We present high resolution images of the Faraday Rotation Measure (RM) structure of the radio galaxy PKS 1246-410, at the center of the Centaurus cluster. Comparison with Halpha-line and soft X-ray emission reveals a correspondence between the line-emitting gas, the soft X-ray emitting gas, regions with an excess in the RM images, and signs of depolarization. Magnetic field strengths of 25 microG, organized on scales of ~1 kpc, and intermixed with gas at a temperature of 5 x 10^6 K with a density of ~0.1 cm^-3 can reproduce the observed RM excess, the depolarization, and the observed X-ray surface brightness. This hot gas may be in pressure equilibrium with the optical line-emitting gas, but the magnetic field strength of 25 microG associated with the hot gas provides only 10% of the thermal pressure and is therefore insufficient to account for the stability of the line-emitting filaments.
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