Alessandra Buonanno Max Planck Institute for Gravitational Physics (Albert Einstein Institute)Department of Physics, University of Maryland
Gravitational-Wave (Astro)Physics: from Theory to Data and Back
May 4, 2018 Spitzer Lectures, Princeton University
Spitzer Lectures
•Lecture I: Basics of gravitational-wave theory and modeling
•Lecture II: Advanced methods to solve the two-body problem in General Relativity
•Lecture III: Inferring cosmology and astrophysics with gravitational-wave observations
•Lecture IV: Probing dynamical gravity and extreme matter with gravitational-wave observations
(visualization credit: Benger @ Airborne Hydro Mapping Software & Haas @AEI)
(NR simulation: Ossokine, AB & SXS @AEI)
• Given current tight constraints on GR (e.g., Solar system, binary pulsars), can any GR deviation be observed with GW detectors?
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)
Solar system:
Binary pulsars:
LIGO/Virgo:
Extreme gravity, dynamical spacetime: tests of General Relativity
PN templates in stationary phase approximation: TaylorF2
�i =Si
m2i
1PN 1.5PN
2PN
spin-orbit
1.5PN
spin-spin
2PN
0PN graviton with non zero mass
1PN
dipole radiation
-1PN
• GW150914/GW122615’s rapidly varying orbital periods allow us to bound higher-order PN coefficients in gravitational phase.
0PN 0.5PN 1PN 1.5PN 2PN 2.5PN 3PN 3.5PNPN order
10�1
100
101
|�'̂|
GW150914GW151226GW151226+GW150914
(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.
(Abbott et al. PRX6 (2016))
• PN parameters take different values in modified theories to GR.
'(f) ='ref + 2⇡ftref + 'Newt(Mf)�5/3
+ '0.5PN(Mf)�4/3 + '1PN(Mf)�3/3
+ '1.5PN(Mf)�2/3 + · · ·
h̃(f) = A(f)ei'(f)
90% upper bounds
Bounding PN parameters: inspiral
Some modified theories to General Relativity
(Yunes & Siemens 2013)
20 50 100 150 200 250 300Frequency (Hz)
1.00
0.10
0.01
|h GW
(f)|/
10�2
2(H
z)
inspiral intermediate mergerringdown
low frequency high frequency
• Merger-ringdown phenomenological parameters (βi and αi) not yet expressed in terms of relevant parameters in GR and modified theories of GR.
Bounding phenom parameters: intermediate/merger-RD
(Abbott et al. PRL 116 (2016) 221101 )
GW150914 + GW151226 + GW170104(Abbott et al. PRL 118 (2017) 221101)
Tests of Lorentz Invariance/Bounding Graviton Mass
(Will 94, Mirshekari, Yunes & Will 12)
vgc
= 1 + (↵� 1)A
2E↵�2
E2 = p2c2 +Ap↵c↵
↵ � 0
mg 7.7⇥ 10�23eV/c2
↵ = 0, A > 0
(Abbott et al. PRL118 (2017))
•Phenomenological approach: modified dispersion relation. GWs travel at speed different from speed of light.
How to test GR and probe nature of compact objects: building deviations from GR & BHs/NSs
• Will GR deviations be fully captured in perturbative-like descriptions during merger-ringdown stage? Likely not. (e.g., Yunes & Pretorius 09, Li et al. 12, Endlich et al. 17)
• Need NRAR waveforms of binaries composed of exotic objects (BH & NS mimickers), such as boson stars, gravastar, etc. (e.g., Palenzuela et al. 17)
• Need NRAR waveforms in modified theories of GR: scalar-tensor theories, Einstein-Aether theory, dynamical Chern-Simons, Einstein-dilaton Gauss-Bonnet theory, massive gravity theories, etc. (e.g., Stein et al. 17, Cayuso et al.17,
Hirschmann et al. 17)
• Do current GR waveform models include all physical effects? Not yet.
• Including deviations from GR in EOB formalism.(Julie & Deruelle 17, Julie 17, Khalil et al. in prep 18)
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)
Probing nature of remnant: quasi-normal modes (QNMs)
•Multiple QNMs can be measured with future detectors, thus testing no-hair conjecture and second-law black-hole mechanics (Israel 69, Carter 71; Hawking 71,Bardeen 73).
(Abbott et al. PRL116 (2016) )
bound viscosity of exotic compact object
•Deformed/perturbed black holes emits quasi-normal modes.
•Measuring at least two modes will be smoking gun that Nature’s black holes are black holes of General Relativity.
Measuring BH’s mass and spin from multiple QNMs (D
reyer et al. 03)• By knowing only one frequency and decay time, we cannot identify final BH’s mass and spin.
• Which SNRs are needed to measure multiple modes?
Black-hole spectroscopy by making full use of GW modeling
200 220 240 260 280 300f220
(Hz)
0
1
2
3
4
5
6
7
8
9
10
τ2
20 (
ms)
GW150914
pEOB
NR
3ms
5ms
1ms
•We employ parametrized inspiral-merger-ringdown waveform model (pEOBNR) that includes modes beyond the dominant (2,2).
•Using pEOBNR we recover more stringent bounds on frequency and decay time of GW150914 QNM, than using damped sinusoid model.
mass ratio = 6(Brito, AB & Raymond 18)
•BH spectroscopy: unveiling nature of merger’s remnant(Dreyer et al. 2004, Berti et al. 2006, Gossan et al. 2012, Meidam et al. 2014, Bhagwat et al. 2017, Yang et al. 2017)
Black-hole spectroscopy by making full use of GW modeling
•We bound quasi-normal mode frequencies & decay times by combining several BH observations.
one event GW150914-like with Advanced LIGO & Virgo
(Brito, AB & Raymond 18)
•Let us assume we did not find deviations from GR.
GW150914-like events in Advanced LIGO & Virgo
• About 30 GW150914-like events are needed to achieve errors of 5% and test no-hair conjecture.
(Cardoso et al. 16)
same ringdown signal
different QNM signals
�t
(Damour & Solodukhin 07, Cardoso, Franzin & Pani 16)
• If remnant is horizonless, and/or horizon is replaced by “surface”, new modes in the spectrum, and ringdown signal is modified: echoes signals emitted after merger.
Remnant: black hole or exotic compact object (ECO)?
horizonless objects
black hole
(Cardoso et al. 16)
wormhole
boson stars, fermion stars, etc. (e.g., Giudice et al. 16)
Constraints on speed of GWs & test of equivalence principle
(Abbott et al. APJ 848 (2017) L12)
• Strong constraints on scalar-tensor and vector-tensor theories of gravity.
• Combining GW and GRB observations:
(Creminelli et al. 17, Ezquiaga et al. 17, Sakstein et al. 17, Baker et al. 17)
�c
c' c
�t
D
�t = tEM � tGW
�c = cGW � c
�4⇥ 10�15 �c
c 7⇥ 10�16
assuming GRB is emitted 10 s after GW signal
assuming observed time delay is entirely due to different speed
�t ' 1.7s
•EM waves & GWs follow same geodesic. Metric perturbations (e.g., due to potential between source and Earth) affect their propagation in same way.
gravitational potential of Milky Way outside sphere of 100 kpc
(Abbott et al. APJ 848 (2017) L12) (Shapiro 1964)
•GR is non-linear theory. Complexity similar to QCD.
- approximately, but analytically (fast way)
- exactly, but numerically on supercomputers (slow way)
• Einstein’s field equations can be solved:
•Synergy between analytical and numerical relativity is crucial.
•GW170817: SNR=32 (strong), 3000 cycles (from 30 Hz), one minute.
last 0.07sec modeled by NRlast minutes
modeled by AR
(Abbott et al. PRL 119 (2017) 161101)
Solving two-body problem in General Relativity (including radiation)
mergerinspiralpost-merger
• PN waveform model was used for: - template bank: to observe GW170817
- Bayesian analyses: to infer astrophysical, fundamental physics information of GW170817
Analytical waveform modeling for GW170817(D
al Canton & H
arry 16)
50,000 PN templates
tail effects tidal effectsspin effects
Probing equation of state of neutron stars(Antoniadis et al. 2016)
tidal interactions (credit: Hinderer)
Neutron Star:
- mass: 1-3 Msun - radius: 9-15 km - core density > 1014g/cm3
• NS equation of state (EOS) affects gravitational waveform during late inspiral, merger and post-merger.
10 50 100 500 1000 500010!25
10!24
10!23
10!22
10!21
f !Hz"
BH!BHInitia
l LIGO
AdvancedLIGO
Einstein Telescope
10 50 100 500 1000 500010!25
10!24
10!23
10!22
10!21
f !Hz"
NS!NS EOS HBInitia
l LIGO
AdvancedLIGO
Einstein Telescope
NS-NS
post merger
effectively point-particle tidal effects
BH-BH
Probing equation of state of neutron stars
(credit: Read)
• measures star’s quadrupole deformation in response to companion perturbing tidal field:
• Tidal effects imprinted on gravitational waveform during inspiral through parameter .
Qij = ��Eij
�
�
PN templates in stationary phase approximation: TaylorF2
�i =Si
m2i
1PN 1.5PN
2PN
spin-orbit
1.5PN
0PN graviton with non zero mass
1PN
dipole radiation
-1PN
· · ·� 39
2⌫�2 ⇤̃ (⇡Mf)10/3
� spin-spin
2PN
tidal
5PN
⇤ =�
m5NS
=2
3k2
✓RNSc2
GmNS
◆5
it can be large
Depends on EOS & compactness
Probing equation of state of neutron stars
•Where in frequency the information about (intrinsic) binary parameters predominantly comes from.
(Harry & Hinderer 17)
•Tidal effects typically change overall number of GW cycles from 30 Hz (about 3000) by one single cycle!
(Dietrich & Hinderer 17) time
State-of-art waveform models for binary neutron stars
• Synergy between analytical and numerical work is crucial.
(Damour 1983, Flanagan & Hinderer 08, Binnington & Poisson 09, Vines et al. 11, Damour & Nagar 09, 12, Bernuzzi et al. 15, Hinderer et al. 16, Steinhoff et al. 16, Dietrich et al. 17)
NREOBNR
Strong-field effects in presence of matter in EOB theory
(Hinderer et al. 2016, Steinhoff et al. 2016)
Tides make gravitational interaction more attractive
1 2 3 4 5 6 7r/M
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
A(r)
EOBNRTEOBNRSchwarzschild
ν
EOBNRSchwarzschild
Schwarzschild
λ
light ringlight ring
ISCO
A(r) = A⌫(r) +Atides(r)
⇤
Constraining Love numbers with GW170817
(Abbott et al. PRL 119 (2017) 161101)
black hole
⇤ =�
m5NS
=2
3k2
✓RNSc2
GmNS
◆5
Depends on EOS & compactness
NS’s Love number
MS1MS1bH4
MPA1APR4
SLy
less compact
more compact
•Effective tidal deformability enters GW phase at 5PN order:
•With state-of-art waveform models, tides are reduced by ~20%. More analyses are ongoing.
Boson stars as black-hole/neutron-star mimickers
(Sennett…AB et al. 17) (see also Cardoso et al. 17)
•Boson stars are self-gravitating configurations of a complex scalar field
•Black holes:
•Boson stars:
⇤ = 0
⇤min ⇠ 1
•Neutron stars:
⇤ = �/M5
(credit: Sennett)
0 2 4 6 8 10
100
101
102
103
104
C =GM
Rc2
⇤min ⇠ 10Boson star
0.08
0.158
0.3
0.349
0.5
Compactness
V (|�|2) Mmax
Mini BS µ2
�
2
⇣85peV
µ
⌘M�
Massive BS
µ2
�
2
+
�2
|�|4p�⇣270MeV
µ
⌘2
M�
Neutron star
2� 4M�
Solitonic BS µ2
�
2
⇣1� 2|�|2
�20
⌘2
⇣µ�0
⌘2
⇣700TeV
µ
⌘3
M�
Black hole
1
The new era of precision gravitational-wave astrophysics
• We can now learn about gravity in the genuinely highly dynamical, strong field regime.
• Theoretical groundwork in analytical and numerical relativity has allowed us to build faithful waveform models to search for signals, infer properties and test GR.
• We have new ways to explore relationships between gravity, light , particles and matter.
• As for any new observational tool, gravitational (astro)physics will likely unveil phenomena and objects never imagined before.
(visualization: Benger @ Airborne Hydro Mapping Software & Haas @AEI)
(NR simulation: Ossokine, AB, SXS)
•We can probe matter under extreme pressure and density.
“Astrophysical & Cosmological Relativity” Department
•Current members
•Past members contributed to work presented
