Gravitational Waves
fromMerging Intermediate-Mass Black Holes
真貝寿明 (大阪工業大)
http://www.oit.ac.jp/is/~shinkai/

Origin of SMBH?
GW event rate?
How many BHs in a galaxy?
How many galaxies in the Universe?
真貝・神田・戎崎, ApJ, 835 (2017) 276 [arXiv:1610.09505]
2017/3/7

東京大理

安東研セミナー1

1. Gravitational Wave >> Expected Waveform

NS-NSNS-BH
BH-BH

1.0

Inspiral−22

Merger Ringdown

重力波の振幅 × 10

ブラックホール形成の重力波波形

0.5

h0.0!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]!50

合体の時刻

5time22http://www.ligo.org/magazine/LIGO-magazine-issue-8.pdf

3

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]

!50

5

合体の時刻

4

1. Gravitational Wave >> Expected Events

p1/2
Strain Sensitivity Sn (f )[Hz]Typical  frequency  of  BH-‐‑‒BH  binary  merger  @  1000Mpc  10-17

5M

10-19

0
1+

5M

fQNM

10fQNM
4M

10-21

4M

01+

103M

3M

01+

2M

10M
0.01

2Rg

10Rg01+1010-45Rg

2M

1010-23fQNM+10M
150Rg
KAGRA
100frequency [Hz]20170307 　真⾙貝 5

1. Gravitational Wave >> Expected Eventsp
1/2
Strain Sensitivity Sn (f )[Hz]Typical  frequency  of  BH-‐‑‒BH  binary  merger  @  100Mpc  5M

10-17

5M

01+

10fQNM

10-19

10-21

fQNM
4M

4M

01+

103M

fQNM

3M

01+

2M

102M

10M
10-4

0.01

10Rg

01+

1010-235Rg

2Rg+

10M50Rg
KAGRA

1100frequency [Hz]20170307 　真⾙貝 6

1. Gravitational Wave >> Expected Events

p1/2
Strain Sensitivity Sn (f )[Hz]Typical  merger  duration  of  BH-‐‑‒BH  binary  merger  @  1000Mpc  10-1789d

10-19

3.4h
8.9d

12m
20m

1.25m

21h

10-21

103 M + 103 M

2m

7.7s
12s

2h

12m

10-23

0.76s
1.2s

70ms

10M + 10M

10-4

0.01

1100

frequency [Hz]20170307 　真⾙貝 7

1. Gravitational Wave >> 2015 Detections
LIGO : Laser Interferometer Gravitational-Wave Observatory

4km
Michelson

8KAGRA : Kamioka Gravitational wave detector(Large-scale Cryogenic Gravitational wave Telescope)

3km Michelson
Cryogenic (20K)in quiet mountain site
Sapphira mirrors

pStrain noise amplitude[1/ Hz]

2016/3/25-31, 4/11-25
initial test run, iKAGRA

10-16

Kagra

10-19

TOBA

aVIRGO
10-22

aLIGO
ET
10-25
1

10

100

1000

104

frequency[Hz]

http://gwcenter.icrr.u-tokyo.ac.jp/plan/history

神楽（かぐら）9

1. Gravitational Wave >> 2015 Detections
LIGO : Laser Interferometer Gravitational-Wave Observatory

https://mediaassets.caltech.edu/gwave

2015/9/16--2016/1/15
Observational run 1
2016/11/30—Observational run 2
10GW150914GW150914:FACTSHEETBACKGROUND IMAGES: TIME-FREQUENCY TRACE (TOP) AND TIME-SERIES( B O T T O M ) I N T H E T W O L I G O D E T E C T O R S ; S I M U L AT I O N O F B L A C K H O L E
HORIZONS (MIDDLE-TOP), BEST FIT WAVEFORM (MIDDLE-BOTTOM)

first direct detection of gravitational waves (GW) and first direct observationof a black hole binary
observed by

LIGO L1, H1

duration from 30 Hz~ 200 ms

source typeblack hole (BH) binary# cycles from 30 Hz~10date

14 Sept 2015

peak GW strain

1 x 10-21

time

09:50:45 UTC
0.75 to 1.9 Gly
230 to 570 Mpc±0.002 fm

likely distancepeak displacement ofinterferometers arms

150 Hz, 2000 km

redshift

0.054 to 0.136

frequency/wavelength
at peak GW strain

signal-to-noise ratio

24

peak speed of BHs~ 0.6 cpeak GW luminosity

3.6 x 1056 erg s-1

false alarm prob.

< 1 in 5 million

radiated GW energy

2.5-3.5 M⊙

false alarm rate

< 1 in 200,000 yr

remnant ringdown freq.

~ 250 Hzremnant damping time

~ 4 ms

Source Masses

M⊙

total mass

60 to 70

primary BH

32 to 41

secondary BH

25 to 33

remnant BH

58 to 67

mass ratio

0.6 to 1

primary BH spin

< 0.7

secondary BH spin

< 0.9

remnant BH spin

0.57 to 0.72

signal arrival timedelay

arrived in L1 7 ms
before H1

likely sky position

Southern Hemispherelikely orientation
resolved toface-on/off~600 sq. deg.

.

.

remnant size, area

180 km, 3.5 x 105 km2

consistent withgeneral relativity?

passes all tests
performed

graviton mass bound< 1.2 x 10-22 eV

coalescence rate ofbinary black holes

2 to 400 Gpc-3 yr-1

online trigger latency~ 3 min# offline analysis pipelines

5CPU hours consumed~ 50 million (=20,000PCs run for 100 days)

papers on Feb 11, 201613

# researchers~1000, 80 institutionsin 15 countries

Detector noise introduces errors in measurement. Parameter ranges correspond to 90% credible bounds.
Acronyms: L1=LIGO Livingston, H1=LIGO Hanford; Gly=giga lightyear=9.46 x 10 12 km; Mpc=megaparsec=3.2 million lightyear, Gpc=10 3 Mpc, fm=femtometer=10 -15 m, M⊙=1 solar mass=2 x 10 30 kg

36Msun + 29 MsunのBHが合体して 62 Msun
（3 Msun分の質量が消失）
13億光年先（400 170 Mpc）
（z=0.054̶0.136）

GW150914:FACTSHEETBACKGROUND IMAGES: TIME-FREQUENCY TRACE (TOP) AND TIME-SERIES( B O T T O M ) I N T H E T W O L I G O D E T E C T O R S ; S I M U L AT I O N O F B L A C K H O L E
HORIZONS (MIDDLE-TOP), BEST FIT WAVEFORM (MIDDLE-BOTTOM)

first direct detection of gravitational waves (GW) and first direct observationof a black hole binary
observed by

LIGO L1, H1

duration from 30 Hz~ 200 ms

source typeblack hole (BH) binary# cycles from 30 Hz~10date14 Sept 2015

peak GW strain

1 x 10-21

time

09:50:45 UTC
0.75 to 1.9 Gly
230 to 570 Mpc±0.002 fm

likely distancepeak displacement ofinterferometers arms

150 Hz, 2000 km

redshift

0.054 to 0.136

frequency/wavelength
at peak GW strain

signal-to-noise ratio

24

peak speed of BHs~ 0.6 cpeak GW luminosity

3.6 x 1056 erg s-1

false alarm prob.

< 1 in 5 million

radiated GW energy

2.5-3.5 M⊙

false alarm rate

< 1 in 200,000 yr

remnant ringdown freq.

~ 250 Hzremnant damping time

~ 4 ms

Source Masses

M⊙

total mass

60 to 70

primary BH

32 to 41

secondary BH

25 to 33

remnant BH

58 to 67

mass ratio

0.6 to 1

primary BH spin

< 0.7

secondary BH spin

< 0.9

remnant BH spin

0.57 to 0.72

signal arrival timedelay

arrived in L1 7 ms
before H1

likely sky position

Southern Hemispherelikely orientation
resolved toface-on/off~600 sq. deg.

重力波が検出された！
重力波が検出できた！
BHが存在した！
BH連星が存在した！
相対論が第0近似として正しい！

.

.

remnant size, area

180 km, 3.5 x 105 km2

consistent withgeneral relativity?

passes all tests
performed

graviton mass bound< 1.2 x 10-22 eV

coalescence rate ofbinary black holes

2 to 400 Gpc-3 yr-1

online trigger latency~ 3 min# offline analysis pipelines5

CPU hours consumed~ 50 million (=20,000PCs run for 100 days)

papers on Feb 11, 201613

# researchers~1000, 80 institutionsin 15 countries

Detector noise introduces errors in measurement. Parameter ranges correspond to 90% credible bounds.
Acronyms: L1=LIGO Livingston, H1=LIGO Hanford; Gly=giga lightyear=9.46 x 10 12 km; Mpc=megaparsec=3.2 million lightyear, Gpc=10 3 Mpc, fm=femtometer=10 -15 m, M⊙=1 solar mass=2 x 10 30 kg

BHs!

7M+14M=20M
29M+36M=62M
why not more?

https://www.ligo.caltech.edu/system/avm̲image̲sqls/binaries/57/page/Black̲Hole̲Mass̲Chart.jpg?1465864737

1. Gravitational Wave >> Expected Waveform

Inspiral

NS-NS
NS-BH
BH-BH

1.0

重力波の振幅 × 10Merger Ringdown−22

ブラックホール形成の重力波波形

0.5

h0.0!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]

!50

合体の時刻

5time
1414

1. Gravitational Wave >> Expected Eventsp
1/2
Strain Sensitivity Sn (f )[Hz]Typical  frequency  of  BH-‐‑‒BH  binary  merger  @  1000Mpc  10-17

5M

10-19

01+

5M

fQNM

10fQNM
4M

10-21

4M

01+

103M

3M

01+

2M

10M
0.01

2Rg

10Rg

01+

1010-45Rg

2M

1010-23

fQNM+10M
150Rg
KAGRA
100

frequency [Hz]1510-16Kagrap

Strain noise amplitude[1/ Hz]

IMBH ringdown freq. is detectable
at LIGO/KAGRA
地上での重力波干渉計感度

BH quasi-normal freq.
(ringdown freq.)
frequency[Hz]104aVIRGO
10-22

aLIGO

100

10Hz

10-25

101000Hz
100c3
fqnm =
12⇡GMT

1010001040.63(1a)0.3

BH < 2000Msun can be a target

100M
10ET

frequency[Hz]a = 0.9
a = 0.5

a = 0.0

10TOBA

11000

100

10-191000M

100

1000

104

MBH /M
162. Model of SMBH

Rees, M.J. 1978. Observatory 98: 210

17

2. Model of SMBH

Volonteri, Science 337 (2012) 54418

2. Model of SMBH

Greene, Nature Comm 3 (2012) [arXiv:1211.7082]

19

2. Model of SMBH

HaloGas Cloud

Massive
Stars

BHs

GlobularCluster

GalaxyRees, M.J. 1978. Observatory 98: 210

IMBHs

SMBHs

20
Ebisuzaki +, ApJ, 562, L19 (2001)

Starburst galaxy M82 has 1000M BH
Matsushita+, ApJ, 545, L107 (2000)
Matsumoto+, ApJ, 547, L25 (2001)

HLX-1 has 20,000M BH!
http://hubblesite.org/newscenter/archive/releases/2012/2012/11/full/

BHs

IMBHs

SMBHs
Yagi, CQG 29 075005 (2012)[arXiv:1202.3512]
21
Ebisuzaki +, ApJ, 562, L19 (2001)

1602.05325
0.15pc from SgrA*
1-2 x 104 Msun

22

PortegiesZwart+, ApJ 641(2006)319

23

'Missing link' founded
Ebisuzaki +, ApJ, 562, L19 (2001)(1)formation of IMBHs by runaway mergers ofmassive stars in dense star clusters,
Marchant & Shapiro 1980; Portegies Zwart et al. 1999;
Portegies Zwart & McMillan 2002;
Portegies Zwart et al. 2004;
Holger & Makino 2003

(2) accumulations of IMBHs at the center region ofa galaxy due to sinkages of clusters by dynamical

BHs

IMBHsfriction
Matsubayashi et al. 2007(3) mergings of IMBHs by multi-body interactions
and gravitational radiation.

SMBHs

Iwasawa et. al. 2010

雰囲気（巡り逢い）＋仲良し成長モデル

24

IMBH-IMBH mergers produce low freq. GW

Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 86427

28

Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 864

29

How many BHs in a galaxy?
How many galaxies in the Universe?

How many BH mergers
in the Universe?
How many BH mergers
we observe in a year?
Detectable Distance ?
KAGRA/aLIGO/aVIRGO
Cosmological model?
BH spin? Signal-to-Noise?

30How many BHs in a Galaxy?
Mass Function of Giant Molecular Clouds
1012
108
104

1

1012 Mgalaxy mass

104

106

109 M

10-4

1100

GMC mass M

A&A 580, A49 (2015) [arXiv:1505.04696]

31

How many BHs in a Galaxy?
Molecular Clouds
Maximum Core

Building Block BHn(M)
Galaxy Mass

105

1012 M
10.000

109 M

0.001

10-7

101309.1223v31001000

BH mass

104

32

How many BHs in a Galaxy?
Count BHs to form a SMBH

Building Block BHn(M)
Galaxy Mass

1051012 Mn(M)10.000

105

109 M

0.001

100

0.1

10-710-4

1010-7101000

105

107

1091011

BH mass

100

1000

104

BH mass

33

How many BHs in a Galaxy?
Count BHs to form a SMBH

dynamical friction
n(M)
105
100

0.1

10-4
10-7101000

105

107

1091011

BH mass

34

How many Galaxies in the Universe?
Count BHs to form a SMBH

(sub-)Galaxy
from Halo modelStar Formation Ratepeak z=3.16

35

How many Galaxies in the Universe?
(1) Halo number density
10-13(3) N of Galaxyz<3within z=51012M

1M

1.95

100

10-15

110-1710-19

z=010-210.01

within z=1

z=510-23
1011

1012

1013

1014

1015

1 × 1011

5 × 1011

1 × 1012

5 × 1012(2) N of seeds of Galaxy (subHalo)
1000
500

100
50

10536
1012

1013

1014

1015

http://iopscience.iop.org/article/10.3847/0004-637X/830/2/83
https://www.ras.org.uk/news-and-press/2910-a-universe-of-two-trillion-galaxies

x10 more than before# of galaxy (z<8) : 2x1012# of galaxy 106>Msun
reduces in evolution
37How many Galaxies in the Universe?
Count BHs to form a SMBH(sub-)Galaxy
from Halo modelStar Formation Ratepeak z=3.16

38

McConnell-Ma
ApJ 764(2013)18439

How many BH mergers in the Universe?
in Standard Cosmology
Nmerger (z)Event Rate R[/yr] =V (D/2.26)

図FStandard Cosmology

zaveraging distances
for all directions

BH massz
BH mass40

√Strain noise amplitude[1/ Hz]

Signal-to-Noise Ratio (SNR)Kagra



TOBA

aVIRGOaLIGOET



frequency[Hz]41

Detectable Distances at bKAGRA
Flanagan&Hughes, PRD57(198)4535✓◆2 ✓ ◆28 ✏r (a)(1 + z)M(1 + z)M4µ2⇢ =SNR
5 fR2 Sh (fR /(1 + z))
dL (z)M

Hierarchical GrowthStandard Cosmology
Energy emission=4% of total M，1% at ringdown

KAGRAKAGRA

a = 0.9

































42

GW150914

2.8% of massemitted by ISCO

4.7% of massemittedin total
1% of massemittedin ringdown?

Slide copy from Hiroyuki Nakano

43How many BH mergers in the Universe?
in Standard CosmologyNmerger (z)Event Rate R[/yr] =V (D/2.26)

図FStandard Cosmology

zaveraging distances
for all directions

BH massz
BH mass44

Event Rates at bKAGRA
BH spin=0.9,0.5,0.0

7 events/yrpeak at 60Mrange 40M-150M

210 events/yr

45

Event Rates at bKAGRA/aLIGO(a1) SNR=10, KAGRA
12LIGO
group [1602.03842]
10

Event Rate [1/yr]

100

Nmerger

1011
1010
109
108
107

1050

100

500

1000

5000

104

BH mass (final BH) [M ]Inoue+ MNRAS461(16)4329

6-400 /Gpc^3/yr

7 events/yr(a2) SNR=10, KAGRA

50

peak at 60M
105range 40M-150M

10.5

10210 events/yr
50

10050010005000104

BH mass (final BH) [M ]Kinugawa+ MNRAS456(15)1093

70-140 /yr
46Event Rates at bKAGRA/aLIGO(a1) SNR=10, KAGRA
LIGO
group PRX6(2016)041015
1210

Event Rate [1/yr]

Nmerger

1011
1010
109
108
107

10100

50100500

1000

5000

104

BH mass (final BH) [M ]Inoue+ MNRAS461(16)4329

6-400 /Gpc^3/yr

7 events/yr(a2) SNR=10, KAGRA

50

peak at 60M
105range 40M-150M

10.510210 events/yr
50

100

500

1000

5000

104

BH mass (final BH) [M ]Kinugawa+ MNRAS456(15)1093

70-140 /yr
47

Sensitivity  of  Space  GW  Interferometersp
1/2
Strain Sensitivity Sn (f )[Hz]

10-17

0M
1+
410-19

M
104M
0+13M
0
1
310-21

0M
1+2M
102

10-23

10-4

0.01

1100

frequency [Hz]48Sensitivity  of  Space  GW  Interferometersp
1/2
Strain Sensitivity Sn (f )[Hz]

10-17

M0
1410-19

M0
14+

M
0+13M
0
1
310-210M
1+2M10210-2310-40.01

1100

frequency [Hz]49

これは遊べる GWplotter
http://rhcole.com/apps/GWplotter/50

Event Rates at eLISA

観測できるBH合体距離[Mpc](S/N=10)10410-17

1000
10-19100eLISA N2A510-211010-23

104
10-40.01

1105

106

107

100109BH質量[Msun]

1年間で観測できるBH数分布(S/N=10) 年55個100観測できるBH数分布
1012101110

spin 0.91010
1109
1080.10107
104108105106

107108BH質量[Msun]

spin 0105106107

108

BH質量[Msun]
51

Event Rates at PreDECIGO

観測できるBH合体距離[Mpc](S/N=10)10510-1710410-191000
10010-211010-23PreDECIGO
10-40.01

111100101001000

104105106

BH質量[Msun]

1年間で観測できるBH数分布(S/N=10)観測できるBH数分布

10001013100

spin 0.910111011090.10100spin 0107

1000

104105106107

BH質量[Msun]

1001000

104105106107

BH質量[Msun]
52

Event Rates at PreDECIGO

観測できるBH合体距離[Mpc](S/N=30)
104

10-17

1000

10-1910010-211010-23

PreDECIGO
10-40.01

11100101000

104105106

BH質量[Msun]

1年間で観測できるBH数分布(S/N=30)観測できるBH数分布

年4850個

10001013100spin 0.910111011090.10spin 0107
1001001000104105106107

BH質量[Msun]

1001000

104105106107

BH質量[Msun]
53まとめSMBHの形成シナリオとして， IMBHsの合体を経由するボトムアップシナリオ
BH spin=0.9,0.5,0.0を仮定して，重力波検出頻度を計算した．
モデルの仮定：分子雲のコアが10Msun以上になったら，BHになると仮定した．
BHは等質量同士のものが次々に合体して成長していくものと仮定した．
BHが形成された後，ガス降着で太ることは考慮していない．
銀河数分布は，サブハローモデルと，星形成率を乗じたものから計算した．
銀河どうしの合体は考えていない．
SMBHは，宇宙初期のガスのdirect collapseによって生じたという説もあるが，そのような形成仮定があれば，このモデルで得た検出頻度は減る．
リングダウン部分の重力波を直接検出できる，と仮定した．
重力波検出のデータを蓄積することによって，銀河分布やSMBH形成シナリオを特定したり，宇宙膨張モデルの検証や，重力理論の検証が可能になる．
20170307 　真⾙貝 54