A Caltech Library Service

Ultrafast effective multilevel atom method for primordial hydrogen recombination

Ali-Haïmoud, Yacine and Hirata, Christopher M. (2010) Ultrafast effective multilevel atom method for primordial hydrogen recombination. Physical Review D, 82 (6). Art. No. 063521. ISSN 1550-7998.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


Cosmological hydrogen recombination has recently been the subject of renewed attention because of its importance for predicting the power spectrum of cosmic microwave background anisotropies. It has become clear that it is necessary to account for a large number n ≳ 100 of energy shells of the hydrogen atom, separately following the angular momentum substates in order to obtain sufficiently accurate recombination histories. However, the multilevel atom codes that follow the populations of all these levels are computationally expensive, limiting recent analyses to only a few points in parameter space. In this paper, we present a new method for solving the multilevel atom recombination problem, which splits the problem into a computationally expensive atomic physics component that is independent of the cosmology and an ultrafast cosmological evolution component. The atomic physics component follows the network of bound-bound and bound-free transitions among excited states and computes the resulting effective transition rates for the small set of ‘‘interface’’ states radiatively connected to the ground state. The cosmological evolution component only follows the populations of the interface states. By pretabulating the effective rates, we can reduce the recurring cost of multilevel atom calculations by more than 5 orders of magnitude. The resulting code is fast enough for inclusion in Markov chain Monte Carlo parameter estimation algorithms. It does not yet include the radiative transfer or high-n two-photon processes considered in some recent papers. Further work on analytic treatments for these effects will be required in order to produce a recombination code usable for Planck data analysis.

Item Type:Article
Related URLs:
URLURL TypeDescription
Hirata, Christopher M.0000-0002-2951-4932
Additional Information:© 2010 The American Physical Society. Received 11 June 2010; published 17 September 2010. We thank Dan Grin for numerous useful and stimulating conversations, and for providing data from RECSPARSE computations for code comparison. We also acknowledge fruitful conversations with the participants of the July 2009 Paris Workshop on Cosmological Recombination. We thank Dan Grin, Marc Kamionkowski, and Jens Chluba for a careful reading of the draft of this paper. Y. A.-H. and C. H. are supported by the U.S. Department of Energy (DEFG03- 92-ER40701) and the National Science Foundation (AST-0807337). C. H. is supported by the Alfred P. Sloan Foundation.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:6
Classification Code:PACS: 98.80.Es, 32.80.Rm, 98.62.Ra, 98.70.Vc
Record Number:CaltechAUTHORS:20101011-095653882
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20363
Deposited By: Tony Diaz
Deposited On:13 Nov 2010 04:06
Last Modified:03 Oct 2019 02:08

Repository Staff Only: item control page