Alessandra Buonanno for the LIGO Scientific Collaboration & Virgo Collaboration

Max Planck Institute for Gravitational Physics (Albert Einstein Institute)Department of Physics, University of Maryland

“Black Holes, GWs & Spacetime Singularities”, Vatican Observatory, Castel Gandolfo May 9-12, 2017

Observing Signatures of Dynamical Space-Time through Gravitational Waves

Outline

• Observation of gravitational waves by Advanced LIGO.

• The science from GW experiments stems on our ability to make precise predictions: theoretical groundwork to identify and interpret the signals.

• Astrophysics. Tests of general relativity in the strong-field, highly dynamical regime. Probing matter at supranuclear densities. Cosmology.

• The bright future of gravitational-wave astronomy comes with new theoretical challenges.

LIGO detections during O1: GW150914 & GW151226

(Abbott et al. PRL 116 (2016) 061102) (Abbott et al. PRL 116 (2016) 241103)

• GW150914: SNR=24 (very loud),10 GW cycles, 0.2 sec.

•GW151226: SNR=13 (quieter), 55 GW cycles, 1.5 sec.

Hanford Livingston

What LIGO detected: binary black-hole coalescences

(Abbott et al. arXiv:1606.04856)

•GW150914: merger in detector’s band, more massive binary

• GW151226: inspiral-plunge in detector’s band, lower mass binary

Characteristics of binary black-hole coalescence

• Early inspiral: low velocity & weak gravitational field.

• Late inspiral/plunge: high velocity & strong gravitational field.

• Merger: nonlinear & non perturbative effects; rapidlyvarying gravitational field

• Ringdown: excitation of quasi-normal modes/spacetime vibrations.

Phase/amplitude evolution encodesunique information about the source

(Abbott et al. PRL 116 (2016) 061102)

Black holes of radius of 90 km at separation of 350 km are making 75 orbits per second before merging!

100 101 102 103 104 105m1/m2

100

101

102

103

104r c

2 /GM

Effective one-body theoryEffective one-body

Numerical Relativity

Post-Newtonian theory

Effective one-body

Post-Newtonian theory

Effective one-body theory

Post-Newtonian theory

theorytheoryPerturbation theorytheory

gravitational self-force

• Two parameters determine the range of validity of each method:

(AB & Sathyaprakash 14)

Waveform modeling to detect and infer source’s properties

Perturbation

• First developed in 1917 (Droste & Lorentz 1917, and Einstein, Infeld & Hoffmann 1938)

(Blanchet, Damour, Iyer, Faye, AB, Bohe’, Marsat; Jaranowski, Schaefer, Steinhoff; Will, Wiseman; Goldberger, Porto, Rothstein, Levi, Foffa, Sturani; Flanagan, Hinderer, Vines …)

+ … +

m1 m2

+ …

m1 m2

+ …

Small parameter is v/c or GM/rc2

Post-Newtonian/post-Minkowskian formalism/effective field theory

Perturbation theory and gravitational self force (GSF)

• First works in 50-70s (Regge & Wheeler 56, Zerilli 70, Teukolsky 72)

(Fujita, Poisson, Sasaki, Shibata, Khanna, Hughes, Bernuzzi, Harms, …)

m1 m2

• GSF: Accurate modeling of relativistic dynamics of large mass-ratio inspirals requires to include back-reaction effects due to interaction of small object with its own gravitational perturbation field.

(Deitweiler, Whiting, Mino, Poisson, Quinn, Sasaki, Tanaka, Barack, Ori, Pound, van de Meent…)

@2

@t2� @2

@r2?+ V`m = S`m

Equation of gravitational perturbations in black-hole spacetime:

m1

m2

Small parameter is m2/m1

Green functions in Schwarzschild/Kerr spacetimes.

Numerical Relativity

-4 0 4

-4

0

4

y/m

x/m

• Breakthrough in 2005 (Pretorius 05, Campanelli et al. 06, Baker et al. 06) Kidder, Pfeiffer, Scheel, Lindblom, Szilagyi; Bruegmann, Hannam, Husa, Tichy; Laguna, Shoemaker; …

• Simulating eXtreme Spacetime (SXS) collaboration

• Numerical-Relativity & Analytical Relativity collaboration (Hinder et al. 13) (Mroue et al. 13)

The effective-one-body (EOB) approach

emission re−written in summed conservative dynamics and GW emission computed as a Taylor

expansion

PN Theoryconservative dynamics and GW

Effective one body Numerical relativity

and/or factorized form

two−body dynamics and GW emission computed with all

non−linearities

• EOB approach introduced before NR breakthrough

• EOB model uses best information available in PN theory, but resums PN terms in suitable way to describe accurately dynamics and radiation during inspiral and plunge.

• EOB assumes comparable-mass description is smooth deformation of test-particle limit. It employs non-perturbative ingredients and models analytically merger-ringdown signal.

AB, Pan, Taracchini, Barausse, Bohe’, Shao, Hinderer, Steinhoff; Damour, Nagar, Bernuzzi, Bini, Balmelli; Iyer, Sathyaprakash; Jaranowski, Schaefer;

1m

2m

1m 2m!ν

g

realE Eeff

realJ Nreal effJ effN

Real description

!νg eff

Effective description

!

The effective-one-body approach in a nutshell

• Two-body dynamics is mappedinto dynamics of one-effective body moving in deformed black-hole spacetime, deformation being the mass ratio.

• Some key ideas of EOB model were inspired by quantum field theory when describing energyof comparable-mass charged bodies.

Map

(AB & Damour PRD59 (1999) 084006 )

-0.2-0.1

00.10.20.3

grav

itatio

nal w

avef

orm inspiral-plunge

merger-ringdown

-250 -200 -150 -100 -50 0 50c3t/GM

0.10.20.30.40.5

frequ

ency

: GM!/c

3 2 x orbital freq inspiral-plunge GW freqmerger-ringdown GW freq

(AB & Damour PRD62 (2000) 064015 )

−!" −#$ −#" −$ " $ #" #$ !"!

−!"

−#$

−#"

−$

"

$

#"

#$

!"

"

#−$%& ν!"!#$%

EOB inspiral-merger-ringdown analytic waveform

(credit: Hinderer)

On the simplicity of merger signal

•Peak of black-hole potential close to “light ring”.

•Once particle is inside potential, direct gravitational radiation from its motion is strongly filtered by potential barrier (high-pass filter).

• Only black-hole spacetime vibrations (quasi-normal modes) leaks outblack-hole potential.

light ring@2

@t2� @2

@r2?+ V`m = S`m

black hole horizon

equation of gravitational perturbations in black-hole spacetime

(Regge & Wheeler 56, Zerilli 70, Teukolsky 72)

Waveforms combining analytical & numerical relativity

emission re−written in summed conservative dynamics and GW emission computed as a Taylor

expansion

PN Theoryconservative dynamics and GW

Effective one body Numerical relativity

and/or factorized form

two−body dynamics and GW emission computed with all

non−linearities

•Effective-one-body (EOB) formalism

0 1000 2000 3000 4000 5000 6000

-0.4-0.20.00.20.4

grav

itatio

nal w

avef

orm

NREOBNR

6000 6100 6200 6300 6400t/M

mass ratio = 1 and spins |S1|/m21 = 0.98, |S2|/m2

2 = 0.98

0.00 0.05 0.10 0.15 0.20 0.25ν

-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

χ

NR nonspinningNR spinningtest-particle limit

(Taracchini, AB, Pan, Hinderer & SXS 14, Puerrer 15)

• Inspiral-merger-ringdown phenomenological waveforms fitting EOB & NR (IMRPhenom) (Khan et al. 16, Hannam et al 16)

38 SXS simulations

100 101 102

m1 [M�]

100

101

m2

[M�

]

|�1| < 0.9895, |�2| < 0.05

|�1,2| < 0.05

|�1,2| < 0.9895

GW150914GW151226LVT151012 (gstlal)LVT151012 (PyCBC)

Detection confidence with modeled search in O1

•Confidence (FAP) > 5.3 (< 2x10-7) that GW150914 & GW151226 were “real” gravitational-wave signals.

200,000 EOBNR templates

•Matched filtering employed

GW150914

GW151226

2� 3� 4� 5� > 5�2� 3� 4� 5� > 5�

8 10 12 14 16 18 20 22 24Detection statistic �̂c

10�810�710�610�510�410�310�210�1100101102103104

Num

ber

ofev

ents

GW150914

Search ResultSearch BackgroundBackground excluding GW150914

• Minimal-assumption search reached high detection confidence (> 4.6 )

only for GW150914.

(Abbott et al. arXiv:1606.04856)

50,000 PN templates

Numerical-relativity simulation of a binary black-hole merger with parameters close to GW150914

-2000 -1500 -1000 -500 0t-tpeak (M)

-0.4

-0.2

0

0.2

0.4

Re[rh

22/M

]

NREOBNR

-50 0 50t-tpeak (M)

-0.4

-0.2

0

0.2

0.4

20 H

z fo

r M =

70

Msu

n

30 H

z fo

r M =

70

Msu

n

(Ossokine, AB & SXS project) (visualization credit: Haas @ AEI)

•Waveform models very closely match the exact solution from Einstein equations around GW150914 & GW151226.

• Systematics due to modeling are smaller than statistical errors.

(Ossokine, AB & SXS project)

(see also Abbott et al. arXiv:1611.07531)

(Ossokine, AB & SXS project)

(visualization credit: Dietrich, Haas @AEI)

(Abbott et al. PRL 116 (2016) 241103)

Numerical-relativity simulation of a binary black-hole merger with parameters close to GW151226

•Systematics due to modeling are smaller than statistical errors.

Unveiling binary black holes properties: masses

GW150914 GW151226

•GW150914: merger in band, total mass well measured, good measurement of individual masses.

• We measure best the “chirp” mass•GW151226: merger outside band, individual masses measured less precisely.

(Abbott et al. PRL 116 (2016) 241103)

M = M ⌫3/5

msource

2

msource

1

(Abb

ott

et a

l. P

RX 6

(20

16) 04

1014

)

Unveiling binary black-holes properties: spins

GW150914 GW151226

• BHs’ spins not maximal, and for GW151226 one BH’s spin larger than 0.2 at 99% confidence.

• Spin of primary BH < 0.7. No information about precession.

(Abb

ott

et a

l. P

RX 6

(20

16) 04

1014

) (Abbott et al. PRL 116 (2016) 241103)

Implications for binary formation scenarios• BHs’ observed heavier than expected for GW150914. How did they form?

•Dynamical capture or massive binary stars undergoing core-collapse or chemically homogeneous stars or primordial BHs or PopIII stars or binaries in AGN disks?

(Heger et al. 03, Mapelli et al. 09, Belczynski et al. 10, Mapelli et al. 13, Spera et al. 15)

(Abbott et al. ApJ L22 (2016) 818)

(Lipunov et al 97, Belczynski et al. 10, Dominik et al. 15, Belczynski et al. 15, Nelemans et al. 01,Rodriguez et al. 16, de Mink et al. 09, Marchant et al. 16,Mckernan et al. 16,Bird et al. 16,de Mink & Mandel 16, Belczynski et al. 16, …)

weak wind

• Given current tight constraints on GR (e.g., Solar system, binary pulsars), can any GR deviation be observed with LIGO?

Tests of GR with LIGO’s sources

highly-dynamical

strong-field

10

�5

10

�4

10

�3

10

�2

10

�1

10

0

10

�8

10

�7

10

�6

10

�5

10

�4

10

�3

10

�2

10

�1

10

0

Solar

System

Binary

Pulsars

Gravitational

Waves

v/c

�

Newton

(credit: Sennett)

• GW150914/GW122615’s rapidly varying orbital periods allow us to bound higher-order PN coefficients in gravitational phase.

Tests of GR with first LIGO’s black holes: inspiral

(Abbott et al. arXiv:1606.04856)

0PN 0.5PN 1PN 1.5PN 2PN 2.5PN 3PN 3.5PNPN order

10�1

100

101

|�'̂|

GW150914GW151226GW151226+GW150914

• First GR test in the genuinelydynamical, strong-field regime.

(Arun et al. 06 , Mishra et al. 10, Yunes & Pretorius 09, Li et al. 12)

• PN parameters describe: tails ofradiation due to backscattering, spin-orbit and spin-spin couplings.

200 220 240 260 280 300QNM frequency (Hz)

0

2

4

6

8

10

12

14

QN

Mde

cay

time

(ms)

1.0

ms

3.0 ms5.0 ms

7.0 ms

7.0ms

IMR (l = 2,m = 2,n = 0)

• We measured frequency & decay time of damped sinusoid in the data after GW150914’s peak.

Could we prove that GW150914’s remnant is a BH?

• Multiple QNMs need to be measured to extract mass and spin of remnant, test no-hair theorem and second-law black-hole mechanics(Israel 69, Carter 71; Hawking 71, Bardeen 73).

(Abbott et al. PRL 116 (2016) 221101 )

Can we probe BH horizon from GW ringdown?

(Cardoso et al. 16)

• What determines ringdown signal? Light ring or horizon?

horizonless object black hole

same ringdownsignal

different QNM signals

�t

radial infall

• QNM spectrum differs in BH and horizonless object.

• Ringdown and QNM signals can be different in horizonless objects. GW echoes!

(Cardoso et al. 16)

same ringdownsignal

different QNM signals

�t

objects. GW echoes!

same ringdownsignal

different QNM signal

�t

(Cardoso, Franzin & Pani 16)

(Cardoso et al. 16)

Inference of cosmological parameters in future LIGO searches

•Measurement of Hubble constant H0 with accuracy of 5% at 95% confidence after 40-50 GW observations with 3 detectors.

• Wide-field galaxy surveys can provide (sky positions and) redshifts(Schutz 1986)

(Del Pozzo 12)

single GW event multiple events

3 detectors

3 detectors

z 0.1

GW catalogue consists of1,000 events sampled fromSDSS at

Upper limits on rates of neutron star mergers

10�2 10�1 100 101 102 103 104

NSBH Rate (Gpc�3yr�1)

aLIGO 2010 rate compendium

Fong et al. GRB

Coward et al. GRB

Petrillo et al. GRB

Jin et al. kilonova

Vangioni et al. r-process

de Mink & Belczynski pop syn

Dominik et al. pop synO1O2O3

100 101 102 103 104

BNS Rate (Gpc�3yr�1)

aLIGO 2010 rate compendium

Kim et al. pulsar

Fong et al. GRB

Siellez et al. GRB

Coward et al. GRB

Petrillo et al. GRB

Jin et al. kilonova

Vangioni et al. r-process

de Mink & Belczynski pop syn

Dominik et al. pop synO1O2O3 (Abbott et al. arXiv:1607.07456)

@90% confidence:• NSNS rate < 12,600/(Gpc)3/yr • NSBH rate < 3,600/(Gpc)3/yr

•Assuming GRB rate of 3-30/(Gpc)3/yr and all GRBs have NSNS (NSBH)progenitors, beaming angle > 1.2-4.0 (2.4-7.4) deg.

• Observed GRB beaming angles 3-25 deg

• NS’s characteristics:

- mass: 1-3 Msun - radius: 9-15 km- core density > 1014 g/cm3

(Baade & Zwicky 1934, Gamow 1937, Landau 1938, Oppenheimer & Volkoff1939, Cameron 1959, Wheeler 1966)

(Antoniadis et al. 16)

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34034

Probing NS’s equation of state with LIGO and Virgo

•NSs are unique laboratoriesto study baryonic matter at supra-nuclear density

(credit: Read)(credit: Hinderer)

With several tens of events, possible to distinguish “some” EOS

• The influence of NS’s internal structure on waveform is characterized by a single (constant) parameter, the tidal deformability

• measures star’s quadrupole deformation in response to the companion perturbing tidal field:

(Kochanek 92, Bildsten & Cutler 92, Lai et al. 93, Lai 94)

(Agathos et al. 15, Del Pozzo et al. 13 (see also Lackey et al. 14; Lynch et al. 14; Yagi et al. 15))

(Kochanek 92, Bildsten & Cutler 92, Lai et al. 93, Lai 94)

mass ratio = 1.5, EOS = MS1b

(Dietrich & Hinderer 17) tidal EOB waveform versus NR waveform

Waveform modeling for NS-NS binaries up to merger

(Damour & Nagar 12; Bernuzzi et al. 15; Hinderer et al. 16, Steinhoff et al. 16)

time

• Results extended to NS-BHs

Advanced detectors’ roadmap and rates

Frequency/Hz

Strainnoise

amplitude/Hz−

1=2

Advanced LIGO

Early (2015 { 16, 40 { 80 Mpc)

Mid (2016 { 17, 80 { 120 Mpc)

Late (2017 { 18, 120 { 170 Mpc)

Design (2019, 200 Mpc)

BNS-optimized (215 Mpc)

101 102 10310−24

10−23

10−22

10−21

(Aasi et al. arXiv:1304.0670)

Detection rates @ design sensitivity:• Binary neutron stars: 0.2 - 200 per year • Binary black holes: tens to hundreds per year!

• Rates: 9 - 240 /(Gpc)3/yr

1 10

hV T i0/hV T iO1

0%

20%

40%

60%

80%

100%

P(N

>{1

0,35

,70}

|{x

j},

hVT

i)O2 O3

(Abbott et al. arXiv:1606.04856)

• To take full advantage of discovery potential in next years and decades we need to make precise theoretical predictions.

The new era of precision gravitational-wave astrophysics

• We can now probe the most extreme astrophysical objects in the universe, and learn how they formed.

• We can now learn about gravity in the genuinely highly dynamical, strong field regime.

• We can now unveil properties of neutron stars unaccessible in other ways.

• We can now provide the most convincing evidence that compact objects in our Universe are black holes as predicted in GR.