Hyrec-2: A highly accurate sub-millisecond recombination code

Abstract

We present the new recombination code hyrec-2, which achieves the same accuracy as the state-of-the-art codes hyrec and cosmorec and, at the same time, surpasses the computational speed of the code recfast commonly used for cosmic microwave background (CMB) anisotropy data analyses. hyrec-2 is based on an effective four-level atom model, accounting exactly for the nonequilibrium of highly excited states of hydrogen, and very accurately for radiative transfer effects with a correction to the Lyman-$\ensuremath{\alpha}$ escape rate. The latter is computed with the original hyrec and tabulated as a function of temperature, along with its derivatives with respect to the relevant cosmological parameters. This enables the code to keep the same accuracy as the original hyrec over the full 99.7% confidence region of cosmological parameters currently allowed by Planck, while running in under one millisecond on a standard laptop. Our code leads to no noticeable bias in any cosmological parameters even in the case of an ideal cosmic-variance-limited experiment up to $\ensuremath{\ell}=5000$. Beyond CMB anisotropy calculations, hyrec-2 will be a useful tool to compute various observables that depend on the recombination and thermal history, such as the recombination spectrum or the 21-cm signal.