Secondary CMB anisotropies from magnetized haloes I. Power spectra of the Faraday rotation angle and conversion rate

Magnetized plasmas within haloes of galaxies leave their footprint on the polarized anisotropies of the cosmic microwave background. The two dominant effects of astrophysical haloes are Faraday rotation, which generates rotation of the plane of linear polarization, and Faraday conversion, which induces a leakage from linear polarization to circular polarization. We revisit these sources of secondary anisotropies by computing the angular power spectra of the Faraday rotation angle and the Faraday conversion rate by the large-scale structures. To this end, we use the halo model and we pay special attention to the impact of magnetic field projections. Assuming magnetic fields of haloes to be uncorrelated, we found a vanishing two-halo term, and angular power spectra peaking at multipoles l similar to 10(4). The Faraday rotation angle is dominated by the contribution of thermal electrons. For the Faraday conversion rate, we found that both thermal electrons and relativistic, non-thermal electrons contribute equally in the most optimistic case for the density and Lorentz factor of relativistic electrons, while in more pessimistic cases the thermal electrons give the dominant contribution. Assuming the magnetic field to be independent of the halo mass, the angular power spectra for both effects roughly scale with the amplitude of matter perturbations as similar to sigma(3)(8), and with a very mild dependence with the density of cold dark matter. Introducing a dependence of the magnetic field strength with the halo mass leads to an increase of the scaling at large angular scales (above a degree) with the amplitude of matter fluctuations up to similar to sigma(9.5)(8) for Faraday rotation and similar to sigma(15)(8) for Faraday conversion for a magnetic field strength scaling linearly with the halo mass. Introducing higher values of the magnetic field for galaxies, as compared to clusters, instead leads to a decrease of such a scaling at arcminute scales down to similar to sigma(0.9)(8) for Faraday rotation.