1. How Massive are the First Stars? Statistical Study of the primordial star formation  M popIII ALMA 時代の宇宙の構造形成理論 @ 北海道大学 / Jan. 26-28, 2013 ○ Shingo Hirano 1 Takashi Hosokawa 1, Naoki Yoshida 1, Kazuyuki Omukai 2, H.W.Yorke 3 1 University of Tokyo, 2 University of Kyoto, 3 JPL/Caltech Variety of PopIII protostellar evolution  3 protostellar accretion paths  M popIII = 10 – a few 100 M sun

2. How Massive are the First Stars? 2 Primordial Halo Cosmological Simulation z =17  Protostar Core ( ~ 0.01 [M sun ] ) 600 kpc/h (comving) Accretion Phase of the Primordial Protostar ■ Different thermal evolution (main coolant is H 2 molecular)  M cloud ~ 1000 [M sun ] ZERO metallicity ■ No Metal & Dust  No radiation pressure (?) (cf, PopII, I star formation) M popIII ~ 1000 [M sun ] (?) UV Radiative Feedback  Stalls mass-accretion

3. UV Radiative Feedback 3 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

5. Accretion History of Protostar 5 M popIII = 43 [M sun ]  moderate massive Accretion Rate [M sun /yrs] … however, M popIII depend on the initial quantities : Primordial Star–Forming Cloud Can be calculated by Cosmological Simulations Can be calculated by Cosmological Simulations Hosokawa et al. (2011) Radiative Hydrodynamics (RHD) Protostar Evolution UV radiative feedback Mass Accretion M star [M sun ]

6. Aim & Method 6 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 M popIII Distribution M popIII Distribution Primordial Gas Clouds Primordial Gas Clouds

7. Cosmological Simulation 7

8. 8 GADGET-2 : parallel SPH+N-body code (Springel 2005) + Primordial Chemistry (Yoshida et al. 2006, 2007) Initial Condition : z ini = 99, WMAP-7 (Komatsu et al. 2011) + zoom-in re-simulation technique  M resolve, init < 500 [M sun ] < M cloud Stop calculations when the collapsing center becomes : n cen ~ 10 13 [cm -3 ] (L resolve ~ 10 -5 ｰ 10 -4 [pc] ~ 2 ｰ 20 [AU]) N sample L box [kpc/h] (comving) N zoom L soft [pc/h] (comving) L soft [pc] (z=19) m sph [M sun ] 7100030726.50.460.867 982000307213.00.926.94

9. Primordial Star-Forming Clouds 9 108 halos @ N cen ~ 10 12 [cm -3 ] R [pc] N H [cm -3 ] Gao et al. (2007)  Density profiles evolve self-similarly

10. Infall Rate of Collapsing Cloud Infall Rate [M sun /yrs] = 10 M enclosed [M sun ] Infall Rate [M sun /yrs] ~ 10 -3 – 10 -1 M enclosed [M sun ] V rad [km/sec] N H [cm -3 ] Characteristic quantities of clouds :

11. Protostellar Accretion Phase 11

12. Protostellar Accretion 12 Using the setting & method in Hosokawa et al. (2011) Radiative Hydrodynamics (RHD) ■ 2D-axsymmetric ■ Self-gravity, Hydro ■ Primordial Chemistry (15 reactions with H, H +, H 2, H -, e) ■ Radiative-transfer : cooling, feedback ■ L cell,min ~ 25 [AU], L box = 1.2 [pc], M total ~ few 1000 [M sun ] 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

13. “Super-Giant” Protostar 13 Hosokawa et al. (2012) M star [M sun ] R star [R sun ] M enclosed [M sun ] Infall Rate [M sun /yrs] dM/dt > 0.04 [M sun /yrs]  No KH contraction (“Super-Giant” Protostar ) dM/dt > 0.004 [M sun /yrs]  L tot (M)| ZAMS > L edd, cannot reach ZAMS

14. Model of “Rebound” Phase 14 Hosokawa et al. (2012) M star [M sun ] R star [R sun ] 1 1 ①②①② 2 2 * Ignore expansion phenomena  By expansion, the effective temperature, T eff, decreases  this phase is not important for the UV radiative feedback L tot ~ L edd  Scaling : R star // R ZAMS L star // L ZAMS dM/dt < 4E–3 [M sun /yrs]  Contraction to ZAMS (KH timescale)

15. Accretion History : one sample 15 ZAMS Mass Accretion  KH Contraction  ZAMS

16. 16 M star [M sun ] 1 10 100 1000 10 3 10 2 10 1 10 4 R star [R sun ] Accretion Histories M star [M sun ] 1 10 100 1000 10 -1 10 -2 10 -3 10 -4 Accretion Rate [M sun /yrs] 10 0 Super-Giant / Rebound / Fiducial  Three paths exist

17. 17 M star [M sun ] 1 10 100 1000 10 5 10 4 10 3 10 2 T eff [K] 5000 [K] Effective Temperature × UV Radiation

18. Accretion History onto Protostar 18 M star [M sun ] 1 10 100 1000 10 -1 10 -2 10 -3 10 -4 Accretion Rate [M sun /yrs] dM/dt > 0.04 [M sun /yrs] dM/dt > 0.004 [M sun /yrs] dM/dt < 0.004 [M sun /yrs] 11 / 108 … “Super-Giant” Phase 36 / 108 … “Rebound” Phase 61 / 108 … Become ZAMS 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

19. Initial infall rate v.s Final M popIII 19 Good Correlation : (4πR 2 ρv rad ) Jeans  M popIII Simple Estimation : M popIII ∝ (4πR 2 ρv rad ) Jeans  Decide M popIII without the calculation of accretion history (* Not consider fragmentation) M popIII [M sun ] (4πR 2 ρv rad ) Jeans [M sun /yrs]

20. Count 20 M popIII [M sun ] Heger & Woosley’02 Final fate of the non-rotating PopIII stars ■ 15 < M PopIII < 40  Core Collapse SNe ■ 40 < M PopIII < 140  Black Hole ■ 140 < M PopIII < 260  Pair-Instability SNe ■ 260 < M PopIII  Black Hole * with rapid rotation M PISN > 65 [M sun ] Chatzopoulos&Wheeler(2012) M popIII Distribution 32 36 21 18

21. 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 M popIII = 10 – a few 100 [M sun ] □ Correlation between (4πR 2 ρv rad ) Jeans – M popIII  Can estimate M popIII by using Jeans quantity 21 M popIII [M sun ] (4πR 2 ρv rad ) Jeans [M sun /yrs] M star [M sun ] 1 10 100 1000 10 3 10 2 10 1 10 4 R star [R sun ] 10 0