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H 3 + cooling in primordial gas

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H3+ 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 ~ 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)

- 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.

- 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?

- 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.

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)

- 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)

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

- 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

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