How many BHs in a galaxy?  

(1)

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  

(2)

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

why not more?

(3)

M1+M2=Mf, Mdiﬀ/Mtotal 

a̲ﬁnal

Mpc

z SNR deg^2

GW150914

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

https://losc.ligo.org/events/GW150914/

https://losc.ligo.org/events/LVT151012/

List of Detected GW events

(4)

!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 Amplitude

Inspiral Merger Ringdown

(5)

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 1000

10^-25 10^-23 10^-21 10^-19 10^-17

f

_QNM

f

_QNM

f

_QNM

f

_QNM

2R

_g

5R

_g

10R

_g

50R

_g

10M + 10M 10

²

M + 10

²

M

10

³

M + 10

³

M

frequency [Hz]

S tr ai n S en si ti v it y p S

n

( f )[ Hz

1/2

]

(6)

6

1. Gravitational Wave >> Expected Events

20170623 　真⾙貝

Typical frequency of BH-‐‑‒BH binary merger @ 1000Mpc

●

■

◆

◆ ◆

▲

▼

0.001 0.100 10 1000

10^-25 10^-23 10^-21 10^-19 10^-17

frequency [Hz]

S tr ai n S en si ti v it y p S

n

( f )[ Hz

1/2

]

f

_QNM

f

_QNM

f

_QNM

f

_QNM

2R

_g

5R

_g

10R

_g

50R

_g

10M + 10M 10

²

M + 10

²

M

10

³

M + 10

³

M

KAGRA

aLIGO

(7)

7 Strainnoiseamplitude[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

a = 0.0

a = 0.5 a = 0.9

M_BH/M

fr eq u en cy [Hz ]

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

1000M 100M

10

100

(8)

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

8

Gas Cloud

BHs

IMBHs

SMBHs

Halo

Galaxy Globular

Cluster Massive

Stars

Ebisuzaki +, ApJ, 562, L19 (2001)

2. Models of SMBH

(9)

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)

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

(11)

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

IMBH-IMBH mergers produce low freq. GW

11

(12)

12

(13)

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

13

(14)

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)

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)

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)

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)

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)

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)

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

10 ¹²

(21)

21 https://www.ras.org.uk/news-and-press/2910-a-universe-of-two-trillion-galaxies

http://iopscience.iop.org/article/10.3847/0004-637X/830/2/83

x10 more than before

# of galaxy (z<8) : 2x10

¹²

# of galaxy 10

⁶

>Msun  

reduces in evolution

(22)

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?

(23)

McConnell-Ma

ApJ 764(2013)184

23

(24)

24

図F

BH mass

z z

BH mass

in Standard Cosmology

How many BH mergers in the Universe?

Event Rate R[/yr] = N_merger(z) V (D/2.26)

Standard Cosmology

averaging distances

for all directions

(25)

Signal-to-Noise Ratio (SNR)

Strainnoiseamplitude[1/√ Hz]

frequency[Hz]

Kagra

TOBA

aLIGO aVIRGO

ET

25

(26)

26

Detectable Distances at bKAGRA

Hierarchical Growth

⇢² = 8 5

✏_r(a) f_R²

(1 + z)M S_h(f_R/(1 + z))

✓(1 + z)M d_L(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

(27)

Slide copy from Hiroyuki Nakano 27

GW150914

4.7% of mass emitted

in total 2.8% of mass

emitted by ISCO

1% of mass

emitted

in ringdown?

(28)

28

図F

BH mass

z z

BH mass

in Standard Cosmology

How many BH mergers in the Universe?

Event Rate R[/yr] = N_merger(z) V (D/2.26)

Standard Cosmology

averaging distances

for all directions

(29)

Event Rates at bKAGRA

BH spin=0.9,0.5,0.0

peak at 60M

range 40M-150M

7 events/yr

210 events/yr

29

(30)

Event Rates at bKAGRA/aLIGO

7 events/yr

peak at 60M

BH mass (final BH) [M ] BH mass (final BH) [M ]

EventRate[1/yr]

(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

(31)

10⁵ 10⁶ 10⁷ 10⁸ 10⁷

10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹²

Observable BH mergers Event Rate

(S/N=10)

spin 0.9

spin 0

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

(32)

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.