How Massive are the First Stars?

Statistical Study of the primordial

star formation MpopIII

ALMA 時代の宇宙の構造形成理論 @ 北海道大学 / Jan. 26-28, 2013

○ Shingo Hirano1

Takashi Hosokawa1, Naoki Yoshida1, Kazuyuki Omukai2, H.W.Yorke3

1University of Tokyo, 2University of Kyoto, 3JPL/Caltech

Variety of PopIII protostellar evolution

3 protostellar accretion paths

MpopIII = 10 – a few 100 Msun

How Massive are the First Stars?2

Primordial HaloCosmological Simulation

z =17

Protostar Core ( ~ 0.01

[Msun] )

600 kpc/h (comving)

Accretion Phase of

the Primordial Protostar

■ Different thermal evolution

(main coolant is H2 molecular)

　 Mcloud ~ 1000 [Msun]

ZERO metallicity

■ No Metal & Dust

　 No radiation pressure (?)

(cf, PopII, I star formation)

MpopIII ~ 1000 [Msun] (?)

UV Radiative Feedback

Stalls mass-accretion

UV Radiative Feedback3

Ultraviolet (UV; hν > 13.6 [eV]) radiation from the protostar Ionizing infalling neutral gas & creating HII region Thermal pressure of the ionized region (high temperature)

is much greater than that in neutral gas of the same density

McKee & Tan (2008)

Gas on the circumstellar disk

is photo-ionized & heated

photo-evaporation

Growth of HII region

Breakout & Expansion

Accreting star emits

the ionizing UV photons

Accretion History of Protostar5

MpopIII = 43 [Msun]

moderate massive

Acc

reti

on R

ate

[Msu

n/y

rs]

… however,

MpopIII depend on the initial quantities :

Primordial Star–Forming Cloud

Can be calculated byCosmological Simulations

Hosokawa et al. (2011)

Radiative Hydrodynamics (RHD)

Protostar Evolution

UV radiative feedbackMass Accretion

Mstar [Msun]

Aim & Method6

Determining the initial mass distribution of the PopIII stars

(massive side; in case of the single-star formation)

■ Cosmological Simulation primordial star-forming halos

■ RHD + Stellar Evolution accretion histories

Cosmological Simulation

Accretion Histories

MpopIII

DistributionPrimordialGas Clouds

Cosmological Simulation

7

Cosmological Simulation8

GADGET-2 : parallel SPH+N-body code (Springel 2005)

+ Primordial Chemistry (Yoshida et al. 2006, 2007)

Initial Condition : zini = 99, WMAP-7 (Komatsu et al. 2011)

+ zoom-in re-simulation technique

Mresolve, init < 500 [Msun] < Mcloud

Stop calculations when the collapsing center becomes :

ncen ~ 1013 [cm-3] (Lresolve ~ 10-5 ｰ 10-4 [pc] ~ 2 ｰ 20

[AU])

Nsample Lbox [kpc/h](comving)

Nzoom Lsoft [pc/h](comving)

Lsoft [pc](z=19)

msph

[Msun]

7 1000 3072 6.5 0.46 0.867

98 2000 3072 13.0 0.92 6.94

Primordial Star-Forming Clouds9

108 halos @ Ncen ~ 1012 [cm-3]

3.2 r

R [pc]

NH [c

m-3]

Gao et al. (2007)

Density profiles evolve self-similarly

Infall Rate of Collapsing Cloud

Infall Rate [Msun/yrs] =

10

Menclosed [Msun]

Infa

ll R

ate

[Msu

n/y

rs]

)()(4 inf2 RvRR all

~ 10-3 – 10-1

Menclosed [Msun]

Vra

d [k

m/s

ec]

NH [c

m-3]

Characteristic quantities of clouds :

Protostellar Accretion Phase

11

Protostellar Accretion12

Using the setting & method in Hosokawa et al. (2011)

Radiative Hydrodynamics (RHD)

■ 2D-axsymmetric

■ Self-gravity, Hydro

■ Primordial Chemistry (15 reactions with H, H+, H2, H-, e)

■ Radiative-transfer : cooling, feedback

■ Lcell,min ~ 25 [AU], Lbox = 1.2 [pc], Mtotal ~ few 1000 [Msun]

Protostar Evolution

Mass Accretion UV radiative feedback

＊ For calculating the case of the high mass accretion rate,

we adopt a simple model of the stellar evolution

“Super-Giant” Protostar13

Hosokawa et al. (2012)

Mstar [Msun]R

star

[Rsu

n]

Menclosed [Msun]

Infa

ll R

ate

[Msu

n/y

rs]

dM/dt > 0.04 [Msun/yrs] No KH contraction (“Super-Giant” Protostar )

dM/dt > 0.004 [Msun/yrs] Ltot(M)|ZAMS > Ledd, cannot reach ZAMS

Model of “Rebound” Phase14

Hosokawa et al. (2012)

Mstar [Msun]

Rst

ar [R

sun]

1

①

②2

* Ignore expansion phenomena

By expansion, the effective temperature, Teff,

decreases

this phase is not important for the UV radiative

feedback

　 Ltot ~ Ledd

Scaling : Rstar //

RZAMS

Lstar // LZAMS　 dM/dt < 4E–3 [Msun/yrs]

Contraction to

ZAMS

(KH timescale)

Accretion History : one sample15

ZAMS

Mass Accretion KH Contraction ZAMS

16

Mstar [Msun]

1 10 　　 100 1000

103

102

101

104

Rst

ar [R

sun]

Accretion Histories

Mstar [Msun]1 10 　 100 1000

10-1

10-2

10-3

10-4Acc

reti

on R

ate

[Msu

n/y

rs]

100

Super-Giant / Rebound / Fiducial

Three paths exist

17

Mstar [Msun]

1 10 　　 100 1000

105

104

103

102

Tef

f [K

]

5000 [K]

Effective Temperature

× UV Radiation

Accretion History onto Protostar18

Mstar [Msun]

1 10 　　 100 1000

10-1

10-2

10-3

10-4

Acc

reti

on R

ate

[Msu

n/y

rs]

dM/dt > 0.04 [Msun/yrs]

dM/dt > 0.004 [Msun/yrs]

dM/dt < 0.004 [Msun/yrs]

11 / 108 … “Super-Giant” Phase

36 / 108 … “Rebound” Phase

61 / 108 … Become ZAMS

Hosokawa et al. (2012)

Star cannot become the Zero-Age

Main-Sequence (ZAMS)

structure Omukai&Palla (2003)

KH contraction & ZAMS directly

KH contraction stage

disappears entirely

Initial infall rate v.s Final MpopIII

19

Good Correlation :

(4πR2ρvrad)Jeans MpopIII

Simple Estimation :

MpopIII (4πR∝ 2ρvrad)Jeans

Decide MpopIII without the

calculation of accretion history

(* Not consider fragmentation)

Mp

opII

I [M

sun]

(4πR2ρvrad)Jeans [Msun/yrs]

Cou

nt

20

MpopIII [Msun]

Heger & Woosley’02Final fate of the

non-rotating PopIII stars

■ 15 < MPopIII < 40

Core Collapse

SNe

■ 40 < MPopIII < 140

Black Hole

■ 140 < MPopIII < 260

Pair-Instability

SNe

■ 260 < MPopIII

Black Hole

* with rapid rotation

MPISN > 65 [Msun]

Chatzopoulos&Wheeler(2012)

MpopIII Distribution

32 36 21 18

Summary

■ more than 100 primordial halos show

the wide range of accretion history

■ Three type of accretion histories

(1) low dM/dt KH contraction

UV radiative

feedback

(2) High dM/dt cannot reach ZAMS

mass accretion

continues

(3) HUGE dM/dt “supergiant” protostar

mass

accretion continues

MpopIII = 10 – a few 100 [Msun]

□ Correlation between (4πR2ρvrad)Jeans – MpopIII

　 Can estimate MpopIII by using Jeans quantity

21M

pop

III [

Msu

n]

(4πR2ρvrad)Jeans [Msun/yrs]

Mstar [Msun]

1 10 100 1000

103

102

101

104

Rst

ar [R

sun]

100