1. Star Formation at Very Low Metallicity Anne-Katharina Jappsen

2. Collaborators  Simon Glover, Heidelberg, Germany  Ralf Klessen, Heidelberg, Germany  Mordecai-Mark Mac Low, AMNH, New York  Spyridon Kitsionas, AIP, Potsdam, Germany

3. The Initial Mass Function

4. From Pop III Stars to the IMF? star formation in the early universe:  30 M sun < M < 600 M sun (e.g. O’Shea & Norman 07)  Z = 0 (Pop III) ➞ Z < 10 -3 Z sun (Pop II.5)  M char ~ 100 - 300 M sun present-day star formation:  0.01 M sun < M < 100 M sun  Z > 10 -5 Z sun, Z = Z sun  M char ~ 0.2 M sun

5. Critical Metallicity Bromm et al. 2001:  SPH-simulations of collapsing dark matter mini-halos  no H 2 or other molecules  no dust cooling  only C and O atomic cooling 10 -4 Z sun < Z cr < 10 -3 Z sun

6. Dependence on Metallicity Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling  = 1 10 2 M sun 1 M sun 10 -2 M sun

7. Present-day star formation Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling  = 1 Z=0

8. Dependence on Z at low  Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling  = 1

9. Numerical Model  Smoothed Particle Hydrodynamics  Gadget-1 & Gadget-2 (Springel et al. 01, Springel 05)  Sink particles (Bate et al. 95)  chemistry and cooling  particle splitting (Kitsionas & Whitworth 02)

10. Chemical Model

11. Cooling and Heating  gas-grain energy transfer  H collisional ionization  H + recombination  H 2 rovibrational lines  H 2 collisional dissociation  Ly-alpha & Compton cooling  Fine-structure cooling from C, O and Si  photoelectric effect  H 2 photodissociation  UV pumping of H 2  H 2 formation on dust grains

12. Dependence on Metallicity at Low Density  gas fully ionized  initial temperature: 10000 K  centrally condensed halo  contained gas mass: 17% of DM Mass  number of gas particles: 10 5 – 10 6  resolution limit: 20 M SUN – 400 M SUN

13. Dependence on Metallicity at Low Density  halo size: 5 x 10 4 M sun – 10 7 M sun  redshift: 15, 20, 25, 30  metallicity: zero, 10 -4 Z sun, 10 - 3 Z sun, 10 -2 Z sun, 0.1 Z sun  UV background: J 21 = 0, 10 -2, 10 -1  dust: yes or no (Jappsen et al. 07)

14. Dependence on Metallicity at Low Density

15. Influence of Different Initial Conditions example I centrally condensed halo hot, ionized initial conditions NFW profile, r s = 29 pc T = 10000 K z = 25 M DM = 8 x 10 5 M sun M res, gas = 1.5 M sun example II solid-body rotating top-hat (cf. Bromm et al. 1999) cold initial conditions with dark matter fluctuations top-hat approximation T = 200 K M DM = 2 x 10 6 M sun M res, gas = 12 M sun

16. Example I CMB after 52 Myrs

17. Example II  Rotating top-hat with dark matter fluctuations and cold gas initially: gas fragments no matter what metallicity, because unstable disk builds up (Jappsen et al. 09) H 2 is the dominant coolant! “critical metallicity” only represents point where metal-line cooling dominates molecular cooling

18. Influence of Different Initial Conditions  example I: centrally condensed halo hot, ionized initial conditions gas does not fragment up to metallicities Z = 0.1 Z sun (n ≤ 10 6 cm -3 )  example II: solid-body rotating top-hat (cf. Bromm et al. 1999) cold initial conditions with dark matter fluctuations gas fragments no matter what the metallicity (n ≤ 10 6 cm -3 ) because unstable disk builds up

19. Conclusions – so far  H 2 is the dominant and most effective coolant  different initial conditions can help or hinder fragmentation ⇒ we need more accurate initial conditions from observations and modeling of galaxy formation  there is no “critical metallicity” for fragmentation at densities below 10 5 cm -3  Transition from Pop III to modern IMF maybe at higher densities due to dust-induced fragmentation:

20. Dependence on Z at high  Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling  = 1

21. Dust-induced Fragmentation  Clark et al. 2008 study dust-induced fragmentation in 3D numerical simulations of star formation in the early universe  dense cluster of low-mass protostars builds up:  mass spectrum peaks below 1 M sun  cluster VERY dense (n stars = 2.5 x 10 9 pc -3)  fragmentation at density n gas = 10 12 - 10 13 cm -3

22. Conclusions  H 2 is the dominant and most effective coolant at n < 10 5 cm -3  there is no “critical metallicity” for fragmentation at densities below 10 5 cm -3  different initial conditions can help or hinder fragmentation ⇒ we need more accurate initial conditions from observations and modeling of galaxy formation  Transition from Pop III to modern IMF maybe at higher densities due to dust-induced fragmentation at Z = 10 -5 Z sun

23. Hierarchical Structure Formation  cold dark matter cosmology  smallest regions collapse first  “bottom-up” formation  observations constrain problem well Credit: S. Gottlöber (AIP)

24. Star Formation in the Early Universe  Population III stars  first potential producers of UV photons that contribute to reionization  first producers of metals  injector of entropy into IGM  so far not observable  Influence on gas in small protogalaxies? Is star formation possible? Credit: NASA, ESA, S. Beckwith (STScI) and the HUDF Team

25. Primordial Gas Cloud Formation Yoshida et al. 2003

26. UV Background Machacek et al. 2001

27. Masses of Pop III Stars star formation in the early universe:  30 M sun < M < 600 M sun (e.g. O’Shea & Norman 07)  Z = 0 (Pop III) ➞ Z < 10 -3 Z sun (Pop II.5)  M char ~ 100 - 300 M sun

28. Questions  What determines the transition from Pop III to modern Initial mass function (IMF)  Is there a critical metallicity?  How does metallicity influence the thermodynamic behaviour and the dynamics of the gas?  What is the influence of initial conditions?  What is the role played by UV background, rotation and turbulence?

29. What determines the mass distribution? Turbulent initial conditions:  determine prestellar core mass function Thermodynamic properties of gas:  determine balance between heating and cooling  determine stiffness of equation of state ability of gas to fragment under gravity Accretion (modulated by feedback):  maps protostellar mass to final mass

30. Hydrodynamics continuity eq. Euler eq. energy eq. Poisson eq. equation of state

31. Effective Equation of State  general EOS: P = P(ρ, T)  ideal gas: P = RρT(ρ)  under certain conditions: energy equation and EOS can be “combined” to an effective polytropic EOS: P = Kρ γ  polytropic exponent γ = 1+dlog T / dlogρ

32. Fragmentation Depends on 

33. how does that work? (1) P ∝    ∝ P 1/  (2) M jeans ∝     –    large density excursion for given pressure  〈 M jeans 〉 becomes small  number of fluctuations with M > M jeans is large   small density excursion for given pressure  〈 M jeans 〉 becomes large  only few and massive clumps exceed M jeans

34. Gravo-turbulent Fragmentation

35. Mass Spectra of Protostellar Cores

36. Polytropic EOS  Fragmentation requires soft equation of state  effective polytropic index  ≤ 1.0  Once EOS stiffens ⇒ fragmentation stops  This happens at different masses for different metallicities:

37. SF in the Early Universe Polytropic Equation of State? Not possible since gas not necessarily in thermal equilibrium Follow coupling of:  chemistry  thermal balance (cooling and heating)  dynamics

38. Smoothed Particle Hydrodynamics Eulerian Lagrangian  Lucy 1977, Gingold & Monaghan 1977  particle based method  resolution follows density  well suited for our problem

39. Sink Particles  replace gas core by single, non-gaseous, massive sink particle  fixed radius – Jeans radius of core  inherit masses, linear momenta, “spin“  accrete gas particles

40. Different Masses

41. UV background

43. Example I + Turbulence CMB after 52 Myrs E turb = 0 E turb = 0.05 E int E turb = 0.1 E int E turb = 0.1 E int, Z = 10 -3

44. Example I + Turbulence  turbulence slows growth of central density slightly  but: collapse continues and sink particle forms in the centre  this is true for both values of turbulent energy input

45. Example I + Rotation  spin parameter of halo   rotation allows for formation of stable disks over large fractions of Hubble time  no fragmentation since Toomre parameter Q > 10 growing metallicity Z

46. Dust-induced Fragmentation  Tsuribe & Omukai (2006) study dust-induced fragmentation in dense, non-rotating cores  Temperature evolution approximated with tabulated EOS, based on Omukai et al. (2005)  Results:  Oblate cores do not fragment  Prolate cores fragment at n~10 16 cm -3

47. 47 t cool, fs > t ff x e = 1.0x e = 10 -2 x e = 10 -4 Cooling Time vs. Free-fall Time