Transcript H 3 + cooling in primordial gas

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