97 research outputs found
Two-photon transitions in hydrogen and cosmological recombination
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-alpha resonance plays a crucial role, we concentrate on
the two-photon corrections in the vicinity of the Lyman-alpha 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 DN_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 (abridged)Comment: 20 pages, 13 figures, 4 tables, accepted versio
The evolution of CMB spectral distortions in the early Universe
The energy spectrum of the cosmic microwave background (CMB) allows
constraining episodes of energy release in the early Universe. In this paper we
revisit and refine the computations of the cosmological thermalization problem.
For this purpose a new code, called CosmoTherm, was developed that allows
solving the coupled photon-electron Boltzmann equation in the expanding,
isotropic Universe for small spectral distortion in the CMB. We explicitly
compute the shape of the spectral distortions caused by energy release due to
(i) annihilating dark matter; (ii) decaying relict particles; (iii) dissipation
of acoustic waves; and (iv) quasi-instantaneous heating. We also demonstrate
that (v) the continuous interaction of CMB photons with adiabatically cooling
non-relativistic electrons and baryons causes a negative mu-type CMB spectral
distortion of DI_nu/I_nu ~ 10^{-8} in the GHz spectral band. We solve the
thermalization problem including improved approximations for the double Compton
and Bremsstrahlung emissivities, as well as the latest treatment of the
cosmological recombination process. At redshifts z <~ 10^3 the matter starts to
cool significantly below the temperature of the CMB so that at very low
frequencies free-free absorption alters the shape of primordial distortions
significantly. In addition, the cooling electrons down-scatter CMB photons
introducing a small late negative y-type distortion at high frequencies. We
also discuss our results in the light of the recently proposed CMB experiment
Pixie, for which CosmoTherm should allow detailed forecasting. Our current
computations show that for energy injection because of (ii) and (iv) Pixie
should allow to improve existing limits, while the CMB distortions caused by
the other processes seem to remain unobservable with the currently proposed
sensitivities and spectral bands of Pixie.Comment: 22 pages, 19 figures, 1 table, accepted by MNRA
Evolution of low-frequency features in the CMB spectrum due to stimulated Compton scattering and Doppler-broadening
We discuss a new solution of the Kompaneets-equation for physical situations
in which low frequency photons, forming relatively narrow spectral details, are
Compton scattered in an isotropic, infinite medium with an intense ambient
blackbody field that is very close to full thermodynamic equilibrium with the
free electrons. In this situation the background-induced stimulated Compton
scattering slows down the motion of photons toward higher frequencies by a
factor of 3 in comparison with the solution that only takes into account
Doppler-broadening and boosting. This new solution is important for detailed
computations of cosmic microwave background spectral distortions arising due to
uncompensated atomic transitions of hydrogen and helium in the early Universe.
In addition we derive another analytic solution that only includes the
background-induced stimulated Compton scattering and is valid for power-law
ambient radiation fields. This solution might have interesting applications for
radio lines arising inside of bright extra-galactic radio source, where
according to our estimates line shifts because of background-induced stimulated
scattering could be amplified and even exceed the line broadening due to the
Doppler-effect.Comment: 5 pages, 2 figures, submitted to A&
Cosmological hydrogen recombination: Lyn line 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}).Comment: 5+epsilon pages, 7 figures, accepted versio
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)Comment: 17 pages, 12 Figures, 1 Table, submitted to A&
Ly alpha escape 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)Comment: 30 pages, 21 figures, submitted to A&
Time-Dependent Corrections to the Ly-alpha Escape Probability During Cosmological Hydrogen Recombination
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-alpha
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-alpha 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
DP/P~5-10%. This is because during recombination the ionization degree changes
significantly over a characteristic time Dz/z~10%, so that at percent level
accuracy the photon distribution is not evolving (abridged)Comment: 18 pages, 12 figures, accepted versio
Cosmological hydrogen recombination: populations of the high level sub-states
We present results for the spectral distortions of the Cosmic Microwave
Background (CMB) arising due to bound-bound transitions during the epoch of
cosmological hydrogen recombination at frequencies down to nu~100MHz. We extend
our previous treatment of the recombination problem 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
density 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 significantly 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.Comment: 12 pages, 11 figures, submitted to MNRAS, revised version, included
two new figures, Sect. 3.4 adde
Cosmological recombination: feedback of helium photons and its effect on the recombination spectrum
In this paper we consider the re-processing of high frequency photons emitted
by HeII and HeI during the epoch of cosmological recombination by HeI and HI.
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 HeII photons on HeI leads to the appearance of
several additional, rather narrow spectral features in the HeI 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 nu ~10GHz, ~35GHz, ~80GHz, and ~200GHz
seem to be affected strongly. In addition, we computed the changes in the
cosmological ionization history, finding that only the feedback of primary HeI
photons on the dynamics of HeII-->HeI recombination has an effect, producing a
change of DN_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
(abridged).Comment: 28 pages, 24 figures, submitted to MNRA
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