宇宙史研究センター

成果報告&交流会

星団形成の輻射流体シミュレーション

福島肇(Hajime Fukushima)

Star cluster formation
Giant molecular cloud

Main sites of star formation.
(Lada & Lada 2003)

M42

Star cluster

SuperNovae

SunGlobular clusters
Open Clusters• Low mass ( ≲ 103 M⊙)• Young ( ≲ 0.3 Gyr)
• Low-density ( ≲ 103 M⊙pc−3)

Globular Cluster• Massive ( ≳ 105 M⊙)• Old ( ≳ 10 Gyr)
• High-density ( ≳ 103 M⊙pc−3)

Globular clusters (GCs) are more massive and compact
than open clusters.

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Star Cluster Formation

Star-forming
cloudsFeedback frommassive stars
Star cluster

HII regions

・Properties of star cluster formation in nearby galaxies:• Duration time of the star formation: 1-5 Myr.

• Star formation efficiencies: 1-10%(e.g., Fukui & Kawamura 2010, Kruijssen et al. 2019, Chevance et al. 2020)

Pre-supernova feedback suppresses the star formation.

Radiative feedback
HII region (ionized gas)

HI & H2 gas (non-ionized gas)

H+

H
C+
O

O+

UV radiation

H2
C+

C

CO

< 103 − 102 K

Tgas ∼ 104 K
Ionization
front

Photoionization feedback (EUV feedback):
Thermal pressure of ionized gas ( ∼ 104 K) pushes ambient gas.
(e.g., Dale et al. 2012, Geen et al. 2015, Kim et al. 2018, 2020, Ali et al. 2018)

To investigate the star cluster formation, we need to perform
radiation hydrodynamics (RHD) simulations.

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4
10
M
105 M
104 MØ 105 MØ<latexit

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40 pc<latexit

RHD simulations of star cluster(2) 4.7 Myr (1.0t↵ )MW

pcmaru sankakui shika 10
mash
20 pc
Æf
Æf
40 pc

101
Z
=
Z

0

101

Ø

10

°1 Z Ø

°
10
2 ZØ

]
Ø pc
Σ = Mcl /(πRcl2ß)[ M: surfacedensity°2

with that of the Milky Way.

The condition for massive star cluster formation is still unclear.
102(HF et al. 2020)

In the previous studies, we performed the simulation of open cluster

formation, and their star formation efficiencies (SFEs) are consistentBound fractions

Cloud

Star cluster

Unbound stars

fbd > 0fbd = 0Bound fraction:

fbd = (Bound stellar mass)/(Total stellar mass)
The bound fraction is determined with the timescale of gas
expulsion and the star formation efficiencies.
(e.g, Adams 2000, Baumgardt & Kroupa 2007, Shukirgaliyev 2019)

Bound fractions & SFE(shukirgaliyev et al. 2019)

Star formation efficiencies (SFEs) is need to be larger than 30% toform bound star cluster. (e.g, Adams 2000, Baumgardt & Kroupa 2007, Shukirgaliyev 2019)
To form bound star cluster, the mechanism which enhances the SFEs.

Method: Radiation hydrodynamic simulation•Self-gravitational AMR (M)HD + Sink particles(Matsumoto 2007, 2015)•Non-Equilibrium chemistry• H, H2, H+, H-, H2+, e, CII, OI, OII, OIII, CO•Heating & Cooling• Photoionization & photodissociation heating• Line cooling (CII, CO, OI, OII, OIII), dust cooling・Chemical heating & cooling(Sugimura et al. 2020, CO network:Nelson & Langer 1997)•Radiation transfer with moment method (M1-closure, reduced speed of light)
・EUV photons
・FUV photons (H2, CO photodissociation)
・Dust thermal emission(HF & Yajima 2021)

Initial conditions
・Uniform density sphere with the turbulent motions
・Cloud masses: Mcl = 105,106 M⊙
・Radius: 5 − 60 pc
・Surface density: Σcl = Mcl /(πRcl2 ) = 80 − 3200 M⊙pc−2
・Virial parameter: α0 = 2K/Ug = 1, σv(λ) ∝ λ 1/2・Sink Particles:
・Sink radius: Rsink = 0.59 pc (Rcl /20pc)(Matsumoto et al. 2015, Gong & Ostriker 2013)

・Light-to-mass ratios are constant (Chabrier IMF)

Sink particles represents
the mini star clusters.

Massive star cluster formation(Fukushima & Yajima 2021, MNRAS, vol506, 5512)

Massive star cluster formation(Fukushima & Yajima 2021, MNRAS, vol506, 5512)

Stars are embedded

Globular clusters

Stellar density is smilar to GCs.

(1) (Mcl, Rcl, Z) = (106M⊙,20pc, Z⊙)
40

103

0

102

−20

y [ pc ](1) 0.6 Myr ( 0.4 tff )(2) 1.9 Myr ( 1.3 tff )(3) 2.9 Myr ( 2.0 tff )(4) 4.4 Myr ( 3.0 tff )

20

1022

0

1021

−20

1020

−40
40

1024

20

1023

0

1022

−20

1021

−40
40

1020

20

1019

0

1018

−20

1017

−40

−25

0
x [ pc ]

25

−25

0
x [ pc ]

25

−25

0
x [ pc ]

25

−25

0
x [ pc ]Nel [ cm−2 ]1023

NH2 [ cm−2 ]y [ pc ]y [ pc ]−40
40

NCO [ cm−2 ]y [ pc ]20Σ [ M" pc−2 ]

104

25

Σ: Surface densities, Nel: Column density of electron, NH2: H2, NCO: CO(1) (Mcl, Rcl, Z) = (106M⊙,20pc, Z⊙)

Core structureappears

40

103

0

102

−20

y [ pc ](1) 0.6 Myr ( 0.4 tff )(2) 1.9 Myr ( 1.3 tff )(3) 2.9 Myr ( 2.0 tff )(4) 4.4 Myr ( 3.0 tff )

20

1022

0

1021

−20

1020

−40
40

1024

20

1023

0

1022

−20

1021

−40
40

1020

20

1019

0

1018

−20

1017

−40

−25

0
x [ pc ]

25

−25

0
x [ pc ]

25

−25

0
x [ pc ]

25

−25

0
x [ pc ]Nel [ cm−2 ]1023

NH2 [ cm−2 ]y [ pc ]y [ pc ]−40
40

NCO [ cm−2 ]y [ pc ]20Σ [ M" pc−2 ]

104

25

Σ: Surface densities, Nel: Column density of electron, NH2: H2, NCO: CO(2) (Mcl, Rcl, Z) = (106M⊙,40pc, Z⊙)y [ pc ]

103

0

°50

102
(1) 2.2 Myr ( 0.5 tÆ )(2) 5.6 Myr ( 1.3 tÆ )(3) 8.5 Myr ( 2.0 tÆ )

ß [ MØ pc°2 ]

104

50

(4) 12.5 Myr ( 3.0 tÆ )y [ pc ]

50

1022

0

1021

°50

1020

Nel [ cm°2 ]1023

y [ pc ]

50

1023

0

1022

°50

1021

NH2 [ cm°2 ]1024

y [ pc ]

50

1019

0

1018

°50

1017
°50

0
x [ pc ]

50

°50

0
x [ pc ]

50

°50

0
x [ pc ]

50

°50

0
x [ pc ]NCO [ cm°2 ]

1020

50

Σ: Surface densities, Nel: Column density of electron, NH2: H2, NCO: COSFEs vs Surface density
Time evolution of total stellar mass
Mcl = 106 M⊙, Rcl = 20, 25, 30, 32.5, 35, 40 pc
0.8
0.7

R cl =

0.6
M§/Mcl

0.5

c
p
0
2

0.4
0.3
0.2

Σcl ≃ 200 M⊙pc−2

Rcl = 40 pc

0.1
0.0
0.5

1.0

1.5

2.0
t/tÆ

2.5

3.0

300 M⊙pc−2

3.5•Rapid increase of SFEs occurs at Σcl ∼ 300 M⊙pc−2.
•The histories of star formation are almost the same until ∼ 1.3 tff.

Relations between SFEs and bound fractions
Time evolution of total stellar massTime evolution of bound fraction ( fbd)

Mcl = 106 M⊙, Rcl = 20, 25, 30, 32.5, 35, 40 pc
0.8
0.7

R cl =

0.6(106MØ, 20 pc)

1.0

c
p
0
2

0.8

0.5

fbd

M§/Mcl

0.6

0.4
0.3

0.4

0.2

0.2

Rcl = 40 pc

0.1
0.0
0.5

1.0

1.5

2.0
t/tÆ

2.5

3.0

3.5

0.0
0.5

1.0

1.5

2.0
t/tÆ

2.5

3.0

• Bound fraction:
fbd = (gravitationally bound stellar mass)/(total stellar mass)• When the bifurcation occurs, the bound fraction of stars rapidly increases.
The epoch of the bifurcation corresponds to that of the stellar
core formation (t ∼ 1.3 tff).

3.5

Stellar core formation(a) Cloud evolution(b) Gravitational potential
ϕ(1) Start of starformationϕ(2) Stars begin to
gravitationally bindeach other.

ϕ(3) Thermal pressurecannot pushes ambientgas. Runaway starformation occurs.

Condition of stellar core formation :Velocity of expanding shell (vsh) < escape velocity from the core vesc

Condition of stellar core formation(1) Σcl = 260 M⊙pc−2 (2) Σcl = 300 M⊙pc−2

0.8
0.7

M§/Mcl

140pc

0.5

130pc

0.6

0.4
0.3
0.2
0.1
0.0
0.5

1.0

1.5

2.0
t/tÆ

2.5

3.0

3.5

Condition of stellar core formation :Velocity of expanding shell (vsh) < escape velocity from the core vesc
vsh < vesc =2GMcoreRcore

Mass: Mcore ∼ 0.1 × 0.1Mcl Radius: Rcore ∼ 0.1Rcl
Shell velocity: vsh,th ≃ 4.9 km /s
−1/5

−2

Σcl > Σth ≃ 280 M⊙pc

Mcl
( 106 M⊙ )Ti
( 8000 K )28/25

The stellar density rapidly increases with the surface density of clouds.

Young massive star clusters
There are two population of young massive star cluster.
・Young massive star cluster (YMCs)
YMCs

⚪︎
⚪︎

Mass: Mcl > 104 M⊙

Stellar density: ρc ≳ 103 M⊙ pc−3

・Leaky Star Clusters (LSCs)
t
LSCs

⚪︎

Mass: Mcl > 104 M⊙⚪︎Stellar density: ρc < 103 M⊙ pc−3
(Portegies Zwart et al. 2010)(Pfalzner 2009)

In addition, we suggest that globular clusters are relics of the morecompact clouds than that of typical one in the Galaxy.

Summary

We perform radiative hydrodynamics simulations of star cluster
formation.
We estimate the condition of the dense stellar core formation:
−1/5

Mcl
−2
Σcl > Σth ≃ 280 M⊙pc
( 106 M⊙ )Ti
( 8000 K )28/25@ Z = Z⊙We will consider the observational signatures of YMC formation.