A code for primordial hydrogen and helium recombination
including radiative transfer

by Yacine Ali-Haïmoud and Chris Hirata,
with contributions from Nanoom Lee

This code includes the following physics:

Helium recombination:

• Hydrogen continuum opacity in the HeI 2¹P^o--1¹S line
• He I] 2³P^o--1¹S intercombination line
• Feedback between these lines

Hydrogen recombination:

• Exact effective multi-level atom calculation
• Time-dependent radiative transfer (through a numerical radiative transfer calculation in HyRec, and correction functions in the default mode of HyRec-2), specifically:
• Feedback between Lyman lines
• Two-photon transitions (emission, absorption, Raman scattering) from 2s and higher levels
• Frequency diffusion in Lyman-α
• This code does not include collisional transitions (yet)

We estimate the residual error of the code to be at the level of a few times 10^-3 during helium recombination and a few times 10^-4 during hydrogen recombination.

In its default swift mode, HyRec-2 computes a full recombination history in less than one millisecond on a standard laptop.

When using the code, please refer to:

N. Lee & Y. Ali-Haïmoud (2020) [arXiv:2007.14114]
Y. Ali-Haïmoud & C. M. Hirata, Phys. Rev. D 83, 043513 (2011) [arXiv:1011.3758]

This work also relies heavily on the following papers:

• Y. Ali-Haïmoud & C. M. Hirata, Phys. Rev. D 82, 063521 (2010) [arXiv:1006.1355]
• C. M. Hirata, Phys. Rev. D 78, 023001 (2008) [arXiv:0803.0808]
• E. R. Switzer & C. M. Hirata, Phys. Rev. D 77, 083006 (2008) [arXiv:0702143]

You may also consider refering to:

• Rubino-Martin et al., MNRAS 403, 439-452 (2010) [arXiv:0910.4384]
• Chluba & Thomas, MNRAS 412, 748-764 (2010), [arXiv:1010.3631]