Helium Recombination

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Helium Recombination

• Christopher Hirata (IAS)
• in collaboration with Eric Switzer (Princeton)
• astro-ph/0609XXX

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Recombination Physics

• Role of recombination in the CMB
• Standard recombination history
• New physics
• Preliminary results for helium(hydrogen coming
  later)

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Cosmic microwave background

• The CMB has revolutionized cosmology- Tight
  parameter constraints (in combination with other
  data sets)- Stringent test of standard
  assumptions Gaussianity, adiabatic initial
  conditions- Physically robust understood from
  first principles

WMAP Science Team (2006)
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Need for CMB Theory

• This trend will continue in the future with
  Planck, ACT/SPT, and E/B polarization
  experiments.
• But the theory will have to be solved to ltlt1
  accuracy in order to make full use of these data.
• Theory is straightforward and tractable linear
  GR perturbation theory Boltzmann equation.

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This is the CMB theory!
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This is the CMB theory!
ne electron density (depends on recombination)
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Recombination history
He2 e- ? He no effect
He e- ? He z damping tail degenerate with ns
H e- ? H z acoustic peak positions degenerate
with DA ?z polarization amplitude
z
as computed by RECFAST (Seager, Sasselov, Scott
2000) The standard recombination code.
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Standard theory of H recombination(Peebles 1968,
Zeldovich et al 1968)

• Effective three level atom H ground state, H
  excited states, and continuum
• Direct recombination to ground state ineffective.
• Excited states originally assumed in equilibrium.
  (Seager et al followed each level individually
  and found a slightly faster recombination.)

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Standard theory of H recombination(Peebles 1968,
Zeldovich et al 1968)

• For H atom in excited level, 3 possible fates
• 2? decay to ground state (?2?)
• Lyman-? resonance escape (?6ALy?Pesc)
• photoionization(? )
• Pesc1/?8?H/3nHIALy??Ly?3.

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Standard theory of H recombination(Peebles 1968,
Zeldovich et al 1968)

• Effective recombination rate is recombination
  coefficient to excited states times branching
  fraction to ground state

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Standard theory of H recombination(Peebles 1968,
Zeldovich et al 1968)

• ? 2-photon decay rate from 2s
• Pesc escape probability from Lyman-? line
• ALy? Lyman-? decay rate
• ?e recombination rate to excited states
• gi degeneracy of level i
• ?i photoionization rate from level i
• R Rydberg

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Standard theory of H recombination(Peebles 1968,
Zeldovich et al 1968)

• ? 2-photon decay rate from 2s
• Pesc escape probability from Lyman-? line
  probability that Lyman-? photon will not
  re-excite another H atom.
• Higher ? or Pesc ? faster recombination. If ? or
  Pesc is large we have approximate Saha
  recombination.

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Standard theory of He ? He recombination

• Essentially the same equation as H.
• Only spin singlet He is relevant in standard
  theory (triplet not connected to ground state).
• Differences are degeneracy factors, rate
  coefficients, and 1s2s-1s2p nondegeneracy.
• Excited states are in equilibrium (even in full
  level code).
• This is exactly the equation integrated in
  RECFAST.

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Is this all the physics?

• Resonance escape from higher-order lines H
  Ly?, Ly?, etc. and He 1s2-1snp (Dubrovich
  Grachev 2005)
• Feedback Ly? photons redshift, become Ly?, and
  re-excite H atoms.
• Stimulated two-photon transitions (Chluba
  Sunyaev 2006)
• Two-photon absorption of redshifted Ly? photons
  H(1s)?CMB?red-Ly??H(2s).

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Is this all the physics?

• Resonance escape from semiforbiddenHe
  1s2(S0)-1snp(S1) transition (Dubrovich
  Grachev 2005)
• Effect of absorption of He resonance and
  continuum photons by hydrogen (increases Pesc)
  (e.g. Hu et al 1995)
• Higher-order two-photon transitions, 1s-ns and
  1s-nd (Dubrovich Grachev 2005)

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Revisiting Recombination

• Project underway at Princeton/IAS to re-solve
  recombination including all these effects.
• Preliminary results are presented here for
  helium.
• Hydrogen will require more work due to higher
  optical depth in resonance lines.

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Effect of Feedback
He I
?xe0.006
H I
?xe0.001
Plot by E. Switzer
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Stimulated 2-photon decays and absorption of
redshifted Lyman-? photons
He I
?xe 0.00003
H I
?xe 0.0008
Stimulated 2? decay Including re-absorption of
redshifted resonance photons
Plot by E. Switzer
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HI effect on Helium recombination I

• Small amount of neutral hydrogen can speed up
  helium recombination
• Issue debated during the 1990s (Hu et al 1995,
  Seager et al 2000) but not definitively settled.
• Must consider effect of H on photon escape
  probability. This is a line transfer problem and
  is not solved by any simple analytic argument.
  We use Monte Carlo simulation (9 days x 32 CPUs).

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HI effect on Helium recombination II

• Must follow 4 effects-- emission/absorption in
  He line (complete redistribution)-- coherent
  scattering in He line (partial redistribution)--
  HI continuum emission/absorption-- Hubble
  redshifting
• Conceptually, as long as complete redistribution
  is efficient, He line is optically thick out to
• Compare to frequency range over which H I is
  optically thick

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Helium recombination history(including effects
1-6)
SAHA EQUILIBRIUM
OLD
NEW
??line lt ??HI
??line gt ??HI
Plot by E. Switzer
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What about 2-photon decays?

• 2-photon decays from excited states n3 have been
  proposed to speed up recombination (Dubrovich
  Grachev 2005)
• Rate (in atomic units)
• Sum includes continuum levels.
• Same equation for He (replace r?r1r2).
• Photon energies EEEnl,1s. (Raman scattering
  if E or Elt0.)
• The 2-photon decays are simply the coherent
  superposition of the damping wings of 1-photon
  processes.

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2-photon decays (cont.)

• How to find contribution to recombination?
  Argument by Dubrovich Grachev rests on three
  points
• Photons emitted in a Lyman line (resonance) are
  likely to be immediately re-absorbed, hence no
  net production of H(1s).
• Largest dipole matrix element from ns or nd state
  is to np
• Therefore take only this term in sum over
  intermediate states and get
• Compare to two-photon rates from 2s 8s-1 (H)
  and 51s-1 (He).

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(No Transcript)
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31S (1 pole)
31D (1 pole)
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Whats going on?

• Large negative contribution to 2-photon rate from
  interference of nn and n?n terms in summation.
• Cancellation becomes more exact as n??.
• For large values of n and fixed upper photon
  energy E, rate scales as n-3, not n. (e.g.
  Florescu et al 1987)
• Semiclassical reason is that 2-photon decay
  occurs when electron is near nucleus. The period
  of the electrons orbit is T?n3, so probability
  of being near nucleus is ?n-3. (Same argument in
  He.)
• Bottom line for recombination n2,3 dominate
  2-photon rate smaller contribution from
  successively higher n.

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Why havent we solved hydrogen yet?

• Its harder than helium!
• Larger optical depths few x 108 vs. few x 107.
• Consequently damping wings of Lyman lines in H
  overlap
• The Lyman series of hydrogen contains broad
  regions of the spectrum with optical depth of
  order unity. This can only be solved by a
  radiative transfer code.

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Summary

• Recombination must be solved to high accuracy in
  order to realize full potential of CMB
  experiments.
• There are significant new effects in helium
  recombination, especially H opacity.
• Extension to H recombination is in progress.
• Is there a way to be sure we havent missed
  anything?