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

2. 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 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

3. Abel, Bryan, Norman (2002) What are the initial conditions for primordial star formation? T min ~= 200 K, n crit ~= 10 4 cm -3 M BE = 380M sun c s =1.2 km/s Centrally concentrated cloud quasi-hydrostatic, subsonic contraction n>n crit, t cool (T=200K)=indep  E grav =-GM  /r T rises Abel, Bryan, Norman (2002)  r -k, k≈2.2 Density structure: ~self-similar,  r -2.2 More chemistry: at high density >10 8 cm -3 H+H+H -> H 2 + H completely moleculer core ~M sun efficient continuum cooling -> dynamical collapse Rotation: core forms from mergers and collapse along filaments: expect J>0 f Kep  v circ / v Kep  ~ 0.5

4. The Accretion Rate and Formation Timescale Density structure: self-similar,  r -k, k≈2.2 ~singular polytropic sphere in virial and hydrostatic equilibrium P = K  ,  =1.1  r -k m * =0.026K’ 15/7 (m * /M sun ) -3/7 M sun /yr t * =41 K’ -15/7 (m * /M sun ) 10/7 yr  m * (t=2Myr) ≈ 2000M sun. Ripamonti et al. 2002 Omukai & Nishi 1998 Abel et al. 2002. Accretion rate: m * =  * m / t ff (m)  f(m,K) K=1.9x10 12 (T/300K)(n H /10 4 cm -3 ) -0.1 cgs K’=K/ 1.9x10 12 cgs  * =1.4 (Hunter 1977) “Isentropic Accretion”

5. Collapse to a Disk Geometry of Streamlines Conserve J during free-fall inside sonic point (Ulrich 1976) r d = f 2 Kep r 0  3.4 (M/M sun ) 9/7 AU Anticipate accretion driven by large scale grav. instabilities and gravitational viscosity (Gammie 2001) viscosity =  c s h,  <0.3 fragmentation t cool < 3  -1

6. Disk Models Surface density Thickness Ionization Temperature T c, T eff Toomre Q  =0.3 : look for fragmentation condition, Q 1 region Disks are Stable with respect to Fragmentation m*m*. 17x10 -3 M sun /yr6.4x10 -3 M sun /yr2.4x10 -3 M sun /yr

7. Energy: E = -  a g Gm * 2 /(2r * ) - f D  D m * dE/dt = - L - (1-f k )Gm * m * /r * Luminosity: L = f  ( L int + L acc ) ; L acc = f k Gm * m * /r *.. Evolution of the Protostar Advection: f  = exp( - 3  v ff / c) Deuterium burning for T c >10 6 K Structural rearrangement after t Kelvin Eddington model for  Solve for r * (m * ), until reach main sequence Assume polytropic structure

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

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

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

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

12. Analytic model for collapse with angular momentum: accretion rate is large and declining most material collapses to disk Conclusions. Understand initial conditions for star formation: set by H 2 physics Analytic model for disk accretion: ionization energy important no fragmentation Analytic model for protostellar evolution: large protostars, contract to main sequence m * >20M sun predict feedback is quite strong compared to spherical case Feedback processes are complicated: m * probably >30M sun, perhaps several 100M sun 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 Find stellar mass at breakout r HII = r g polar; equatorial Breakout mass vs rotation Infall likely to be suppressed for r HII >r g, where v esc =c i

14.  1 in HI around HII region : P  = u  /3 = 4  J  /3c Photons diffuse in freq. and space Normalize J  to appropriate F   1/r 2 Velocity field: Voigt profile  D ; x   /  D Line profile: damping wings  x =  x ;  x = a/  x 2 Escape after n scatterings, or 2 photon decay freq. shift x e = n 1/2 ; mean free path at escape l e = 1/  e diffusion scale n 1/2 l e = n 1/2 /  e must equal size of region, L= L / n 1/2 = L  e and x e = L  e ≈ (a L ) 1/3 total path length of photons is n 1/2 L so mean intensity boosted by factor n 1/2 = L a/  x e 2 ≈ (a L ) 1/3 (Neufeld 90) : P  / (F  /c) = 36.7 N H,20 1/3 /  v D,6 2/3 Evaluate N H from harmonic mean of sightlines from star Ly-  and FUV Radiation Pressure L

15. Disk Photoevaporation Weak wind case: m evap = 6.1x10 -5 S 49 1/2 (m * /100M sun ) 1/2 M sun /yr =1.7x10 -4 (m * /100M sun ) 5/4 M sun /yr for zero age main sequence Equate with mass accretion rate  m *max = 480 K’ 60/47  40/47 M sun. Hollenbach et al. 94

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

18. Overview of Structure Formation 1. Recombination z ≈1200, start of “dark ages” 2. Thermal equilibrium matter-CBR until z ≈160 M Jeans ≈ 10 5 M sun  (T/  1/3 ) 3/2 : independent of z e.g. globular clusters 3. Thermal decoupling, T  (1+z) 2 ; M Jeans  (1+z) 3/2 4. “First Light” 5. Reionization, T ≈10 4 K, M Jeans ≈ 10 9-10 ((1+z ion )/10) 3/2 M sun e.g. galaxies Madau (2002)

19. Numerical Simulations: Results Abel, Bryan, Norman (2002): 1. Form pre-galactic halo ~10 5-6 M sun at intersection of filaments 2. Form quasi-hydrostatic gas core inside halo: M≈4000M sun, r ≈10pc, n H ≈10cm -3, f H2 ≈10 -3, T>=200K H 2 formation: H+e —  H — +  H+H —  H 2 +e -— Gradual contraction driven by cooling in dense central region. Rapid 3-body H 2 formation for n H >10 10 cm -3 : fully molecular region; strong cooling  supersonic inflow. Line cooling is optically thick for n>10 13 cm -3 :end of sim. 3. 1D simulations (Omukai & Nishi 1998): Form quasi-hydrostatic protostar n H ≈10 16-17 cm -3, T ≈2000K: optically thick, adiabatic contraction  hydrostatic core with m * ≈0.005M sun,r * ≈14R sun (also Ripamonti et al.02)

20. Abel, Bryan, Norman (2002)

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

22. Mass Limits vs. Core Rotation

23. core rotation (ABN)

24. 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) 8<M<40NS“normal” enrichment 40<M<130BHinefficient enrichment 130<M<260no remnantefficient enrichment 260<MBHinefficient enrichment Nucleosynthetic yields may reveal themselves in metal-poor stars (Aoki et al. 02; Christlieb et al. 02)

25. Hydrogen Ionizing Luminosities along the Primordial Main Sequence Tumlinson & Shull 00; Bromm et al. 01; Ciardi et al. 01; Schaerer 02

26. Rotating Infall f Kep  v circ / v Kep  0.5 (ABN)r d = f 2 Kep r 0  3.4 (M/M sun ) 9/7 AU Geometry of Streamlines Density along radii,  =0,  /3, 9  /20 Optical Depth Conserve J during free-fall (Ulrich 76)