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It has recently been suggested that conduction-driven magnetohydrodynamic(MHD) instabilities may operate at all radii within an intracluster medium(ICM), and profoundly affect the structure of a cluster's magnetic field. WhereMHD instabilities dominate the dynamics of an ICM, they will re-orient magneticfield lines perpendicular to the temperature gradient inside a cooling core, orparallel to the temperature gradient outside it. This characteristic structureof magnetic field could be probed by measurements of polarized radio emissionfrom background sources. Motivated by this possibility we have constructed 3-dmodels of a magnetized cooling core cluster and calculated Faraday rotationmeasure (RM) maps in the plane of the sky under realistic observing conditions.We compare a scenario in which magnetic field geometry is characterized byconduction driven MHD instabilities to that where it is determined by isotropicturbulent motions. We find that future high-sensitivity spectro-polarimetricmeasurements of RM, such as will be enabled by the Expanded Very Large Arrayand Square Kilometer Array can distinguish between these two cases withplausible exposure times. Such observations will test the existence ofconduction-driven MHD instabilities in dynamically relaxed cooling coreclusters. More generally, our findings imply that observations of Faraday RMshould be able to discern physical mechanisms that result in qualitativelydifferent magnetic field topologies, without a priori knowledge about thenature of the processes.

Using Faraday Rotation to Probe MHD Instabilities in Intracluster Media