A code for primordial hydrogen and helium recombination
including radiative transfer

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

New (07/2020): HyRec-2 is available on Nanoom Lee's github repository .

The previous stable versions of HyRec are available here: October 2012, May 2012, and January 2011.
See details in the readme file and the technical explanatory supplement

This code includes the following physics:

Helium recombination:

  • Hydrogen continuum opacity in the HeI 21Po--11S line
  • He I] 23Po--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:

For questions or issues, please email yah2[at]nyu[dot]edu

This material is based upon work supported by NSF awards AST-0807337, AST-0807444, PHY-1820861, and NASA award 80NSSC20K0532.

Last revised: August 3rd, 2020