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Pop III IMF

Pop III IMF. Michael L. Norman Laboratory for Computational Astrophysics UC San Diego (with thanks to Andrea Ferrara & Mario Livio). General Comments. Definition: Pop III = zero metallicity IMF not observationally constrained at this time We don’t observe Pop III stars directly

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Pop III IMF

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  1. Pop III IMF Michael L. Norman Laboratory for Computational Astrophysics UC San Diego (with thanks to Andrea Ferrara & Mario Livio)

  2. General Comments • Definition: Pop III = zero metallicity • IMF not observationally constrained at this time • We don’t observe Pop III stars directly • Interpretation of “fossil evidence” highly uncertain • Must rely on theory/simulations (yikes!) • Robust prediction: first stars were massive • But not all Pop III stars may form this way

  3. Why do we care? • Fate of Pop III depends sensitively on mass • IMF controls early radiative and chemical evolution of the universe, and the population of seed black holes Figure courtesy Alex Heger

  4. Defining the Pop III IMF • What is the statistical ensemble? • First stars are believed to form in isolation, one per low mass halo (Mcrit ~ 5x105 Ms) (Abel, Bryan & Norman 2002) • Simply not enough cool baryons to form 2 cores • High z IMF may be strongly peaked about the characteristic mass scale Mc~100 Ms, with dispersion reflecting halo properties (O’Shea & Norman 2006b) • If some more massive halos at lower z remain pristine (chemical feedback), Pop III clusters may form with a broader, but still top-heavy IMF (Larson 1998) • Primordial stars formed through secondary processes (shocked slabs, relic HII regions), may have lower Mc, and a broader dispersion • It is highly likelyn(M)=n(M,z) • My proposal: ensemble is the entire Pop III era

  5. Topics • Characteristic fragmentation mass scale of “first star” halos • Origin (old) • cosmological evolution (new) • 1st generation Pop III stars: role of sub-fragmentation and accretion • 2nd generation Pop III: Variations on a theme • FUV, relic HII regions, shocked slabs • Chemical feedback and 2nd generation stars • The rise and fall of Pop III: a schematic

  6. Formation of the first stars(Abel et al, Bromm et al.) • DM halos of M~5x105 Ms at z~30 attract enough primordial gas to achieve significant baryonic core densities and temperatures • H2 formation proceeds, and by z~20 cools core baryons to T~200K, n~104 cm-3, precipitating gravitational instability • Collapse proceeds quasi-statically until n~108 cm-3, and dynamically at higher densities as core becomes fully molecular • Collapsing core does not fragment, but forms a single massive star with MFS =O(100 Ms) as inferred by its accretion rate • These results are numerically converged

  7. Pop III Star formation: the current paradigm Range of resolved scales = 1010 From Abel, Bryan and Norman 2002, Science, 295, 93

  8. Origin of mass scale: H2 • H2 cooling rate (per particle) becomes independent of density above n=104 cm-3 (“critical density”) • 0-1 ro-vib. exitation temperature =590K • Tmin~200K • Cloud core “loiters” at these conditions until a Jeans mass of gas accumulates

  9. Evolution of cloud core Gravitationally unstable Z=19 + 9 Myr + 300 Kyr + 30 Kyr + 3 Kyr + 1.5 Kyr + 200 yr (z=18.18) Gravitationally stable Abel, Bryan & Norman (2002)

  10. tms Schaerer (2002) primordial stars If we bound MFS from below by tkh, get ~100 Ms If we bound MFS from above by tms, get 600-1000 Ms 100 < MFS/Ms < 1000 (neglecting feedback) Shu

  11. Cosmological Evolution of Characteristic Mass Scale(O’Shea & Norman (2006b)) • The Issue • How representative are these results? • Are Pop III halos forming at different redshifts different? • The Simulations • 12 simulations (4 random realizations) x (3 box sizes) • Run to core collapse • Analyzed when central density had reached 1012 cm-3 DM halo mass function (PS) Pop III halos 5x105 < Mhalo < 5x107

  12. mass range 20-4000 Ms

  13. Conclusions: cosmological evolution of characteristic fragmentation scale • Pop III halos forming at higher redshifts have: • Higher mean temperature • Higher core H2 fraction • Lower core temperature, and hence • Lower accretion rates • The first Pop III stars to form may be less massive than those forming later • Pop III epoch may start modestly and build to a crescendo • Or it might be the other way around…..

  14. Fragmentation and Accretion • Turbulent fragmentation and competitive accretion both seem to account for present day IMF • Both rely on Mcloud >> Mc • Could these mechanisms operate in high mass primordial halos? • If so, might expect a Pop III IMF with shape like present-day IMF, but shifted to high mass (Larson 1998) • Can massive primordial halos from? • What about good-old gravitational fragmentation? (Hoyle 1953) • CAUTION!

  15. 0-D free-fall models Not dynamically self-consistent Omukai (2001)

  16. 1-D hydrodynamical models • Spherical symmetric • no fragmentation • Dynamically self-consistent • Rate chemistry, EOS, radiative transfer • entire massive envelope eventually accretes Mstar=Mcore Omukai & Nishi (1998)

  17. collapsing rotating core ABN02 density 0.6 pc 0.06 pc 1200 AU disk temperature

  18. Fragmentation and Accretion • Yes, both happen • But, in low mass halos at least, only one central fragment forms, which then accretes • Angular momentum important on small scales, but no centrifugal barrier found to n~1015 cm-3 • Disk not an accretion disk per se, but a rotating, collapsing core • Could possibly fragment into a binary • Evidence of turbulent transport of AM and AM “segregation” (O’Shea & Norman 2006c)

  19. Accretion rate may determine the final stellar mass (Omukai & Palla 2003)

  20. Protostar growth with time-dependent accretion history In the absence of other effects, ABN02 star should grow to ~600 Ms Omukai & Palla (2003)

  21. Effects of Rotation (Tan & McKee 2004) • Collapse becomes supersonic when core becomes fully molecular • Assuming gas conserves AM inside sonic radius, TM04 argue that an accretion will form • Most of the mass is accreted via this disk • Eddington limited accretion is bypassed • Protostellar evolution similar to OP03 subcritical case (all mass is accreted)

  22. Variations on a Theme 1.Effect of FUV Background • The issue: • FUV photons from first stars easily escape primordial halos, building up soft UV background • will photo-dissociate H2, inhibiting cooling and hence Pop III star formation (Dekel & Rees 1987; Haiman, Rees & Loeb 1997; Haiman, Abel & Rees 2000) Solomon process Does negative feedback quench star formation in low mass halos?

  23. Machacek, Bryan & Abel 2001 Mass Thresholdto Cool • H2 in photo- dissociation equilibrium wrtFLW • H2 cooling still effective for M>106 Msun • Soft UVB delays, but does not suppress star formation

  24. FUVB delays collapse, and raises accretion rate (O’Shea & Norman 2006d) FLW=10-22 FLW=5x10-23 Mvir FLW=10-23 FLW=10-24 10-2 Ms/yr Accretion rate increases with increasing FLW Above Omukai-Palla critical accretion rate Final mass may be smaller zcoll

  25. Variations on a Theme 2.Pop III star formation in a relic HII region(O’Shea et al. 2005) Log(Xe) Log(T) 100 kpc (com)

  26. Log(T)

  27. Primordial 2nd Generation Objects • z ~ 11, Mdyn/ M = 4 x 107, Tvir=14,000 K • well above minimum halo mass to form H2 in the presence of a SUV background (Machacek, Bryan & Abel 2001) •  2 x 106 Msol of cold (200K) gas • 100 x the amount that formed the 1st star due to abundant electrons • Will it form a star 100x as massive (SMS)? • Will it form a cluster of Pop III stars? IMF? • AMR simulations with more levels can answer these questions (O’Shea & Norman, in prep)

  28. Variations on a Theme 3.Pop III star formation in SN shells(Uehara & Inutsuka 2000; Mackey, Bromm & Hernquist 2003) • Blast waves in primordial halos will sweep up shells of gas which from H2 and HD • Gas cools below 100 K due to HD • Shell fragments due to gravitational instability • Mass scale: brown dwarfs Uehara & Inutsuka (2000)

  29. Chemical Feedback from Pop III(O’Shea & Norman 2006c, poster) 4x105 yr 6x107 yr

  30. 2nd generation stars • At Z=7x10-3 Zs, metal line cooling will dominate primordial gas cooling (Bromm & Loeb 2003) • Assuming gas cools down to CMB temperature (47 K), then MJ~6 Ms for our core density. This is resolution-dependent and hence an upper limit. • Expect extreme Pop II to have a universal IMF shifted slightly to higher mass • IMF will depend of properties of molecular cloud turbulence (Padoan & Nordlund 2002), which we can (and will) quantify

  31. Evolution of Pop III Halo fraction(Schneider et al. 2006) • Procedure: construct merger tree from N-body simulation • Assume fraction fSN host metal-producing SN • Mergers with polluted halos form Pop II • If fSN=0.1, Pop III halos from to z=0; Pop III stars dominate SF history • If fSN=1, Pop III halos continue to form at negative feedback threshold; Pop II stars dominate SF history

  32. Rise and Fall of Pop III: A schematic 30 20 15 10 z Pop II protogalaxy threshold Pop III halo Low mass Pop III halo Enriched Pop III halo

  33. Slides in reserve

  34. Turbulent AM transport Reynolds stress

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