重力波観測とデータ解析
真貝寿明
大阪工業大学情報科学部
http://www.oit.ac.jp/is/~shinkai/

https://scimeter.org says.

1.重⼒波 / 2. KAGRA / 3. データ解析
2018-10-31 京都産業⼤ 理学部 宇宙物理・気象学科 談話会1重⼒波観測とデータ解析

1. 重力波2016年2月，LIGOが重力波を初めて検出した，と発表 GW150914

四国新聞だけちがった．．．残念（笑）

2017年10月，LIGO/Virgo
中性子星連星合体観測を発表
GW170817

2017年10月，ノーベル財団が，重力波検出に貢献した３名をノーベル物理学賞として顕彰
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤2

重力波の発生と伝播
ブラックホール連星や中性子星連星レーザー干渉計
LIGO＝Laser Interferometer
Gravitational-Wave Observatory重力波の発生と伝播
ブラックホール連星や中性子星連星レーザー干渉計
LIGO＝Laser Interferometer
Gravitational-Wave Observatory重力＝時空のゆがみ
質点が加速度運動＝重力波発生大質量の天体が激しく加速度運動＝観測できる重力波が発生

www.phdcomics.com“gravitational waves explained”

重⼒波観測とデータ解析

1. 重力波

重力波の波源http://gwcenter.icrr.u-tokyo.ac.jp

連星合体を予測が難しい振幅が小さい真⾙ 寿明 (⼤阪⼯⼤)

振幅が小さい2018/10/31 @ 京都産業⼤ターゲットに6

重⼒波観測とデータ解析

1. 重力波

重力波観測によって解明できること
一般相対性理論は正しいか？
強い重力場で重力理論の検証ができる

ブラックホール合体後のふるまいは？
no hair になるか．
（質量，角運動量，電荷の3物理量のみか？）

ガンマ線バースト現象の起源は？
加速メカニズムは？

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤7重⼒波観測とデータ解析

1. 重力波

重力波観測によって解明できること
超新星爆発のメカニズムは？
ブラックホールと中性子星の質量差？

中性子星の最大質量は？
高密度物質の状態方程式は？

重元素の起源？
r-processは充分に発生するか？

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤8重⼒波観測とデータ解析

1. 重力波

重力波観測によって解明できること（ちょっと将来）
銀河中心の超巨大ブラックホールの起源は？
合体成長か，初期にできていたか？

宇宙の膨張速度の測定
星形成モデルの特定
CMB以前の初期宇宙の解明

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤9連星中性子星の発見 (1974)

パルサー＝中性子星
半径 10km位
質量 1.4x太陽

Arecibo, Puerto Rico

http://www.nobelprize.org/nobel̲prizes/physics/laureates/1993/illpres/discovery.html

連星中性子星の発見 (1974)

重力波を放出してエネルギーを失うので，星が近づいてゆく．

重力波の存在が間接的に確かめられた．

連星中性子星の発見 (1974)"for the discovery of a new type of pulsar, a
discovery that has opened up new
possibilities for the study of gravitation""重力についての新しい研究を開いた，新種のパルサーの発見に対して"重力波の存在が間接的に確かめられた．

重力波の存在は連星パルサーの発見で，間接的に確かめられていた．
重力波の直接観測をしたい！

連星中性子星連星ブラックホール
Inspiral
1.0

重力波の振幅 × 10

Merger Ringdown−22

ブラックホール形成の
重力波波形

0.5

0.0

!0.5

!1.0

連星のインスパイラル運動からの
重力波波形

!25

!20

!15

!10

時間 [ミリ秒]

!5

0

合体の時刻

5

2015年9月14日

太陽の36倍と29倍のブラックホールが合体して，太陽の62倍のブラックホールになった．
3倍の質量が消失
2

E = mc

13億光年先（440 Mpc）

Animation of the inspiral and collision of two black holes consistent with the masses and spins of GW170104. The top part of the movie shows the black hole horizons (surfaces of "no return"). The initial two
black holes orbit each other, until they merge and form one larger remnant black hole. The shown black holes are spinning, and angular momentum is exchanged among the two black holes and with the orbit. This results
in a quite dramatic change in the orientation of the orbital plane, clearly visible in the movie. Furthermore, the spin-axes of the black holes change, as visible through the colored patch on each black hole horizon, whichindicates the north pole.
The lower part of the movie shows the two distinct gravitational waves (called 'polarizations') that the merger is emitting into the direction of the camera. The modulations of the polarizations depend sensitively on theorientation of the orbital plane, and thus encode information about the orientation of the orbital plane and its change during the inspiral. Presently, LIGO can only measure one of the polarizations and therefore obtains
only limited information about the orientation of the binary. This disadvantage will be remedied with the advent of additional gravitational wave detectors in Italy, Japan and India.
Finally, the slowed-down replay of the merger at the end of the movie makes it possible to observe the distortion of the newly formed remnant black hole, which decays quickly. Furthermore, the remnant black hole is"kicked" by the emitted gravitational waves, and moves upward. (Credit: A. Babul/H. Pfeiffer/CITA/SXS.) - See more at: http://ligo.org/detections/GW170104.php#sthash.NZPaW2LT.dpuf

http://ligo.org/detections/GW170104.php

16

arXiv:1606.01262

重⼒波観測とデータ解析

List of Detected GW eventsref.
GW150914
LVT151012
GW151226
GW170104
GW170608
GW170814
GW170817

M1+M2=Mf,

spin

Mpc

Mdiﬀ/Mtotala̲ﬁnalz

PRL116, 061102

36.2+29.1=62.3+3.0(2016/2/11)

4.59%(2016/2/11)

23+13=35+1.5
2.78%

PRL116, 241103

14.2+7.5=20.8+0.9(2016/6/15)

4.15%

PRL118, 221101

31.2+19.4=48.7+1.9(2017/6/1)

3.75%

ApJ 851, L35

12+7=18.0+1.0(2017/12/18)

5.2%

PRL119,141101

30.5+25.3=53.2+2.6(2017/10/6)

4.66%

PRL119, 161101

1.36〜1.60 + 1.17〜1.36(2017/10/16)= 2.74 + ?

真⾙ 寿明 (⼤阪⼯⼤)

0.68

0.66

0.74

0.64

0.69

0.70

?

2018/10/31 @ 京都産業⼤410Mpc0.09
1000Mpc
0.20
440Mpc0.09
880Mpc0.18
340Mpc0.07
540Mpc
0.11
40Mpc

SNR

deg^2

23.7

600

9.7

13.0

850

13

1300

13

520

18

60

32.4

28

18

https://www.ligo.caltech.edu/image/ligo20171016a

【宇宙物理】

連星中性子星合体

2017/10/16

重力波検出，多くの天文台が同時観測
GW170817

これまでのBHBH合体による重力波

今回のNSNS合体による重力波

【宇宙物理】

連星中性子星合体

2017/10/16

重力波検出，多くの天文台が同時観測
GW170817

【宇宙物理】

連星中性子星合体

2017/10/16

重力波検出，多くの天文台が同時観測
GW170817
The Astrophysical Journal Letters, 848:L12 (59pp), 2017 October 20

Ab

Figure 2. Timeline of the discovery of GW170817, GRB 170817A, SSS17a/AT 2017gfo, and the follow-up observations are shown by messenger and w
relative to the time t of the gravitational-wave event. Two types of information are shown for each band/messenger. First, the shaded dashes represent the ti

重⼒波観測とデータ解析

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤23重⼒波観測とデータ解析

2. KAGRA 日本の重力波観測
http://gwplotter.com

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤24

重⼒波観測とデータ解析

aLIGO, aVirgo & KAGRA : 目標感度曲線

Living Reviews in Relativity; 21:3; 2018

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤25

signal = gw + noise
Science 256 (1992) 325

strain noise
spectral density [sec]26重⼒波観測とデータ解析

2. 重力波観測計画（主に KAGRA)

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤27

1. Gravitational Wave >> Expected Amplitude

1.0

重力波の振幅 × 10

−22

ブラックホール形成の
重力波波形

0.5

0.0

!0.5

!1.0

連星のインスパイラル運動からの
重力波波形

!25

!20

!15

!10

時間 [ミリ秒]

!5

0

5

合体の時刻

28

重力波レーザー干渉計に対する工夫(１)ª%­ŜRĿŃŭŝRĿĺŢŗĺĺƷ
干渉計は，大きければ大きいほどよい．
ƧƮƶ!
ƧƮƶ!

ƜƶƨƈƠƯƏƌƶ!

Ʊƶƅƶ!

ƍƶžƥƶƓ!

Kokeyama!@!SSH,!Kamioka苔山圭似子氏（東京大宇宙線研究所）のスライドからĩĩ重力波レーザー干渉計に対する工夫(２)

ŇŪř<ŰNkŊŬfUさらに，信号を増幅させるƧƮƶ!

=ůŌēśũĻřňŔĳ!
ƱƶƅƶŰqŧy}ŇŌŬ!
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パワーリサイクリングƧƮƶ!

ƜƶƨƈƠƯƏƌƶ!

Ʊƶƅƶ!

Đ,³<śŽƫƏƎŕĿŬ!
A³hKŰońŬŎŦśƧƮƶ!

シグナルリサイクリング
Kokeyama!@!SSH,!Kamioka苔山圭似子氏（東京大宇宙線研究所）のスライドからĩĪ重力波レーザー干渉計に対する工夫(3)

さらに，さらに，雑音を減らすŇŪřŇŪřĳěġŰŨőŒŃŬ②¾ěġ!

①IĠ.

③đWěġ
Kokeyama!@!SSH,!Kamiokaĩī苔山圭似子氏（東京大宇宙線研究所）のスライドから

KAGRAŕśěġaÝƓƴƗư!
①IĠ.!
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Kokeyama!@!SSH,!KamiokaĩĬ苔山圭似子氏（東京大宇宙線研究所）のスライドから

KAGRAŕśěġaÝ②¾ěġ!

ēśîĠś&WŨūWľ¾Č.ňŔŭĳ!
ÛĖśŪŀŖ0(ľŒĽŋřěġŖŘŬ!
!
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• ƄƞŲŵųƧƮƶŰĻ!
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③đWěġ!
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• 180WśƙŵƛƳƶƱƶƅƶŰĻ!
!
Kokeyama!@!SSH,!Kamiokaĩĭ苔山圭似子氏（東京大宇宙線研究所）のスライドから

KAGRA sensitivity

−19

10

IĠ

Residual gas
Mirror thermal noise
Seismic noise
Suspension thermal noise
Quantum noise
Total

−20

10

.


Sensitivity [1/rtHz]¯Ťšśq

−21

10

−22

10

−23

10

¾ěġ

ƹƧƮƶ

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−24

10

−25

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←ċĺ<

210Frequency
A³ [Hz]Kokeyama!@!SSH,!Kamioka

3

4

10

10

Ĉĺ<→
ĩĮ

苔山圭似子氏（東京大宇宙線研究所）のスライドから

bKAGRA phase-1 operation (Apr 28 - May 6, 2018)• All vacuum• Cooled ETMY (18K for 30 days).
• Duty cycle (88.6% ﬁrst 5 days; 26.8% May 3 & 4;
59.8% May 5 &6)• Longest lock was >10 hrs• Sensitivity 2x10^{-17} / rHz• PEM injection, hardware injection tests35重⼒波観測とデータ解析

baseline KAGRA 構成図

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤36

Kamioka Gravitational Observatory
former name LCGT = large cryogenic gravitational telescope

named by public naming contest, 神楽（かぐら）dance music in front of Gods

3km Laser Interferometer, Cryogenic
1000m under thesummit of the Mt.

Mozumicontrol office.
(15 min)Toyama City
(60 min)

358m above thesea level.

http://gwcenter.icrr.u-tokyo.ac.jp/en/37Schedule (2) (Construction and Operation)
Already one year has passed after theiKAGARrun.
slide
from Kajita
2010 2011 20102012 20112013 20122014 20132015 20142016 20152017 20162018 2019 2020

Calendar year
Project start
Tunnel excavation
iKAGRA
operation

Adv. vibration isolation, optics, …

bKAGRAphase 2, 3, 4

Cryogenic system
operationphase 1
Cryogenic
mirrorsiKAGRAbKAGRA(*) The configurationin 2019 is still to be
decided referring themilestones.

baseline KAGRA
3• Phase-1 operation (Apr 28 ̶ May 6) ﬁnished• Phase-2 starts on May 7.
38

重⼒波観測とデータ解析

KAGRA（かぐら：大型低温重力波望遠鏡）

KAGRA

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤39

スーパー・カミオカンデ（ニュートリノ観測装置）
Super-Kamiokande

http://www-sk.icrr.u-tokyo.ac.jp/sk/

直径40m
高さ40m

岐阜県・神岡の鉱山跡の空洞に巨大な水槽をつくり，宇宙から飛来するニュートリノを観測する．
ノーベル物理学賞を受賞

小柴昌俊（2002年）
梶田隆章（2015年）

重⼒波観測とデータ解析

KAGRA（かぐら：大型低温重力波望遠鏡）
2018年8月

2016年4月

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤41

重⼒波観測とデータ解析

KAGRA（かぐら：大型低温重力波望遠鏡）
2015年8月

Seiji Kawamura
Kieran Craig
Martynov Denis

Hisaaki Shinkai

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤42

重⼒波観測とデータ解析

KAGRA（かぐら：大型低温重力波望遠鏡）
2018年8月

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤43

KAGRA collaboration: as of June 2018
385 collaborators(8 B students, 73 M students, 35 D students, 10 PDs)
90 institutes
15 countries(Australia 5, China 35, France 1, German 1, India 3, Italy 17, Japan 253,
Korea 23, The Netherlands 1, Poland 2, Russia 1, Taiwan 34, UK 2, USA 10, Vietnam 2)

PI: Takaaki Kajita
梶田隆章

Face-to-Face meetingat Osaka City Univ.
May 2018 ⇨重⼒波観測とデータ解析

KSC（KAGRA Scientiﬁc Congress）
)
0 28

PI

2/
2

2
(
1

0 /66

(

F

EO

KSC

sharing information & idea

SEO

KH

Collaborator-list
ManagerKH
CFC H CK

Computing &Software

CF

CHFH

GC
KC

HC

Editorial board
JJJ

C

*

Author-list
Committee
CHFH

KSC newsletter
editor

GC

F

F
K A

* *
C
-

C *
C

C
H
LH

H

* *

-

CF

Committees with violet color are joint ones with LIGO/Virgo

真⾙ 寿明 (⼤阪⼯⼤)

C

K A
CI
A

WG fordefinition of
KAGRA data

F
CG

HLH

WG for authorlist policy in
CPC rules

Detector
Characterization

Meeting

JJJ

JJJ

Calibration

Detection

JJJ

JJJ

2018/10/31 @ 京都産業⼤

K F

K A

CF C

Computing &SoftwareF -C
G C CAC

CF

C

C

Diversity
Committee

CA H

F
KH

K
CF

FC
LH

H

C *
H

*H

Data Analysis
Council
KH

KH

C

C HKH

K A

A ACGC

C

. K

H

KH

Stochastic
Wave

CPC

AH

International
Cooperation WG

GC

C

C
C

C

C

Burst Wave
LH

.

-

Continuos Wave

CHFH

HG

CF

Compact Binary
Coalesence

Joint Run Planning
Committee

board

A
LH

C HKH

Data Analysis
Committee (DAC)
KH

H

C

46

重⼒波観測とデータ解析

LIGO/Virgo joint observation plans“Scenario Paper”

Living Rev Relativ (2018) 21:3
https://doi.org/10.1007/s41114-018-0012-9

GW150914

BHBH@440Mpc

GW151226

BHBH@440Mpc
10-25
Mpc

GW170104

BHBH@880Mpc

GW170608

BHBH@340Mpc

GW170814
GW170814
BHBH@540Mpc
GW170817

today

NSNS@40Mpc

真⾙ 寿明 (⼤阪⼯⼤)“We try to catch up with O3”

2018/10/31 @ 京都産業⼤47

重⼒波観測とデータ解析

Roadmap of bKAGRA phase2 &3, Join LIGO/Virgo O3 runtime limited, we have to compromise
2018
July

Aug

Sep

2019

Oct

Nov

Dec

Jan

Feb

Mar

Apr

May

Jun

Jul

2020
Aug

Sep

Oct

Nov

Dec

Jan

Feb

LIGO/VIRGO Observation 3
ITMX

X-arm
com.

Xend
ETMY

ITMY

FPMI

post com.
ETMX
Y-arm
com.

FPMI

DRFPMI (RSE)
Laser

mode cleaner

data analysis rehearsal

plan A

post
com.

DRFPMI(RSE)

plan B

Data Sharing with KAGRA-LIGO-Virgo̶ either DRFPMI(RSE) (-25Mpc, Oct?) or FPMI (-10Mpc, June?)checking points: Sep/2018, Dec/2018 and Mar/2019

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤48

Re-organizing KAGRA groups for joint observations

VIRGO

LIGO

KAGRA

Observatory
Observatory
Observatory

KAGRA
Muti-Messenger
Astronomy

Outreacheducation
promotion…

Publication

Detector Science

OpticsSeismic
LasersQuantum
…

LIGO
VIRGO

Joint xxx
Committees

Data Analysis

Burst
CBC
continuous…

talks
articles…

Test GR
Event Rates
Waveforms
EOS
New Sources…

49

KAGRA SCIENTIFIC CONGRESS: COLLABORATORS’ INFORMATION EXCHANGE

2018/04/01

KSC NewsLetter
The premiere issue
KAGRA SCIENTIFIC CONGRESS: COLLABORATORS’ INFORMATION EXCHANGE

2018/08/01

KSC Newsletter
Second Issue
What is this
NewsLetter?

From Phase 1 to Phase 2

Nobody knows if thisis the first issue of aseries of information
letters, or just a April
fool’s day joke.

Nine-day operation with wild weather & earthquakes
KAGRA now has the world's tallest vibration isolation systems (13.5 m)
which help to reduce seismic noise at low frequencies. The volume of thevacuum system is third largest in the world. Two 23-kg sapphire mirrors
have been installed at each end, and one of them was kept for 30 days atcryogenic temperature (18K).
A leakage of the vacuum system was found in April 2018, therefore thePhase-1 experimental activity was delayed for 5 days. Despite thedifficulties, the phase-1 operation was a success: it lasted from April 28
to May 6, 2018, and during this period many injection tests were
AG JGS O R
9 (performed.
The interferometer duty cycle during the Phase-1
operation reached 88.6% between April 28 and May 2,
while it dropped to 26.8% on May 3 and 4. Finally itslightly improved to 59.8% over the final days (May 5 & 6).
The longest lock was over 10 hours. The low duty cycle on
May 3 and on the following days was mainly attributed tothe high micro-seismic noise caused by a heavy storm, local
earthquakes, volcano eruptions in Hawaii, and visits oftheorists.
The achieved sensitivity during Phase 1 was still worse
than the final sensitivities of TAMA and CLIO, except at thelower frequencies (40 Hz), where KAGRA's sensitivity wasContents of this issue
better than that of TAMA. KAGRA started Phase 2 from May
p-2 Directions
7: the final installation work before the real observation
Steps to the Observation 2019run.
p-3 Kamioka local
Subgroup orientation
Kagra River / Science Cafe
p-5 Meetings
F2F at Osaka City U.
KIW5 at Seoul
Poster Award Winners
Group LOGO
Next F2F at Toyama
p-8 Virgo Visit
p-9 We hear that …

1

Phase-1 operation starts on April 23
First cryogenic interferometer test will start soon.
After two years from the iKAGRA run, we will start phase-1 operation on April 23
to May 6. Due to the tight schedule for our upcoming real observation, systemengineering office (SEO) decided to operate phase-1 with one cryogenic mirror (Yarm), and the other at normal temperature. We do not know what will be theoutcomes. So it might become a sort of fun. A detail list of tests planned during
the run is at page-3.
The above photo, taken in a clean room in the University of Toyama, is our 23kgSapphire mirror for X-end, which is now under installation. The installation of thecryo-payload at X-end is almost done and the main beam is coming back to the

O3=Ozone.

We are in a rush forO3 this year. Let’sfinish looking for O2.

center now ! .
DLAA

1L M S O MD OG I N

GWFind GW.
Here GW is not“Gravitational Wave”,
but “Golden Week”.

2

MM I OL

IPALM N I

3

CRYOGENICO3

Not an oxygenallotrope. Not apathogenic Vibrio
Parahaemolyticus.

Buy refrigerator, set
freezing chamber,feel chilly, but try not tocatch a cold.

We call forvolunteers

We welcome youreditorial participation
to this journal. It will
give you a career
update definitely.

1

http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/KAGRA!50

重⼒波観測とデータ解析

３. 重力波のデータ解析

https://www.iscie.or.jp/pub/journal
http://www.oit.ac.jp/is/~shinkai/

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤51

重⼒波観測とデータ解析

重力波のデータ解析

1. 連星合体解析
波形が既知．マッチド・フィルタ解析．
gstlal, pycbc, lalinference (MCMC法)
2. バースト重力波解析
超新星爆発・中性子星グリッチ現象
cWB (コヒーレント解析)
3. 連続重力波解析
中性子星回転Einstein@Home (分散型コンピューティング)
4. バックグラウンド重力波解析
宇宙論起源，白色矮星フォアグラウンド

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤52

重⼒波観測とデータ解析

Ideal vs Reality(Theory vs Data Analysis)
GW150914(S/N=23.7)

h(t)

16.25

16.45

challenging for data analysis
GW data is with noise
signal quickly decays(M=60Msun, a=0.75 ̶> 300Hz, tau = 3 ms)
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤53

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sha1_base64="nC5LppoHqIoWfFfilG8wbqqsbLQ=">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</latexit><latexit

sha1_base64="nC5LppoHqIoWfFfilG8wbqqsbLQ=">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</latexit><latexit

sha1_base64="nC5LppoHqIoWfFfilG8wbqqsbLQ=">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</latexit><latexit<latexit

重⼒波観測とデータ解析

３. 重力波のデータ解析

Matched Filter 解析

signal = gw + noise
gw templateh(t)signal/noise ratio
GW151226

真⾙ 寿明 (⼤阪⼯⼤)
2018/10/31 @ 京都産業⼤(S/N=13.0)

54

重⼒波観測とデータ解析

List of Detected GW eventsref.
GW150914
LVT151012
GW151226
GW170104
GW170608
GW170814
GW170817

M1+M2=Mf,

spin

Mpc

Mdiﬀ/Mtotala̲ﬁnalz

PRL116, 061102

36.2+29.1=62.3+3.0(2016/2/11)

4.59%(2016/2/11)

23+13=35+1.5
2.78%

PRL116, 241103

14.2+7.5=20.8+0.9(2016/6/15)

4.15%

PRL118, 221101

31.2+19.4=48.7+1.9(2017/6/1)

3.75%

ApJ 851, L35

12+7=18.0+1.0(2017/12/18)

5.2%

PRL119,141101

30.5+25.3=53.2+2.6(2017/10/6)

4.66%

PRL119, 161101

1.36〜1.60 + 1.17〜1.36(2017/10/16)= 2.74 + ?

真⾙ 寿明 (⼤阪⼯⼤)

0.68

0.66

0.74

0.64

0.69

0.70

?

2018/10/31 @ 京都産業⼤410Mpc0.09
1000Mpc
0.20
440Mpc0.09
880Mpc0.18
340Mpc0.07
540Mpc
0.11
40Mpc

SNR

deg^2

23.7

600

9.7

13.0

850

13

1300

13

520

18

60

32.4

28

55

重⼒波観測とデータ解析

LIGO Computing Latencies

12!

12!

Sharon Brunett, 2015/10
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤56

⾃⼰回帰モデルを⽤いた重⼒波データ解析：
ブラックホール合体のリングダウン波形の抽出
真貝寿明，山本峻 元M2（大阪工大）
H. Shinkai, S. Yamamoto (OIT)
MergerRingdown

InspiralBH 準固有モード(quasi-normal modes)⇦ BH 摂動理論⇨ (M, a)
強い重⼒場の表れ⇨ ⼀般相対論の検証ができる

新しい方法を提案． テンプレートを使わず，データから波形を再構築．

2018/9/14 物理学会 ＠ 信州大学

重⼒波観測とデータ解析

Mock data example (0) : QNM extraction contest

modiﬁed ringdown signals from GR
with LIGO detectorʼs noise

真⾙ 寿明 (⼤阪⼯⼤)

1. Standard Matched-ﬁltering method
2. Improved Matched-ﬁltering method
3. Hilbert-Huang transformation method
4. Auto-Regressive method
5. Neural network method

2018/10/31 @ 京都産業⼤58

重⼒波観測とデータ解析

1. Auto-Regressive model (Method, general) I
Fitting data with linear func.

e.g. xn = Ae rn t cos(!n t)
Z1 = e (r j!) t
Z2 = e (r+j!) t
1.0

0.8

0.6

0.4

0.5

0.2

5

10

15

20

25

30
5

10

15

-0.2

-0.4
-0.5

-0.6

can be applied also to noisy data by adjusting M
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤59

重⼒波観測とデータ解析

1. Auto-Regressive model (Method, general) II
Fitting data with linear func.

• 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

・・・・・

・・・・・

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤60

重⼒波観測とデータ解析

Auto-Regressive modelvs Short FFTsegment = 1/128 sec = 32 points

h(t)shift = 1/1024 sec = 4 points
The order M can be ﬁxed at 2〜8.
Even for short segment,
AR model shows precise
power-spectrum.

P(f)
FFT
AR
freq.

[mock data, SNR=40, inspiral part]
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤61重⼒波観測とデータ解析

1. Auto-Regressive model (Method, general) III
Fitting data with linear func.

• 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

characteristic eq.

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤62

重⼒波観測とデータ解析

Mock data example (1) ﬁtting well
Mock Data (Nakano02 p)

freq.

h(t)

spectrogramx original data, ̶ ﬁtted

8"mockN02p_segmentH.txt""mockN02p_segmentR.txt"

6
4
2
0
-2
-4
-6
1.593 1.594 1.595 1.596 1.597 1.598 1.599

1.6

1.601 1.602

Fitting data with linear func.

a.1
a.2
a.3
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤= -2.235e+00= 1.869e+00= -5.545e-01
63

重⼒波観測とデータ解析

Mock data example (2) spectrogram
Mock Data (Nakano02 p)

freq.

spectrogram

power spectrum

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤64

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sha1_base64="N6OULxLyV4n+YDLj4gzs3pFIM1g=">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</latexit><latexit<latexit

重⼒波観測とデータ解析

Mock data example (3) characteristic eq.

Mock Data (Nakano02 p)

Fitting data with linear func.

a.1
a.2
a.3

characteristic eq.

1
2
3
x.r
0.962
0.962
1.447
x.i
0.566
-0.5660.000
f_R[Hz]346.800-346.800
0.000

真⾙ 寿明 (⼤阪⼯⼤)
2018/10/31 @ 京都産業⼤= -2.235e+00= 1.869e+00= -5.545e-01

xn 1 = zxn
z = exp[ 2⇡if t]|x|
f_I[Hz]8.025e-01 71.721
8.025e-01 71.721
4.775e-01 240.931

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重⼒波観測とデータ解析

Mock data example (4) identify ring-down freq.
Mock Data (Nakano02 p)

characterestic eq.

1
2
3
x.r
0.962
0.962
1.447
x.i
0.566
-0.5660.000

xn 1 = zxn
z = exp[ 2⇡if t]

f_R[Hz]346.800-346.800
0.000

真⾙ 寿明 (⼤阪⼯⼤)|x|
f_I[Hz]8.025e-01 71.721
8.025e-01 71.721
4.775e-01 240.931

t
f_R (z_plane) f_I (z_plane) f_Rh(spectr) f_Rmax(spectr)
0.159375E+01
0.363837E+03
0.280414E+02
0.340000E+03
0.363000E+03
0.159668E+01
0.344258E+03
0.166608E+02
0.331000E+03
0.344000E+03
0.159766E+01
0.346800E+03
0.717212E+02
0.240000E+03
0.329000E+03
0.161230E+01
0.357677E+03
0.122067E+03
0.213000E+03
0.338000E+03
0.161328E+01
0.361098E+03
0.948919E+02
0.261000E+03
0.350000E+03
0.161523E+01
0.379918E+03
0.772796E+02
0.304000E+03
0.373000E+03
average & variance zfr =0.359E+03
0.118E+02 fr(sp) =0.350E+03
average & variance zfi =0.684E+02
0.365E+02
2018/10/31 @ 京都産業⼤f_Rh(spectr)
0.384000E+03
0.357000E+03
0.382000E+03
0.431000E+03
0.422000E+03
0.432000E+03
0.148E+0266

重⼒波観測とデータ解析

Application to the LIGO/Virgo data

List of Detected GW eventsref.
GW150914
LVT151012
GW151226
GW170104
GW170608
GW170814
GW170817

M1+M2=Mf,

spin

Mpc

Mdiﬀ/Mtotala̲ﬁnalz

PRL116, 061102

36.2+29.1=62.3+3.0(2016/2/11)

4.59%(2016/2/11)

23+13=35+1.5
2.78%

PRL116, 241103

14.2+7.5=20.8+0.9(2016/6/15)

4.15%

PRL118, 221101

31.2+19.4=48.7+1.9(2017/6/1)

3.75%

ApJ 851, L35

12+7=18.0+1.0(2017/12/18)

5.2%

PRL119,141101

30.5+25.3=53.2+2.6(2017/10/6)

4.66%

PRL119, 161101

1.36〜1.60 + 1.17〜1.36(2017/10/16)= 2.74 + ?

真⾙ 寿明 (⼤阪⼯⼤)

0.68

0.66

0.74

0.64

0.69

0.70

?

2018/10/31 @ 京都産業⼤410Mpc0.09
1000Mpc
0.20
440Mpc0.09
880Mpc0.18
340Mpc0.07
540Mpc
0.11
40Mpc

SNR

deg^2

23.7

600

9.7

13.0

850

13

1300

13

520

18

60

32.4

28

67

重⼒波観測とデータ解析

Ringdown wave of GW150914

LIGO paper

4096 sampling rate
100-400 Hz ﬁlter
1 segment = 1/64 sec= 64 points
1 shift = 1/512 sec = 8 points

AR modelHanfordP(f)max M = 3
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤

freq.
68

重⼒波観測とデータ解析

Ringdown wave of GW150914

16384 sampling rate

AR modelHanford4096 sampling rate
100-400 Hz ﬁlter
1 segment = 1/64 sec= 64 points
1 shift = 1/512 sec = 8 points

AR modelHanfordP(f)max M = 3
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤

freq.
69

重⼒波観測とデータ解析

Ringdown wave of GW150914

16384 sampling rate

AR modelHanford真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤70

重⼒波観測とデータ解析

Ringdown wave of GW150914
t

f realf imagWe see QNM at 300Hz, 0.003s after the merger.

Berti, Cardoso & Will PRD 73, 064030 (2006).

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤71

重⼒波観測とデータ解析

Ringdown wave of GW150914, GW170814, GW170104

真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤72

重⼒波観測とデータ解析

Ringdown wave of GW150914, GW170814, GW170104

Ｎ/A
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤73

重⼒波観測とデータ解析

Summary & Outlook
⾃⼰回帰モデル x(t)短いデータ (〜 30 pts) に対しても精度よく周波数・減衰率を特定できる．
シグナルを⾒つけるのにテンプレートは不要．
LIGO/Virgo の 3 実イベントデータに適⽤，リングダウン部分の抽出を試みた．
LIGO/Virgoのは発表している (M, a) とGW150914, GW170814よく⼀致
S/Nの低い GW170104 ではいまいち(S/N=23.7)(S/N=18)(S/N=13)★リングダウン部分だけを検出できれば，強い重⼒場の重⼒理論検証ができる．
他の⽅法と組み合わせ，検出データ数が稼げれば，相対論検証ができるだろう．
★テンプレートを使わない⽅法は，今後，未知の重⼒波シグナルの候補検出に役⽴つかも．
真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤74

重⼒波観測とデータ解析

重力波観測の将来計画
late 2010s

early 2020s

O3
USA

aLIGO

late 2020s

Cosmic Explorer
40km L-shapeearly 2030s

O4

A+

Voyager

Cosmic Explorer ?
LIGO-India

EuropeaVirgoaVirgo+Einstein Telescope ?
Europe

KAGRA

Japan

eLISA

Einstein Telescope
10km Triangle

?
Japan

DECIGO?

EM counterparts(certain)

1

Evan Hall, MIT真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤75

マルチ・メッセンジャー天文学の誕生

ガンマ線

X線

可視光

赤外

電波

重力波
は 重
じ 力
波
め 天
ま 文
し 学

Black Widow Spider
Fermi Bubbles
ColosseumEiﬀel Tower
Einstein
Fermi Satellite
Godzilla
Golden Gate
Hulk
The Little Prince
Mjolnir
Mount Fuji
CastleObelisk
PharosRadio Telescope
Saturn V Rocket
Schrödinger's Cat
Starship Enterprise
TARDIS
Vasa

2018/10
Fermi衛星チーム，ガンマ線バースト天体
カタログで21星座を命名!77
https://fermi.gsfc.nasa.gov/science/constellations/重力波源が特定されたのは，まだ１つ．

http://www.virgo-gw.eu/skymap.html

しかし2019年の観測がはじまれば，
週に１回，BH-BH
月に１回，NS-NS
202x/xx
LIGO/Virgo/KAGRAチーム，
重力波天体カタログで108星座を命名

宇宙空間での観測がはじまれば，
1日に10回，BH-BH ??
!78

重⼒波観測とデータ解析

まとめ
１．重力波観測時代がはじまった
BH-BH, NS-NS．次はBH-NS? SN?
２．日本のKAGRAも2019年から実観測開始
LIGO/Virgoとの共同観測体制構築中．
３．データ解析には，まだまだ試すべきアイデアがたくさんある．
将来計画もたくさんある．

新規参入，大歓迎！
LIGO

KAGRA
Virgo
ET LISA真⾙ 寿明 (⼤阪⼯⼤)

2018/10/31 @ 京都産業⼤79