Ultrafast effective multilevel atom method for primordial hydrogen recombination

Abstract

Cosmological hydrogen recombination has recently been the subject of renewed attention because of its
\nimportance for predicting the power spectrum of cosmic microwave background anisotropies. It has
\nbecome clear that it is necessary to account for a large number n ≳ 100 of energy shells of the hydrogen
\natom, separately following the angular momentum substates in order to obtain sufficiently accurate
\nrecombination histories. However, the multilevel atom codes that follow the populations of all these levels
\nare computationally expensive, limiting recent analyses to only a few points in parameter space. In this
\npaper, we present a new method for solving the multilevel atom recombination problem, which splits the
\nproblem into a computationally expensive atomic physics component that is independent of the
\ncosmology and an ultrafast cosmological evolution component. The atomic physics component follows
\nthe network of bound-bound and bound-free transitions among excited states and computes the resulting
\neffective transition rates for the small set of ‘‘interface’’ states radiatively connected to the ground state.
\nThe cosmological evolution component only follows the populations of the interface states. By pretabulating
\nthe effective rates, we can reduce the recurring cost of multilevel atom calculations by more than
\n5 orders of magnitude. The resulting code is fast enough for inclusion in Markov chain Monte Carlo
\nparameter estimation algorithms. It does not yet include the radiative transfer or high-n two-photon
\nprocesses considered in some recent papers. Further work on analytic treatments for these effects will be
\nrequired in order to produce a recombination code usable for Planck data analysis.

Keywords

Affiliated Institutions

• California Institute of Technology US

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