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H 3 + cooling in primordial gas

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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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slide1

H3+ cooling in primordial gas

S. Glover (A.I.P.)

D. W. Savin (Columbia)

slide2

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)
slide3

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.
slide4

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?
slide5

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.
slide6

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)
slide7

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)
slide8

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
slide9

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
slide17

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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