Gravitational Waves
fromMerging Intermediate-Mass Black Holes
Hisaaki Shinkai 真貝寿明
(Osaka Inst. Tech., Japan)
http://www.oit.ac.jp/is/~shinkai/Counting BHs
How many BHs in a galaxy?
How many galaxies in the Universe?
How many BH mergers in the Universe?
Event Rates at aLIGO/KAGRA/DECIGO/LISA
Ref: HS, Kanda & Ebisuzaki, ApJ, 835 (2017) 276 [arXiv:1610.09505]
2017/7/4 The 13th International Conference on Gravitation, Astrophysics, & Cosmology (ICGAC-XIII)@ Seoul, Korea1

why not more?

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

List of Detected GW events
M1+M2=Mf,
Mdiﬀ/Mtotala̲ﬁnalMpc
zSNRdeg^2

PRL116,061102(2016/2/11)

36.2+29.1=62.3+3.0
4.59%
0.68

410Mpc
0.09

23.7

600

LVT151012(2016/2/11)

23+13=35+1.5
2.78%
0.66

1000Mpc
0.20

9.7

GW151226

PRL116,241103(2016/6/15)

14.2+7.5=20.8+0.9
4.15%
0.74

440Mpc
0.09

13.0

850

GW170104

PRL118,221101(2017/6/1)

31.2+19.4=48.7+1.9
3.75%
0.64

880Mpc
0.18

13.0

1300

GW150914

https://losc.ligo.org/events/GW150914/https://losc.ligo.org/events/LVT151012/
https://losc.ligo.org/events/GW151226/
https://losc.ligo.org/events/GW170104/

1. Gravitational Wave >> Expected Amplitude

1.0InspiralMerger Ringdown

重力波の振幅 × 10

ブラックホール形成の−22

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

Typical  frequency  of  BH-‐‑‒BH  binary  merger  @  100Mpc  p
1/2
Strain Sensitivity Sn (f )[Hz]●10-1710-19●▼▼▲3310 M + 10 M2◆▲

fQNM
▲

▲

◆210 M + 10 M

■fQNM

◆10M + 10M

◆◆■
●50Rg

10-21■

■

●

10Rg
5Rg

fQNM

●

10-23

10-25

fQNM

■

●

●2Rg
KAGRA
aLIGO

0.001

0.100

101000frequency [Hz]20170623 　真⾙貝 5

1. Gravitational Wave >> Expected Events

Typical  frequency  of  BH-‐‑‒BH  binary  merger  @  1000Mpc  p
1/2
Strain Sensitivity Sn (f )[Hz]●▼▲

10-17▼▼▼▲

3310 M + 10 M

◆▲

fQNM
▲
▲

10-192210 M + 10 M

fQNM◆■◆◆

10-21

10M + 10M

◆■●

■50Rg

■
●fQNM
10Rg ●●5Rg ●
KAGRA
2Rg

10-2310-25

■fQNM

aLIGO

0.001

0.100

101000frequency [Hz]20170623 　真⾙貝 6

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]

104

TOBA

aVIRGO
10-22

aLIGO
ET

10Hz

10-25
1101000Hz
100

1000

104

frequency[Hz]a = 0.9
a = 0.51000

10010-19100
a = 0.01010BH < 2000Msun can be a target

100M
101000M

1001000104

MBH /M72. Models of SMBH

HaloGas Cloud

MassiveStars

BHs

GlobularCluster

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

IMBHs

SMBHs

8Ebisuzaki +, 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]
9Ebisuzaki +, ApJ, 562, L19 (2001)

'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

IMBHs

friction
Matsubayashi et al. 2007(3) mergings of IMBHs by multi-body interactionsand gravitational radiation.

SMBHs

Iwasawa et. al. 201010

IMBH-IMBH mergers produce low freq. GW

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

11

12

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

13

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?

14How many BHs in a Galaxy?
Mass Function of Giant Molecular Clouds
101210810411012 Mgalaxy mass

104

106

109 M

10-4

1

100

GMC mass M

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

15

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

101309.1223v3100

1000

BH mass

104

16

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

10-4

1010-7101000105

1071091011

BH mass

1001000

104

BH mass

17

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

18

How many Galaxies in the Universe?
Count BHs to form a SMBH(sub-)Galaxy
from Halo modelStar Formation Ratepeak z=3.16

19

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

1

10-17

10-19

z=010-21

0.01

within z=1z=510-23
1011

1012

1013

1014

1015

1 × 1011

5 × 1011

1 × 1012

5 × 1012(2) N of seeds of Galaxy (subHalo)
100050010050105201012

1013

10141015

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
21

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

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

22

McConnell-Ma
ApJ 764(2013)18423

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

図FStandard Cosmologyzaveraging distances
for all directions

BH massz
BH mass24

√Strain noise amplitude[1/ Hz]

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

TOBAaVIRGO
aLIGOET







frequency[Hz]25Detectable Distances at bKAGRA
Flanagan&Hughes, PRD57(1998)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

KAGRAKAGRAa = 0.9







26

GW150914

2.8% of massemitted by ISCO

4.7% of massemittedin total
1% of massemittedin ringdown?

Slide copy from Hiroyuki Nakano

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

図FStandard Cosmologyzaveraging distances
for all directions

BH massz
BH mass

28

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

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

210 events/yr29Event Rates at bKAGRA/aLIGO(a1) SNR=10, KAGRA
LIGO
group PRX6(2016)041015
1210

Event Rate [1/yr]

Nmerger

10111010
109108107

1010050100500

10005000

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

100500

1000

5000

104

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

70-140 /yr30

Event Rates at eLISA[Mpc]

Horizon Distance(S/N=10)10410-171000
10-19100eLISA N2A510-211010-23

104
10-40.01

1105

106

100

108

109

BH mass [Msun]

Event Rate(S/N=10)

Observable BH mergers

10010121011

1055 events/year
1

spin 0.91010
1091080.10

107
104

107

105

106

107

108

BH mass [Msun]

spin 0105

106

107

108

BH mass [Msun]
31

Summary
Based 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.

If we will observe BH-BH mergers above 100 Msun, this model is the only
one to predict such an event.
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.