Gravitational Waves
from Intermediate-Mass Black Holes
真貝寿明 (大阪工業大)Hisa-aki Shinkai(Osaka Institute of Technology, Japan)
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?
HS, N.Kanda, T.Ebisuzaki, arXiv:1610.09505
2016/12

Colloquim @ KASI, Korea

1

“Physicists start thinking from spherical model”
Black Holes,
Cosmology,… … even for a cow

contents
1. Gravitational Wave
2. Model of SMBH via IMBHs
3. How many BHs in a galaxy?
4. How many galaxies in the Universe?
5. Event Rates, Proﬁles

http://www.oit.ac.jp/is/~shinkai/

HS, N.Kanda, T.Ebisuzaki, arXiv:1610.09505
2016/12

Colloquim @ KASI, Korea

3

1. Gravitational Wave >> 1.1 Expected Waveform

BHs, Expanding Universe,and GWs (HS, 2015/9)

Korean version (2017)from Kachi Books

Inspiral

NS-NS
NS-BH
BH-BH

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

h

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

合体の時刻

5time45

1. Gravitational Wave >> 1.2 Detectors
LIGO : Laser Interferometer Gravitational-Wave Observatory

4kmMichelson

1. Gravitational Wave >> 1.2 Detectors
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
7

GW150914

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~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

GW150914
36Msun + 29 Msun=> 62 Msun
13 x109 lyr（400 170 Mpc）
（z=0.054̶0.136）
GW exists！
GW was detected！
BH exists！
BH binary exists！
GR is right！

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, H1duration from 30 Hz~ 200 mssource 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
performedgraviton 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

1. Gravitational Wave >> 1.2 Detectors
KAGRA : Kamioka Gravitational wave detector(Large-scale Cryogenic Gravitational wave Telescope)

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

pStrain noise amplitude[1/ Hz]

Sapphira mirrors

10-16

Kagra

10-19

TOBA

aVIRGO
10-22

aLIGO
ET
10-25
1101001000

frequency[Hz]

神楽（かぐら）
Sinto Music
http://gwcenter.icrr.u-tokyo.ac.jp/plan/history

104

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 >> 1.3 Sources

12

IMBH-IMBH mergers produce low freq. GW

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

1. Gravitational Wave >> 1.1 Expected Waveform

Inspiral

NS-NS
NS-BH
BH-BH

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

h

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

合体の時刻

5time
14

10-16

KagrapStrain 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
10-22aLIGO

10010Hz

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

1001000

104

MBH /M15

2. Model of SMBH

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

16

2. Model of SMBH

Volonteri, Science 337 (2012) 544

2. Model of SMBH

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

2. Model of SMBH

HaloGas Cloud

MassiveStars

BHs

GlobularCluster

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

IMBHs

SMBHs

19Ebisuzaki +, 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]
20Ebisuzaki +, ApJ, 562, L19 (2001)

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

PortegiesZwart+, ApJ 641(2006)319

IMBH-IMBH mergers produce low freq. GW

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

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

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?

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

11012 Mgalaxy mass

104

106

109 M

10-4

1100

GMC mass M

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

27

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

10-7101309.1223v3100

1000

BH mass

10428

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

Building Block BHn(M)
Galaxy Mass

105

1012 Mn(M)10.000

105

109 M

0.001

100

0.1

10-7

10-41010-7101000

105

1071091011

BH mass

100

1000

104

BH mass

29

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

dynamical friction
n(M)
105
100

0.1

10-4
10-7
101000105

1071091011

BH mass

30

PortegiesZwart+, ApJ 641(2006)319

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

(sub-)Galaxy
from Halo modelStar Formation Ratepeak z=3.1632

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

1M

1.95

10010-15

110-1710-19

z=010-21

0.01within z=1z=510-23
1011

1012

1013

10141015

1 × 1011

5 × 1011

1 × 1012

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

100
50

10533
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
34

How many Galaxies in the Universe?
Count BHs to form a SMBH(sub-)Galaxy
from Halo modelStar Formation Ratepeak z=3.1635

McConnell-Ma
ApJ 764(2013)184

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 mass37

√Strain noise amplitude[1/ Hz]

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



TOBA

aVIRGOaLIGOET







frequency[Hz]

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







39

GW150914

2.8% of massemitted by ISCO

4.7% of massemittedin total
1% of massemittedin ringdown?

Slide copy from Hiroyuki Nakano

40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 mass

41

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

7 events/yr
peak at 60Mrange 40M-150M

210 events/yr

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

50peak at 60M
105range 40M-150M

10.5

10210 events/yr
50

100

500

1000

5000

104

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

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

Event Rate [1/yr]

Nmerger

1011
1010
109108107

1010050

100500

1000

5000

104

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

6-400 /Gpc^3/yr

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

50peak at 60M
105range 40M-150M

10.5

10210 events/yr
50

100500

1000

5000

104

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

70-140 /yrSummaryBased on a bottom up formation model of a SMBH via IMBHs, we estimate
BH spin=0.9,0.5,0.0
expected observational proﬁle of gravitational wave at ground-based
detectors.
We simply modeled that cores of molecular clouds become BHs if it is more than 10Msun, which become building blocks of forming larger BHs. We also modeled that BH
mergers are accumulations of equal-mass ones and suppose these occurs
hierarchically. We did not include gas accretion after a BH is formed.
Details numbers are, of course, depend on model settings and model parameters.
We assume all the galaxies in the Universe evolve in the single scenario, which will overestimate the event rate if some SMBHs are formed from the direct collapse of gas
cloud. We also ignore galaxy mergers, which are another route of forming SMBHs.

The statistics of the signals will tell us both a galaxy distribution and aformation model of SMBHs, and also in future cosmological models/
gravitational theories.