FORMATION OF PRIMORDIAL STARS

Transcription

1 UW, July 5, 2006 FORMATION OF PRIMORDIAL STARS Naoki Yoshida Department of Physics Nagoya University

2 Outline Thermal evolution of a primordial gas - Physics at high densities (cooling, chem. etc. ) - Chemo-thermal instability - Accretion rate onto proto-stars Yoshida, Omukai, Hernquist, Abel (2006, astro-ph/ ) Formation and evolution of early HII/HeIII regions - re-collapse of HII regions - primordial star formation with HD cooling - providing the initial conditions of the formation of (proto-)galaxies Yoshida (2006, NewA); Yoshida et al., in prep.

3 Thermal evolution of a primordial gas (See e.g. Palla, Stahler, Salpeter 1983) T adiabatic molecule formation and cooling 3-body react. (NLTE) mostly molecular, heat release loitering (~LTE) opaque to line absorption collision induced emission Previous Simulations (Abel et al. 02, Bromm Loeb 04) number density

4 Why did we need the improvement? Gas mass accretion rate Omukai & Nishi 98 self-similar solution Msun / year Abel, Bryan, Norman 2002 log M/Msun New result accurate cooling rate correct temperature reasonable accretion rate proto-stellar evolution

5 Three-body reactions and heat release Main formation paths at high densities: Reaction rates density 3. The core becomes nearly fully molecular. Significant heat (4.48eV per molecule) is released.

6 Molecular line opacity Example) J=6 4 transition at T~1000 K For τ >0.1, the cloud core is optically thick to H2 linesand then line cooling becomes inefficient τ 4,6 ~1 for Lcore~0.0001pc

7 Line transfer problem: the Sobolev length V thermal L sobolev = dv/dr We compute the Sobolev lengths from local velocity gradients dvx/dx, dvy/dy, dvz/dz *Also tested local column densities, local Jean lengths

8 Net molecular cooling rate Λthick = Σ β escape n k,l A k,l hν optically thick / thin 3D calculation Ripamonti Omukai98 1D full RT CIE cooling log (n) NY, Omukai, Hernquist, Abel (2006)

9 Collision Induced Emission hν continuum emission During collisions, a collision pair acts as a super-molecule, generating an induced electric dipole.

10 Optically thin CIE cooling rate 2hν η (ν) = 3 σ nh2 exp(- c hν/kt ) 2 H2-H2 (Borysow et al. 2001) H2-He (Jorgensen et al 2000) pairs dominates over other collisions at n ~

11 Cosmological Simulations Standard ΛCDM model Multi-level zoom-in technique initial mass resolution 0.01 M sun final mass resolution 60 M earth Hydro, neq-chemistry (H, He), radiative processes, etc. etc. NY, Omukai, Hernquist, Abel (2006)

12 100pc 5pc 5AU 0.01pc

13 Radial profiles r density temperature fh2 radial velocity

14 Chemo-thermal instability and fragmentation Yoshii & Sabano (1977) Silk (1983) The strong density dependence of 3-body reactions can trigger chemo-thermal instability. Condensation larger density larger molecular fraction larger cooling rate It is very important to examine whether or not the instability is triggered and multiple (small-mass) clouds are formed.

15 L cooling rate F reaction (formation) rate, f molecular fraction Dispersion relation For perturbations of the form exp(ωt): a 0 ω 2 + a 1 ω + a 2 0 (t growth = 1/ω) a /2 (µ/µ a )

16 Dispersion relation a 0 ω 2 + a 1 ω + a 2 0 (t growth = 1/ω) Yoshii & Sabano (1977) Omukai & Yoshii (2003)

17 Chemo-thermal instability: Numerical results growth rate tff/tg becomes larger than 1, but always below 2. t free fall / t growth The growing perturbation has L ~ c s t g, while the central region size is L J ~ c s t ff Although the thermal instability occurs, the cloud does not fragment to multiple objects - Collapse is just accelerated. log (n)

18 Primordial proto-star: a tiny seed in a large cloud

19 Accretion rate and proto-stellar evolution dm/dt = Msun/yr M ZAMS = M sun We used the obtained accretion rate as an input to the proto-stellar evolution code of Omukai & Palla (2003)

20 Primordial Star Formation: Summary 1. No fragmentation is observed during the prestellar collapse. A single ~300 Msun cloud in a Msun halo. 2. The cloud is stable against gravitational deformation, too, yielding a single tiny proto-stellar seed. 3. Proto-stellar evolution calculations give M ZAMS ~ Msun

21 Three important issues: 1. Further evolution up to the final adiabatic phase 2. (Possible) disk accretion 3. Radiative feedback from the proto-star

22 Feedback from the first star First star First light First HII region Fossil HII region Re combination First galaxy? Yoshida (2006, NewA)

23 Ionization front propagation in 3-D Ray-tracing to all the gas particles (~ millions particles) to compute photon arrival times t i Ri dt t i+1 Ri+1 N ne,np

24 Comparison: vs full Radial profiles at t=2.2 Myr Initial profile Density Temp. 1D full 3D Initial profile 1D results from Kitayama, NY, Susa, Umemura (2004, ApJ)

25 Comparisons with 1D full RT Radial profiles at t=2 Myr Radial velocity Neutral fraction (_not_ ionized fraction)

26 Helium ionization A 100 Msun PopIII star QLW = /s QH = /s QHe = /s QHe+ = /s Photo-dissociation region HII / HeII HeIII Ionized region could be similar to planetary nebula rather than local HII regions

27 Early HeIII region Almost fully ionized within the HeIII region. 2 kpc HeIII HII H in HeIII region kept ionized by recombination (HeII Ly-a, HeII-Balmer, HeII two-photon) photons (Osterbrook 1989) HII/HeII regions have (almost) the same extent. Yoshida (2006, New A.)

28 Early HeIII region Temperature profile With helium Helium ionization raises the gas temperature, and the outgoing gas velocity. hydrogen only 1 kpc HeIII HII Yoshida (2006, New A.)

29 Radial velocity profile t=2.2 Myr t=0

30 Evolution of the baryon fraction t=100 Myr Density profile Initially outward motion is reverted due to gravity by the growing dark halo and infalling gas t=2.2 Myr

31 Effect of HD cooling H2 formation is promoted in relic HII region (ionized gas). The temperature becomes so low that HD cooling becomes important. CMB temperature

32 Accretion rate and proto star evolution first star

33 Summary If the first stars are massive. 1 They cause significant radiative feedback, evacuating the surrounding gas and hence quenching star-formation for ~100 Myrs. This may set characteristic velocity scales for early (proto-)galaxies ~ 30 km/sec. 2 Early reionization models by first galaxies (and by mini-quasars) need to be revisited.

34 Halo mass evolution in the CDM model σ peaks ~100Myrs ~100Myrs 2 nd, V=30 km/s 1 st, T=2000 K From Barkana & Loeb (2001)