Time-Dependent Corrections to the Ly-alpha Escape Probability During Cosmological Hydrogen Recombination (original) (raw)
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Time-dependent corrections to the Ly αescape probability during cosmological recombination
Astronomy & Astrophysics, 2009
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.
Signals from the epoch of cosmological recombination - Karl Schwarzschild Award Lecture 2008
Astronomische Nachrichten, 2009
(ii) with the advent of high precision CMB data, e.g. as will be available using the Planck Surveyor or CMBpol, a very accurate theoretical understanding of the ionization history of the Universe becomes necessary for the interpretation of the CMB temperature and polarization anisotropies. Here we show that the uncertainty in the ionization history due to several processes, which until now were not taken in to account in the standard recombination code Recfast, reaches the percent level. In particular He ii → He i-recombination occurs significantly faster because of the presence of a tiny fraction of neutral hydrogen at z 2400. Also recently it was demonstrated that in the case of H i Lyman α photons the timedependence of the emission process and the asymmetry between the emission and absorption profile cannot be ignored. However, it is indeed surprising how inert the cosmological recombination history is even at percent-level accuracy. Observing the cosmological recombination spectrum should in principle allow us to directly check this conclusion, which until now is purely theoretical. Also it may allow to reconstruct the ionization history using observational data.
Two-photon transitions in hydrogen and cosmological recombination
Astronomy & Astrophysics, 2008
We study the two-photon process for the transitions ns → 1s and nd → 1s in hydrogen up to large n. For n ≤ 20 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 (n > 2) likely do not reach the percent-level. For conservative assumptions we find a correction ∆N e /N e ∼ −0.4% at redshift z ∼ 1160. 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.
Cosmological hydrogen recombination: influence of resonance and electron scattering
Astronomy and Astrophysics, 2009
In this paper we consider the effects of resonance and electron scattering on the escape of Lyman α 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 α 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 quantummechanical corrections related to the two-photon nature of the 3d/3s-1s emission and absorption process on the exact shape of the Lyman α emission profile. We show here that due to the redistribution of photons over frequency hydrogen recombination is sped up by ∆N e /N e ∼ −0.6% at z ∼ 900. For the CMB temperature and polarization power spectra this results in |∆C 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 (∆N e /N e ∼ −1.2% at z ∼ 900), while Doppler boosting and Doppler broadening partially cancel this correction, again slowing hydrogen recombination down by ∆N 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. We also give the cumulative results when in addition including the time-dependent correction, the thermodynamic factor and the correct shape of the emission profile. This amounts in ∆N e /N e ∼ −1.8% at z ∼ 1160 and |∆C l /C l | ∼ 1% − 3% at l 1500.
Ly alpha escape during cosmological hydrogen recombination: the 3d-1s and 3s-1s two-photon processes
Astron Astrophys, 2010
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 ∆P/P ∼ +11% at z ∼ 1400 in comparison with the one obtained using the Sobolev approximation. This speeds up of hydrogen recombination by ∆N e /N e ∼ −1.6% at z ∼ 1190, implying |∆C 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 α 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 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) lead to the largest separate contributions to the result, however they partially cancel each other close to z ∼ 1100. At z ∼ 1100 the modification due to the shape of the line profile contributes about ∆N e /N e ∼ −0.4%, while the sum of the other two contributions gives ∆N e /N e ∼ −0.9%.
Cosmological recombination: feedback of helium photons and its effect on the recombination spectrum
Monthly Notices of the Royal Astronomical Society, 2010
In this paper we consider the reprocessing of high frequency photons emitted by He ii and He i during the epoch of cosmological recombination by He i and H i. We demonstrate that, in comparison to computations which neglect all feedback processes, the number of cosmological recombination photons that are related to the presence of helium in the early Universe could be increased by ∼ 40% − 70%. Our computations imply that per helium nucleus ∼ 3 − 6 additional photons could be produced. Therefore, a total of ∼ 12 − 14 helium-related photons are emitted during cosmological recombination. This is an important addition to cosmological recombination spectrum which in the future may render it slightly easier to determine the primordial abundance of helium using differential measurements of the CMB energy spectrum. Also, since these photons are the only witnesses of the feedback process at high redshift, observing them in principle offers a way to check our understanding of the recombination physics. Here most interestingly, the feedback of He ii photons on He i leads to the appearance of several additional, rather narrow spectral features in the He i recombination spectrum at low frequencies. Consequently, the signatures of helium-related features in the CMB spectral distortion due to cosmological recombination at some given frequency can exceed the average level of ∼ 17% several times. We find that in particular the bands around ν ∼ 10 GHz, ∼ 35 GHz, ∼ 80 GHz, and ∼ 200 GHz seem to be affected strongly. In addition, we computed the changes in the cosmological ionization history, finding that only the feedback of primary He i photons on the dynamics of He ii → He i recombination has an effect, producing a change of ∆N e /N e ∼ +0.17% at z ∼ 2300. This result seems to be ∼ 2 − 3 times smaller than the one obtained in earlier computations for this process, however, the difference will not be very important for the analysis of future CMB data.
Cosmological hydrogen recombination: Lyn line feedback and continuum escape
Astronomy and Astrophysics, 2007
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 ∆N e /N e ∼ 0.22% at z ∼ 1050. Including only Lyman-β feedback onto the Lyman-α transition, accounts for most of the effect. We find corrections to the cosmic microwave background T T and EE power spectra with typical peak to peak amplitude |∆C T T l /C T T l | ∼ 0.15% and |∆C EE l /C EE l | ∼ 0.36% at l 3000. The escape in the Lymancontinuum and feedback of Lyman-α photons on the photoionization rate of the second shell lead to modifications of the ionization history which are very small (less than |∆N e /N e | ∼ few × 10 −6).
Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination
Astronomy and Astrophysics, 2006
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.
Free-bound emission from cosmological hydrogen recombination
Astronomy & Astrophysics, 2006
In this letter 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 in the recombination spectrum within the frequency range 1 GHz ≤ ν ≤ 100 GHz. In particular, the Balmer-continuum emission increases the distortion at ν ∼ 690 GHz by roughly 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 ν < ∼ 30 GHz is completely featureless.
Monthly Notices of The Royal Astronomical Society, 2009
The fraction of ionizing photons that escape their host galaxies and so are able to ionize hydrogen in the inter-galactic medium (IGM) is a critical parameter in analyses of the reionization era and early galaxy formation. Studies of the reionization history normally suffer from a degeneracy between the unknown values for the efficiency with which high redshift galaxies turn mass into stars and the escape fraction of ionizing photons. Recent gamma-ray burst (GRB) measurements of the star formation rate density during reionization provide the first opportunity to break this degeneracy. We confront a semi-analytic model for reionization with the GRB-derived star formation rate, as well as observations of the Ly-alpha forest and the CMB. Assuming that UV photons produced in star-forming galaxies dominate the reionization process, we show that the escape fraction of ionizing photons from high redshift galaxies is ~5% [log(f_esc)=-1.35+/-0.15 (68%)] for our fiducial model. This value is reasonably stable against uncertainties in the modeling, including the implementation of radiative feedback, the possibility of an evolving escape fraction, and the unknown shape of the IMF, which in sum contribute ~0.2 dex of additional systematic uncertainty on the value of escape fraction.