重力波観測による巨大ブラックホール形成シナリオ解明 の可能性
真貝寿明 (大阪工業大)神田展行 (大阪市立大)戎崎俊一 (理化学研究所)

IMBH から SMBH のモデル
銀河内のBH数，銀河分布を仮定し，KAGRAでのEvent Rateを予測する．

2016年９月15日 天文学会@愛媛大学
セッション「重力波初検出の意義と重力波天文学の幕開け」
1

BHs!

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

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

HaloGas Cloud

MassiveStars

BHs

GlobularCluster

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

IMBHs

SMBHs
3

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]
4

'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 dynamicalBHs

IMBHs

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

SMBHs

Iwasawa et. al. 20105

宇宙空間での重力波干渉計で形成過程がわかる

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

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

10-16

KagrapStrain noise amplitude[1/ Hz]

地上重力波干渉計で形成過程がわかるか？
地上での重力波干渉計感度

frequency[Hz]104a = 0.9
a = 0.5

1000

10-19

TOBA

aVIRGO
10-22

aLIGO
ET10-251101001000

104

frequency[Hz]BH 準固有振動(ringdown freq.)

100a = 0.0
10

数100MのBHまではターゲットになる．

101001000

MBH /M

104

銀河内のBH数，銀河分布を仮定し，9KAGRAでのEvent Rateを予測する．

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]

10

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

11

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

10-7

10-4

1010-7101000

105

107

109

1011

BH mass

100

1000

104

BH mass

12

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

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

13

How many Galaxies in the Universe?
(1) Halo number density
10-13(3) N of Galaxy
100

within z=510-15

M

1M

1.95

110-17

10-19z=010-21

0.01

within z=1z=510-2310111012101310141015

1 × 1011

5 × 1011

1 × 1012

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

10050

105141012

101310141015

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

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

15

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

図Fz

BH massz
BH mass16

Detectable Distances at bKAGRA
SNR

8 ✏r (a)(1 + z)M⇢ =5 fR2 Sh (fR /(1 + z))
2✓(1 + z)MdL (z)◆2 ✓4µMHierarchical Growth◆2合体のGW放出=全質量の4%，ringdownで1%(a) SNR=10KAGRA

KAGRA

Detectable Distance [Mpc]SNR at d=1000 Mpc



a = 0.9

a = 0.5

a = 0.0









BH Mass (ﬁnal BH)



[M⊙ ]






a = 0.9
a = 0.5

a = 0.0










BH mass (final BH) [M⊙ ]17

Event Rates at bKAGRA(a1) SNR=10, KAGRA100

BH spin=0.9,0.5,0.0Nmerger

10111010
109108107

105010050010005000

104

Event Rate [1/yr]

1012

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

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

10.5

10

BH mass (final BH) [M ]

50

100

500

1000

5000

104

BH mass (final BH) [M ]210 events/yr
Summary
By accumulating data, we can discuss astrophysics:
formation scenario of SMBH, number counts of galaxies,…(and later) cosmological models/gravitational theories.