subsequent measurements → probing black hole mass distribution

2 / 21

A New Population of Black Holes

3 / 21

Overview

This talk: an introduction to gravitational wave (GW) observations of

binary black hole (BBH) mergers

1 BBH Observations

GW150914

GW151226

GW170104

GW170608

GW170814

2 Astrophysical Implications

Progenitor SystemsImage: butterfly1

4 / 21

BBH Observations

GW150914

On September 14, 2015. . . first detection at > 5σ (FAR< 10−7 yr−1)

SNR=24, (m1, m2) = (36, 29) M�, D ∼ 410 Mpc [1]5 / 21

Inferring Source Properties

Binary parameter space:

• Component masses: m1, m2

• 2 × 3 = 6 spin components

• Binary orientation: θJN , φc, ψ

• Sky-location & distance: (α, δ) & D15-dimensional waveform model!

Inspiral phase evolution accurately modeled via post-Newtonian theory:

• Leading-order amplitude and phase evolution: chirp mass [2]:

Mc =(m1m2)3/5

(m1 + m2)1/5

• Additional parameters (q = m2/m1 ≤ 1), effective spin χeff enter at

higher PN-order

• Effective spin – most important combination of spins for evolution of

inspiral [3]:

χeff =c

GM

(~χ1

m1+~χ1

m2

)· L̂

6 / 21

Inferring Source Properties

Source properties (generally) determined from Bayesian analysis of a

given waveform model:

• Time series data output from detector, given a signal h(t), noise

n(t):

d(t) = h(t) + n(t)

• Signal h(t) is a linear combination of polarizations, weighted by

antenna beam patterns F+,×:

h(t) = F+(α, δ, ψ)h+(t; ~θ) + F×(α, δ, ψ)h×(t; ~θ)

• Source properties ~θ = {Mc , q, χeff ,D, θJN , φc, . . . }

Information about source properties ~θ is determined from posterior

probability density function:

p(~θ|~d) ∼ p(~θ)L(~d |~θ)

Assumes signal model faithfully models the underlying signal!7 / 21

GW150914: Masses

Component mass distributions [4]

⇒

Final mass & spin [4]

• Fitting formula from numerical relativity (NR) for final mass, spin

• Initial Mtot = 65.0+4.5±0.8−4.0±0.7 M�, Final Mtot = 62.0+4.1±0.7

−3.7±0.6 M�

• Erad ∼ 3 M�c2: peak luminosity >> than entire electromagnetic

(EM)-observable Universe!

8 / 21

GW150914: Cross-validation

Two approaches to waveform reconstruction:

1. h(t) = h(t;Mc , q, χeff ,D, θJN , φc, . . . )

2. h(t) = wavelet decomposition dictated by coherent network signal

Excellent agreement → validation of BBH waveform models [4, 5]9 / 21

GW151226

SNR=13, (m1, m2) = (14.2, 7.5) M�, D ∼ 440 Mpc [6]10 / 21

GW151226 Source Properties: spin configuration

Mass-weighted spin χeff and in-plane

spin-components χp [6]

Figure 1: Component spin magnitudes &

orientations

• Lower mass → merger at higher frequency, longer inspiral

• Longer inspiral → more informative spin measurement

• p(χeff > 0|D) > 99% → at least 1 BH has non-zero spin

11 / 21

GW150914, LVT151012 & GW151226: durations & spins

12 / 21

GW170104

More distant cousin of GW150914:

SNR=13, (m1,m2) = (31.2, 19.4) M�,

D ∼ 880 Mpc [7]

Waveform reconstructions remain consistent

p(χeff < 0|D) = 0.82 → large total

spin aligned with orbital angular

momentum is disfavored 13 / 21

GW170608

Most recent result, lightest BBH so far!

SNR=13, (m1,m2) = (12, 7) M�,

D ∼ 340 Mpc [8]

Potential selection bias → systems with

uninformative precession (χp)

measurementsSpin inferences for GW170608 [8]

14 / 21

GW170814

First Virgo observation, first triple-detector detection! [9]

0

2

4

6

8

10

12

14

SNR

Hanford Livingston Virgo

16

32

64

128

256

Fre

quen

cy[H

z]

0.46 0.48 0.50 0.52 0.54 0.56

Time [s]

−1.0

−0.5

0.0

0.5

1.0

Whi

tene

dSt

rain

[10-

21]

0.46 0.48 0.50 0.52 0.54 0.56

Time [s]0.46 0.48 0.50 0.52 0.54 0.56

Time [s]

−5

0

5

−5

0

5

−2

0

2

σno

ise

0.00.51.01.52.02.53.03.54.04.55.0

Nor

mal

ized

Am

plitu

de

SNR=18, (m1,m2) = (30.5, 25.3) M�, D ∼ 540 Mpc [9]

15 / 21

GW170814: Sky localization

Triple-coincident observations → sky localization

• 1 GW detector: omni-directional

but non-uniform

• 2 GW detectors: time-delay

constrains source to annulus +

amplitude ratio constraints

• 3 GW detectors: intersection of 2

annuli → sky-patches

Localization of GW170814 [9]

Geometry of HLV network and signal travel

times [10]

• Initial HL rapid localization: 1160 deg2

• Rapid localization +Virgo: 100 deg2

• Full parameter estimation: 60 deg216 / 21

Observation Summary: Sky localization

90% credible sky-areas

GW150914: 230 deg2 [11]

LVT151012:

1600 deg2 [11]

GW151226: 850 deg2 [11]

GW170104: 1200 deg2 [7]

GW170814: 50 deg2 [9]

17 / 21

Astrophysical Implications

Massive BH Progenitor Systems

• GW150914: m1,m2 > all

known BH masses

• BH formation:

1. Supernova + fall-back

2. Failed SN + prompt collapse

• Key factor: stellar wind

metallicity Z :

Low Z → lower opacity,

weaker winds & less

mass-loss

Figure 2: Dependence of maximum BH mass on

metallicity [12] (Bands: GW150914 m1, m2)

Conclusion: GW150914 BBH formed

in a low-metallicity environment

18 / 21

Constraining Binary Evolution Scenarios

BBH formation channels (see e.g., [11]):

1. dense stellar environment → dynamical formation 3

2. isolated binary evolution with a common envelope phase 3

3. chemically homogeneous evolution, tidally-locked binaries 7

Expect large, aligned spins: implausible in light of GW170104

Dynamical BBH formation [13] BBH through isolated evolution [14]

19 / 21

Summary

• GW BBH observations

becoming “routine” (!)

• GWs encode source parameters

Some parameters measured

well (e.g., chirp mass)

Others much harder (e.g.,

mass ratio, spin orientations)

• GW observations starting to

probe black hole formation &

evolution

Expected BBH detection rates from O1 [11]Just scraping the surface:

• Whole suites of tests of general relativity!

• Higher-order multipoles + precession in waveform models

• Direct comparisons with numerical relativity

• Searches for “intermediate” mass BBH (> 100 M�)

20 / 21

Observation Summary: Spins & Masses

Watch this space!

21 / 21

O1 Source Parameters

Figure 3: Trigger characteristics and source parameters for the O1 BBH triplet [11]

GW170104

Figure 4: Trigger characteristics and source parameters for GW170104 [7]

GW170608, GW170814

Figure 5: Trigger characteristics and source

parameters for GW170608 [8]

Figure 6: Trigger characteristics and source

parameters for GW170814 [9]

References

[1] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], ,

“Observation of Gravitational Waves from a Binary Black Hole Merger”,

Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837

[2] B. S. Sathyaprakash & B. F. Schutz, “Physics, Astrophysics and

Cosmology with Gravitational Waves”, Living Rev. Relativ. (2009)

[3] P. Ajith et al, “Inspiral-Merger-Ringdown Waveforms for Black-Hole

Binaries with Nonprecessing Spins” Phys. Rev. Lett. 106, 241101 (2011)

[4] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], ,

“Properties of the binary black hole merger GW150914”, Phys. Rev.

Lett. 116, 241102 (2016), arXiv:1602.03840

References

[5] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], “Tests of

general relativity with GW150914”, Phys. Rev. Lett. 116, 221101 (2016),

arXiv:1602.03841

[6] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], ,

“GW151226: Observation of Gravitational Waves from a 22-Solar-Mass

Binary Black Hole Coalescence”, Phys. Rev. Lett. 16 241103 (2016)

arXiv:1606.04855

[7] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations],

“GW170104: Observation of a 50-Solar-Mass Binary Black Hole

Coalescence at Redshift 0.2”, Phys. Rev. Lett. 118, 221101 (2017)

[8] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations],

“GW170608: Observation of a 19-solar-mass Binary Black Hole

Coalescence”, Submitted to Astrophys. J. Lett (2017), arxiv:1711.05578

References

[9] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations],

“GW170814: A Three-Detector Observation of Gravitational Waves from

a Binary Black Hole Coalescence”, Phys. Rev. Lett. 119, 141101 (2017),

arxiv:1709.09660

[10] S. Chatterji et al., “Coherent network analysis technique for

discriminating gravitational-wave bursts from instrumental noise”, Phys.

Rev. D 74, 082005 (2006)

[11] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], , “Binary

Black Hole Mergers in the first Advanced LIGO Observing Run”, Phys.

Rev. X 6, 041015 (2016), arXiv:1606.04856

[12] B. P. Abbott et al. [Virgo and LIGO Scientific Collaborations], ,

“Astrophysical Implications of the Binary Black-Hole Merger

GW150914”, Astrophys. J. Lett., 818, L22, (2016), arXiv:1602.03846

References

[13] C. Rodriguez, et al., “Dynamical Formattion of the GW150914 Binary

Black Hole”, Astrophys. J. Lett. 824 1 (2016)

[14] K. Belczynski et al., “The first gravitational-wave source from the

isolated evolution of two stars in the 40100 solar mass range”, Nature

534, 512–515 (2016)