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H 3 + cooling in primordial gas

H 3 + cooling in primordial gas. S. Glover (A.I.P.) D. W. Savin (Columbia). A brief introduction to galaxy formation. The first protogalaxies form at z ~ 20 - 30 Typical masses ~ 10 6 M  , sizes ~ 100 pc Composed of primordial gas: no enrichment by heavy elements:

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H 3 + cooling in primordial gas

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  1. H3+ cooling in primordial gas S. Glover (A.I.P.) D. W. Savin (Columbia)

  2. A brief introduction to galaxy formation • The first protogalaxies form at z ~ 20 - 30 • Typical masses ~ 106 M, sizes ~ 100 pc • Composed of primordial gas: no enrichment by • heavy elements: • xHe = 0.083 • xD = 2.6  10-5 • xLi = 4.3  10-10 • (Cyburt, 2004)

  3. At low density, cooling dominated by H2 H + e- H- + h H- + H  H2 + e- • Gas-phase reactions produce only a small H2 fraction. • Typically, no more than 0.1% of the gas is molecular. • BUT: this is enough to cool the gas to ~ 200K. • This allows runaway gravitational collapse to occur, • which leads to star formation.

  4. Detailed numerical simulations follow collapse • down to scales ~ 10,000 AU (Abel et al. 2000, 2002) • These simulations suggest that each protogalaxy • forms only one single massive star (at least initially) • Models assume H2 cooling dominates at ALL densities. • But is this true?

  5. H2 is not a very effective coolant, particularly at high n. • In LTE, cooling rate per H2 molecule at 1000K is: •  = 1.4  10-21 erg s-1 molecule-1 • For comparison, the LTE value for H3+ is: •  = 2.8  10-12 erg s-1 molecule-1 • (Neale, Miller & Tennyson, 1996) • So cooling from H3+ is potentially very important.

  6. Modeling protogalactic H3+ • Very simple dynamical model: single zone, free-fall • Detailed chemical model: 162 reactions between 23 • species. • Rates primarily taken from two existing compilations: • Galli & Palla (1998), Stancil, Lepp & Dalgarno (1998) • Include some additional three-body reactions, e.g: • H2 + H+ + H2 H3+ + H2 • (Gerlich & Horning, 1992)

  7. Radiative cooling from: H2, HD, LiH, H2+, H3+, HeH+… • Also include cooling due to Compton scattering of • CMB photons • At n > 104 cm-3, include H2 formation heating • At n > 1010 cm-3, include effects of H2 line opacity • following prescription of Ripamonti & Abel (2004)

  8. The H3+ cooling function • In LTE limit, use values from Neale et al (1996) • But what do we do at low density? • No complete set of vibrational excitation rates for • H3+ - H or H3+ - H2 collisions exists, so we can’t • treat the low density regime accurately. • Approximate the cooling rate per H3+ ion as: •  = LTE n > ncr •  = LTE (n / ncr) n < ncr

  9. What’s an appropriate value for ncr? • Assume that at 1000 K, there is a total excitation rate • coefficient kex ~ 10-9 cm3 s-1 • Assume that each collision leads, on average, to the loss • of approximately kT of energy • Then the low density cooling rate per H3+ ion is:  ~ 10-9 nkT ~ 10-22 n erg s-1 ion-1 • Comparison with the LTE rate then implies ncr ~ 1010 cm-3

  10. Summary • H3+ cooling can be important in the density range • n = 107 - 1011 cm-3 if: • The H3+ critical density ncr < 1010 cm-3 • OR: • The ionization rate  > 10-19 s-1 at n > 107 cm-3 • H3+ cooling is unimportant at n > 1011 cm-3, as too • little H3+ survives at these densities

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