Cosmological Hydrogen Recombination Research Articles

Level-mixing effect induced by blackbody radiation and its influence on the cosmological hydrogen recombination problem

An effect of atomic line broadening induced by the blackbody radiation is discussed. The level mixing effect and anti-Stokes Raman scattering are compared. It is shown that the mixing effect gives the most significant contribution to the line broadening and it is indicated how to distinguish these two effects in laboratory experiments. The influence of the level mixing on the recombination history of primordial plasma is also discussed.

Investigation of the electromagnetically induced transparency in the era of cosmological hydrogen recombination

Investigation of cosmic microwave background formation processes is one of the most compelling problems at the present time. In this paper we analyse the response of the hydrogen atom to external photon fields. Field characteristics are defined via conditions corresponding to the recombination era of the universe. Approximation of the three-level atom is used to describe the ‘atom–field’ interaction. It is found that the phenomena of the electromagnetically induced transparency (EIT) take place in this case. Consideration of EIT phenomena makes it necessary to update the astrophysical description of the processes of cosmic microwave background formation and, in particular, the Sobolev escape probability. Additional terms to the optical depth entering in the Sobolev escape probability are found to contribute on the level about 1%.

QED model of the radiation escape from matter

A simple model based on quantum electrodynamics (QED) is presented to estimate the contribution of the excited-level few-photon decays to the radiation escape from the matter in the epoch of cosmological hydrogen recombination. It is shown that apart from the widely studied two-photon decays, some specific three-photon decays can contribute with an accuracy of 0.1%, which is required by recent astrophysical observations.

Radiative transfer effects in primordial hydrogen recombination

The calculation of a highly accurate cosmological recombination history has been the object of particular attention recently, as it constitutes the major theoretical uncertainty when predicting the angular power spectrum of Cosmic Microwave Background anisotropies. Lyman transitions, in particular the Lyman-alpha line, have long been recognized as one of the bottlenecks of recombination, due to their very low escape probabilities. The Sobolev approximation does not describe radiative transfer in the vicinity of Lyman lines to a sufficient degree of accuracy, and several corrections have already been computed in other works. In this paper, the impact of some previously ignored radiative transfer effects is calculated. First, the effect of Thomson scattering in the vicinity of the Lyman-alpha line is evaluated, using a full redistribution kernel incorporated into a radiative transfer code. The effect of feedback of distortions generated by the optically thick deuterium Lyman-alpha line blueward of the hydrogen line is investigated with an analytic approximation. It is shown that both effects are negligible during cosmological hydrogen recombination. Secondly, the importance of high-lying, non overlapping Lyman transitions is assessed. It is shown that escape from lines above Ly-gamma and frequency diffusion in Ly-beta and higher lines can be neglected without loss of accuracy. Thirdly, a formalism generalizing the Sobolev approximation is developed to account for the overlap of the high-lying Lyman lines, which is shown to lead to negligible changes to the recombination history. Finally, the possibility of a cosmological hydrogen recombination maser is investigated. It is shown that there is no such maser in the purely radiative treatment presented here.

Towards a complete treatment of the cosmological recombination problem

A new approach to the cosmological recombination problem is presented, which completes our previous analysis on the effects of two-photon processes during the epoch of cosmological hydrogen recombination, accounting for ns-1s and nd-1s Raman events and two-photon transitions from levels with n>=2. The recombination problem for hydrogen is described using an effective 400-shell multi-level approach, to which we subsequently add all important recombination corrections discussed in the literature thus far. We explicitly solve the radiative transfer equation of the Lyman-series photon field to obtain the required modifications to the rate equations of the resolved levels. In agreement with earlier computations we find that 2s-1s Raman scattering leads to a delay in recombination by DN_e/N_e~0.9% at z~920. Two-photon decay and Raman scattering from higher levels (n>3) result in a small additional modifications, and precise results can be obtained when including their effect for the first 3-5 shells. This work is a major step towards a new cosmological recombination code (CosmoRec) that supersedes the physical model included in Recfast, and which, owing to its short runtime, can be used in the analysis of future CMB data from the Planck Surveyor.

Ultrafast effective multilevel atom method for primordial hydrogen recombination

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 $n\ensuremath{\gtrsim}100$ 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.

Cosmological hydrogen recombination: The effect of extremely high-nstates

Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and re-ionization. The Planck} mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as l~2500, necessitating a calculation of recombination with fractional accuracy of ~10^{-3}. Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculations separately follow angular momentum sublevels of the hydrogen atom to accurately treat non-equilibrium effects at late times (z<900). The inclusion of extremely high-n (n>100) states of hydrogen is then computationally challenging, preventing until now a determination of the maximum n needed to predict CMB anisotropy spectra with sufficient accuracy for Planck. Here, results from a new multi-level-atom code (RecSparse) are presented. For the first time, `forbidden' quadrupole transitions of hydrogen are included, but shown to be negligible. RecSparse is designed to quickly calculate recombination histories including extremely high-n states in hydrogen. Histories for a sequence of values as high as n_max=250 are computed, keeping track of all angular momentum sublevels and energy shells of the hydrogen atom separately. Use of an insufficiently high n_max value (e.g., n_max=64) leads to errors (e.g., 1.8 sigma for Planck) in the predicted CMB power spectrum. Extrapolating errors, the resulting CMB anisotropy spectra are converged to 0.5 sigma at Fisher-matrix level for n_max=128, in the purely radiative case.

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

We give a formulation of the radiative transfer equation for Lyman alpha 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 alpha 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 DP/P ~+ 11% at z~1400 in comparison with the one obtained using the Sobolev approximation. This speeds up of hydrogen recombination by DN_e/N_e ~- 1.6% at z~1190, implying |DC_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 for 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 alpha line from the normal Lorentzian, and (iii) a thermodynamic correction factor, which occurs to be very important. All 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 alpha 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 (abridged)

Cosmological hydrogen recombination: influence of resonance and electron scattering

In this paper we consider the effects of resonance and electron scattering on the escape of Lyman alpha photons during cosmological hydrogen recombination. We pay particular attention to the influence of atomic recoil, Doppler boosting and Doppler broadening using a Fokker-Planck approximation of the redistribution function describing the scattering of photons on the Lyman alpha resonance of moving hydrogen atoms. We extend the computations of our recent paper on the influence of the 3d/3s-1s two-photon channels on the dynamics of hydrogen recombination, simultaneously including the full time-dependence of the problem, the thermodynamic corrections factor, leading to a frequency-dependent asymmetry between the emission and absorption profile, and the quantum-mechanical corrections related to the two-photon nature of the 3d/3s-1s emission and absorption process on the exact shape of the Lyman alpha emission profile. We show here that due to the redistribution of photons over frequency hydrogen recombination is sped up by DN_e/N_e~-0.6% at z~900. For the CMB temperature and polarization power spectra this results in |DC_l/C_l|~0.5%-1% at l >~ 1500, and therefore will be important for the analysis of future CMB data in the context of the PLANCK Surveyor, SPT and ACT. The main contribution to this correction is coming from the atomic recoil effect (DN_e/N_e~-1.2% at z~900), while Doppler boosting and Doppler broadening partially cancel this correction, again slowing hydrogen recombination down by DN_e/N_e~0.6% at z~900. The influence of electron scattering close to the maximum of the Thomson visibility function at z~1100 can be neglected. (abridged)

Pre-recombinational energy release and narrow features in the CMB spectrum

Energy release in the early Universe (z<~ 2x10^6) should lead to some broad spectral distortion of the cosmic microwave background (CMB) radiation field, which can be characterized as y-type distortion when the injection process started at redshifts z<~ 5x10^4. Here we demonstrate that if energy was released before the beginning of cosmological hydrogen recombination (z~1400), closed loops of bound-bound and free-bound transitions in HI and HeII lead to the appearance of (i) characteristic multiple narrow spectral features at dm and cm wavelengths, and (ii) a prominent sub-millimeter feature consisting of absorption and emission parts in the far Wien tail of CMB spectrum. The additional spectral features are generated in the pre-recombinational epoch of HI (z>~1800) and HeII (z>~7000), and therefore differ from those arising due to normal cosmological recombination in the undisturbed CMB blackbody radiation field. We present the results of numerical computations including 25 atomic shells for both HI and HeII, and discuss the contributions of several individual transitions in detail. As examples, we consider the case of instantaneous energy release (e.g. due to phase transitions) and exponential energy release because of long-lived decaying particles. Our computations show that due to possible pre-recombinational atomic transitions the variability of the CMB spectral distortion increases when comparing with the distortions arising in the normal recombination epoch. The existence of these narrow spectral features would open an unique way to separate y-distortions due to pre-recombinational ($1400<~ z <~5x10^4) energy release from those arising in the post-recombinational era at redshifts z<~800. (abridged)

Equivalent two-level atom method for calculating the kinetics of cosmological hydrogen recombination

The effective coefficient of recombination to the second level, which enters the equations describing the recombination kinetics in the cosmological HII region, is calculated. The calculation method is based on the quasi-steady-state approximation and makes it possible to adequately consider cascade transitions and induced processes without the necessity to numerically solve a complete set of corresponding kinetic equations.

Two-photon transitions in primordial hydrogen recombination

The subject of cosmological hydrogen recombination has received much attention recently because of its importance to predictions for and cosmological constraints from cosmic microwave background observations. While the central role of the two-photon decay $2s\ensuremath{\rightarrow}1s$ has been recognized for many decades, high-precision calculations require us to consider two-photon decays from the higher states $ns$, $nd\ensuremath{\rightarrow}1s$ ($n\ensuremath{\ge}3$). Simple attempts to include these processes in recombination calculations with an effective two-photon decay coefficient analogous to the $2s$ decay coefficient ${\ensuremath{\Lambda}}_{2s}=8.22\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ have suffered from physical problems associated with the existence of kinematically allowed sequences of one-photon decays, e.g. $3d\ensuremath{\rightarrow}2p\ensuremath{\rightarrow}1s$, that technically also produce two photons. These correspond to resonances in the two-photon spectrum that are optically thick to two-photon absorption, necessitating a radiative transfer calculation. We derive the appropriate equations, develop a numerical code to solve them, and verify the results by finding agreement with analytic approximations to the radiative transfer equation. The related processes of Raman scattering and two-photon recombination are included using similar machinery. Our results show that early in recombination the two-photon decays act to speed up recombination, reducing the free electron abundance by 1.3% relative to the standard calculation at $z=1300$. However, we find that some photons between $\mathrm{Ly}\ensuremath{\alpha}$ and $\mathrm{Ly}\ensuremath{\beta}$ are produced, mainly by $3d\ensuremath{\rightarrow}1s$ two-photon decay and $2s\ensuremath{\rightarrow}1s$ Raman scattering. At later times, these photons redshift down to $\mathrm{Ly}\ensuremath{\alpha}$, excite hydrogen atoms, and act to slow recombination. Thus, the free electron abundance is increased by 1.3% relative to the standard calculation at $z=900$. Our calculation involves a very different physical argument than the recent studies of Wong and Scott and Chluba and Sunyaev, and produces a much larger effect on the ionization history. The implied correction to the cosmic microwave background power spectrum is negligible for the recently released WMAP and ACBAR data, but at Fisher matrix level will be $7\ensuremath{\sigma}$ for Planck.

Two-photon transitions in hydrogen and cosmological recombination

We study the two-photon process for the transitions and in hydrogen up to large n. For we provide simple analytic fitting formulae to describe the non-resonant part of the two-photon emission profiles. Combining these with the analytic form of the cascade-term yields a simple and accurate description of the full two-photon decay spectrum, which only involves a sum over a few intermediate states. We demonstrate that the cascade term naturally leads to a nearly Lorentzian shape of the two-photon profiles in the vicinity of the resonances. However, due to quantum-electrodynamical corrections, the two-photon emission spectra deviate significantly from the Lorentzian shape in the very distant wings of the resonances. We investigate up to which distance the two-photon profiles are close to a Lorentzian and discuss the role of the interference term. We then analyze how the deviation of the two-photon profiles from the Lorentzian shape affects the dynamics of cosmological hydrogen recombination. Since in this context the escape of photons from the Lyman-α resonance plays a crucial role, we concentrate on the two-photon corrections in the vicinity of the Lyman-α line. Our computations show that the changes in the ionization history due to the additional two-photon process from high shell () likely do not reach the percent-level. For conservative assumptions we find a correction at redshift . This is numerically similar to the result of another recent study; however, the physics leading to this conclusion is rather different. In particular, our calculations of the effective two-photon decay rates yield significantly different values, where the destructive interference of the resonant and non-resonant terms plays a crucial role in this context. We also show that the bulk of the corrections to the ionization history is only due to the 3s and 3d-states and that the higher states do not contribute significantly.

Is there a need and another way to measure the cosmic microwave background temperature more accurately?

The recombination history of the Universe depends exponentially on the temperature, T0, of the cosmic microwave background. Therefore tiny changes of T0 are expected to lead to significant changes in the free electron fraction. Here we show that even the current 1σ-uncertainty in the value of T0 results in more than half a percent ambiguity in the ionization history, and more than 0.1% uncertainty in the TT and EE power spectra at small angular scales. We discuss how the value of T0 affects the highly redshifted cosmological hydrogen recombination spectrum and demonstrate that T0 could, in principle, be measured by looking at the low frequency distortions of the cosmic microwave background spectrum. For this no absolute measurements are necessary, but sensitivities on the level of ∼30 nK are required to extract the quasi-periodic frequency-dependent signal with typical ∆ν/ν ∼ 0.1 coming from cosmological recombination. We also briefly mention the possibility of obtaining additional information on the specific entropy of the Universe, and other cosmological parameters.

Cosmological hydrogen recombination: Lynline feedback and continuum escape

We compute the corrections to the cosmological hydrogen recombination history due to delayed feedback of Lyman-series photons and the escape in the Lyman-continuum. The former process is expected to slightly delay recombination, while the latter should allow the medium to recombine a bit faster. It is shown that the subsequent feedback of released Lyman-n photons on the lower lying Lyman-(n-1) transitions yields a maximal correction of DN_e/N_e 0.22% at z~ 1050. Including only Lyman-\beta feedback onto the Lyman-\alpha transition, accounts for most of the effect. We find corrections to the cosmic microwave background TT and EE power spectra \change{with typical peak to peak amplitude |DC^{TT}_l/C^{TT}_l|~0.15% and |\Delta C^{EE}_l/C^{EE}_l|~0.36% at l<~3000. The escape in the Lyman-continuum and feedback of Lyman-\alpha photons on the photoionization rate of the second shell lead to modifications of the ionization history which are very small (less than |DN_e/N_e|~few x 10^{-6}).

The effect of forbidden transitions on cosmological hydrogen and helium recombination

More than half of the atoms in the Universe recombined via forbidden transitions, so that accurate treatment of the forbidden channels is important in order to follow the cosmological recombination process with the level of precision required by future microwave anisotropy experiments. We perform a multilevel calculation of the recombination of hydrogen (H) and helium (He) with the addition of the 2 3 P 1 -1 1 S 0 spin-forbidden transition for neutral helium (He I), plus the nS-1S and nD-1S two-photon transitions for H (up to n = 40) and among singlet states of He I (n ≤ 10 and e ≤ 7). The potential importance of such transitions was first proposed by Dubrovich & Grachev using an effective three-level atom model. Here, we relax the thermal equilibrium assumption among the higher excited states to investigate the effect of these extra forbidden transitions on the ionization fraction Χ e and the cosmic microwave background (CMB) angular power spectrum C e . The spin-forbidden transition brings more than 1 per cent change in Χ e . The two-photon transitions may also give non-negligible effects, but currently accurate rates exist only for n ≤ 3. We find that changes in both Χ e and C e . would be at about the per cent level with the approximate rates given by Dubrovich & Grachev. However, the two-photon rates from 3S to IS and 3D to IS of H appear to have been overestimated, and our best numerical calculation puts the effect on Χ e and C e at below the per cent level. Nevertheless, we do not claim that we have the definite answer, since several issues remain open; sub-per cent level computation of the C e values requires improved calculations of atomic transition rates as well as increasingly complex multilevel atom calculations.

Cosmological hydrogen recombination: populations of the high-level substates

We present results for the spectral distortions of the Cosmic Microwave Background (CMB) arising due to bound-bound transitions during the epoch of cosmological hy- drogen recombination at frequencies down to ν � 100MHz. We extend our previous treatment of the recombination problem (Rubino-Mart´on et al. 2006) now including the main collisional processes and following the evolution of all the hydrogen angular momentum sub-states for up to 100 shells. We show that, due to the low baryon den- sity of the Universe, even within the highest considered shell full statistical equilibrium (SE) is not reached and that at low frequencies the recombination spectrum is signifi- cantly different when assuming full SE for n > 2. We also directly compare our results for the ionization history to the output of the Recfast code, showing that especially at low redshifts rather big differences arise. In the vicinity of the Thomson visibility function the electron fraction differs by roughly 0.6% which affects the temperature and polarization power spectra by � 1%. Furthermore we shortly discuss the influence of free-free absorption and line broadening due to electron scattering on the bound- bound recombination spectrum and the generation of CMB angular fluctuations due to scattering of photons within the high shells.

Free-bound emission from cosmological hydrogen recombination

In this paper we compute the emission coming from the direct recombination of free electrons to a given shell (n>=2) during the epoch of cosmological hydrogen recombination. This contribution leads to a total of one photon per recombined hydrogen atom and therefore a ~30-88% increase of the recombination spectrum within the frequency range 1 GHz<=nu<=100 GHz. In particular the Balmer-continuum emission increases the distortion at nu~ 690 GHz by ~92%. With our 100 shell calculations for the hydrogen atom we find that a total of ~5 photons per hydrogen atom are emitted when including all the bound-bound transitions, the 2s two-photon decay channel and the optically thin free-bound transitions. Since the direct recombination continuum at high n is very broad only a few n-series continuua are distinguishable and most of this additional emission below nu<~30 GHz is completely featureless.

Lines in the cosmic microwave background spectrum from the epoch of cosmological hydrogen recombination

We compute the spectral distortions of the cosmic microwave background (CMB) arising during the epoch of cosmological hydrogen recombination within the standard cosmological (concordance) model for frequencies in the range 1–3500 GHz. We follow the evolution of the populations of the hydrogen levels including states up to principle quantum number n= 30 in the redshift range 500 ≤z≤ 3500. All angular momentum substates are treated individually, resulting in a total number of 465 hydrogen levels. The evolution of the matter temperature and the fraction of electrons coming from He ii are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, for example Lyman and Balmer series, as well as the emission due to the two-photon decay of the hydrogen 2s level. Furthermore, we investigate the robusteness of the results against changes in the number of shells considered. The resulting spectral distortions have a characteristic oscillatory behaviour, which might allow experimentalists to separate them from other backgrounds. The relative distortion of the spectrum exceeds a value of 10−7 at wavelengths longer than 21 cm. Our results also show the importance of detailed follow-up of the angular momentum substates, and their effect on the amplitude of the lines. The effect on the residual electron fraction is only moderate, and mainly occurs at low redshifts. The CMB angular power spectrum is changed by less than 1 per cent. Finally, our computations show that if the primordial radiation field is described by a pure blackbody, then there is no significant emission from any hydrogen transition at redshifts greater than z∼ 2000. This is in contrast to some earlier works, where the existence of a ‘pre-recombination’ peak was claimed.

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

Induced emission due to the presence of soft CMB photons slightly increases the two-photon decay rate of the 2s level of hydrogen defining the rate of cosmological recombination. This correspondingly changes the degree of ionization, the visibility function and the resulting primordial temperature anisotropies and polarization of the CMB on the percent level. These changes exceed the precision of the widely used Cmbfast and Camb codes by more than one order of magnitude and can be easily taken into account.