Radiative transfer effects during primordial helium recombination

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In this paper we refine the calculation of primordial helium recombination, accounting for several additional effects that were neglected or treated more approximately in previous studies. These include consideration of (i) time-dependent radiative transfer interaction between the 2¹ P₁ - 1¹ S₀ and 2³ P₁ - 1¹ S₀ resonances; (ii) time-dependent radiative transfer for the partially overlapping n¹ P₁ - 1¹ S₀, n¹ D₂ - 1¹ S₀ and n³ P₁ - 1¹ S₀ series with 3 <= n <= 10; (iii) electron scattering within a kernel approach. We also briefly discuss the effect of electron scattering and HI quadrupole lines on the recombination of hydrogen. Although the physics of all the considered processes is interesting and subtle, for the standard cosmology, with Yₚ 0.24, the overall correction to the ionization history during helium recombination with respect to the previous implementation of CosmoRec remains smaller than |DeltaNe/Ne| 0.05%. The dominant improvement is caused by consistent inclusion of resonance scattering for the 2¹ P₁ - 1¹ S₀ resonance. For cosmologies with a large helium fraction, Yₚ 0.4, the difference reaches |D Nₑ/Nₑ| 0.22% at z 1800, however, the overall correction to the CMB power spectra is small, exceeding |D Cₗ/Cₗ| 0.05 % only at l> 3000. In comparison to the current version of Recfast the difference reaches |D Cₗ/Cₗ| 0.4% at l 3000 for Yₚ 0.4, and also for the standard value Yₚ 0.24 we find differences |DCₗ/Cₗ|> 0.1% at l 2500. The new processes are now included by the cosmological recombination code CosmoRec and can be activated as needed for most settings without affecting its runtime significantly.