Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination

Chluba, Jens; Sunyaev, R.

doi:10.1051/0004-6361:20053988

Cited by 123 publications

(161 citation statements)

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“…For the 2s-1s two-photon process, this behavior was also seen earlier (Chluba & Sunyaev 2006b). In the case of 3s and 3d twophoton decays, this enhances the emission of photons close to the Lyman β resonance (cf.…”

Section: Appendix C: Computation Of Two-photon Profilessupporting

confidence: 77%

“…After the seminal works of Zeldovich et al (1968) and Peebles (1968) on cosmological recombination, and the later improvements to the theoretical modeling of this epoch (e.g., Jones & Wyse 1985;Seager et al 2000), leading to the widely used standard recombination code Recfast (Seager et al 1999), over the past few years the detailed physics of cosmological recombination has again been reconsidered by several independent groups (e.g., Dubrovich & Grachev 2005;Chluba & Sunyaev 2006b;Kholupenko & Ivanchik 2006;Rubiño-Martín et al 2006;Switzer & Hirata 2008;Wong & Scott 2007). It is clear that understanding the cosmological ionization history at the level of ∼0.1% (e.g., see Fendt et al 2009, for a more detailed overview of the different previously neglected physical processes that are important at this level of accuracy) will be very important to accurate theoretical predictions of the cosmic microwave background (CMB) temperature and polarization angular fluctuations (e.g., see Hu et al 1995;Seljak et al 2003) to be measured by the Planck Surveyor 1 , which will be launched later this year.…”

Section: Introductionmentioning

confidence: 99%

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Lyαescape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes

Chluba

Sunyaev

2010

A&A

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We give a formulation of the radiative transfer equation for Lyman α photons, which allows us to include the two-photon corrections for the 3s-1s and 3d-1s decay channels during cosmological hydrogen recombination. We use this equation to compute the corrections to the Sobolev escape probability for Lyman α photons during hydrogen recombination, which then allow us to calculate the changes in the free electron fraction and CMB temperature and polarization power spectra. We show that the effective escape probability changes by ΔP/P ∼ +11% at z ∼ 1400 in comparison with the one obtained using the Sobolev approximation. This accelerates hydrogen recombination by ΔN e /N e ∼ −1.6% at z ∼ 1190, implying that |ΔC l /C l | ∼ 1−3% at l > ∼ 1500 with shifts in the positions of the maxima and minima in the CMB power spectra. These corrections will be important to the analysis of future CMB data. The total correction is the result of the superposition of three independent processes, related to (i) time-dependent aspects of the problem; (ii) corrections due to quantum mechanical deviations in the shape of the emission and absorption profiles in the vicinity of the Lyman α line, from the normal Lorentzian; and (iii) a thermodynamic correction factor, which is found to be very important. All of these corrections are neglected in the Sobolev-approximation, but they are important in the context of future CMB observations. All three can be naturally obtained in the two-photon formulation of the Lyman α absorption process. However, the corrections (i) and (iii) can also be deduced in the normal "1 + 1" photon language, without necessarily going to the two-photon picture. Therefore, only (ii) is really related to the quantum mechanical aspects of the two-photon process. We show here that (i) and (iii) represent the largest individual contributions to the result, although they partially cancel each other close to z ∼ 1100. At z ∼ 1100, the modification due to the shape of the line profile contributes about ΔN e /N e ∼ −0.4%, while the sum of the other two contributions gives ΔN e /N e ∼ −0.9%.

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Section: Appendix C: Computation Of Two-photon Profilessupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Lyαescape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes

Chluba

Sunyaev

2010

A&A

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“…Important corrections include feedback from higher-order lines [16,17], time-dependent effects in Ly-α [18], and frequency diffusion due to resonant scattering [19][20][21]. An accurate 2s − 1s two-photon decay rate also requires following the radiation field to account for stimulated decays [22] and absorption of non-thermal photons [23,24]. Dubrovich & Grachev [25] suggested that two-photon transitions from higher levels may have a significant effect on the recombination history.…”

Section: Introductionmentioning

confidence: 99%

HyRec: A fast and highly accurate primordial hydrogen and helium recombination code

2011

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We present a state-of-the-art primordial recombination code, HyRec, including all the physical effects that have been shown to significantly affect recombination. The computation of helium recombination includes simple analytic treatments of hydrogen continuum opacity in the He I 2 1 P o − 1 1 S line, the He I] 2 3 P o − 1 1 S line, and treats feedback between these lines within the on-the-spot approximation. Hydrogen recombination is computed using the effective multilevel atom method, virtually accounting for an infinite number of excited states. We account for two-photon transitions from 2s and higher levels as well as frequency diffusion in Lyman-α with a full radiative transfer calculation. We present a new method to evolve the radiation field simultaneously with the level populations and the free electron fraction. These computations are sped up by taking advantage of the particular sparseness pattern of the equations describing the radiative transfer. The computation time for a full recombination history is ∼ 2 seconds. This makes our code well suited for inclusion in Monte Carlo Markov chains for cosmological parameter estimation from upcoming high-precision cosmic microwave background anisotropy measurements.

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“…see Fendt et al 2008, for detailed overview), including subtle physical processes during hydrogen (e.g. see Dubrovich & Grachev 2005;Chluba & Sunyaev 2006b;Kholupenko & Ivanchik 2006;Rubiño-Martín et al 2006;Hirata 2008) and helium recombination (e.g. see Switzer & Hirata 2008a,b;Hirata & Switzer 2008;Kholupenko et al 2007;Wong & Scott 2007;Rubiño-Martín et al 2008;Kholupenko et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Time-dependent corrections to the Ly αescape probability during cosmological recombination

Chluba

Sunyaev

2009

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We consider the effects connected with the detailed radiative transfer during the epoch of cosmological recombination on the ionization history of our Universe. We focus on the escape of photons from the hydrogen Lyman α resonance at redshifts 600 z 2000, one of two key mechanisms defining the rate of cosmological recombination. We approach this problem within the standard formulation, and corrections due to two-photon interactions are deferred to another paper. As a main result we show here that within a non-stationary approach to the escape problem, the resulting correction in the free electron fraction, N e , is about ∼1.6-1.8% in the redshift range 800 z 1200. Therefore the discussed process results in one of the largest modifications to the ionization history close to the maximum of Thomson-visibility function at z ∼ 1100 considered so far. We prove our results both numerically and analytically, deriving the escape probability, and considering both Lyman α line emission and line absorption in a way different from the Sobolev approximation. In particular, we give a detailed derivation of the Sobolev escape probability during hydrogen recombination, and explain the underlying assumptions. We then discuss the escape of photons for the case of coherent scattering in the lab frame, solving this problem analytically in the quasi-stationary approximation and also in the time-dependent case. We show here that during hydrogen recombination the Sobolev approximation for the escape probability is not valid at the level of ΔP/P ∼ 5-10%. This is because during recombination the ionization degree changes significantly over a characteristic time Δz/z ∼ 10%, so that at percent level accuracy the photon distribution is not evolving along a sequence of quasi-stationary stages. Non-stationary corrections increase the effective escape by ΔP/P ∼ +6.4% at z ∼ 1490, and decrease it by ΔP/P ∼ −7.6% close to the maximum of the Thomson-visibility function. We also demonstrate the crucial role of line emission and absorption in distant wings (hundreds and thousands of Doppler widths from the resonance) for this effect, and argue that the final answer probably can only be given within a more rigorous formulation of the problem using a two-or multi-photon description.

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Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination

Cited by 123 publications

References 17 publications

Lyαescape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes

Lyαescape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes

HyRec: A fast and highly accurate primordial hydrogen and helium recombination code

Time-dependent corrections to the Ly αescape probability during cosmological recombination

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