TITLE:
Two-photon transitions in primordial hydrogen recombination.
AUTHOR(S):
Christopher M. Hirata (Caltech).
DATE:
2008 Mar 06 (arXiv, v1, posted); 2008 Mar 11 (Phys. Rev. D, submitted);
2008 May 15 (revised);
2008 May 20 (Phys. Rev. D, accepted);
2008 May 20 (arXiv, v2, posted);
2008 Jul 01 (Phys. Rev. D, published).
AVAILABILITY:
arXiv 0803.0808 (free);
APS (requires subscription).
PUBLICATION INFORMATION:
Phys. Rev. D 78, 023001, 2008.
ABSTRACT:
The subject of cosmological hydrogen recombination has received much attention recently because of its importance to predictions for and cosmological
constraints from CMB observations. While the central role of the two-photon decay 2s-->1s has been recognized for many decades,
high-precision calculations require us to consider two-photon decays from the higher states ns,nd-->1s (n>=3). Simple attempts to
include these processes in recombination calculations with an effective two-photon decay coefficient analogous to the 2s decay coefficient
L2s=8.22 s-1 have suffered from physical problems associated with the existence of kinematically
allowed sequences of one-photon
decays, e.g. 3d-->2p-->1s, that technically also produce two photons. These correspond to resonances in the two-photon spectrum
that are optically thick to two-photon absorption, necessitating a radiative transfer calculation.
We derive the appropriate equations, develop a numerical code to solve them, and verify the results by finding agreement with analytic
approximations to the radiative
transfer equation. The related processes of Raman scattering and two-photon recombination are included using similar machinery.
Our results show that early in recombination the two-photon decays act to speed up recombination, reducing the free electron abundance by 1.3%
relative to the standard calculation at z=1300. However we find that some photons between Lya and Lyb are produced, mainly by
3d-->1s two-photon decay and 2s-->1s Raman scattering. At later times these photons redshift down to Lya, excite hydrogen
atoms, and act to slow recombination. Thus the free electron abundance is increased by 1.3% relative to the standard calculation at z=900. Our
calculation involves a very different physical argument than the recent studies of Wong & Scott and Chluba & Sunyaev, and produces a much
larger
effect on the ionization history. The implied correction to the CMB power spectrum is neligible for the recently released WMAP and ACBAR
data, but at Fisher matrix
level will be 7s for Planck.
ADS BIBLIOGRAPHIC CODE: N/A.
COMMENTS: Paper I in a long series on hydrogen recombination. See Paper II.