  , (Tohoku University)1Motivation:
Super Massive Black Holes at high z

2

SMBH with 109 M8 at z ~ 7 (8)
BHEddington

ṀBH

MBH mpL
G=R24 cR2
2L = Ṁ cṀBH = (1)ṀMBH

MBH = Mini exp (t/tE)
where tE  50 Myr

30 20 15

redshift
108

Mini=30 M⊙ at z=30
Mini=105 M⊙ at z=20

10log10 MBH / M⊙

BH

87⋆6⋆⋆⋆ ⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆ ⋆⋆⋆⋆ ⋆⋆⋆⋆⋆⋆⋆⋆ ⋆⋆⋆⋆⋆⋆ ⋆⋆ ⋆Massiveseed

64GW150914



200.2

0.4

: Eddington: Eddington60%0.60.8

1

cosmic age [Gyr] !
3

Massive Seed Formation(1) First Star

102-103 M8(2) Direct Collapse
gas cloudprotostarstar

BH~105 M8(3) ~103 M8(Volonteri, 2012)3

Massive Seed Formation
high-z SMBHs~~

atomic-cooling halo105
mihi-halo(2) Direct Collapse



[M8]

109

(3) 

103(1) First Star
z=20-30

z=20-10

4

Massive Seed Formation
high-z SMBHs

 [M8]109~~

atomic-cooling halo105(2) Direct Collapsemihi-halo
103

(3)
(1) First Star
z=20-30

 SMBH(z7.5)!Eddington(i)    %
 (ii)  "$#%

z=20-10

5

Direct Collapse#$$%(⇒ !  '"&#%
T[K]Under strong UV: T8000K

104

no UV case
Typical PopIII T200K

102

higher density(Omukai.2001)

Ṁ

MJ /tff

c3s /G~ 0.1 – 1 M8 yr -1

T

32(Omukai 01)

星の最終質量 ~ 105 M86

Direct Collapse
/2#!%239⇒ )- *&+7.(6 /3 
T[K]Under strong UV: T8000K

104

no UV case
102

Typical PopIII T200K
higher density(Omukai.2001)(Omukai 01)

3 3)3'"2SMBH(1-10/Gpc
 (Dijkstra+2014)
3Ṁ MJ /tff cs /G T 2~ 105 M8450SMBH(0.01-0.1/Mpc3) 8星の最終質量
,613*$50(7~ 0.1 – 1 M8 yr -1

Direct Collapse&(()2!
'*,

/.01(/.0

Omukai+2008'*+$-."(%'*,$#2or 28

Direct Collapse;
Latif+2016

Tagawa+2019

Sakurai+2017
105

103
101

103

104

105106$ [yr]dust 87.)9:&
2collapse8

9:&1 +
,7-0
 2" 8N1D/)429:%0<=02 8⇒ 3576+)
' 42(*9:⇒ runaway collision103 M82+⇒ 105 M82!
+

#
9

Direct CollapseC

3C&'8!9;2?>3-6Latif+2016

Tagawa+2019

Sakurai+2017
105

103101103

104

105

106

' [yr]dust @>3,AB)
8collapse@!

AB)7 .
/>15
 8$ @N!

1D4,:8AB(5D E58 @!

⇒ &'8$
9 <>=.,
9*:8+-AB⇒ runawaycollision
 3 8910 M88.

⇒ 105 M88#"%.!03-6-03-=10

Purpose of this work56#/collapse)2 1374'+-,%

!

.(*3  /

403&105

[M8]

atomic-cooling halo

103

8





$





"

11

Numerical Setup Gadget2 (SPH + N-body) barotropic-EOS(Z/Z8 = 10-3, 10-4, 10-5, 5×10-6, 10-6 )Z/Z8 = 10-6
125 10-6
3

Spherical Cloud
11

10-5
10-4

210-3
510log n [cm-3]

 multiple sink, merger
 sink radius

109nadib104 AU158pc
z 30= 12.77(created at n = 2×1016 – 2×1017 cm-3)
Hosokawa+2013

・ Initial Condition ⇒ Spherical Cloud (SC+16,18)

12log < density >log T [K]410 Mpc

Accretion Phase
Z = 10-6 Z8

Z = 10-4 Z8

 M>10 M8massive sink,  M<10 M8small sink

Z = 10-3 Z813

Accretion Phase
Z = 10-6 Z8

Z = 10-4 Z8"-/$%*#
Massive star$ (0()consistent)

Dust+./'&+massive star$ (Z/Z8 = 10-6))Z = 10-3 Z8+.0+./*$ 
+./$ (0!

1 M>10 M8,massive sink, 1 M<10 M8,small sink14

Mass Evolution@ Z/Z8<10-4 48metallicity69:
3+1 M8 yr-17?A>4&⇒ dust 8="+7$" ='25⇒ $.

Z < 10-4 Z8
10-3 Z8@ Z/Z8=10-3 48+$(./0.<(0.01 M8 yr-1)⇒ %!69< 4+9;4# .1<,⇒ 7&8) 6,@(M∝ T3/2)⇒ * .
05000
Time [yr]

10000
15

Merger v.s. Accretion
1gas accretion

0.8fraction

Z/Z8 = 10-4
10-5510-6 10-310-60.4
0.2
0Time [yr]Mergers withM* > 100 M80.6

Mergers with M* < 100 M8

10-310-410-5

5 10-6

10-6

Metallicity [Z8]

 '$!!%' ⇒ )(*!%& "'
!%& # '

! '16

Summary• D8<K*)
PE")' L&@?6CE$")(DA7B5• Z/Z8 < 10-4 CF 6-84103 M8E96
Ø NMO DIJ!F>KHEE5FD")+>K6• Z/Z8 = 10-3 CF 350 M8E96
Ø *%  DIJ5IJC 9#=K6Ø GE-F:;/2123.M8 yr-10[M8]

atomic-cooling halo

Z/Z8 < 10-4105103

Z/Z8 > 10-3,1718

NumberNumberMass distribution (1 )
100
10100
101Z = 10-4 Z810
1100
100

NumberNumberNumber100

1010∝ M -1

5 10-6 Z8

100
10
111-2
100
100

02 -5 410 Z
log Mass [M8] 8
Number024log Mass [M8]
NumberNumber-2-2

100

02-64log Mass10[MZ88]-6
Low mass star 10
!Z/Z>51081010⇒ dust '&)("#111High mass star  ! '&)( %' flow$
024-2024 -2
#log10 Mass [M⊙]log10 Mass [M⊙]100⇒   #
Numbernumber1

1019(a)(b)(c)
1016log < density >1214log < density >Collapse phase10-5 Z88106 au
2(a)5 104 au
46log < density >812200 au

6(b)

10(c)

10-3 Z8

22200 au

5 104 au

106 au464log < density6 >8810121012log < density>

10141410121412log < density 14>1616log n [cm-3]

Z/Z8 < 10-4  ⇒ dustsmall scale (< 103 au)  20

Onset of the gravitational collapse
3log M(< R) / MBE

log n [cm-3]

1510Z/Z8= 10-3

10-4

51

12time [106 yr]

3

Z/Z8= 10-3

10-4

010-6
0

Gravitationallyunstable2

Gravitationally stable

4-1

2

46log M(<R) [M⊙]  ⇒   
21

Mass distribution (1)
1000

Number-2

10
1-2

1000

Number-6-4

10-2

1000

Number1-4⇒sink 100
10-61-21000-4⇒ competitive accretion(e.g. Bonnel+2001),
 -1100-6Number

log10 Mdot [M8 yr-1]-4

Mass function

100

100
101-6-202

log10 Mass [M⊙]4-6-4-2-1

log10 Mdot [M⊙ yr ]028

Supermassive star or dense cluster?
(Sakurai+2017) 



300 au29

Detection rate of GWs
Nmerge = NDC fbinary fmerge /24(Haehnelt, 1994)(Habouzit et al, 2016)9 ,0SMS/.*#+"-%(6+#57 8!
,0 %$-4 &#%/GW,#'3$,&5$1)6-#!

Agarwal+2012
Habouzit+2016

this work

Dijkstra+201430metallicity
massive binary binaryseparation (SC+19)
mass ratio1

(a)

3000

2000

1000

08(b)
mass ratio

Z = 10-4 Z

separation [AU]

Massive binaries

10.5

00

5000

Time [yr]1000031