Abstract
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 ∼ 104. 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 ∼σ38, 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 ∼σ9.58 for Faraday rotation and ∼σ158 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 ∼σ0.98 for Faraday rotation.
Highlights
One of the main challenges in observational cosmology is a complete characterization of cosmic microwave background (CMB) polarization anisotropies, targeted by a large number of ongoing, being deployed, or planned experiments either from ground or space-borne missions
For the Faraday conversion, we first recall that irrespective of the nature of free electrons the conversion rate is proportional to B2⊥e±2iθB, where B⊥ is the norm of the projected magnetic field on the plane orthogonal to n, and θB is the angle between the projected magnetic field and the first basis vector in the plane orthogonal to n
We investigate the degeneracy between a scaling in mass of the magnetic field at the centre of the halo and the σ8 scaling, as what we have done for the Faraday rotation angle; see Fig. 7
Summary
One of the main challenges in observational cosmology is a complete characterization of cosmic microwave background (CMB) polarization anisotropies, targeted by a large number of ongoing, being deployed, or planned experiments either from ground or space-borne missions (see e.g. Simons Observatory Collaboration 2019; Suzuki et al 2018). With the significant increase of sensitivity of the forthcoming observatories aimed at an accurate mapping of the CMB polarization on wide ranges of angular scales, clear predictions for such additional secondary anisotropies are of importance for many reasons These secondary anisotropies contain some cosmological and/or astrophysical informations and could be used to probe, for example parity violation in the Universe (Li & Zhang 2008; Lue et al 1999; Pospelov et al 2009; Yadav 2009), intra-halo magnetic fields, or gas evolution at early epochs (Takada et al 2001; Ohno et al 2003; Tashiro et al 2008, 2009).
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