471 research outputs found
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.Comment: 17 pages, 8 figures, minor typos corrected, accepted by MNRAS,
CosmoRec available at http://www.Chluba.de/CosmoRe
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
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
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
Could the Cosmological Recombination Spectrum Help Us Understand Annihilating Dark Matter?
In this paper we explore the potential effects of DM annihilations on the
cosmological recombination spectrum. With this example we want to demonstrate
that the cosmological recombination spectrum in principle is sensitive to
details related to possible extra energy release during recombination. We
restrict ourselves to DM models which produce a negligible primordial
distortion of the CMB energy spectrum. However, since during the epoch of
cosmological recombination a large fraction of the deposited energy can
directly go into ionizations and excitations of neutral atoms, both the
cosmological recombination spectrum and ionization history can still be
affected significantly. We compute the modifications to the cosmological
recombination spectrum using our multi-level HI and HeI recombination code,
showing that additional photons are created due to uncompensated loops of
transitions which are induced by DM annihilations. As we illustrate here, the
results depend on the detailed branching of the deposited energy into heating,
ionizations and excitations. This dependence in principle should allow us to
shed light on the nature of the underlying annihilating DM model (or more
generally speaking, the mechanism leading to energy injection) when measuring
the cosmological recombination spectrum. However, for current upper limits on
the potential DM annihilation rate during recombination the cosmological
recombination spectrum is only affected at the level of a few percent.
Nevertheless, we argue here that the cosmological recombination spectrum would
provide another independent and very direct way of checking for the presence of
sources of extra ionizing or exciting photons at high redshifts. This would
open an new window to possible (non-standard) processes occurring (abridged)Comment: 14 pages, 11 figure, submitted to MNRA
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&
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
Precise cosmological parameter estimation using CosmoRec
We use the new cosmological recombination code, CosmoRec, for parameter
estimation in the context of (future) precise measurements of the CMB
temperature and polarization anisotropies. We address the question of how
previously neglected physical processes in the recombination model of Recfast
affect the determination of key cosmological parameters, for the first time
performing a model-by-model computation of the recombination problem. In
particular we ask how the biases depend on different combinations of
parameters, e.g. when varying the helium abundance or the effective number of
neutrino species in addition to the standard six parameters. We also forecast
how important the recombination corrections are for a combined Planck, ACTPol
and SPTpol data analysis. Furthermore, we ask which recombination corrections
are really crucial for CMB parameter estimation, and whether an approach based
on a redshift-dependent correction function to Recfast is sufficient in this
context.Comment: 12 pages, 7 figures, submitted to MNRA
Semi-blind Eigen-analyses of Recombination Histories Using CMB Data
Cosmological parameter measurements from CMB experiments such as Planck,
ACTpol, SPTpol and other high resolution follow-ons fundamentally rely on the
accuracy of the assumed recombination model, or one with well prescribed
uncertainties. Deviations from the standard recombination history might suggest
new particle physics or modified atomic physics. Here we treat possible
perturbative fluctuations in the free electron fraction, \Xe(z), by a
semi-blind expansion in densely-packed modes in redshift. From these we
construct parameter eigenmodes, which we rank order so that the lowest modes
provide the most power to probe the \Xe(z) with CMB measurements. Since the
eigenmodes are effectively weighed by the fiducial \Xe history, they are
localized around the differential visibility peak, allowing for an excellent
probe of hydrogen recombination, but a weaker probe of the higher redshift
helium recombination and the lower redshift highly neutral freeze-out tail. We
use an information-based criterion to truncate the mode hierarchy, and show
that with even a few modes the method goes a long way towards morphing a
fiducial older {\sc Recfast} into the new and improved {\sc
CosmoRec} and {\sc HyRec} in the hydrogen recombination
regime, though not well in the helium regime. Without such a correction, the
derived cosmic parameters are biased. We discuss an iterative approach for
updating the eigenmodes to further hone in on if large
deviations are indeed found. We also introduce control parameters that
downweight the attention on the visibility peak structure, e.g., focusing the
eigenmode probes more strongly on the \Xe (z) freeze-out tail, as would be
appropriate when looking for the \Xe signature of annihilating or decaying
elementary particles.Comment: 28 pages, 26 Fig
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