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Register a new userLines in the cosmic microwave background spectrum from the epoch of cosmological helium recombination
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J. A. Rubino-Martin
Publication date
2008
fields
Physics
and research's language is
English
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The main goal of this work is to calculate the contributions to the cosmological recombination spectrum due to bound-bound transitions of helium. We show that due to the presence of helium in the early Universe unique features appear in the total cosmological recombination spectrum. These may provide a unique observational possibility to determine the relative abundance of primordial helium, well before the formation of first stars. We include the effect of the tiny fraction of neutral hydrogen atoms on the dynamics of HeII -> HeI recombination at redshifts $zsim 2500$. As discussed recently, this process significantly accelerates HeII -> HeI recombination, resulting in rather narrow and distinct features in the associated recombination spectrum. In addition this process induces some emission within the hydrogen Lyman-$alpha$ line, before the actual epoch of hydrogen recombination round $zsim 1100-1500$. We also show that some of the fine structure transitions of neutral helium appear in absorption, again leaving unique traces in the Cosmic Microwave Background blackbody spectrum, which may allow to confirm our understanding of the early Universe and detailed atomic physics.
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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 GHz-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 $500leq zleq 3500$. All angular momentum sub-states 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 HeII are also included. We present a detailed discussion of the distortions arising from the main dipolar transitions, e.g. 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 21cm. Our results also show the importance of detailed follow-up of the angular momentum sub-states, 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%. 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 $z sim 2000$. This is in contrast to some earlier works, where the existence of a `pre-recombination peak was claimed.
By using N-body hydrodynamical cosmological simulations in which the chemistry of major metals and molecules is consistently solved for, we study the interaction of metallic fine-structure lines with the CMB. Our analysis shows that the collisional induced emissions in the OI 145 $mu$m and CII 158 $mu$m lines during reionization introduce a distortion of the CMB spectrum at low frequencies ($ u < 300$ GHz) with amplitudes up to $Delta I_{ u}/B_{ u}(T_{rm CMB})sim 10^{-8}$-$10^{-7}$, i.e., at the $sim 0.1$ percent level of FIRAS upper limits. Shorter wavelength fine-structure transitions (OI 63 $mu$m, FeII 26 $mu$m, and SiII 35 $mu$m) typically sample the reionization epoch at higher observing frequencies ($ u > 400$ GHz). This corresponds to the Wien tail of the CMB spectrum and the distortion level induced by those lines may be as high as $Delta I_{ u}/B_{ u}(T_{rm CMB})sim 10^{-4}$. The angular anisotropy produced by these lines should be more relevant at higher frequencies: while practically negligible at $ u=145 $GHz, signatures from CII 158 $mu$m and OI 145 $mu$m should amount to 1%-5% of the anisotropy power measured at $l sim 5000$ and $ u=220 $GHz by the ACT and SPT collaborations (after assuming $Delta u_{rm obs}/ u_{rm obs}simeq 0.005$ for the line observations). Our simulations show that anisotropy maps from different lines (e.g., OI 145 $mu$m and CII 158 $mu$m) at the same redshift show a very high degree ($>0.8$) of spatial correlation, allowing for the use of observations at different frequencies to unveil the same snapshot of the reionization epoch. Finally, our simulations demonstrate that line-emission anisotropies extracted in narrow frequency/redshift shells are practically uncorrelated in frequency space, thus enabling standard methods for removal of foregrounds that vary smoothly in frequency, just as in HI 21 cm studies.
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets.
The advent of precise measurements of the cosmic microwave background (CMB) anisotropies has motivated correspondingly precise calculations of the cosmic recombination history. Cosmic recombination proceeds far out of equilibrium because of a bottleneck at the $n=2$ level of hydrogen: atoms can only reach the ground state via slow processes: two-photon decay or Lyman-$alpha$ resonance escape. However, even a small primordial abundance of molecules could have a large effect on the interline opacity in the recombination epoch and lead to an additional route for hydrogen recombination. Therefore, this paper computes the abundance of the H$_2$ molecule during the cosmic recombination epoch. Hydrogen molecules in the ground electronic levels X$^1Sigma^+_g$ can either form from the excited H$_2$ electronic levels B$^1Sigma^+_u$ and C$^1Pi_u$ or through the charged particles H$_2^+$, HeH$^+$ and H$^-$. We follow the transitions among all of these species, resolving the rotational and vibrational sub-levels. Since the energies of the X$^1Sigma^+_g$--B$^1Sigma^+_u$ (Lyman band) and X$^1Sigma^+_g$-C$^1Pi_u$ (Werner band) transitions are near the Lyman-$alpha$ energy, the distortion of the CMB spectrum caused by escaped H Lyman-line photons accelerates both the formation and the destruction of H$_2$ due to this channel relative to the thermal rates. This causes the populations of H$_2$ molecules in X$^1Sigma^+_g$ energy levels to deviate from their thermal equilibrium abundances. We find that the resulting H$_2$ abundance is $10^{-17}$ at $z=1200$ and $10^{-13}$ at $z=800$, which is too small to have any significant influence on the recombination history.
We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a $Delta chi^{2}$ statistic, simulate the measurements of MAXIMA-1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals to Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15%, and confidence interval-widths that agree within 30%. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of Omega=0.89{+0.26atop -0.19}, Omega_{rm B}h^2=0.026{+0.020atop -0.011} and n=1.02{+0.31atop -0.10}, and the Bayesian analysis gives values of Omega=0.98{+0.14atop -0.19}, Omega_{rm B}h^2=0.0.029{+0.015atop-0.010}, and $n=1.18{+0.10atop -0.23}$, all at the 95% confidence level.
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