Simulating Pop III multiple formation
under radiation feedback
Kazuyuki Sugimura(Univ. of Maryland, Tohoku Univ.)
Collaborators: T. Matsumoto (Hosei., Princeton)
T. Hosokawa (Kyoto), K. Omukai (Tohoku)
S. Hirano (Kyushu)
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Contents
pIntroduction• Pop III (binary/multiple) formation

pMethods• code, simulation set-up

pResults• simulations of multiple Pop III star formation

pConclusions
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INTRODUCTION

3Formation of Pop III stars
pFrom Big Bang to first objects (= Pop III stars)

z = 1100ⒸNASAzform 〜 20-30• Well-established initial condition and relevant physics
make first principle study possible• Former analytical/numerical works have revealed the outline• A next important step is to properly follow binary/multipleformation

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Why Pop III binaries/multiples?
1. They can be of dominant population of Pop III stars• most of present-day massive stars found in binaries/multiples> 80% of O stars are in multiple systems (Duchene and Kraus 2013)vssingle starbinary/multiple

2. They are also interesting because...
•they can be progenitors of observed GW events•

their contribution to the cosmic evolution is likely quite
different from that of single Pop III stars

GWBHBH(reionization, first galaxy formation, Pop III to Pop II transition, ...)
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Pop III multiple formation in former
3D simulations(Hosokawa+16)(see also Stacy+16)

p SPH simulation (Susa+14)

p Spherical grid simulation
The Astrophysical Journal, 824:119 (26pp), 2016 June 20• effectively
NO feedback byionizing photons→ multiple stars• fragmentation
not well resolved• radiation onlyfrom central star→ single starAll former simulations miss at least one of the essential
processes in Pop III multiple formation

New simulations with new code!!

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METHODS
Simulation code & setup

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Recipe for new codeü self-gravitational (M)HDü AMR
ü sink particle
ü Ray tracing ofEUV, FUV photons(Matsumoto 2007)

Adaptive Ray-Tracing(Abel&Wandelt 2002)

ü prim. chem./thermodynamics
ü protostellar radiation

Pop III physics(Hosokawa+ 2016)

New code for Pop III binary formation!!
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SFUMATO(Matsumoto 2007)• MHD (AMR)
Adaptive Mesh Refinement= high resolution where you need it

Level 0minimum unit = cell
grid = collection of cells

Level 1• Selfgravity• Sink particle

refinement of gridOct-tree type block structure

9Adaptive Ray Tracing (ART) Method
p HEALPix (Górski+ 2005)
ü Library originally for CMB analysis
ü Split sphere into 12 x 4level patchesp Adaptive Ray Tracing method

level 0level 1level 2

(Abel&Wandelt 2002, Wise&Abel 2011)

ü Rays are split with HEALPix to ensure the minimum # ofrays penetrating each cell surface
ü Tracing direct EUV/FUV photons from protostars

EUV (>13.6eV)
FUV (11.2-13.6eV)protostarH photo-ionization
H2 photo-dissociation
10Figure 2. Illustration of how one base ray spawns child rays to sample

Physics modelof Pop III formation(basically same as Hosokawa+ 2016)

p Prim. chemistry (H, H2, e, H+, H-, H2+, (He))• chemical reactions
H photo-ion., H2 photo-dis., H- photo-det., H+ rec.,
H-/H2+-channel & 3-body H2 formation, etc.

• cooling/heating processes
H photo-ion heat., H+ rec. cool., Lyα cool,free-free cool., H2 line cool (w/ fesc),chemical heat/cool, etc.

chemistry module check by1-zone evolution calculation

10-2 Msun/yr
10-3 Msun/yr

p Pop III proto-stellar radiation
pre-calculated table from stellar evolution code(𝑀∗ : 10-1—103 Msun, 𝑀̇: 10-5—10-1 Msun/yr)(𝑀∗ , 𝑀̇) → (𝑅∗ , 𝐿∗ )→ (𝑁̇,-. , 𝑁̇/-. ) (blackbody)pre-calc. Pop III star model

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Initial conditions forSFUMATO
cosmologicalinitial condition
Mass of primordial stars

571

SFUMATO
initial conditioncomp. box
Gadget cosmo.
sim. (Hirano+15)

12Simulation Parameters•

Initial conditions

typicalHosokawa+16 (H16)

The Astrophysical Journal, 824:119 (26pp), 2016 June 20

low-mass

Minihalos “C” and “D” in H16•box size•

sink radius/minimum cell size

〜105 au
64 au/4 au•

refinement condition for AMR>16 cells per λJ•

computational cost〜 512 cores x 6 months

What’s new?

Figure 2. Time evolution of the stellar masses (a) and accretion rates (b) forcases A (green), B (blue), C (black), D (red), and E (magenta). The time t= 0
corresponds to the formation of embryo protostars.

ü AMR makes it possible to achieve 10 times better resolution comparedwith H16 in the outer part of disks wherefragmentation
isgasmostactivehomogeneous,zero-metallicity
cloud insolid body rotation
üwith constant density, temperature, and chemical composition.
ART makes it possible to treat radiation
multiple
proto-Pop
IIIdiscussed
stars in13theThefrom
results ofthese idealized
simulations areAppendix. These more simpliﬁed initial conditions allow us toRESULTS

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a typical pop III formation site

CASE OF MINIHALO “C”

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3D movieyr

8000auhalo C (typical Pop III formation site)150 (a)M [M ]

Sink particle
evolutionhalo C (typical Pop III formation site)Ṁ [M /yr](a) grav. collapse(b) initial frag.
(c) binary evl. via acc.

(c)

(d)

(e)

100S250
05 Evolutionary phases(b)

S1S4S3S5S6S8S710−2
10−3
10−410−5(d) late-time frag.
(e) photo-evaporation∆r [au]104
3 -4103
2

1 -7

1 -3

1 -5
1 -2Merger

10−15 0

6 -8

1 -6

1

(t: time after 1st sink formation)

2t [104 yr]

3 468 10

halo C (typical Pop III formation site)

Five Evolutionary Phases(a) gravitational collapse−1.5×105 yr(b) initial fragmentation

4 km/s

2.7×103 yr

10105 au(e) photo-evaporation
7.2×104 yr

Ionization front-3

H54

1.8×104 yr

S3
S1 n [cm ]10S4nH [cm-3]
106
10(c) binary accretion

10 km/s

111010S3

1091000 au

S1(d) late-time fragmentation
30 km/s

2.2×104 yr

S7S3
S1 + S6 + S7

S1104 au

4000 auΣ [g cm-2]
1 10 102

15 km/s

S6S34000 auΣ [g cm-2]
10 102 103

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Summary of simulation for Case C• We use the initial condition from which a single 300 Msun
Pop III star was formed in Hosokawa+16• Although we are still running the simulation, the mainaccretion phase has (hopefully) ended• The final(?) product is a massive wide binary of single andclose triplet
200 au60 Msun

103 au>104 au
50+10+10 Msun

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a formation site of small Pop III star(s)CASE OF MINIHALO “D”

20halo D (formation site of small Pop III)au

Surface density (face-on)

au

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100

M [M ]

Sink particle
evolution

halo D (formation site of small Pop III)(b)(a)Ṁ [M /yr](a) grav. collapse(b) initial frag.

(d)

50S104 Evolutionary phases(c)

S2S310−210−310−410−5(d) photo-evaporation104∆r [au](c) binary accretion

1 -3103210−31

1 -2Merger

02(t: time after 1st sink formation)

4t [10 yr]
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Summary of simulation for Case D• We use the initial condition from which a single 80 Msun
Pop III star was formed in Hosokawa+16• The entire formation process has been followed in thesimulation (accretion rate of each star reaches zero)• The final product is a massive wide binary

60 Msun〜104 au30 Msun
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CONCLUSIONS

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Summary• We have performed simulations of entire Pop III multiple
formation: from cosmological initial conditions to theend of accretion phase• We have developed a new code with AMR + Pop III phys.
+ ART, capable of following both fragmentation andionization feedback• In two out of two different halos studied in this work,
the final products are massive Pop III binaries/multiples

Pop III stars typically form as massive multiple stars!
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