Probing Intracluster Magnetic Fields with Cosmic Microwave Background Polarization

Intracluster magnetic fields with $ \sim \mu G $ strength induce Faradayrotation on the cosmic microwave background (CMB) polarization. Measurements of this effect can potentially probe thedetailed structure of intracluster magnetic fields across clusters, since theCMB polarization is a continuously varying field on the sky, in contrast to theconventional method restricted by the limited number of radio sources behind orinside a cluster. We here construct a method for extracting information onmagnetic fields from measurements of the effect, combined with possibleobservations of the Sunyaev-Zel'dovich effect and X-ray emission for the samecluster which are needed to reconstruct the electron density fields. Employing the high-resolution magneto-hydrodynamic simulations performed byDolag, Bartelmann & Lesch (1999) as a realistic model of magnetizedintracluster gas distribution, we demonstrate how our reconstruction techniquecan well reproduce the magnetic fields, i.e., the spherically average radialprofiles of the field strength and the coherence length.Comment: 20pages, 10figures, accepted for publication in AP