A code to calculate the recombination history of the
This code is meant to reproduce the calculations described in the paper
"A new calculation of the recombination epoch",
Seager, S., Sasselov, D. & Scott, D., 1999, ApJ, 523, L1
which is a fast
approximation to the detailed calculations described in
"How exactly did the Universe become neutral?"
Seager, S., Sasselov, D. & Scott, D., 2000, ApJS, 128, 407
And with some updates (to He etc.) which are described in
Wong, W.Y., Moss, A. & Scott, D., 2008, MNRAS, 386, 1023
together with the Compton coupling treatment in
Scott, D. & Moss A., 2009, MNRAS, 397, 445
It solves a modified 3-level atom for each of hydrogen and helium, along
with some corrections motivated by more detailed calculations. It is thus
fast, while being accurate enough for current CMB experiments.
Here are things that the code treats:
This results in xe(z) producing (it is believed)
better than 0.1 percent accuracy for CMB anisotropy Cl.
- Solves H and He simultaneously
- Kinetic temperature of matter evolved separately, including Compton
and adiabatic cooling
- Careful consideration of dependency of quantities on
TM and TR
- Accurate values of all relevant physical constants
- Full treatment of background cosmology, including radiation, Lambda
and curvature (but no explicit "w")
- Saha assumed for ionized helium
- Accurate look-up table for recombination coefficients
- Approximation for H recombination at low redshift, to account for
out of equilibrium
- Singlet and triplet states considered for neutral He
- Additional "fudge factor" for He recombination
- Solves for temperature difference between matter and radiation,
giving smoother transition in TM evolution
- Includes an extra "fudge" function to correct K(z) to
approximate the H physics corrections from detailed codes (see Rubino-Martin
et al. 2010)
- Extra "fudge factor" Gaussians, designed to make correction for
additional He physics for cosmologies near the standard one
There are 2 separate versions of the code, one in
(developed by DS), and one in
C (developed by SS).
Current version 1.5.2 (September 2012)
You can get recfast.for
and recfast.readme here.
You can also still get
version1.5.0 (January 2010),
version1.4.2 (September 2008),
version1.4.1 (August 2008),
as well as version1.3 (October 2006),
version1.2 (June 2003)
and version1.0 (October 2001).
A bug has been fixed that caused overflow on some types of computer (Feb 2000).
Other minor bugs have also been noted and fixed. Some problems with
Helium recombination were also pointed out and corrected (June 2003).
Version 1.3 includes 3 minor corrections (value of G,
mHe/mH ratio and an
error of x for
Version 1.4 includes modifications to account for the effects of Helium,
especially the new fudge factor.
Heswitch should be set to
6 to include all the He effects. Version 1.5 includes a correction
to the optical depth in order to approximate the change in xe
coming from additional H physics.
Hswitch should be set to 1
to include these new effects. Version 1.5.2 includes a change to the fudge
factors (including "fu") to match new He physics (see Chluba et al. 2012).
It is believed that the current version of recfast.for is sufficiently accurate
(i.e. effectively negligible bias on parameters) for use with Planck
data, for theories not too disimilar to the standard cosmology.
Note: this code is not currently up-to-date with bug fixes etc.
It is only included for historical reasons and to help people who want to
write their own
C code, with
makefile etc. is available
The current version of the code links to Numerical Recipes (NR), which is
copyright - hence users will require their own NR library. Details of
the modifications to NR routines and how to link are fully explained at
French translation of this page
Please e-mail any comments to
(or seager"AT"mit.edu for
Last revised: 30th September 2012