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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)