Signature of patchy reionization in the polarization anisotropy of the CMB

Olivier Doré, Gil Holder, Marcelo Alvarez, Ilian T. Iliev, Garrelt Mellema, Ue-Li Pen, and Paul R. Shapiro

Phys. Rev. D 76, 043002 – Published 3 August 2007

Abstract

The inhomogeneous ionization state of the Universe when the first sources of ionizing radiation appeared should lead to anisotropies in the polarization of the cosmic microwave background. We use cosmological simulations of the process by which the first sources ionized the intergalactic medium to study the induced polarization anisotropies. We find that the polarization anisotropies have rms of order $\sim 0.01 μ K$ , and local peak values of $\sim 0.1 μ K$ , smaller than those due to gravitational lensing on small scales. The polarization direction is highly coherent over degree scales. This directional coherence is not expected from either primary anisotropy or gravitational lensing effects, making the largest signals due to inhomogeneous ionization relatively easy to isolate, should experiments achieve the necessary very low noise levels.

Received 30 January 2007

DOI:https://doi.org/10.1103/PhysRevD.76.043002

Authors & Affiliations

Olivier Doré¹, Gil Holder², Marcelo Alvarez³, Ilian T. Iliev¹, Garrelt Mellema⁴, Ue-Li Pen¹, and Paul R. Shapiro⁵

¹Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
²Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada
³Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, P.O. Box 20450, MS 29, Stanford, California, 94309, USA
⁴Stockholm Observatory, AlbaNova University Center, Stockholm University, SE-106 91 Stockholm, Sweden
⁵Department of Astronomy, University of Texas, Austin, 78712-1083, USA

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Vol. 76, Iss. 4 — 15 August 2007

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Images

Figure 1
Left panel: Quadrupole $C_{2}$ as a function of $z$ . Right panel: Correlation $⟨ a_{2 m} (0, 0, τ (z)) a_{2 m^{'}}^{*} (0, 0, τ (z^{'})) ⟩$ for $(m, m^{'}) = (2, 2)$ , where $z$ and $z^{'}$ correspond to the center of each box. Each line/color corresponds to a given $z^{'}$ . The correlation peaks to 1 of course when $z = z^{'}$ . Similar results are obtained for $(m, m^{'}) = (1, 1)$ or (0, 0).Reuse & Permissions
Figure 2
Map of optical depth (color scale) and direction of polarization (shown by sticks denoting the orientation of the electric field) at each location in a typical map for the WMAP3 cosmology and the f250 ionization model. Note that the polarization amplitude is proportional to the optical depth (and also to the primordial quadrupole at that location), and that the amplitude of the polarization is not proportional to the length of the sticks.Reuse & Permissions
Figure 3
Polarization maps for a typical realization for the WMAP3 cosmology and the f250 ionization model. Top panels show E and B maps, while bottom panels show Q and U maps. The mean was subtracted from each of these maps to ease the comparison.Reuse & Permissions
Figure 4
Angular power spectrum of EE and BB polarization anisotropy, compared with primordial EE and BB signals (tensor to scalar ratio, $r = 0.2$ ) and EE and BB signals including the effects of gravitational lensing (solid lines) or not (dashed lines). Several analytical computations as in Hu [6] are shown as well. The model that peaks around $ℓ ≃ 80$ receives most of its contribution from $≃ 200 Mpc$ (comoving) bubbles, whereas the one that peaks around $ℓ ≃ 800$ is dominated by the contribution of $≃ 40 Mpc$ (comoving) bubbles. Note, however, that this model is not meant to reproduce our simulations (see text for details). The power level is smaller than the lensing-induced BB signal by several orders of magnitude on small scales. Planck sensitivity is shown by the dash-triple-dot line, while an estimate for something like ACT or SPTPol is shown as a dashed line for a bin of width $Δ ℓ = 10$ . For comparison, we also display an additional BB spectrum with $r = 0.001$ .Reuse & Permissions
Figure 5
Measured angular power spectra of individual simulation volumes at different redshifts, showing (left panel) the projection of the 3D power spectrum of the ionized hydrogen distribution using the Limber approximation, (middle panel) the angular power spectrum of the optical depth maps at each redshift deduced from this 3D power spectrum, and (right panel) the measured angular power spectra for each redshift.Reuse & Permissions
Figure 6
Angular power spectra of EE polarization generated with various assumptions concerning either the cosmology (WMAP1 versus WMAP3 model) or the physics of reionization (various photon production efficiency, $f_{γ}$ , and with or without subcell gas clumping), as labeled by color. The primordial CMB is shown by the dashed line, whereas the lensed one is shown by the solid line. Analytic computation is as in Fig. 4.Reuse & Permissions

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