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Hisaaki Shinkai 真貝寿明 (Osaka Inst. Tech., Japan)
1
2017/7/4 The 13th International Conference on Gravitation, Astrophysics, & Cosmology (ICGAC-XIII) @ Seoul, Korea
Gravitational Waves from
Merging Intermediate-Mass Black Holes
http://www.oit.ac.jp/is/~shinkai/
Ref: HS, Kanda & Ebisuzaki, ApJ, 835 (2017) 276 [arXiv:1610.09505]
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
M1+M2=Mf, Mdiff/Mtotal
a_final
Mpc z SNR deg^2
GW150914PRL116, 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
1000Mpc0.20
9.7
GW151226PRL116, 241103
(2016/6/15)
14.2+7.5=20.8+0.94.15%0.74
440Mpc 0.09
13.0 850
GW170104PRL118, 221101
(2017/6/1)
31.2+19.4=48.7+1.93.75%0.64
880Mpc 0.18
13.0 1300
https://losc.ligo.org/events/GW150914/
https://losc.ligo.org/events/GW151226/https://losc.ligo.org/events/LVT151012/
https://losc.ligo.org/events/GW170104/
List of Detected GW events
!25 !20 !15 !10 !5 0 5
!1.0
!0.5
0.0
0.5
1.0
時間 [ミリ秒] 合体の時刻
重力波の振幅
連星のインスパイラル運動からの重力波波形
ブラックホール形成の重力波波形
× 10−22
4
1. Gravitational Wave >> Expected AmplitudeInspiral Merger Ringdown
KAGRA aLIGO
20170623 真⾙貝 5
1. Gravitational Wave >> Expected Events
Typical frequency of BH-‐‑‒BH binary merger @ 100Mpc
●
●
●● ●
● ●
■
■
■■ ■
◆
◆◆
◆ ◆
▲▲
▲ ▲
▼ ▼
0.001 0.100 10 100010-25
10-23
10-21
10-19
10-17
fQNM
fQNM
fQNM
fQNM
2Rg5Rg
10Rg
50Rg
10M� + 10M�
102M� + 102M�
103M� + 103M�
frequency [Hz]
Strain
Sen
sitivitypSn(f)[Hz�
1/2]
6
1. Gravitational Wave >> Expected Events
20170623 真⾙貝
Typical frequency of BH-‐‑‒BH binary merger @ 1000Mpc
●
●
●●
●
●
■
■
■■
■
◆
◆◆
◆◆
▲
▲▲
▲▲
▼▼
▼▼
0.001 0.100 10 100010-25
10-23
10-21
10-19
10-17
frequency [Hz]
Strain
Sen
sitivitypSn(f)[Hz�
1/2]
fQNM
fQNM
fQNM
fQNM
2Rg5Rg
10Rg
50Rg
10M� + 10M�
102M� + 102M�
103M� + 103M�
KAGRA aLIGO
7
Strain
noiseamplitude[1/p
Hz]
frequency[Hz]1 10 100 1000 104
10-25
10-22
10-19
10-16
Kagra
TOBA
aLIGO
aVIRGO
ET
10 100 1000 104
10
100
1000
104
a = 0.0
a = 0.5a = 0.9
MBH/M�
frequen
cy[H
z]
地上での重力波干渉計感度
BH quasi-normal freq. (ringdown freq.)
BH < 2000Msun can be a target
IMBH ringdown freq. is detectable at LIGO/KAGRA
10Hz 1000Hz
1000M100M10
100
8Rees, M.J. 1978. Observatory 98: 210
Gas Cloud
BHs
IMBHs
SMBHs
Halo
Galaxy
Globular Cluster
Massive Stars
Ebisuzaki +, ApJ, 562, L19 (2001)
2. Models of SMBH
9
Yagi, CQG 29 075005 (2012) [arXiv:1202.3512]
HLX-1 has 20,000M BH!http://hubblesite.org/newscenter/archive/releases/2012/2012/11/full/
Starburst galaxy M82 has 1000M BH
BHs
IMBHs
SMBHs
Matsushita+, ApJ, 545, L107 (2000) Matsumoto+, ApJ, 547, L25 (2001)
Ebisuzaki +, ApJ, 562, L19 (2001)
10
BHs
IMBHs
SMBHs
'Missing link' founded Ebisuzaki +, ApJ, 562, L19 (2001)
(1)formation of IMBHs by runaway mergers of massive stars in dense star clusters,
(2) accumulations of IMBHs at the center region of a galaxy due to sinkages of clusters by dynamical friction
(3) mergings of IMBHs by multi-body interactions and gravitational radiation.
Marchant & Shapiro 1980; Portegies Zwart et al. 1999; Portegies Zwart & McMillan 2002; Portegies Zwart et al. 2004; Holger & Makino 2003
Matsubayashi et al. 2007
Iwasawa et. al. 2010
Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 864
IMBH-IMBH mergers produce low freq. GW
11
12
Matsubayashi, HS, Ebisuzaki, ApJ 614 (2004) 864 13
How many BH mergers in the Universe?
How many BH mergers we observe in a year?
How many BHs in a galaxy? How many galaxies in the Universe?
Detectable Distance ? KAGRA/aLIGO/aVIRGO
Cosmological model? BH spin? Signal-to-Noise?
14
15
Mass Function of Giant Molecular Clouds
1 100 104 106
10-4
1
104
108
1012
M�
1012M�
109M�
galaxy mass
GMC mass
A&A 580, A49 (2015) [arXiv:1505.04696]
How many BHs in a Galaxy?
16
10 100 1000 104
10-7
0.001
10.000
105
1309.1223v3
1012M�
109M�
Galaxy Mass
n(M)
BH mass
Molecular Clouds Maximum Core
Building Block BH
How many BHs in a Galaxy?
17
Count BHs to form a SMBH
10 1000 105 107 109 1011
10-7
10-4
0.1
100
105
10 100 1000 104
10-7
0.001
10.000
105
1012M�
109M�
Galaxy Mass
n(M)
BH mass
Building Block BH
BH mass
n(M)
How many BHs in a Galaxy?
18
Count BHs to form a SMBH
10 1000 105 107 109 1011
10-7
10-4
0.1
100
105
dynamical friction
BH mass
n(M)
How many BHs in a Galaxy?
19
(sub-)Galaxy from Halo model
Star Formation Rate peak z=3.16
Count BHs to form a SMBH
How many Galaxies in the Universe?
20
1011 1012 1013 1014 1015
10-23
10-21
10-19
10-17
10-15
10-13
z = 0
z = 5
1012 1013 1014 1015
5
10
50
100
500
1000
(1) Halo number density
(2) N of seeds of Galaxy (subHalo)
(3) N of Galaxy
within z=1
within z=5
M�1
1×1011 5×1011 1×1012 5×1012
0.01
1
100
M�1.95
How many Galaxies in the Universe?z<3 1012
21
https://www.ras.org.uk/news-and-press/2910-a-universe-of-two-trillion-galaxieshttp://iopscience.iop.org/article/10.3847/0004-637X/830/2/83
x10 more than before
# of galaxy (z<8) : 2x1012
# of galaxy 106>Msun reduces in evolution
22
(sub-)Galaxy from Halo model
Star Formation Rate peak z=3.16
Count BHs to form a SMBH
How many Galaxies in the Universe?
McConnell-Ma ApJ 764(2013)184
23
24
図F
BH mass
z
z
BH mass
in Standard Cosmology
How many BH mergers in the Universe?
Event Rate R[/yr] =Nmerger(z)
V (D/2.26)
Standard Cosmology
averaging distances for all directions
Signal-to-Noise Ratio (SNR)
Strainnoise
amplitude[1/√Hz]
frequency[Hz]� �� ��� ���� ���
�����
�����
�����
�����
Kagra
TOBA
aLIGO
aVIRGO
ET
25
26
Detectable Distances at bKAGRAHierarchical Growth
⇢2 =8
5
✏r(a)
f2R
(1 + z)M
Sh(fR/(1 + z))
✓(1 + z)M
dL(z)
◆2 ✓4µ
M
◆2
SNR
Energy emission=4% of total M，1% at ringdown
Flanagan&Hughes, PRD57(1998)4535
Standard Cosmology
�� ��� ���� ���
�
��
���
����
���
���
a = 0.9
�� ��� ���� ���
�
��
���
����
���
���KAGRA KAGRA
27Slide copy from Hiroyuki Nakano
GW1509144.7% of mass
emitted in total
2.8% of mass emitted by ISCO
1% of mass emitted
in ringdown?
28
図F
BH mass
z
z
BH mass
in Standard Cosmology
How many BH mergers in the Universe?
Event Rate R[/yr] =Nmerger(z)
V (D/2.26)
Standard Cosmology
averaging distances for all directions
Event Rates at bKAGRA
BH spin=0.9,0.5,0.0peak at 60M
range 40M-150M
7 events/yr
210 events/yr
29
Event Rates at bKAGRA/aLIGO
7 events/yrpeak at 60M
BH mass (final BH) [M�] BH mass (final BH) [M�]
Event
Rate[1/y
r]
(a1) SNR=10, KAGRA (a2) SNR=10, KAGRA
10 50 100 500 1000 5000 104
0.5
1
5
10
50
100
Nmerger
10 50 100 500 1000 5000 104
107
108
109
1010
1011
1012
range 40M-150M
210 events/yr
LIGO group PRX6(2016)041015
Inoue+ MNRAS461(16)4329
6-400 /Gpc^3/yr
Kinugawa+ MNRAS456(15)1093
70-140 /yr
30
105 106 107 108
107
108
109
1010
1011
1012
Observable BH mergersEvent Rate (S/N=10)
spin 0.9
spin 0
BH mass [Msun]BH mass [Msun]
55 events/year
104 105 106 107 108
0.10
1
10
100
104 105 106 107 108 109
10
100
1000
104
Horizon Distance (S/N=10)
BH mass [Msun]
[Mpc]
10-4 0.01 1 100
10-23
10-21
10-19
10-17
eLISA N2A5
31
Event Rates at eLISA
BH spin=0.9,0.5,0.0
Summary
The statistics of the signals will tell us both a galaxy distribution and a formation model of SMBHs, and also in future cosmological models/gravitational theories.
Based on a bottom up formation model of a SMBH via IMBHs, we estimate 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 10 Msun, 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 over-estimate 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.
