Metal-­‐poor	  star	  formation	  through	  fragmentation	  of	  accretion	  disks
Gen	  Chiaki	  (Georgia	  Tech)
Naoki	  Yoshida	  (University	  of	  Tokyo)
Nagoya, November	  11, 2019

Research	  aim

To	  know	  Mass	  scale and	  multiplicity ofMetal-­‐free	  (Pop	  III)	  star and	  metal-­‐poor	  (Pop	  II)	  star	  formation	  Population	  Metal-­‐free	  Supernova
III	  
cloudstar
Metal	  enrichment

He24%

H76%

Metal-­‐poor	  cloudSupernova
Metal-­‐poor	  stars
Metal	  enrichment

Present-­‐day	  stars
Metal
1.3%
He24%

Metal	  enrichment

H76%

also	  see	  T.	  Hartwig,	   T.	  Kirihara and	  A.	  Choplin’s talks

Mass	  scale:Observations	  of	  metal-­‐poor	  stars.
Low-­‐mass	  stars	  are	  dominant
Salpeter IMF
Mass	  func.

Small	  number	  of	  EMP	  stars.
Still	  top-­‐heavy IMF?
but	  low-­‐mass	  stars	  form
Mass	  func.

9

Carbon abundance
A(C)
A(C)

Mass	  func.

No	  metal-­‐free	  stars.
Top-­‐heavy IMF?

810	  	   	  	  	  	  	  	  	  	   	  1000
7 [M☉]
Stellar	  mass	  Our	  sun0.1	  	  	  	  	  	   	  	  	  	  1Stellar	  mass	  [M☉]?
Stellar	  mass	  [M☉]65

SAGA	  database	  (Suda et	  al.	  2008)

4-9-8-7-6-5-4-3[Fe/H] [Fe/H]
Iron abundance-2-10

Multiplicity:
Binary	  Ultra	  metal-­‐poor	  stars

2MASS	   J18082002–5104378

0.76	  M☉B

0.2	  au
0.14	  M☉

[Fe/H]	  =	  −3.50

Stellar	  mass	  and	  multiplicity	  are	  affected	  by	  fragmentation
Two	  modes	  of	  fragmentation••

Cloud	  fragmentation	  (thermal	  instability)
Disk	  fragmentation	  (gravitational	  instability)
Larson	  (1969);	  Penston (1969);	  Chiaki	  et	  al.	  (2016)

Collapsing	   phase

MolecularCloudcloudfragmentation
Accretion	  phase
Protostar(s)DiskAccretion
fragmentation
disk

Cloud	  fragmentation(Omukai et al. 2000; Schneider et al. 2003)

condensates	   of	  metal<0.1	  μm in	  ISMlog [Temperature / K]

Dust	  grains

MJ=106M⊙ 104M⊙ 102M⊙

32−2−1

100

Moyce et	  al.	  ( 2015)−5−4−301M⊙

10-2M⊙

481216log [Hydrogen number density / cm-3]

CCTime	  sequenceüDust	  cooling	  operates	  high	  density (~1014 cm−3),=ülow Jeans	  mass	  (~0.01-­‐0.1	  M☉)

Cloud	  fragmentationTsuribe &	  Omukai (2006)

Safranek-­‐Shrader et	  al.	  (2014)

Smith	  et	  al.	  (2015)

Chiaki	  et	  al.	  (2016)

also	  see	  D.	  Nakauchi and	  H.	  Fukushima’s	   talks

Disk	  fragmentation

Clark	  et	  al.	  (2011)

Greif	  et	  al.	  (2012)

Machida	  &	  Nakamura	  (2015)

Hosokawa	  et	  al.	  (2016)

Hirano	  et	  al.	  (2017)

Susa	  et	  al.	  (2019)

also	  see	  H.	  Washinoue,	   T.	  Hosokawa,	  S.	  Chon,	   K.	  Higuchi,	   and	  N.	  Yoshida’s	  talks

In	  this	  work,	  we	  investigate	  conditions	  for	  cloud/disk	  fragmentationin	  metal-­‐free	  and	  metal-­‐poor	  gas	  clouds
with	  numerical	  simulations
Collapsing	   phase

Accretion	  phase

Cloudfragmentation

Disk
fragmentation100-­‐400	  yrWe	  do	  not	  use	  sink	  particle	  techniqueand	  follow	  accretion	  phase	  for 100-­‐400	  yr.

Numerical	  method•

Code
Chemistry

AREPO

Box	  Size
Boundary	  condition
Refinement
Cell	  massDM	  particle mass1.15	  kpcPeriodic
Jeans	  criterion
λJ >	  32	  Δx
5	  M☉→ ~10-­‐7 M☉
25	  M☉
No	  refinement

GRACKLE

Springel et	  al.	  (2010)
Smith	  et	  al.	  (2017);	  Chiaki	  &	  Wise	  (2019)

In	  high	  density	  region	  (>	  1016 cm-­‐3),	  we	  impose	  stiff	   EoS (γ=4).
(Machida	  &	  Nakamura	  2015;	  Susa	  2019)••

We	  do	  not	  employ	  sink-­‐particle	  technique	  but	  resolve hydrodynamics	  of	  protostars.

100	  chemical	  reactions	  for	  48	  species	  in	  three-­‐dimensional	  simulations
48	  primordial	   chemistry38	  metal	  chemistry10	  grain	  growth	   reactions

H2 formation	  on	   grain	  surfaces
2H + grain → H2(g) gas-­‐phase, (s) solid-­‐phase+	  Detailed	  radiative	  cooling	  processesC	  II,	  C	  I,	  and	  O	  I fine-­‐structure	  cooling
calculate	  level	  populations
opacity	  for	  each	  transition	  line	  ( one-­‐zone	  m odel)
integrate	  cooling	  rates
C II

3	  vibrational levels(1) P3/2
157.7 µm

(1) 3P1(0) 3P02(0) P1/2

369.0 µm

CO,	  OH,	  and	  H2O	  rotation	  transition	  line

609.2 µminterpolated	  from	  tables	  presented	  byCO	  (Omukai et	  al.	  2010)
OH	   (Neufeld	  &	  Kaufman	  1993)
H2O	   (Neufeld	  et	  al.	  1995)
from	  Nmol,	  T,	  and	  nH2 of	  each	  cell

OI(4) 1S0(2) 3P05577 Å(1) 3P1(3) 1D2

145.6 µm
63.1 µm

×1006300 Å3(0) P2

H2 formation	  heatingBinding	  energy	  of	  H2	  is	  converted	   into	  thermal	  energy

HH
4.48	  eVH H

3 vibrational levels
20 rotational	  levels

HD	  rotation	  transition	  line	  coolingCI2(2) 3P2

H2 ro-­‐vibration	  transition	  line	  cooling

Dust	  physics

calculated	  for	  each grain	  size bininterpolated	  from	  a	  table

Dust	  cooling	  rate
Dust	  continuum	   opacity
H2 formation	  rate	  on	  dust
Grain	  growth	  ratecomposition	   of	  grain	  species
with	  arbitrary grain	  size	  distribution

Initial	  conditions:	  2	  minihalos
with	  longest/shortest	  collapse	  time
taken	  from	  Hirano	  et	  al.	  (2014)

Longest	  col.	  time

Shortest	  col.	  timeID

H1

H2Formation	   redshift

15.15

20.46

Virial mass	  (DM)
Virial mass	  (gas)8.1×104 M☉
1.6×104 M☉

1.4×105 M☉
2.0×104 M☉

Virial radius

37.5	  pc

26.5	  pc

Collapse	  timescale	  depends	  on	  gravitational	  potential	  of	  MHslog [ tcol / tcol,0 ]Collapse timescale~100	  MHs	  from	  Hirano	  et	  al.	  (2014)

𝑡"#$	   = 	  𝜌𝜌̇𝑡"#$,*	   = 	  124𝜋𝐺𝜌

Slowlycollapse
Shallow
potential

H2

H1

Rapidlycollapse
Deep
potential

log [ GMhalo / Rhalo ]Gravitational potential of MHs

Metal/dust	  model
Metal/dust	  is	  uniformly	  distributed	  in	  the	  minihalos.
Nucleosynthesis	  and	  dust	  formation/destruction	  model(Umeda &	  Nomoto 2002;	  Nozawa et	  al.	  2007)• Pop	  III	  SN	  with	  MPopIII =	  30 M☉• Ambient	   gas	  density	  nH,amb =	  1	  cm-­‐3Collapsing	  phase

With	  cell	  refinement,	  we	  can	  resolve
0.01	  AU in	  ~1	  kpc	  simulation	  box!

Chemical	  evolution
log [ Abundance ]H1 Z = 10−4 Z☉
SiMg

MgSiO3 (dust)
Mg2SiO4 (dust)
SiO

Grain	  growthlog [ Density / cm−3 ]Temperature	  evolution	  in	  collapsing	  phase• Higher	  metallicity	  → Lower	  temperature• Shorter	  collapse	  time	  for	  H2 → Higher	  temperature

Collapsing	  phaseH2 form.	  heating

H2 form.	  heating

1.	  HD	  cooling	  → Filamentary	  structure
2.	  H2 formation	  heating	  → Stable	  core
3.	  Dust	  cooling	  → Filamentary	  structureAccretion	  phase
H1 10-5 Z☉

No	  cloud	  fragmentation
but	  disk	  fragmentation occurs
0.14
1.8

0.71
0.10

0.80

0.33 0.14

0.31

0.58

0.58

0.47

0.097

0.026 0.025

Unit: M☉
0.018

0.012
0.82
2.1

0.13
0.35
0.37

5.6

1.7

1.1
0.011

0.16
0.39

0.015

1.4

0.012

Similar	  morphology	  of	  accretion	  disksregardless	  of	  metallicity!

Unit: M☉

Cloud	  fragmentation	  does	  not	  occur	  because…

••

For	  <	  10-­‐5 Z☉,	  insufficient	  dust	  cooling.
For	  >	  10-­‐5 Z☉,	  clouds	  become	  stable	  through	  rapid	  gas	  heating	  through	  H2 formation.

HH
4.48	  eVH H

Mass	  evolution	  of	  protostars• Protostellar mass: 0.52-­‐3.8	  M☉ for	  100-­‐400	  yr• Average	  mass	  accretion	  rate:• H1:	  1.30×10-­‐3-­‐1.30×10-­‐2 M☉/yr• H2:	  7.11×10-­‐3-­‐3.77×10-­‐2 M☉/yr

At	  most	  26	  protostars	  form	  but	  only	  1-­‐5	  protostars	  survive#	  of	  forming	  protostars#	  of	  surviving	  protostars

Criteria	  for	  protostar	  formation
Formation	  paths
1. Gas	  accretion
2. Break-­‐up	  of	  protostars
3. Interaction	  of	  spiral	  arms

Protostar	  formation	  (1)Gas	  accretion

Criterion	  for	  mass	  accretion• dM/dt >~	  10-­‐2 M☉/yr• Z <	  10-­‐6 Z☉

Protostar	  formation	  (2)Break-­‐up	  of	  rapidly	  rotating	  protostar

0 Z☉

10-6 Z☉

10-5 Z☉

Criterion	  for	  break-­‐up>	  0.02

10-4 Z☉

10-3 Z☉

J:	  angular	  momentum
ρ*:	  density
M*:	  mass	  of	  each	  protostar

Protostar	  formation	  (3)Interaction	  of	  spiral	  arms

Criterion	  for	  protostar	  formation< 0.6along	  the	  spiral	  arms	   (Takahashi	  et	  al.	  2016)

Criteria	  for	  protostar	  destruction
Destruction	  paths
1. Merger
2. Tidal	  disruption	  events	  (TDEs)

Protostar	  destruction:	  Merger/TDEs

MergerTDE

Merger

TDE

v2

a1bv1

v2
ba1

b < a1v1

b > a1

Survival	  of	  protostars

Even	  in	  the	  case	  with	  highest	  accretion	  rate,	  •>	  20	  protostars	  form
•but	  most	  of	  them	  merge	  with	  each	  other.
•Oligarchical	  growth occurs.	  Summery	  and	  conclusion• We	  study	  mass	  scale	  and	  multiplicity	  for	  Pop	  III	  to	  Pop	  II	  stars.
•Numerical	  simulations	  with	  complete	  chemical	  models.

• Disk	  fragmentation	  occurs	  for	  all	  runs	  u Two	  minihalos	  with	  large/small	  accretion	  rates
1. 1.30×10-­‐3-­‐1.30×10-­‐2 M☉/yr
2. 7.11×10-­‐3-­‐3.77×10-­‐2 M☉/yru Metallicity	  with	  0-­‐10-­‐3 Z☉• Evolution	  of	  accretion	  disks	  for	  100-­‐400	  yru Protostellar mass: 0.52-­‐3.8	  M☉
u At	  most	  26	  protostars	  formu Through	  merger/TDEs,	  1-­‐5	  protostars	  survive• Conclusion	  u Binary/Cluster	  formation occurs	  in	  general with	  <	  10-­‐3 Z☉.

Cloud	  fragmentation
Bromm et	  al.	  (1999);	  Omukai (2000);	  Hanawa &	  Matsumoto	  (2000);
Schneider	   et	  al.	  (2002);	  Frebel et	  al.	  (2005);	  Tsuribe &	  Omukai (2006)

With	  metallicities	  Z <	  10−5 Z☉

Temperature

only	  H2 cooling→ collapsing	  clouds	  are	  stable	  against	  deformation→ collapse	  into	  a	  single	  massive	  starTroughTimeCloud	  fragmentation
Bromm et	  al.	  (1999);	  Omukai (2000);	  Hanawa &	  Matsumoto	  (2000);
Schneider	   et	  al.	  (2002);	  Frebel et	  al.	  (2005);	  Tsuribe &	  Omukai (2006)

With	  metallicities	  Z >	  10−5 Z☉

Temperature

additional	  cooling→ collapsing	  clouds	  are	  unstable	  against	  deformation→ collapse	  into	  low-­‐mass	  star	  cluster

TroughTimeConditions	  for	  disk	  fragmentation	  and	  survival	  of	  protostars
What	  condition	  for	  disk	  fragmentation?
Still	  under	  the	  debate.

•••••<	  1	  (Toomre 1964)
Cooling	  time	  <	  dynamical	  time	  (Gammie et	  al.	  2001)
Q	  <	  0.6	  in	  spiral	  arm	  (Takahashi	  et	  al.	  2016)
Modified	  linear	  analysis	  (Inoue	   et	  al.	  2018)
Avoid	  Type	  I,	  II,	  and	  Roche-­‐lobe	  overflow	  migration (Chon	  &	  Hosokawa	  2019)	  • Avoid	  Type	  I	  migration	  and	  tidal	  disruption (Liao	  et	  al.	  subm.)

In	  Pop	  II	  star	  formation,	  several	  othercooling	  processes	  are	  also important.
Chiaki	  et	  al.	  (2015; 2016)

Grain	  growthlog [Temperature / K]

6MJeans=10 M⊙410 M⊙

3enhances	  gas	  cooling

21 M⊙

10 M⊙

metalmolecule

10−6Z6Z☉

dustgrain

10Z5−5 Z☉

2H2 formation	  heatingstabilize	  the	  gas

-2

MJeans=10 M⊙

Z410−4 Z☉

w/o grain growth
w grain growth

N07M30n1
04

812-3log [Density / cm ]16H

H
4.48	  eVH H

Future	  works• To	  follow	  further	  evolution	  of	  accretion	  disks• with	  sink	  particle	  technique	  coupled	  with	  RT.
• To	  start	  from	  cosmological	  simulations	  with	  metal	  enrichment	  from	  Pop	  III	  SNe (with	  M.	  Magg).
• To	  see	  the	  effect	  of	  magnetic	  fields	  on	  fragmentation	  and	  amplification	  of	  magnetic	  fields	  (with	  W-­‐T.	  Liao).

Disk	  Fragmentation
Thomas	  Greif’s	  contributions

Thomas Greif(*Feb 17 1981- †Sep 27 2019)

Greif	  et	  al.	  (2012)