All Figures

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{fig1.ps}\end{figure}$ Figure 1: Distortion of the power spectrum due to coherent scattering in the H $\alpha$ line, as a function of the observing frequency today. The maximum distortion (in absolute value) is obtained at $\nu =452$ GHz for $\ell =873$ . We show that shifting the observing multipole in a region of $\Delta \ell = \pm 70$ around the maximum, we still have the signal within the 70% of the peak intensity.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{fig2.ps}\end{figure}$ Figure 2: Distortion of the power spectrum due to scattering in the H $\alpha$ line as a function of angular scale.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{fig3.eps}\end{figure}$ Figure 3: Multilevel hydrogen recombination as computed in this paper (using 10 levels for quantum number n, and following independently all the states of angular momentum), compared with the standard "effective three level'' computation from RECFAST. It is shown $x_{\rm e}$ (= $n_{\rm e}/n_{\rm H}$ ) as a function of redshift in the vicinity of the epoch of cosmic recombination for the cosmological model with parameters $\Omega _{\rm b}=0.044$ , $\Omega _{{\rm tot}}=1$ and h=0.71 (Bennett et al. 2003).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{fig4.eps}\end{figure}$ Figure 4: Optical depths for several lines considered in this paper, as a function of redshift z. All values were computed using method I. For the H $\alpha$ line, it is also shown the computation using the Saha approximation (method II), to show that with this method, deviations with respect to the detailed calculation (method I) only appear when the Universe is practically transparent, which corresponds to the high frequency wing of the line and where the expected effect is not important.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{fig5.eps}\end{figure}$ Figure 5: Dependence of the optical depth with the redshift for the H $\alpha$ line. For comparison, we also show the Thomson visibility function ( $\mathcal{V}_{\rm T}(\eta) = ({\rm d}\tau_{\rm T}/{\rm d}\eta) \exp(-\tau_{\rm T})$ ), the function $\exp(-\tau_{\rm T})$ , and the function $\tau_{{\rm H}\alpha} \exp(-\tau_{\rm T})$ . To display all of them on the same scale, they were rescaled by the indicated factors.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{fig6.ps}\end{figure}$ Figure 6: Linear term of the correction to the angular power spectrum originated from coherent scattering in a line located at the specified redshift. These curves have to be multiplied by the optical depth in the line to obtain the first order correction to $\delta C_\ell$ . Thick lines correspond to positive values, and thin lines to negative ones. For comparison, it is also shown the primary CMB power spectrum (dotted lines). Note that at high- $\ell$ , the correction is roughly $-2 C_\ell$ for the case z=850 or z=950, as we would expect for a line located between us and recombination. This property disappears when we go to higher redshifts, because in that case the line is located inside recombination where radiative viscosity and thermal conductivity are important. (See movie in the electronic version.)
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{fig7.eps}\end{figure}$ Figure 7: Correction to the visibility function in the presence of coherent scattering in the H $\alpha$ line. To first order in the optical depth of the line ( $\tau _{nm}$ ), there are two terms. One is associated with suppression (Eq. (7)), and the other one with the generation of new anisotropies (Eq. (8)). Both terms are plotted (dot-dashed and dashed lines, respectively) together with their sum (solid line), for the case of observing the H $\alpha$ line placed at z=1000. For comparison, we also show the Thomson visibility function (dotted line).
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{fig8.ps}\end{figure}$ Figure 8: Correction to the power spectrum due to coherent scattering in the H $\alpha$ line. We plot three curves for three different redshifts, namely z=900, 1150 (which correspond to 507 GHz and 397 GHz, respectively), and also z=1010 (452 GHz), which is the redshift (frequency) at which we have the maximum amplitude for signal, at multipole $\ell =873$ . Note how the z=900 case mimics the shape of the power spectrum at high multipoles, but with negative sign, and how this behavior disappears as we go to higher redshifts. Observing at different frequencies with sufficiently narrow spectral bands, we can perform tomography of the recombination epoch using the H $\alpha$ line.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{fig9.ps}\end{figure}$ Figure 9: Relative correction ( $\vert\delta C_\ell \vert / C_\ell$ ) to the power spectrum due to scattering in the H $\alpha$ line, as a function of angular scale ( $\ell$ ). Thick lines correspond to positive values whereas thin lines represent negative ones. The distortions are larger at small angular scales, approaching the asymptotics of $-2\tau _{{\rm H}\alpha }$ (dotted line) for redshifts before the peak of the visibility function. The region where this asymptotic behavior is valid changes with redshift, and for redshifts well inside the recombination, it disappears. This behavior could give us information about the process of dissipation of short wavelength adiabatic perturbations due to radiative viscosity and thermal conductivity during recombination.
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In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{fig10a.eps}\vspace*{2mm} \... ...10b.eps}\vspace*{2mm} \includegraphics[width=6.2cm,clip]{fig10c.eps}\end{figure}$ Figure 10: Angular power spectrum arising from the Balmer recombination lines of hydrogen during cosmological recombination, as a function of the redshifted (observed) frequency. We plot the values at $\ell =20$ ( top panel), at $\ell =300$ ( middle panel), and at $\ell =800$ ( bottom panel). Thick lines corresponds to region where the $\delta C_\ell$ are positive, whereas thin lines correspond to negative values.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{fig11.ps}\end{figure}$ Figure 11: Same as Fig. 10, but only for the H $\alpha$ line which gives the maximum contribution. The vertical axis is now presented in a linear scale so we can explicitly see the change of sign. We plot values for five multipole scales, $\ell =100, 350, 750, 1200$ , and also $\ell =873$ , which is the multipole at which we have the maximum signal at $\nu =452$ GHz. (See movie in the electronic version.)
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In the text

$\begin{figure} \par\includegraphics[height=5.2cm,width=7.6cm,clip]{fig12a.eps}\i... ...g12c.eps}\includegraphics[height=5.2cm,width=7.4cm,clip]{fig12d.eps}\end{figure}$ Figure 12: Angular power spectrum arising from the P $\alpha$ ( top row) and B $\alpha$ ( bottom row) hydrogen lines during recombination, as a function of the redshifted frequency ( left column) and the angular multipole ( right column). The solid lines in all panels refer to the cases in which the signal is maximum, according to Table 2.
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In the text

$\begin{figure} \par\includegraphics[height=8.6cm,width=15cm,clip]{fig13.eps}\end{figure}$ Figure 13: a) Maximum contribution of the coherent scattering in the H $\alpha$ line to the angular CMB power spectrum, as seen by an hypothetical experiment measuring at 430 GHz and 130 GHz. The upper thick solid line gives the reference power spectrum. b) Contribution of foregrounds at these frequencies. All thin lines refer to the foreground model as quoted in T00: free-free emission is shown as dotted line; synchrotron emission as solid line; the thermal SZ effect produced in filaments as dot-dashed line and the thermal dust emission is shown by dashed lines. Rayleigh scattering contribution is shown as a thick long-dashed line, whereas the cosmic variance contribution associated to this effect is shown as a thin long-dashed line.
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In the text

$\begin{figure} \par\includegraphics[width=7.75cm,clip]{fig14.eps}\end{figure}$ Figure 14: Multilevel hydrogen recombination computed in this paper. It is presented the evolution of the relative fraction of electrons ( $x_{\rm e}$ ), neutral hydrogen atoms ( $x_{{\rm HI}}=n_{{\rm HI}}/n_{\rm H}$ ) and the population of the 2p level ( $x_{{\rm 2p}}=n_{{\rm 2p}}/n_{\rm H}$ ), as a function of the redshift z in the vicinity of the epoch of recombination (near the peak of the visibility function). The $x_{{\rm 2p}}$ values were multiplied by 10¹⁰ to display all lines in the same scale. The cosmological model adopted here is the same as in Fig. 3.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{fig2.ps}\end{figure}$	Figure 2: Distortion of the power spectrum due to scattering in the H $\alpha$ line as a function of angular scale.
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$\begin{figure} \par\includegraphics[height=5.2cm,width=7.6cm,clip]{fig12a.eps}\i... ...g12c.eps}\includegraphics[height=5.2cm,width=7.4cm,clip]{fig12d.eps}\end{figure}$	Figure 12: Angular power spectrum arising from the P $\alpha$ ( top row) and B $\alpha$ ( bottom row) hydrogen lines during recombination, as a function of the redshifted frequency ( left column) and the angular multipole ( right column). The solid lines in all panels refer to the cases in which the signal is maximum, according to Table 2.
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