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The Accretion Physics of Primordial Protostars

The Accretion Physics of Primordial Protostars. Jonathan C. Tan Christopher F. McKee. Chemical Composition Trace H 2 formation: H + e —  H — +  H + H —  H 2 + e —. T min ~= 200 K, n crit ~= 10 4 cm -3 M BE = 380M sun c s =1.2 km/s.

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The Accretion Physics of Primordial Protostars

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  1. The Accretion Physicsof Primordial Protostars Jonathan C. Tan Christopher F. McKee

  2. Chemical Composition Trace H2 formation: H + e—  H— +  H + H—  H2 + e— Tmin ~= 200 K, ncrit ~= 104 cm-3 MBE = 380Msun cs=1.2 km/s What are the initial conditions for primordial star formation? Core Mass Core Size Density Structure Bulk Velocities: Rotation Radial infall Internal Velocities: Turbulence Sound Speed Chemical Composition

  3. r -k, k≈2.2 Centrally concentrated cloud quasi-hydrostatic, subsonic contraction Abel, Bryan, Norman (2002) n>ncrit , tcool(T=200K)=indep  Egrav=-GM/r T rises Abel, Bryan, Norman (2002) What are the initial conditions for primordial star formation? Tmin ~= 200 K, ncrit ~= 104 cm-3 MBE = 380Msun cs=1.2 km/s Density structure: ~self-similar, r -2.2 More chemistry: at high density >108cm-3 H+H+H -> H2 + H completely moleculer core ~Msun efficient continuum cooling -> dynamical collapse Rotation: core forms from mergers and collapse along filaments: expect J>0 fKep vcirc / vKep  ~ 0.5

  4. r -k . Accretion rate: m*= * m / tff(m)  f(m,K) Ripamonti et al. 2002 . m*=0.026K’15/7(m*/Msun)-3/7Msun/yr t* =41 K’-15/7(m*/Msun)10/7yr  m*(t=2Myr) ≈ 2000Msun Omukai & Nishi 1998 Abel et al. 2002 The Accretion Rateand Formation Timescale Density structure: self-similar, r -k, k≈2.2 ~singular polytropic sphere in virial and hydrostatic equilibrium P = K , =1.1 K=1.9x1012(T/300K)(nH/104cm-3)-0.1cgs K’=K/ 1.9x1012cgs *=1.4 (Hunter 1977) “Isentropic Accretion”

  5. Anticipate accretion driven by large scale grav. instabilities and gravitational viscosity (Gammie 2001) viscosity = cs h, <0.3 fragmentation tcool< 3-1 Collapse to a Disk rd = f2Kepr0 3.4 (M/Msun)9/7 AU Geometry of Streamlines Conserve J during free-fall inside sonic point (Ulrich 1976)

  6. Disk Models =0.3 : look for fragmentation condition, Q<1 in >1 region Surface density Thickness Ionization Disks are Stable with respect to Fragmentation Temperature Tc , Teff Toomre Q . m* 17x10-3Msun/yr 6.4x10-3Msun/yr 2.4x10-3Msun/yr

  7. Evolution of the Protostar Assume polytropic structure Energy:E = -agGm*2/(2r*) - fD Dm* dE/dt = - L - (1-fk)Gm*m*/r* Luminosity:L = f ( Lint + Lacc );Lacc = fk Gm*m*/r* . . Advection:f = exp( - 3 vff / c) Deuterium burning for Tc>106K Structural rearrangement after tKelvin Eddington model for  Solve for r*(m*), until reach main sequence

  8. Photosphere Accretion Shock Main Sequence (Schaerer 2002) :Radius Evolution of the Protostar Comparison with Stahler et al. (1986), Omukai & Palla (2001) Initial condition m* = 0.04 Msun r* = 14 Rsun (Ripamonti et al. 02) Protostar is large (~100 Rsun) until it is older than tKelvin Contraction to Main Sequence Accretion along Main Sequence

  9. Total Internal :Luminosity Evolution of the Protostar Boundary Layer Accretion Disk

  10. Total Internal Boundary Layer fKep=0.05 Accretion Disk Spherical, fKep=0 Main Sequence (Schaerer 2002) :Ionizing Luminosity Evolution of the Protostar fKep=0.5 Spectrum depends on initial rotation

  11. Feedback Processes When does accretion end? See Poster: JT, McKee, Blackman m* >~ 20-30 Msun (polar) Ly- Radiation Pressure Ionization Disk Evaporation Hydromagnetic Outflows m* >~ 100 Msun m* ~ 100-200 Msun m* >~ 100-500 Msun JT & Blackman (2003)

  12. Conclusions Understand initial conditions for star formation: set by H2 physics Analytic model for collapse with angular momentum: accretion rate is large and declining most material collapses to disk Analytic model for disk accretion: ionization energy important no fragmentation . Analytic model for protostellar evolution: large protostars, contract to main sequence m*>20Msun predict feedback is quite strong compared to spherical case Feedback processes are complicated: m* probably >30Msun, perhaps several 100Msun Implications of massive star formation in each mini-halo? How effective is external feedback? Are low-mass zero metallicity stars possible?

  13. Growth of the HII Region Balance ionizing flux vs recombinations and infall Infall likely to be suppressed for rHII>rg , where vesc=ci Find stellar mass at breakout rHII = rg polar; equatorial Breakout mass vs rotation

  14. Ly- and FUV Radiation Pressure 1 in HI around HII region :P = u/3 = 4J/3c Photons diffuse in freq. and space Normalize J to appropriateF 1/r2 Velocity field: Voigt profile D ;x /D Line profile: damping wingsx = <> x ; x = a/x2 Escape after n scatterings, or 2 photon decay freq. shiftxe = n1/2; mean free path at escapele = 1/<>e diffusion scalen1/2 le = n1/2/<>emust equal size of region,L=<>L/<> n1/2 = <>L eandxe = <>L e ≈ (a <>L)1/3 total path length of photons is n1/2L so mean intensity boosted by factor n1/2 = <>L a/xe2 ≈ (a <>L )1/3 (Neufeld 90) :P / (F/c) = 36.7 NH,201/3 / vD,62/3 Evaluate NH from harmonic mean of sightlines from star L

  15. Disk Photoevaporation Weak wind case: mevap= 6.1x10-5 S491/2 (m*/100Msun)1/2Msun/yr =1.7x10 -4(m*/100Msun)5/4Msun/yr for zero age main sequence Equate with mass accretion rate m*max = 480 K’60/47 40/47 Msun . Hollenbach et al. 94

  16. Mass Limits vs. Core Rotation Disk Photo- evaporation

  17. Overview of Structure Formation Recombination z ≈1200, start of “dark ages” Thermal equilibrium matter-CBR until z ≈160 MJeans ≈105Msun(T/1/3)3/2 : independent of z e.g. globular clusters Thermal decoupling, T (1+z)2 ; MJeans (1+z)3/2 “First Light” Reionization, T ≈104K, MJeans ≈109-10 ((1+zion)/10)3/2Msun e.g. galaxies Madau (2002)

  18. Numerical Simulations: Results 1. Form pre-galactic halo ~105-6Msun at intersection of filaments 2. Form quasi-hydrostatic gas core inside halo: M≈4000Msun, r ≈10pc, nH ≈10cm-3, fH2 ≈10-3, T>=200K H2 formation: H+e—H— +  H+H— H2+e-— Gradual contraction driven by cooling in dense central region. Rapid 3-body H2 formation for nH>1010cm-3: fully molecular region; strong cooling supersonic inflow. Line cooling is optically thick for n>1013cm-3:end of sim. Abel, Bryan, Norman (2002): 3. 1D simulations (Omukai & Nishi 1998): Form quasi-hydrostatic protostar nH ≈1016-17cm-3, T ≈2000K: optically thick, adiabatic contraction hydrostatic core with m* ≈0.005Msun,r* ≈14Rsun (also Ripamonti et al.02)

  19. Abel, Bryan, Norman (2002)

  20. Initial Conditions for Star Formation from Abel, Bryan, Norman 02

  21. Mass Limits vs. Core Rotation

  22. core rotation (ABN)

  23. Stellar Evolution to Supernovae Primordial high-mass main sequence is relatively stable with little mass loss (Baraffe, Heger, Woosley 01) Calculations of stellar evolution and supernovae (Fryer, Woosley, Heger 01) Nucleosynthetic yields may reveal themselves in metal-poor stars (Aoki et al. 02; Christlieb et al. 02)

  24. Hydrogen Ionizing Luminositiesalong the Primordial Main Sequence Tumlinson & Shull 00; Bromm et al. 01; Ciardi et al. 01; Schaerer 02

  25. Rotating Infall fKep vcirc / vKep 0.5 (ABN) rd = f2Kepr0 3.4 (M/Msun)9/7 AU Geometry of Streamlines Density along radii, =0,/3, 9/20 Optical Depth Conserve J during free-fall (Ulrich 76)

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