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How Massive are the First Stars? Statistical Study of the primordial star formation  M popIII

How Massive are the First Stars? Statistical Study of the primordial star formation  M popIII. Variety of PopIII protostellar evolution  3 protostellar accretion paths  M popIII = 10 – a few 100 M sun. ○ Shingo Hirano 1

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How Massive are the First Stars? Statistical Study of the primordial star formation  M popIII

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  1. How Massive are the First Stars? • Statistical Study of the primordial • star formation  MpopIII Variety of PopIIIprotostellar evolution  3 protostellar accretion paths  MpopIII = 10 – a few 100 Msun • ○ Shingo Hirano1 • Takashi Hosokawa1, Naoki Yoshida1, Kazuyuki Omukai2, H.W.Yorke3 • 1University of Tokyo, 2University of Kyoto,3JPL/Caltech • ALMA時代の宇宙の構造形成理論@北海道大学 / Jan. 26-28, 2013

  2. How Massive are the First Stars? z =17 600kpc/h (comving) Accretion Phase of the Primordial Protostar Primordial Halo Cosmological Simulation  Protostar Core ( ~ 0.01 [Msun] ) ZERO metallicity ■Different thermal evolution (main coolant is H2 molecular)  Mcloud ~ 1000 [Msun] MpopIII ~ 1000 [Msun] (?) ■No Metal & Dust  No radiation pressure (?) (cf, PopII, I star formation) UV Radiative Feedback  Stalls mass-accretion

  3. UV Radiative Feedback • 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) Accreting star emits the ionizing UV photons Growth of HII region  Breakout & Expansion Gas on the circumstellar disk is photo-ionized & heated  photo-evaporation

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

  5. Aim & Method 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 Primordial Gas Clouds MpopIII Distribution Accretion Histories

  6. 7 Cosmological Simulation

  7. Cosmological Simulation 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])

  8. Primordial Star-Forming Clouds 108 halos @ Ncen~ 1012 [cm-3] Gao et al. (2007) NH[cm-3] R [pc]  Density profiles evolve self-similarly

  9. Infall Rate of Collapsing Cloud Characteristic quantities of clouds : Infall Rate[Msun/yrs] = NH[cm-3] Infall Rate [Msun/yrs] Vrad[km/sec] ~ 10-3 – 10-1 Menclosed[Msun] Menclosed[Msun]

  10. Protostellar Accretion Phase

  11. Protostellar Accretion Using the setting & method in Hosokawa et al. (2011) Protostar Evolution UV radiative feedback Mass Accretion 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] ＊ For calculating the case of the high mass accretion rate, we adopt a simple model of the stellar evolution

  12. “Super-Giant” Protostar Hosokawa et al. (2012) Rstar[Rsun] Infall Rate [Msun/yrs] Mstar[Msun] Menclosed[Msun] 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

  13. Model of “Rebound” Phase Hosokawa et al. (2012) Ltot ~ Ledd  Scaling : Rstar // RZAMS Lstar // LZAMS ① ② Rstar[Rsun] 2 dM/dt < 4E–3 [Msun/yrs]  Contraction to ZAMS (KH timescale) 1 Mstar[Msun] * Ignore expansion phenomena  By expansion, the effective temperature, Teff, decreases  this phase is not important for the UV radiative feedback

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

  15. Accretion Histories 104 10-1 103 10-2 Accretion Rate [Msun/yrs] Rstar[Rsun] 102 10-3 101 10-4 100 1 10 100 1000 1 10 100 1000 Mstar[Msun] Mstar[Msun] Super-Giant / Rebound / Fiducial  Three paths exist

  16. Effective Temperature 105 104 5000 [K] Teff[K] × UV Radiation 103 102 1 10 100 1000 Mstar[Msun]

  17. Accretion History onto Protostar 11 / 108 … “Super-Giant” Phase 36 / 108 … “Rebound” Phase 61 / 108 … Become ZAMS dM/dt > 0.04 [Msun/yrs] •  KH contraction stage • disappears entirely Hosokawa et al. (2012) 10-1 dM/dt > 0.004 [Msun/yrs] 10-2 Accretion Rate [Msun/yrs]  Star cannot become the Zero-Age Main-Sequence (ZAMS) structure 10-3 Omukai&Palla (2003) dM/dt < 0.004 [Msun/yrs] 10-4 1 10 100 1000  KH contraction & ZAMS directly Mstar[Msun]

  18. Initial infall rate v.s Final MpopIII Good Correlation : (4πR2ρvrad)Jeans MpopIII MpopIII[Msun] Simple Estimation : MpopIII ∝ (4πR2ρvrad)Jeans  Decide MpopIII without the calculation of accretion history (* Not consider fragmentation) (4πR2ρvrad)Jeans[Msun/yrs]

  19. MpopIIIDistribution Heger & Woosley’02 Final fate of the non-rotatingPopIIIstars ■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) Count 32 36 18 21 MpopIII[Msun]

  20. Summary 104 ■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)HUGEdM/dt  “supergiant” protostar  mass accretion continues MpopIII = 10 – a few 100 [Msun] □ Correlation between (4πR2ρvrad)Jeans – MpopIII  Can estimate MpopIII by using Jeans quantity 103 Rstar[Rsun] 102 101 100 1 10 100 1000 Mstar[Msun] MpopIII[Msun] (4πR2ρvrad)Jeans[Msun/yrs]

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