Gravitational wave and test of general relativity
Planned Contents

Hisaaki Shinkai (Osaka Inst. Tech.)
http://www.oit.ac.jp/is/shinkai/

GW projects: KAGRA
LIGO-Virgo: GWTC-2 release & Test of GR
Auto-Regressive method for data analysis◀ In 1989, when Kei-ichi Maeda started a group at Waseda．
Kei-ichi suggested me to work in numerical relativity.
My thesis was on numerical analysis on the generality ofinﬂationary cosmology.
I mainly worked formulation problem in NR, simulations in
modiﬁed gravity theories, … and now in GW data analysis.

HS, Kei-ichi Maeda, Andy Birkin, Nobuyuki Sakai

December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

Gravitational Wave
from binary BH-BH, NS-NS, BH-NSPart 1: Gravitational Wave Projects

We need moredetectors
forbetter
localization!
GW International Network

4 km

4 km

600 m
3 km

3 km
7Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe3

Part 1: Gravitational Wave Projects

KAGRA
Underground and Cryogenic interferometric 3 km gravitational-wave detector at Kamioka, Japan112groups, 14 countries/regions
410+ active members

http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/KAGRA

HSTakaaki Kajita (PI)

Masatake Ohashi (vice PI)

board chair of KAGRA Scientiﬁc Congress(2017-2021)

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

4

Part 1: Gravitational Wave Projects

North [deg]Fourth 2nd generation detector on the Earth
LHO

KAGRA

50

Virgo

Virgo

KAGRA

LLO

LIGO-Hanford

South [deg]0

LIGO-Livingston
-50

KAGRA
-150-100

West [deg]-50050100150

East [deg]more precise GW source localization
more certain GW source parameters
more chances to hunt GW events
more ideas for GW researches
more man power

LIGO-Hanford

Virgo

LIGO-Livingston

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

5Part 1: Gravitational Wave Projects

Target Sensitivity & Schedule“Scenario Paper”[1304.0670ver2020Jan]

LVK collaboration, Living Rev Relativ (2020) 23:3
https://link.springer.com/article/10.1007/s41114-020-00026-9

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

6Part 1: Gravitational Wave Projects

Joint Research MoA signed LIGO-Virgo-KAGRA＊ 1 Mpc (BNS) is required to join the observation.

Aug 24, 2019

Dec 19, 2019

October 4, 2019 @ Ceremony of MoA signing

March 26, 2020

main part (10 pages)
Concept, Deﬁnitions,Purposes

Appendix A (17 pages)
Organizations, Procedures

Letter of Intent (3 pages)
KAGRAʼs Join to O3＊ Finally, over 1 Mpc in the end of March 26, 2020.

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

7

Part 1: Gravitational Wave Projects

Target Sensitivity & Schedule“Scenario Paper”[1304.0670ver2020Jan]

LVK collaboration, Living Rev Relativ (2020) 23:3
https://link.springer.com/article/10.1007/s41114-020-00026-9

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

8Part 1: Gravitational Wave Projects

Target Sensitivity & Schedule
2015

2016

“Scenario Paper”[1304.0670ver2020Jan]

LVK collaboration, Living Rev Relativ (2020) 23:3
https://link.springer.com/article/10.1007/s41114-020-00026-9

2020

2021

2022

O2

O3a O3bO350 Mpc

90-120Mpc

O3a O3bO4

2016

GW170608 BHBH@340Mpc
GW170814
BHBH@540Mpc
GW170817
NSNS@40Mpc

O1

GW170104 BHBH@880Mpc

160-190 Mpc

GW151226 BHBH@440Mpc

120-130 Mpc

iKAGRA2015

2019

60-100Mpc

GW150914 BHBH@440Mpc

KAGRA

2018

60-80Mpc

LIGO

Virgo

2017

O2

30
Mpc

bKAGRAphase1
2017

2018

1Mpc

25-70Mpc

bKAGRAphase2

O3O4

2019

2020

2021

2022

today

COVID-19 terminated O3bO4 will likely start no earlier thanJune 2022

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe9O1 (2015/9/12 - 2016/1/19)

3 BHBH

GW150914: the first ever detection of gravitational waves from the merger of two black holes more than a billion light years away

https://media.ligo.northwestern.edu/gallery/mass-plot

O2 (2016/11/30 - 2017/8/25)

After O2：GWTC1 (2018/12/3 released)

10 BHBH
1 NSNS• GW170814: the first GW signal measured by the three-detector network, also from a binary black hole (BBH) merger;• GW170817: the first GW signal measured from a binary neutron star (BNS) merger — and also the first event observed in light,
by dozens of telescopes across the entire electromagnetic spectrum.
https://media.ligo.northwestern.edu/gallery/mass-plot

O3a (2019/4/1 - 2019/9/30)

After O3a：GWTC2 (2020/10/28 released)

46 BHBH
2 NSNS
2 BH+?

••••••••GW190412: the first BBH with definitively asymmetric component masses, which also shows evidence for higher harmonics
GW190425: the second gravitational-wave event consistent with a BNS, following GW170817
GW190426_152155: a low-mass event consistent with either an NSBH or BBH
GW190514_065416: a BBH with the smallest effective aligned spin of all O3a events
GW190517_055101: a BBH with the largest effective aligned spin of all O3a events
GW190521: a BBH with total mass over 150 times the mass of the Sun
GW190814: a highly asymmetric system of ambiguous nature, corresponding to the merger of a 23 solar mass black hole with a 2.6 solar masscompact object, making the latter either the lightest black hole or heaviest neutron star observed in a compact binary
GW190924_021846: likely the lowest-mass BBH, with both black holes exceeding 3 solar masses

Part 2: Gravitational Wave Science Now

GWTC-2
Gravitational Wave Transient Catalog 2
arXiv:2010.14527
https://dcc.ligo.org/LIGO-P2000223/public

39 events in O3a36BHBH, 1 NSNS, 2 BH+unknown
GWyymmdd̲hhmmss for new events••••••••GW190412: the first BBH with definitively asymmetric component masses, which also
shows evidence for higher harmonics
GW190425: the second gravitational-wave event consistent with a BNS, following
GW170817
GW190426_152155: a low-mass event consistent with either an NSBH or BBH
GW190514_065416: a BBH with the smallest effective aligned spin of all O3a events
GW190517_055101: a BBH with the largest effective aligned spin of all O3a events
GW190521: a BBH with total mass over 150 times the mass of the Sun
GW190814: a highly asymmetric system of ambiguous nature, corresponding to themerger of a 23 solar mass black hole with a 2.6 solar mass compact object, making
the latter either the lightest black hole or heaviest neutron star observed in a compact
binaryGW190924_021846: likely the lowest-mass BBH, with both black holes exceeding 3
solar masses

arXiv:2010.14529

Test of GR
arXiv:2010.14533 Population properties
Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe13

Part 2: Gravitational Wave Science Now

arXiv:2010.14529

GWTC-2: Test of General Relativity by LIGO-Virgo
1. Residuals test
2. Inspiral‒merger‒ringdown consistency test
3. Hierarchical analysis
4. Parametrized test
5. Spin-induced quadrupole moment
6. Ringdown
7. Echoes
8. Dispersion

Subtract the best ﬁt template for the event from the strain data andcompute the 90% upper limit on residual SNR.

9. Polarizations
Check whether the residual SNR is consistent with SNR from noise:measure SNR from noise-only times around the event times,
yielding a p-value
All p-values consistent with residual SNR produced by noiseNo statistically signiﬁcant deviations from GR
Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe14

Part 2: Gravitational Wave Science Now

arXiv:2010.14529

GWTC-2: Test of General Relativity by LIGO-Virgo
1. Residuals test
2. Inspiral‒merger‒ringdown consistency test
3. Hierarchical analysis
4. Parametrized test
5. Spin-induced quadrupole moment
6. Ringdown

Waveform models
IMRPhenom - phenomenological PN-based models, calibrated to NR

7. Echoes

SEOB - aligned-spin eﬀective-one-body models, calibrated to NR

8. Dispersion(note: only includes quadrupole)

9. Polarizations

GW190814

GW170823
GW190408 181802◀ IMRPhenom waveform test
mostly consistent, but …
GW170823
GW190408 181802
GW190814◀ 39.5M+29.5M, SNR@ inspiral < 8◀ 24.5M+18.3M, with multimodal posterior◀ 23M+2.6M, large mass ratio everNo statistically signiﬁcant deviations from GR
Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe15

Part 2: Gravitational Wave Science NowarXiv:2010.14529

GWTC-2: Test of General Relativity by LIGO-Virgo
1. Residuals test
2. IMR consistency test
3. Hierarchical analysis
4. Parametrized test
5. Spin-induced quadrupole moment
6. Ringdown
7. Echoes
8. Dispersion
9. Polarizations

No statistically signiﬁcant deviations from GR
Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

16Part 2: Gravitational Wave Science Now

arXiv:2010.14529

GWTC-2: Test of General Relativity by LIGO-Virgo
1. Residuals test
2. IMR consistency test
3. Hierarchical analysis
4. Parametrized test
5. Spin-induced quadrupole moment
6. Ringdown
7. Echoes
8. Dispersion
9. Polarizations

No signiﬁcant evidence for higher-mode in ringdown part

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

17Part 3: New Approach to GW data analysis

Ringdown GW search using Auto-Regressive model
AR modelrn t
x=Aecos(!n t)e.g.
nZ1 = e (r j!) t
Z2 = e (r+j!) t
1.0

0.8

0.6

0.40.50.251015202530
51015-0.2-0.4-0.5-0.6

can be applied also to noisy data by adjusting M

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe18

Part 3: New Approach to GW data analysis

Ringdown GW search using Auto-Regressive model
sampling rate=4096

AR modelh(t)• ﬁnd aj (Burg method)• ﬁnd M (FPE ﬁnal prediction error method)• re-construct wave signal from ﬁtted function• apply FFT with arbitrary precision.
power spectrum

segment = 1/64 sec = 64 points

shift = 1/512 sec = 8 points
The order M can be ﬁxed at 2〜8.

characteristic eq.
P(f)
FFT

Even for short segment,
AR model shows precise
power-spectrum.

AR
freq.

[mock data, SNR=40, inspiral part]

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

19Part 3: New Approach to GW data analysis

Ringdown GW search using Auto-Regressive model
GW150914 case
LIGO paper
freq [Hz]AR modelHanford▲mergertimeAR-method enables us to extract waves
from original signal
without preparing any wave templates.
freq.

4096 sampling rate
150-450 Hz ﬁlter
1 segment = 1/64 sec= 64 points
1 shift = 1/512 sec = 8 points

tar

P
Inap
re

nio

AR-method can be an alternative approachto test general relativity.

Hisaaki Shinkai (Osaka Institute of Technology); December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe

20Congratulations Maeda-san, for your 70th birthday
You left various footprints in GR, but also you made continuouscontributions for growing GR community in Japan, in the Asia, andof course in the world.
As Roger Penrose received Nobel Prize at his age 89, the theorists
have to live long. The next task for you is to develop a light-speed
rocket or a way to escape from the strong gravity region.

YOU MUST BUY THEM (not from me)

Hisaaki Shinkai (Osaka Inst. Tech.)

December 10, 2020 @ 7th Korea-Japan Workshop on Dark Energy: Maeda's Universe