Probing Intracluster Magnetic Fields with Cosmic Microwave Background Polarization

Intracluster magnetic fields with $\sim \mu G$ strength induce Faraday rotation on the cosmic microwave background (CMB) polarization. Measurements of this effect can potentially probe the detailed structure of intracluster magnetic fields across clusters, since the CMB polarization is a continuously varying field on the sky, in contrast to the conventional method restricted by the limited number of radio sources behind or inside a cluster. We here construct a method for extracting information on magnetic fields from measurements of the effect, combined with possible observations of the Sunyaev-Zel'dovich effect and X-ray emission for the same cluster which are needed to reconstruct the electron density fields. Employing the high-resolution magneto-hydrodynamic simulations performed by Dolag, Bartelmann & Lesch (1999) as a realistic model of magnetized intracluster gas distribution, we demonstrate how our reconstruction technique can well reproduce the magnetic fields, i.e., the spherically average radial profiles of the field strength and the coherence length.