2. Feedback Effects of the First Stars on Nearby Halos Kyungjin Ahn The University of Texas at Austin The End of the Dark Ages STSCI March 13, 2006

3. Outline Introduction Code Description Initial Setup Result Conclusion

4. Dark Ages and Reionization End of dark ages – reionization – is only observed indirectly  WMAP 1st year result : Need for high-redshift reionization sources  Gunn-Peterson Effect  Ly Forest Temperature First Stars  Prime candidate for early reionization sources  Forms by H 2 cooling  Feedback effects may be self-regulating (e.g. Haiman, Abel, Rees 2000)

5. Feedback effects of the First Stars Feedback Effects (positive vs. negative for further star formation)  Negative – star formation quenched H 2 is fragile: dissociation by Lyman-Werner band photons (Haiman, Abel, Rees 2000; Machacek, Bryan, Abel 2001)  Positive – star formation promoted Hard photons partially ionize IGM to create H 2 (Haiman, Rees, Loeb 1996; Ricotti, Gnedin, Shull 2002)

6. Feedback effects of the First Stars Feedback Effects of the First Stars onto Nearby Collapsed Objects (study by 3-D simulations)  O'shea et al. (2005) Assume full ionization of nearby halos of M~5*10 5 M solar Quick formation of H 2 after source dies Inner core collapses; Outer region evaporates  Alvarez, Bromm, Shapiro (2005) Track I-front propagation through nearby halos of M~5*10 5 M solar I-front slows down and being trapped. I-front fails to reach the center: Center remains neutral Neutral center: no further formation of H 2 after source dies at the center Negative feedback then??

7. Feedback effects of the First Stars Alvarez, Bromm, Shapiro (2005) Fig. 8.— Volume visualization at z = 20 of neutral density field (blue – low density, red – high density) and I- front (translucent white surface). Top row panels show a cubic volume ∼ 13.6 kpc (proper) across, middle row ∼ 6.8 kpc, and bottom row ∼ 3.4 kpc. Left column is at the initial time, middle column shows simulation at t ∗ = 3 Myr for the run with stellar mass M ∗ = 80M ⊙, and the right column shows simulation at t ∗ = 2.2 Myr for the run with stellar mass M ∗ = 200M ⊙. The empty black region in the lower panels of middle and right columns indicates fully ionized gas around the source, and is fully revealed as the volume visualized shrinks to exclude the I-front that obscures this region in the larger volumes above.

8. Feedback effects of the First Stars (In collaboration with Paul Shapiro) Feedback Effects of the First Stars onto Nearby Collapsed Objects (study by 1-D simulation)  Use 1-D radiation, hydrodynamics code Full treatment of primordial chemistry, radiative transfer, cooling/heating, hydrodynamics 1-D spherical geometry  Ultra high resolution possible  Analysis relatively easier than 3-D  Follow I-front propagation of the radiation from outer source in detail Is I-front trapped? What happens to the center? Any H 2 formation/dissociation interesting? Is it positive or negative feedback effect?

9. 1-D Spherical, Radiation-Hydro Code Radiative transfer  inner point souce: radial only, easy. (ex) one star at the center of halo  outer isotropic source: 3-D type ray tracing. Practical. (ex) background radiation field  outer plane-parallel source (with care). (ex) source far from halo.  N of frequency bins: >~200 bins are OK.  Optical depth calculated for each frequency bin.  Radiative rates calculated for each frequency bin.  H 2 self-shielding: special and simple treatment by Draine & Bertoldi (optical depth ~ 1 at n HI ~10 14 cm -2 )

10. 1-D Spherical, Radiation-Hydro Code Radiative transfer for outer isotropic source  7 discrete ordinates for angle, using Gaussian quadrature (with N Gaussian, 2N Simpson achieved)

11. 1-D Spherical, Radiation-Hydro Code Gravity  Dark matter: use fluid approximation. Better than radial shells. Ocasionally frozen gravity is not a bad approximation.  Baryon: Gravity involved hydrodynamics. Chemistry  Solve primordial chemistry, neglecting HD and HLi. H, H -, H +, H 2, He, He +, He ++, e  ionization, dissociation, recombination, radiative transfer Cooling/Heating  excitation, recombination, free-free, H 2  photoheating  adiabatic compression/rarefaction

12. Initial Setup Experiment 1 (Artificial)  Test O'shea et al. result Fully ionize the target halo without disturbing the structure Let it evolve without source Experiment 2 (Realistic)  Start out with a halo profile (TIS profile)  Abundance of electron and H 2 molecule with equilibrium value of a given halo: Departs from primodial values x e =10 -4, x H2 =2x10 -6  Send plane-parallel, black-body radiation from outside 120M solar, 10 5 K, 10 6.24 L solar, tstar=2.5 Myr  Place different-mass target halos at 360pc.

13. Rule of Thumbs H atomic cooling : down to ~10000K collisional ionization : at > ~10000K photo-ionization front : thickness ~ mean free path of ionizing photons R-type ionization front: I-front moves supersonically into neutral region; gas doesn’t respond dynamically D-type ionization front: I-front moves subsonically into neutral region; gas responds, shock-front develops Primary H 2 formation mechanism H + e  H - + H - + H  H 2 + e H 2 cooling : down to ~100K at H 2 /H >~ 10 -4 Low temperature, T ~ 10 -4 to be safe from collisional dissociation H 2 self-shielding effective at N(H 2 )>~10 14 cm -2 in static.

14. Experiment 1 (O’shea et al. type) No radiation (after star died) Fully-ionized gas quickly forms a lot of H 2 Core region quickly cools to ~100K Outer region evaporates Again, can this full ionization happen in the first place?

15. Initial Setup Experiment 2 (Realistic)

16. Result: Experiment 2 (collapse fails) 10 5 M solar target halo Movie during the lifetime of star (2.5 Myr) E net =kinetic energy + thermal energy + potential energy E net <0  collapse E net >0  exodus

17. 10 5 M solar target halo Movie after the lifetime of star Result: Experiment 2 (collapse fails)

18. Result: Experiment 2 (collapse successful) 4x10 5 M solar target halo Movie during the lifetime of star (2.5 Myr)

19. 4x10 5 M solar target halo Movie after the lifetime of star Cooling at the center & in H 2 precursor shell leads to negative net energy  collapse of neutral region. Result: Experiment 2 (collapse successful)

20. Result: Features to note I-front slows down, finally gets trapped. Transition to D-type front Precursor H 2 shell formation  Long mean-free-path of ionizing photons  Partial ionization -> H - formation -> H 2 formation  Shielding + H 2 molecule cooling Shock-front is driven, with T~1000 - 10000 K  Heating!!  Shock-front accelerates in constant-density core  Accelerates up to >~ 10000K  heated enough to lead to collisional ionization  electron, H 2 formation: Basically identical to Shapiro & Kang 1987, with v s ~15 km s -1  H atomic cooling + H 2 molecule cooling

21. H 2 Shell Forms through electrons in the partially ionized region Gains substantial column density, of order ~10 16 -10 18 cm -2. Self-shields against dissociating photons. (Not completely, though, because of peculiar motion of H 2 precursor shell) Neutral region sees weakned dissociating photons. Helps cool the gas against shock-heating  fragmentation?

22. H 2 Shell Structure Ricotti, Gnedin, Shull 2001 Into static IGM Our result Into minihalos

23. Conclusion Minihalos (target) nearby the first Stars (source) I-front trapped; Ionized gas evaporates H 2 formation in evaporating gas doesn’t help, just evaporates H 2 shell forms ahead of I-front: shielding dissociation + cooling Shock is driven to the neutral region: active heating  collisional ionization. (universal?) Competition between H 2 cooling & shock-heating determines the fate of neutral region. Higher the mass, more efficient the cooling -> critical minihalo mass for hosting 2 nd generation stars. In preparation  Wider parameter search  Jeans mass?  IMF?  Sequential star formation? Photon budget? See Brian O’shea’s talk too (Another feedback).