超大質量星形成過程における星周円盤の進化松木場

亮喜 (東北大学)

E. I. Vorobyov (ウィーン大学)
杉村 和幸(メリーランド大学)
細川 隆史(京都大学)
大向 一行(東北大学)

Outline
1. Introduction

2. Model3. Result

4. Summary and discussion

1. Introduction

Supermassive Black Holes (SMBHs)
High-z QSOs observation (e.g. SDSS and HSC)
111011z > 6 (cosmic age ≲ 1 Gyr)observed.
・ BH mass : 107-1010 Msun
Most distant one
z=7.54 (cosmic age~0.7 Gyr)
~Banados+18

7.5
7.5

7
7.0

6.5
6.5

66.0

SMBHs at z>6
BH mass (Msun)

・ More than 100 QSOs are

redshift

1010101099

1088

z = 7.54, 8×108 Msun
1077

0.7
0.7

0.8
0.9 De Rosa+11,
Willott+10,
Mazzucchelli+17,0.80.9
Chehade+18, Mortlock+11, Banados+18
Pons+19, Wang+18,
Tang+19
Onoue+19,
and Shen+19
cosmicage(Gyr)Jiang+07,Matsuoka+19,Reed+19,Wu+15,
Fan+19The origin of those BHs is still a mystery.

What is the formation scenario of high-z massive BHs?

bombarded by infalling gas. The resulting system (a“quasi-star”) is composed of a black hole that growsby eating its surrounding cocoon from the inside,although clues to the seeds’ properties may be foundin the lowest-mass MBHs, which may be the mostpristine objects due to their limited growth.

Formation scenarios of seed BHs
Pop IIIGas cools
very slowly
forming astable disc

Direct collapserrk matte
aD

Globally
unstable gas
infalls rapidly
toward thegalaxy centerand asupermassive
Supermassive star(SMS)
star forms

If the star isFirst stars:
more massive
maybe onethan ~300 solar
star permasses, itgalaxy, up
collapses intoto several
a black hole,hundred times~200 times thelarger than
2-3
MBH=10Msun
mass of Sun
the sunThe stellar
core collapses
into a small
black hole,embedded inwhat is leftof the star
MThe black holeswallows
the envelope
growing up
to ~one million
solar masses
BH=105 Msun

Stellar collisions
Locally
unstablegas flows
toward thegalaxy centersame fate
Digital S
TelescopGas
fragments
into stars,
and a densestar cluster
forms

Stars merge intoa very massive
star thatcollapses into a
black hole ~1000
times more
massive than3
MBH=10 Msun
the SunFig. 1. Illustration showing three pathways to MBH formation that can occur in a distant galaxyVolonteri(56). The12starting
point is a primeval galaxy, composed of a dark matter halo and a central condensation of gas. Most of this gas will
eventually form stars and contribute to making galaxies as we know them. However, part of this gas has also gone into

Thermal evolution of SMS formation
H2 formation is suppressedby FUV radiation.

temperature (K)105

・ Photodissociation

H2 +! H2 ⇤ ! 2H・ Photodetachment

H +!H+eH atomic cooling
104

103

H2 molecular cooling102

Accretion rate of H atomic cooling cloudMJṀ ⇠⇠ 0.1 Mt↵

yr 1

⇣

108

1012

1020

number density (cm-3)
Omukai 01

T ⌘3/2104 K

High accretion rate
✔ Stellar mass can reach 105 Msun within its lifetime.
✔ Protostar becomes ʻʻsupergiantʼʼ.

Hosokawa+12, 13

✔ Disk structurecsΩ
Q==1πGΣcsΩ
Σ=πG✔ Fragmentation conditionνΣ
α= 2 >1cs

maximum value of α parameter

Stability of the steady accretion disk
10Fragment
1Not fragment

0.1
10-3

10-2

10-1100accretion rate (Msun yr-1)
RM+19

When the accretion rate > 0.1 Msun yr-1, the disk becomes
gravitationally unstable and fragments.

The accretion ﬂow has time variation.

Motivation
If the accretion rate has time variation,
stellar radius decreases and the eﬀective temperature rises.
Ionization feedback becomes eﬃcient.
The length of time that accretion rate falls below 4x10-2 Msun yr-1.
is important.

Sakurai+15

We should investigate the time evolution ofthe accretion rate.
Previous work

Sakurai et al. (2016)

They used barotropic relation as EOS,
but gravitational instability depends on the temperature.

In this work, we follow the disk formation processwith detailed thermal and chemical treatments.

2. Model

Calculation model2D simulation, face-on●Sink cellradius rsink = 300 au●ChemistryH, H2, H+, e●Thermalheating : viscous, compression, stellar radiation
cooling : H2 line, continuum, Ly α, chemical cooling●Central stellar radiation
Lstar=LEdd, Teﬀ=5000 K

Hosokawa+12

Initial condition
Chon et al. (2016)
They identiﬁed two direct collapsecloud from the cosmological simulation.

Two dimensionalization●Core mass

Chon et al. (2018)

Sph : 5.2x104 Msun●

(Thermal energy)／(grav. energy)
α=0.24 (Fil), α=0.30 (Sph)●(rotation energy)／(grav. energy)
β=2.5x10-2 (Fil), β=3.6x10-2 (Sph)number density (cm-3)

Fil : 4.6x104 Msun
66
1010

core
551010initial proﬁle of density
4410101033

101044

1055

1010
radial distance (au)

1066

10

3. Result

Time evolution of gas density
log nH

6000

ﬁlamentary cloud4000

distance (au)20000-2000-4000-6000-6000-4000

-2000

02000

distance (au)

4000

6000

Spatial distributions
ﬁlamentary

10spherical4000

80-4000

number density

6clumps

5105

4000

104
T (K)

distance (au)7log nH (cm-3)

90
103
-4000

temperature
-4000

0102
4000

-4000

distance (au)04000

Gravitational instability of the disk
2100
10Q parameter1 kyr after disk formation

11010

Q∼11001

-1
100.1

5x102

3

10 3
102x103

radial distance (au)

Toomre Q parametercsΩ
Q=(>1stable,<1unstable)
πGΣ
Q~1 at 400 au < r < 800au
Spiral arms and fragments are formed by gravitational instability.

4. Summary and discussion

Time evolution of accretion rate
stellar mass [Msun]

4400004x1030000

15000 Msun
4200002x10
1000000

-1000

1020
2030

40
40

5060
60

70

1

101
10010010accretion rate [Msun yr-1]

spherical
ﬁlamentary

50000

stellar mass (Msun)

accretion rate (Msun yr-1)

4600006x10-11010-1

4x10-2 Msun yr-1

-21010-23000 yr-3-3
1010-1000

10time [kyr]20203040
40

50

time [kyr]time (kyr)time (kyr)spherical : Accretion rate is always greater than the critical value Mcrit.
ﬁlamentary : Accretion rate becomes less than Mcrit.
1/2

Surface KH time

M*tKH,surf ∼ 10 yr( 500 M⊙ )3

Sakurai+15tKH,surf = 6300 yr when 15000 Msun
Ionization feedback may aﬀect stellar evolution.

60
60

70

10000
104

disk

31000
10our model
barotropic
210100
3x102

103
103

3x103

104
104

1
101
10010010accretion rate [Msun yr-1]

temperature (K)5 kyr after disk formation

accretion rate (Msun yr-1)

Diﬀerence from the barotropic model-110-110-210-210-3
1010-3-10-1000

radial distance (au)1020

10 time [kyr] 20

3030time (kyr)The temperature at the disk is lower than in the case of barotropic.
More gravitationally unstable
The time variation of accretion rate becomes strenuous
due to the disk fragmentation.

More diﬃcult to form SMS

4040

Summary
We followed the SMS formation process using hydrodynamical
simulation with detailed thermal and chemical treatments.
✔ The formed disks are gravitationally unstable.
✔ Spherical : The accretion rate is always greater than the critical value.

Filamentary : The accretion rate becomes less than Mcrit for 3000 yr.
Ionization feedback may aﬀect the stellar evolution.
How massive can formed seed black holes be?

Future work✔ We should consider the stellar evolution and the eﬀect of ionization.
✔ What about other initial conditions?