Star Formation at Very Low Metallicity Anne-Katharina Jappsen

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<ul><li>Slide 1</li></ul> <p>Star Formation at Very Low Metallicity Anne-Katharina Jappsen Slide 2 Collaborators Simon Glover, Heidelberg, Germany Ralf Klessen, Heidelberg, Germany Mordecai-Mark Mac Low, AMNH, New York Spyridon Kitsionas, AIP, Potsdam, Germany Slide 3 The Initial Mass Function Slide 4 From Pop III Stars to the IMF? star formation in the early universe: 30 M sun &lt; M &lt; 600 M sun (e.g. OShea &amp; Norman 07) Z = 0 (Pop III) Z &lt; 10 -3 Z sun (Pop II.5) M char ~ 100 - 300 M sun present-day star formation: 0.01 M sun &lt; M &lt; 100 M sun Z &gt; 10 -5 Z sun, Z = Z sun M char ~ 0.2 M sun Slide 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 &lt; Z cr &lt; 10 -3 Z sun Slide 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 Slide 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 Slide 8 Dependence on Z at low Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling = 1 Slide 9 Numerical Model Smoothed Particle Hydrodynamics Gadget-1 &amp; Gadget-2 (Springel et al. 01, Springel 05) Sink particles (Bate et al. 95) chemistry and cooling particle splitting (Kitsionas &amp; Whitworth 02) Slide 10 Chemical Model Slide 11 Cooling and Heating gas-grain energy transfer H collisional ionization H + recombination H 2 rovibrational lines H 2 collisional dissociation Ly-alpha &amp; 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 Slide 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 Slide 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) Slide 14 Dependence on Metallicity at Low Density Slide 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 Slide 16 Example I CMB after 52 Myrs Slide 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 Slide 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 Slide 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: Slide 20 Dependence on Z at high Omukai et al. 2005: one-zone model, H 2, HD and other molecules, metal cooling, dust cooling = 1 Slide 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 Slide 22 Conclusions H 2 is the dominant and most effective coolant at n &lt; 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 Slide 23 Hierarchical Structure Formation cold dark matter cosmology smallest regions collapse first bottom-up formation observations constrain problem well Credit: S. Gottlber (AIP) Slide 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 Slide 25 Primordial Gas Cloud Formation Yoshida et al. 2003 Slide 26 UV Background Machacek et al. 2001 Slide 27 Masses of Pop III Stars star formation in the early universe: 30 M sun &lt; M &lt; 600 M sun (e.g. OShea &amp; Norman 07) Z = 0 (Pop III) Z &lt; 10 -3 Z sun (Pop II.5) M char ~ 100 - 300 M sun Slide 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? Slide 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 Slide 30 Hydrodynamics continuity eq. Euler eq. energy eq. Poisson eq. equation of state Slide 31 Effective Equation of State general EOS: P = P(, T) ideal gas: P = RT() under certain conditions: energy equation and EOS can be combined to an effective polytropic EOS: P = K polytropic exponent = 1+dlog T / dlog Slide 32 Fragmentation Depends on Slide 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 &gt; M jeans is large small density excursion for given pressure M jeans becomes large only few and massive clumps exceed M jeans Slide 34 Gravo-turbulent Fragmentation Slide 35 Mass Spectra of Protostellar Cores Slide 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: Slide 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 Slide 38 Smoothed Particle Hydrodynamics Eulerian Lagrangian Lucy 1977, Gingold &amp; Monaghan 1977 particle based method resolution follows density well suited for our problem Slide 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 Slide 40 Different Masses Slide 41 UV background Slide 42 Slide 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 Slide 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 Slide 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 &gt; 10 growing metallicity Z Slide 46 Dust-induced Fragmentation Tsuribe &amp; 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 Slide 47 47 t cool, fs &gt; t ff x e = 1.0x e = 10 -2 x e = 10 -4 Cooling Time vs. Free-fall Time </p>