  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.
